diff --git a/edison-trajectories/heterogeneous-params/README.md b/edison-trajectories/heterogeneous-params/README.md new file mode 100644 index 00000000..87c832a9 --- /dev/null +++ b/edison-trajectories/heterogeneous-params/README.md @@ -0,0 +1,60 @@ +# Heterogeneous (per-member) BO parameter axes — Edison literature trajectory + +Source: PR #24 comment +[4520542433](https://github.com/vertical-cloud-lab/tensegrity-optimization/pull/24#issuecomment-4520542433) +(sgbaird relaying @me-madsen): + +> noting that we could also allow for diameters of individual struts/cables +> to vary, rather than assuming a fixed diameter. Similar for other +> parameters perhaps. Mostly thinking in context of #35 right now + +PR #35 currently sweeps a single `strut_d_mm` and a single `cable_d_mm` per +T3-prism specimen (all 3 struts and all 9 cables tied to one diameter each). +The proposal is to expand selected scalar parameters into vector / per-member +parameters — taking the per-specimen design vector from ~5-D to O(12-30+) D. + +## Trajectory + +| File | Notes | +| --- | --- | +| `heterogeneous-params-5191cf4d-873a-4e3e-9077-9565a2602ba1.md` | Verbatim `formatted_answer` from Edison `LITERATURE_HIGH` task `5191cf4d-873a-4e3e-9077-9565a2602ba1` (job: `LITERATURE_HIGH`, status: `success`). 466 lines covering (a) precedent in Skelton/Nagase/Goyal/Zegard/Pajunen/Xu/Zhang minimal-mass tensegrity sizing, (b) form-finding / bistability / energy-absorption implications under D3 symmetry, (c) FFF manufacturability on Bambu H2D, (d) high-dim BO methodology (SAASBO, TuRBO, ALEBO, additive GPs, hierarchical search spaces, equivariant GPs, MTGP), (e) symmetry exploitation under C3/D3, (f) numeric recommendations + Ax/BoTorch recipe, (g) ranked failure modes, (h) numbered references. | +| `heterogeneous-params-5191cf4d-873a-4e3e-9077-9565a2602ba1.json` | Full structured `model_dump_json` for reproducibility. | +| `../../scripts/edison/submit_heterogeneous_params.py` | Idempotent submission + polling driver (reads `EDISON_PLATFORM_API_KEY` or mirrors `EDISON_API_KEY`; uses `client.get_task(task_id=...)` polling; writes a `-SUBMITTED.json` placeholder so a follow-up session can resume on wall-clock timeout). | + +## Headline recommendation (Edison §f) + +For the first heterogeneous PR #35 follow-on batch on a single T3-prism: + +- **Keep scalar:** `R_mm`, `H_mm`, `twist_deg`, infill %. +- **Expand to per-orbit (not per-member)** the strut and cable diameters, + exploiting the T3-prism `C3 → D3` symmetry that decomposes the 9 cables + into 3 orbits (saddle / top / bottom triangles): one `strut_orbit_d_mm` + continuous axis ∈ [3.5, 9.0] mm + three `cable_orbit_d_mm` categorical + axes ∈ {1.2, 1.8, 2.4, 3.0, 4.5} mm (FFF-resolvable bins on a 0.4 mm + nozzle, per Tuncel 2024 dimensional-accuracy data). +- **Expand to fully per-member** only the per-cable prestress fraction + simplex (sum = 1), per Skelton's minimal-mass prestress optimization + (Nagase & Skelton 2014; Goyal, Skelton & Peraza Hernandez 2020). +- **BO engine:** SAASBO for ≤25-D campaigns (Eriksson & Jankowiak 2021), + escalate to TuRBO + qNEHVI for tilings that push into O(100+) D + (Eriksson 2019; Daulton 2020). Initialize with stratified Sobol (≥3 + specimens per topology family / orbit configuration). +- **Symmetry handling:** hard-enforce orbit symmetry as the default + search space (Approach (i) in §e); only relax to per-member axes if + the symmetric Pareto front is exhausted, since the lab budget is + 50–100 specimens. + +## Cross-references + +- PR #24 hierarchical search space synthesis: + [`../tpu-petg-bo-variables-additions-from-pr22.md`](../tpu-petg-bo-variables-additions-from-pr22.md) + §D recasts the topology axes as an Ax `HierarchicalSearchSpace` per + [facebook/Ax#140](https://github.com/facebook/Ax/issues/140). This per-member + expansion nests one level *below* that hierarchy — inside any chosen + `topology_family` branch, selected scalar parameters expand into + per-orbit / per-member vector parameters. +- PR #35 (`bo/t3_prism_sobol_batch.py`) is the concrete target for the + Edison §f recipe. +- PR #33 sim-ladder (MuJoCo → Newton/Warp XPBD → PolyFEM+IPC / DiffPD) is + the recommended host for the MTGP / multifidelity escalation discussed + in Edison §d. diff --git a/edison-trajectories/heterogeneous-params/heterogeneous-params-5191cf4d-873a-4e3e-9077-9565a2602ba1.json b/edison-trajectories/heterogeneous-params/heterogeneous-params-5191cf4d-873a-4e3e-9077-9565a2602ba1.json new file mode 100644 index 00000000..812aea7d --- /dev/null +++ b/edison-trajectories/heterogeneous-params/heterogeneous-params-5191cf4d-873a-4e3e-9077-9565a2602ba1.json @@ -0,0 +1,23 @@ +{ + "status": "success", + "query": "Per-member (heterogeneous) design parameters in tensegrity / lattice BO campaigns — when to vary strut and cable diameters independently, and how to keep the resulting high-dimensional search space tractable.\n\nProject context (read in full before answering):\n\n* Hardware: multi-material 3D-printed tensegrity-inspired energy absorber.\n Strut material PETG (or PLA in the current PR #35 batch), tendon material\n TPU 85A (NinjaFlex-class, E ~12 MPa secant, sigma_break ~26 MPa, rho\n ~1200 kg/m^3, strain-at-break ~550-660%). Printed on a Bambu H2D\n dual-extrusion FFF system with manual-painted supports. Baseline topology\n is a T3-prism (3 struts, 9 cables = 3 saddle + 3 top + 3 bottom). Stretch\n goals: 6-bar SUPERball icosahedron, stacked / tiled prisms, Pajunen\n truncated-octa.\n* Existing BO setup (PR #30 + PR #33 + PR #35): an Ax / BoTorch qNEHVI\n multi-objective campaign. PR #35 specifically — `bo/t3_prism_sobol_batch.py`\n — currently sweeps FIVE T3-prism design variables as a single Sobol batch\n of 9 specimens on the H2D plate:\n - `R_mm` (cell radius)\n - `H_mm` (cell height)\n - `twist_deg` (rotation between top and bottom triangles)\n - `strut_d_mm` (ONE diameter — applies to all 3 struts)\n - `cable_d_mm` (ONE diameter — applies to all 9 cables)\n Frozen: topology=t3_prism, tiling=1x1x1, joint geometry (captive TPU core\n inside hollow PLA shell), build_orientation=vertical, tpu_shore=85A.\n* Proposal under discussion (PR #24 comment 4520542433): allow the diameter\n of every individual strut and every individual cable to vary independently\n (so a T3-prism specimen would have ~3 strut-diameter axes + 9 cable-\n diameter axes = 12 diameter axes, instead of 2). The user also asks\n \"similar for other parameters perhaps\" — i.e. per-member length,\n per-cable prestress, per-member material assignment, per-cable shore,\n per-strut layer-height, etc.\n* Companion PR #24 design-space docs already encode a hierarchical\n `topology_family` -> conditional child parameters search space (per\n facebook/Ax#140). The per-member proposal sits one level below that —\n inside any chosen topology family, expand selected scalar parameters into\n vector / per-member parameters.\n\nAnswer EVERY sub-question below with primary, peer-reviewed citations\n(DOIs where available). When recommending a numeric value or a default\nchoice, justify from a cited source rather than rule-of-thumb. Do not\nfabricate DOIs.\n\n(a) MOTIVATION / LITERATURE PRECEDENT. In peer-reviewed tensegrity, cable\n dome, deployable space-structure, lattice-metamaterial, and ground-\n structure topology optimization work, when have authors deliberately\n allowed individual struts and individual cables to have heterogeneous\n (per-member) cross-section, length, prestress, or material — vs.\n enforcing a uniform value across the cell? Identify the canonical\n references (e.g. Skelton & de Oliveira 2009 minimal-mass tensegrity\n sizing; Masic, Skelton & Gill 2006 form-finding with member-wise force\n densities; Adam & Smith active-tensegrity bridges; Pellegrino &\n Calladine self-stress; Tibert & Pellegrino reviews; Achtziger /\n Bendsoe / Sigmund ground-structure topology optimization; Zegard &\n Paulino GRAND/Polytop; Hanaor double-layer grids; Goyal & Skelton\n minimum-mass tensegrity dynamics; Bel Hadj Ali, Rhode-Barbarigos,\n Smith active control; Wang, Senatore, Marano 2021+ optimal tensegrity\n sizing under impact; Veuve, Safaei, Smith deployable tensegrity).\n For each, summarise: what was varied per-member, what objective was\n optimized, what variation actually emerged at the optimum (i.e. do\n the per-member sizes converge to a few discrete clusters, or do they\n populate a continuum?), and how the heterogeneity compared\n quantitatively against a uniform-member baseline.\n\n(b) MECHANICAL / FORM-FINDING IMPLICATIONS. For a class-1 prismatic\n tensegrity (T3-prism, T4-prism), what is the literature on the\n feasibility envelope of heterogeneous member properties?\n Specifically:\n - Form-finding & self-stress: does varying individual cable\n cross-sections break the symmetric self-stress state, force an\n unsymmetric prestress distribution, or shift the cell's\n equilibrium geometry (R, H, twist)? Cite force-density-method\n and dynamic-relaxation references.\n - Buckling: per-strut diameter governs Euler buckling at known\n slenderness; what is the published trade-off between SEA and\n peak-force when individual struts are deliberately under-sized\n to act as sacrificial buckling fuses?\n - Bistability / multistability (Schenk & Guest 2014; Defossez 2003;\n Sumi & Miyashita): does per-member heterogeneity unlock bistable\n modes not accessible to uniform cells?\n - Anisotropy: how much directional stiffness / energy-absorption\n tailoring can be achieved by per-cable cross-section selection\n in a single T-prism vs. by going to multi-cell tilings?\n - Cycle life / fatigue: per-tendon shore / cross-section\n heterogeneity in TPU-tendon tensegrities — any reuse-count\n data?\n Cite numbers (peak-force reduction %, SEA gain %, prestress shift\n in % of uniform self-stress) where available.\n\n(c) MANUFACTURABILITY ON FFF MULTI-MATERIAL FDM (BAMBU H2D / IDEX).\n The lab prints PETG struts + TPU 85A cables in a single multi-\n material job. Per the PR #35 captive-TPU-core-inside-PLA-shell\n joint design, every joint shell has a uniform bore size set by\n the (currently single) cable diameter. If individual cables get\n independent diameters, what manufacturability gotchas appear?\n Specifically:\n - Bore tolerance: how many distinct cable diameters can a single\n joint sphere accommodate before the PLA shell becomes\n impractically thick (cable_d + 0.8 mm bore clearance, then\n +3 mm core, then +3.2 mm PLA wall)?\n - TPU bridging: can a 1.5 mm cable transition mid-print into a\n 4.5 mm cable on the same TPU extruder pass, or does the\n extruder retraction / line-width mismatch force a layer\n boundary at the transition?\n - Strut diameter discretization: PETG FFF practical strut\n diameters quantize on the 0.4 mm nozzle line-width. Cite\n published recommendations (Khatri 2024; Yavas 2022; Lopes\n 2018; Ye 2023; Bambu Lab / Prusa application notes) for\n discrete-set vs. continuous treatment.\n - Print time: how does the H2D wipe-tower volume scale with\n N_distinct_filament_diameters?\n - Variability noise: if the BO can request 12 different cable\n diameters per specimen but FFF reliably resolves only 3-4\n bins, the additional \"axes\" are noise. Cite repeatability /\n CoV numbers (Khatri 2024; Yavas 2022 PLA+TPU FFF tensile;\n Intrigila 2022; Davami 2025 SLA Tough 2000 + double-T3).\n\n(d) HIGH-DIMENSIONAL BO METHODOLOGY. Once the per-member expansion is\n taken, the design vector becomes O(10) to O(30) dimensional for a\n single T3-prism cell, and O(100+) for a 3x3x2 tiling. Survey peer-\n reviewed and well-cited workshop / preprint methodology for high-\n dim BO over structured design vectors. Cover at minimum:\n - Random embeddings (REMBO — Wang et al. 2016; BOCK; ALEBO —\n Letham et al. 2020).\n - Sparse / SAASBO (Eriksson & Jankowiak 2021) — strong fit\n for \"most members do not matter, a few do\" sparse-effect\n regimes. Recommend specific Ax / BoTorch hooks.\n - Additive / decomposed GPs (Kandasamy 2015; Gardner 2017;\n Wang & Jegelka 2018) — natural fit when per-member effects\n are largely independent.\n - Trust-region BO (TuRBO — Eriksson 2019) and SCBO — strong\n empirical performance in O(100+) dims, especially on\n physically-constrained problems.\n - Hierarchical / conditional search spaces (Ax HierarchicalSearch\n Space, facebook/Ax#140; SMAC; Auto-WEKA; HyperBand) — the\n natural way to nest per-member parameters under a topology\n choice.\n - Latent / generative parameterizations (VAE-BO; LSO — Tripp 2020;\n Maus et al. 2022 LOL-BO; differentiable-CAD or differentiable\n physics priors). Particularly relevant when there are physically\n meaningful symmetries (the 3-fold T-prism is permutation-\n invariant; the 9 cables decompose into 3 saddle + 3 top + 3\n bottom orbits — encode that symmetry explicitly).\n - Symmetry-aware / permutation-invariant kernels (Cohen & Welling;\n Bronstein et al. geometric deep learning; cited in\n Bayesian-optimization-with-symmetry preprints if any).\n - Multi-fidelity / multi-task GPs (PR #33 sim ladder maps\n cleanly onto MTGP / MF-GP — Kandasamy 2017; Wu 2020; Astudillo &\n Frazier 2021) as a way to amortize the high-dim cost.\n - Constraint handling: heterogeneity often introduces feasibility\n constraints (TPU bore set must be ≤4, strut slenderness L/D ≤\n some max, mass ≤ 500 g). Cite NEI / SCBO / cNEHVI.\n For each method, recommend whether to adopt it as the primary BO\n engine for PR #35, as a fallback if dimensionality blows up, or as\n a wrong-fit. Give a concrete recommended progression starting from\n the current 5-D Sobol → next-step BO step.\n\n(e) SYMMETRY EXPLOITATION. The T3-prism has a natural C3 rotational\n symmetry (rotate by 120 deg). All 3 struts are in one orbit; the 9\n cables decompose into 3 orbits of 3 (saddle, top, bottom triangles).\n Under that symmetry, the \"12 diameter axes\" reduce to 4 orbit\n diameters (1 strut orbit + 3 cable orbits). What does the literature\n say about exploiting this symmetry in BO, in form-finding, and in\n optimal-control of tensegrity? Cite Sultan & Skelton symmetry-\n decomposed self-stress; group-theoretic stability (Kangwai & Guest);\n invariant / equivariant GPs (van der Wilk 2018; Holderrieth, Hutchinson\n & Teh 2021). Recommend whether to (i) hard-enforce orbit symmetry as\n the default search space (so the BO never sees a symmetry-broken\n design), (ii) use orbit symmetry only as a kernel prior so symmetry\n breaking can emerge when warranted, or (iii) ignore symmetry and\n let the per-member axes float independently. Justify quantitatively\n in terms of expected sample efficiency given the lab's 50-100\n specimen budget.\n\n(f) NUMERIC RECOMMENDATIONS for the lab's next BO batch (PR #35 follow-on).\n For a single T3-prism cell on the H2D, recommend:\n - Which scalar parameters to keep scalar (R, H, twist, infill %).\n - Which scalar parameters to expand to per-orbit (strut diameter,\n cable diameter — recommend per-orbit, not per-member, for the\n first heterogeneous batch).\n - Which scalar parameters to expand to fully per-member\n (per-cable prestress fraction is the strongest candidate —\n cite Skelton's minimum-mass prestress optimization).\n - Recommended bounds and discretization for each new axis\n (e.g. strut_orbit_d_mm ∈ [3.5, 9.0] continuous; cable_orbit_d_mm\n ∈ (1.2, 1.8, 2.4, 3.0, 4.5) categorical for FFF resolvability;\n per-cable prestress fraction simplex with sum = 1).\n - Recommended BO engine + acquisition + batch size for the\n 50-100 specimen total budget. Give a specific Ax / BoTorch\n configuration recipe (model_class, surrogate_spec,\n acquisition_function_class, batch_size, n_init_sobol).\n - Recommended sample-efficiency analytic: how many specimens does\n SAASBO / TuRBO / orbit-symmetric GP each need on a published\n problem of comparable dimension to reach within 10% of the\n Pareto-front hypervolume? Cite the benchmark.\n\n(g) FAILURE MODES AND OPEN QUESTIONS. Top 5-10 ranked gotchas /\n pitfalls of adopting per-member heterogeneous BO axes for the\n lab's PETG + TPU 85A tensegrity-on-H2D context. For each: cite\n the failure mode from peer-reviewed work and propose a mitigation.\n\n(h) NUMBERED REFERENCES section (DOI when available) supporting every\n quantitative claim in (a)-(g).\n\nCite only primary, peer-reviewed sources or established standards\n(ASTM, ISO, JEDEC, NASA / NIST technical reports, well-cited workshop\npapers at NeurIPS / ICML / AISTATS). Do NOT fabricate DOIs.\n", + "user": null, + "created_at": "2026-05-22T16:26:31.994716Z", + "job_name": "job-futurehouse-paperqa3-high", + "share_status": "private", + "permitted_accessors": { + "users": [], + "organizations": [] + }, + "build_owner": "FutureHouse", + "environment_name": null, + "agent_name": null, + "task_id": "5191cf4d-873a-4e3e-9077-9565a2602ba1", + "project_id": null, + "answer": "\n# Per-Member Heterogeneous Design Parameters in Tensegrity/Lattice BO Campaigns\n\n## (a) Literature Precedent for Per-Member Heterogeneous Sizing\n\nThe canonical framework for per-member heterogeneous tensegrity sizing is the Skelton–de Oliveira minimal-mass formulation, where per-member force densities (γ_i for cables, λ_j for bars) and per-member cross-sectional areas (A_si, A_bj) serve as explicit optimization variables. The total mass is minimized subject to equilibrium and material-yield/buckling constraints, formulated as a linear program for single-load cases or a multi-load LP when areas are shared across load cases (nagase2014minimalmassdesign pages 1-3, nagase2014minimalmassdesign pages 5-7). Nagase & Skelton (2014) demonstrated this framework on 2D and 3D box tensegrities, reporting optimized per-member force densities that take distinct values (e.g., γ_i(1) = 0.00 N/m and γ_i(2) = 10.00 N/m in a 2D box) and per-member cross-sections on the order of 10⁻² mm² (nagase2014minimalmassdesign pages 10-12).\n\nGoyal, Skelton & Peraza Hernandez (2020) extended this to 3D T-bar (D-bar) tensegrity lattices, finding a global minimum mass ratio μ_3D = 0.2159 (≈78% mass reduction versus a monolithic column) at complexity q = 3 and aperture angle α = 31°. Critically, optimizing per-member string cross-section areas yielded lower mass than optimizing prestress distribution alone (goyal2020designofminimal pages 6-8). Chen et al. (2021) formulated minimal-mass deployable tensegrity towers where per-member areas A_si and A_bj appear explicitly in the mass and stiffness expressions, with prestress ε₀ as a lower bound on string force densities (chen2021deployabletensegritylunar pages 3-6).\n\nIn topology optimization, Xu et al. (2018) formulated tensegrity sizing using discrete candidate cross-section sets with binary selection variables per member. They introduced global indicators N_As and N_Ac to explicitly count and constrain the number of distinct cross-sectional sizes adopted, enabling manufacturing-aware clustering (xu2018topologyoptimizationof pages 3-4, xu2018topologyoptimizationof pages 2-3). In the ground-structure approach, Zegard & Paulino (2014, 2015) treat per-member areas as continuous LP variables; the optimal truss is statically determinate with at most N_dof nonzero members, implying natural sparsity/clustering (zegard2015grand3—ground pages 1-3, zegard2014grand—ground pages 3-4).\n\nZhang et al. (2021) optimized energy absorption of truncated-octahedral tensegrity lattices, treating per-member-type cross-sectional areas and overall prestress level as design variables, with bar post-buckling explicitly modeled for energy absorption (zhang2021optimizationforenergy pages 1-2). Pajunen et al. (2019) demonstrated 3D-printable tensegrity-inspired structures where adjusting strut and cable diameters independently (ds/dc ratios of 1.44–2.23) yielded a 3.1× increase in strain energy at 0.4 strain and ~1.5× higher normalized strain energy per mass (pajunen2019designandimpact pages 4-5, pajunen2019designandimpact pages 2-3).\n\n**Key finding:** In all per-member sizing studies, the optimized cross-sections cluster into a small number of discrete groups corresponding to member types (e.g., top cables, saddle cables, bottom cables, struts) rather than populating a continuum. This is a direct consequence of symmetry orbits and the structure of the equilibrium constraints.\n\n## (b) Mechanical and Form-Finding Implications\n\n### Form-Finding and Self-Stress\nFor class-1 prismatic tensegrities (T3, T4), group-theoretic analysis under D3 symmetry decomposes the equilibrium matrix into four irreducible blocks (A1, A2, E1, E2). The A1 block (full symmetry) yields the integral self-stress state in which all cables of the same orbit carry equal prestress and all struts carry equal compression (chen2018grouptheoreticexploitationsof pages 8-10, chen2012initialprestressdistribution pages 7-9). Varying individual cable cross-sections breaks this symmetric self-stress: members with different EA values will carry different forces under the same elongation, forcing an asymmetric prestress distribution. The equilibrium geometry (R, H, twist) shifts because the force-density method couples geometry to the self-stress coefficients (masic2005pathplanningand pages 2-2).\n\n### Bistability\nMicheletti (2013) showed that T3-prism bistability arises when geometry and prestrain exceed critical thresholds — specifically, at the equilibrium twist angle ϕ = π/6, high prestrain can destabilize the symmetric configuration, creating two low-symmetry stable equilibria (micheletti2013bistableregimesin pages 9-11, micheletti2013bistableregimesin pages 5-7). Crucially, per-member heterogeneity (different spring constants k_a ≠ k_b) produces asymmetric energy wells — the two bistable minima have different energy values, so heterogeneity in cable/strut diameters shifts bistability thresholds and relative well depths (micheletti2013bistableregimesin pages 13-14). Vangelatos et al. (2020) confirmed experimentally that fabrication heterogeneities localize or confine bistability to specific layers in multi-cell tensegrity lattices (vangelatos2020designandtesting pages 13-16).\n\n### Energy Absorption\nPajunen et al. (2019) demonstrated that modifying strut-to-cable diameter ratios (from ds/dc = 2.23 to 1.44) in a spherically-jointed tensegrity produced 3.1× higher strain energy absorption at 0.4 strain with only 3.6% mass increase (pajunen2019designandimpact pages 4-5). Repeated impact tests showed excellent resilience: average remaining strain of only ~2.28% after 24 impacts (~0.11% per impact) (pajunen2019designandimpact pages 5-7).\n\n### Stability\nPer-member heterogeneity modifies both material stiffness K_M and geometric stiffness K_G; a prestress-stable configuration for one set of member properties may become unstable for another. This is because K_T = K_M + K_G depends on per-member EA products and rest-length mismatches (micheletti2013bistableregimesin pages 2-4).\n\n## (c) Manufacturability on FFF Multi-Material (Bambu H2D)\n\n### Dimensional Accuracy\nFDM/FFF dimensional studies report width deviations averaging ~1.5% and thickness deviations averaging ~9.5% for PLA, PETG, and ABS with a 0.4 mm nozzle at 0.2 mm layer height (tuncel2024theinfluenceof pages 5-7, tuncel2024theinfluenceof pages 1-2). PETG shows higher dimensional deviations than PLA and ABS. Cross-sectional areas consistently exceed nominal values by ~11.5% (tuncel2024theinfluenceof pages 2-4).\n\n### Practical Constraints\n- **Nozzle quantization:** With a 0.4 mm nozzle, practical minimum wall/line width is ~0.4–0.5 mm. Circular strut/cable cross-sections are built from concentric perimeters; reliable diameter steps are approximately 0.8 mm (2 × line width). This means cable diameters below ~1.2 mm are unreliable, and the practical resolution for diameter variation is ~0.6 mm steps.\n- **Bore tolerance:** Each joint shell must accommodate the largest cable entering it. If independent cable diameters range from 1.2 to 4.5 mm, the bore must be sized to the maximum, wasting clearance for thinner cables. Practically, 3–4 distinct cable diameter bins suffice.\n- **TPU bridging:** TPU 85A has poor bridging and retraction performance. Mid-print diameter transitions (e.g., 1.5 mm to 4.5 mm) require significant flow-rate changes that produce inconsistent geometry at the transition. Layer boundaries at transitions are recommended.\n- **Wipe tower:** On the H2D, wipe-tower volume scales with the number of tool changes per layer, not directly with the number of distinct diameters. However, more diameter variation increases slicer complexity.\n- **Recommendation:** Treat cable diameters as categorical with 4–5 bins (e.g., 1.2, 1.8, 2.4, 3.0, 4.5 mm) rather than continuous, and strut diameters similarly discretized in ~1 mm steps.\n\n## (d) High-Dimensional BO Methodology\n\n### SAASBO (Primary Recommendation for 7–12D)\nEriksson & Jankowiak (2021) introduced the SAAS GP prior with half-Cauchy priors on inverse-squared lengthscales, enabling automatic identification of important dimensions. SAASBO uses fully Bayesian inference via NUTS with recommended settings: num_warmup = 256, num_samples = 256, thinning = 32, α = 0.1 (santoni2024comparisonofhighdimensional pages 21-23). On BBOB benchmarks at D=10, SAASBO achieves the highest fraction of solved targets throughout the budget range; at D=20 it remains competitive with TuRBO (santoni2024comparisonofhighdimensional pages 32-36). SAASBO is initialized with as few as m=10 Sobol points and shows strong performance within 50 evaluations (eriksson2021highdimensionalbayesianoptimization pages 14-16). **This is the recommended primary engine for the orbit-reduced 7D search space.**\n\n### TuRBO (Fallback for >20D or Tiled Designs)\nTuRBO maintains multiple local trust regions with adaptive sizing, using Thompson Sampling for batch selection (eriksson2019scalableglobaloptimization pages 2-4). On BBOB at D=40–60, TuRBO clearly surpasses SAASBO, becoming the most effective method for larger budgets (santoni2024comparisonofhighdimensional pages 32-36). TuRBO is designed for scenarios allowing tens to thousands of evaluations and scales well to 100+ dimensions (eriksson2019scalableglobaloptimization pages 8-10). **Recommended as the fallback for fully per-member parameterizations or multi-cell tilings.**\n\n### MORBO (Multi-Objective High-Dimensional)\nDaulton et al. (2022) developed MORBO for multi-objective BO in high-dimensional spaces (tested up to d=222). MORBO achieves best average rank across DTLZ benchmarks at d=100 with batch size q=50, and provides order-of-magnitude computational savings over global GP methods (daulton2022multiobjectivebayesianoptimization pages 22-24, daulton2022multiobjectivebayesianoptimization pages 9-10). **Recommended for multi-objective campaigns if dimensionality exceeds ~20D.**\n\n### SCBO (Constrained BO)\nSCBO extends TuRBO with per-constraint GP models and constrained Thompson Sampling, handling feasibility constraints scalably (maathuis2025scalingbayesianoptimization pages 4-6). **Recommended for enforcing slenderness, mass, and bore-clearance constraints.**\n\n### REMBO/ALEBO (Not Recommended)\nREMBO uses random projections but suffers from distorted objective values; ALEBO addresses some issues but both have high runtime and memory constraints at moderate dimensions (santoni2024comparisonofhighdimensional pages 32-36). **Not recommended** for this application.\n\n### Recommended Progression\n1. **Current (5D):** Continue qNEHVI with Sobol initialization (9 specimens).\n2. **Next batch (7D, orbit-reduced):** Switch to SAASBO surrogate with qNEHVI acquisition. Use `SaasFullyBayesianSingleTaskGP` in BoTorch with NUTS inference (256 warmup, 256 samples). Initialize with 14 Sobol points (2D rule of thumb), then run sequential/small-batch (q=3–5) BO for 36–50 additional specimens.\n3. **If expanding to fully per-member (12D):** Stay with SAASBO but increase Sobol init to 24 points; monitor for lengthscale collapse.\n4. **For multi-cell tilings (30D+):** Switch to TuRBO-based MORBO with local GPs.\n\n## (e) Symmetry Exploitation\n\nThe T3-prism has D3 (≅ C3 × C2) rotational symmetry. Under C3, the 3 struts form one orbit; the 9 cables decompose into 3 orbits of 3 (saddle, top, bottom) (chen2012initialprestressdistribution pages 3-5, chen2012initialprestressdistribution pages 1-3). Group-theoretic block-diagonalization reduces the equilibrium matrix to four independent blocks, with the integral self-stress residing in the fully symmetric A1 block (chen2018grouptheoreticexploitationsof pages 8-10, chen2012initialprestressdistribution pages 7-9). This reduces 12 diameter axes to 4 orbit diameters.\n\nBrown et al. (2024) proved that invariant GP kernels constructed via k_G(x,y) = (1/|G|) Σ_{σ∈G} k(σ(x), y) achieve provably lower maximum information gain, with sample-complexity improvement scaling linearly with group size |G| (brown2024sampleefficientbayesianoptimisation pages 4-6). For C3 (|G|=3), this translates to roughly a 3× reduction in required samples. Empirically, invariant kernels substantially outperform non-invariant baselines on synthetic tasks, and the gains grow with dimension and group size (brown2024sampleefficientbayesianoptimisation pages 6-8). In a nuclear fusion application (12D, permutation-invariant), invariant UCB found high-performance solutions that non-invariant methods missed entirely (brown2024sampleefficientbayesianoptimisation pages 9-11, brown2024sampleefficientbayesianoptimisation pages 27-28).\n\n**Recommendation:** Hard-enforce orbit symmetry as the default search space (option i). With a 50–100 specimen budget, reducing from 12D to 4D (via orbit enforcement) is critical — SAASBO at 4D orbit parameters needs ~30–50 evaluations to converge, well within budget. Allow symmetry-breaking exploration only as a stretch goal after the orbit-symmetric Pareto front is characterized, using an invariant kernel prior (option ii) rather than fully independent axes.\n\n## (f) Numeric Recommendations\n\n### Parameters to Keep Scalar\n- `R_mm` (cell radius): scalar, [15, 45] mm continuous\n- `H_mm` (cell height): scalar, [20, 70] mm continuous \n- `twist_deg`: scalar, [15, 45]° continuous\n- `infill_%`: scalar (if varied), [20, 100]% in 20% steps\n\n### Parameters to Expand to Per-Orbit\n- `strut_orbit_d_mm`: 1 orbit × 1 value, [3.5, 9.0] mm continuous (all 3 struts equal)\n- `cable_saddle_d_mm`: 1 orbit, categorical {1.2, 1.8, 2.4, 3.0, 4.5} mm\n- `cable_top_d_mm`: 1 orbit, categorical {1.2, 1.8, 2.4, 3.0, 4.5} mm\n- `cable_bottom_d_mm`: 1 orbit, categorical {1.2, 1.8, 2.4, 3.0, 4.5} mm\n\n**Total: 7D** (3 continuous + 1 continuous strut + 3 categorical cable orbits)\n\n### Candidates for Fully Per-Member Expansion (Future)\nPer-cable prestress fraction (as in Skelton's minimal-mass formulation where force densities γ_i are independent variables) is the strongest candidate for per-member treatment (nagase2014minimalmassdesign pages 5-7). This would add 3 independent prestress ratios (one per orbit, constrained to sum to 1 on a simplex).\n\n### BO Configuration Recipe\n```python\n# Ax/BoTorch configuration for 7D orbit-symmetric T3-prism\nfrom ax.models.torch.botorch_modular.surrogate import Surrogate\nfrom botorch.models.fully_bayesian import SaasFullyBayesianSingleTaskGP\n\nexperiment_config = {\n \"model_class\": SaasFullyBayesianSingleTaskGP,\n \"acquisition_function\": \"qNEHVI\", # multi-objective\n \"num_warmup\": 256, # NUTS warmup (per Santoni 2024)\n \"num_samples\": 256, # NUTS samples\n \"thinning\": 32,\n \"n_init_sobol\": 14, # 2 × D for 7D\n \"batch_size\": 5, # H2D plate fits ~9, use 5 for BO batches\n \"total_budget\": 50-100,\n \"objectives\": [\"SEA_J_per_g\", \"neg_peak_force_kN\"],\n \"constraints\": [\"mass_g <= 500\", \"strut_slenderness <= 40\"],\n}\n```\n\n### Sample-Efficiency Estimates\nBased on BBOB benchmarks (Santoni et al. 2024): SAASBO at D=10 achieves the highest target-hit rate within budgets of 10D+50 = 150 evaluations (santoni2024comparisonofhighdimensional pages 32-36). At the lab's 7D, convergence to within 10% of optimal is expected within 40–70 evaluations. TuRBO requires larger budgets (>100 evaluations) to outperform SAASBO at D≤20.\n\n## (g) Failure Modes and Pitfalls\n\n1. **Symmetry-breaking artifacts from printing:** FFF layer-by-layer construction inherently breaks the C3 rotational symmetry due to build orientation, seam placement, and support differences. Mitigation: vertical build orientation (already adopted); rotate seam positions; include build-orientation noise in the GP noise model.\n\n2. **Cable diameter below FFF resolution:** Requesting cable diameters finer than ~1.2 mm with a 0.4 mm nozzle produces unreliable geometry. Mitigation: enforce categorical cable diameters with a 1.2 mm lower bound (tuncel2024theinfluenceof pages 2-4).\n\n3. **Prestress-stability loss under heterogeneity:** Per-member cable heterogeneity can inadvertently destabilize the self-stress equilibrium, shifting the cell into an unintended bistable or collapsed configuration (micheletti2013bistableregimesin pages 13-14, micheletti2013bistableregimesin pages 2-4). Mitigation: include a self-stress feasibility check (eigenvalue of tangent stiffness > 0) as a BO constraint.\n\n4. **GP model misspecification in mixed continuous/categorical space:** SAASBO assumes continuous parameters; categorical cable diameters require probabilistic reparameterization or one-hot encoding. Mitigation: use Ax's mixed-parameter support with probabilistic reparameterization for discrete parameters.\n\n5. **NUTS computational cost:** Fully Bayesian inference scales as O(N³D) per sample. At 100 observations × 7D with 256 NUTS samples, wall-clock overhead is ~5–15 minutes per iteration. Mitigation: use MAP fallback if budget is time-constrained (eriksson2021highdimensionalbayesianoptimization pages 4-5).\n\n6. **Bore-tolerance feasibility:** If three cable orbits have three different diameters, each 6-way joint must accommodate multiple bore sizes. The PLA shell becomes impractically thick if the spread is large. Mitigation: constrain max(cable_d) - min(cable_d) ≤ 2.0 mm as a BO feasibility constraint.\n\n7. **Overfitting with small data:** With only 50–100 specimens, a 12D fully per-member space is severely undersampled (curse of dimensionality). Mitigation: use orbit-reduced 7D as default; SAASBO's sparsity prior provides natural regularization (eriksson2021highdimensionalbayesianoptimization pages 3-4).\n\n8. **Fatigue/cycle-life data gap:** No published reuse-count data exists for TPU 85A tendons in tensegrity configurations under cyclic loading. Mitigation: include 5-cycle repeated compression in the test protocol to capture degradation as an additional BO objective.\n\n9. **Wipe-tower waste scaling:** Each additional distinct filament diameter per layer increases purge volume on the H2D. With 4 cable bins + 1 strut, this is manageable; fully per-member treatment with 12 diameters would be wasteful. Mitigation: the orbit-reduced approach naturally limits distinct diameters.\n\n10. **Interaction effects between orbit diameters and global geometry:** Cable orbit diameters interact strongly with twist angle and cell radius (they jointly determine prestress and buckling modes). SAASBO may underestimate these interactions if the sparse prior suppresses cross-terms. Mitigation: monitor GP lengthscales; if multiple dimensions show short lengthscales, consider switching to a non-sparse GP or TuRBO.\n\n## (h) References\n\n1. Skelton, R.E. & de Oliveira, M.C. (2009). *Tensegrity Systems*. Springer. DOI: 10.1007/978-0-387-74242-7\n2. Nagase, K. & Skelton, R.E. (2014). Minimal mass design of tensegrity structures. *SPIE Proceedings* 9061:90610W. DOI: 10.1117/12.2044869\n3. Goyal, R., Skelton, R.E. & Peraza Hernandez, E.A. (2020). Design of minimal mass load-bearing tensegrity lattices. *Mechanics Research Communications* 103:103477. DOI: 10.1016/j.mechrescom.2020.103477\n4. Goyal, R., Peraza Hernandez, E.A. & Skelton, R.E. (2019). Analytical study of tensegrity lattices for mass-efficient mechanical energy absorption. *Int. J. Space Structures* 34:21–39. DOI: 10.1177/0956059919845330\n5. Masic, M. & Skelton, R.E. (2004). Optimization of class 2 tensegrity towers. *SPIE Proceedings* 5390. DOI: 10.1117/12.540363\n6. Masic, M. & Skelton, R.E. (2005). Path planning and open-loop shape control of modular tensegrity structures. *J. Guidance Control and Dynamics* 28:421–430. DOI: 10.2514/1.6872\n7. Chen, M. et al. (2021). Deployable tensegrity lunar tower. *Earth and Space 2021*, pp. 1079–1092. DOI: 10.1061/9780784483374.100\n8. Xu, X. et al. (2018). Topology optimization of tensegrity structures considering buckling constraints. *J. Structural Engineering* 144(10). DOI: 10.1061/(ASCE)ST.1943-541X.0002156\n9. Zegard, T. & Paulino, G.H. (2014). GRAND — Ground structure based topology optimization. *Struct. Multidisc. Optim.* 50:861–882. DOI: 10.1007/s00158-014-1085-z\n10. Zegard, T. & Paulino, G.H. (2015). GRAND3 — 3D ground structure topology optimization. *Struct. Multidisc. Optim.* 52:1161–1184. DOI: 10.1007/s00158-015-1284-2\n11. Zhang, J. et al. (2021). Optimization for energy absorption of 3D tensegrity lattice with truncated octahedral units. *Composite Structures* 267:113903. DOI: 10.1016/j.compstruct.2021.113903\n12. Pajunen, K. et al. (2019). Design and impact response of 3D-printable tensegrity-inspired structures. *Materials & Design* 182:107966. DOI: 10.1016/j.matdes.2019.107966\n13. Micheletti, A. (2013). Bistable regimes in an elastic tensegrity system. *Proc. R. Soc. A* 469:20130052. DOI: 10.1098/rspa.2013.0052\n14. Vangelatos, Z. et al. (2020). Design and testing of bistable lattices with tensegrity architecture. *Nanomaterials* 10:652. DOI: 10.3390/nano10040652\n15. Guest, S.D. (2000). Tensegrities and rotating rings of tetrahedra: a symmetry viewpoint. *Phil. Trans. R. Soc. A* 358:229–243. DOI: 10.1098/rsta.2000.0529\n16. Chen, Y. & Feng, J. (2012). Initial prestress distribution and natural vibration analysis of tensegrity structures based on group theory. *Int. J. Struct. Stab. Dyn.* 12:213–231. DOI: 10.1142/S0219455412500010\n17. Chen, Y. & Feng, J. (2018). Group-theoretic exploitations of symmetry in novel prestressed structures. *Symmetry* 10:229. DOI: 10.3390/sym10060229\n18. Eriksson, D. & Jankowiak, M. (2021). High-dimensional Bayesian optimization with sparse axis-aligned subspaces. *Proc. UAI 2021*. DOI: 10.48550/arxiv.2103.00349\n19. Eriksson, D. et al. (2019). Scalable global optimization via local Bayesian optimization (TuRBO). *NeurIPS 2019*. DOI: 10.48550/arxiv.1910.01739\n20. Eriksson, D. & Poloczek, M. (2021). Scalable constrained Bayesian optimization (SCBO). *ICML 2021*. DOI: 10.48550/arxiv.2002.08526\n21. Daulton, S. et al. (2022). Multi-objective Bayesian optimization over high-dimensional search spaces (MORBO). *NeurIPS 2022*. DOI: 10.48550/arxiv.2109.10964\n22. Santoni, M.L. et al. (2024). Comparison of high-dimensional Bayesian optimization algorithms on BBOB. *ACM Trans. Evol. Learn. Optim.* 4:1–33. DOI: 10.1145/3670683\n23. Brown, T. et al. (2024). Sample-efficient Bayesian optimisation using known invariances. *arXiv:2410.16972*. DOI: 10.48550/arxiv.2410.16972\n24. Letham, B. et al. (2020). Re-examining linear embeddings for high-dimensional Bayesian optimization (ALEBO). *NeurIPS 2020*. DOI: 10.48550/arxiv.2001.11659\n25. Baird, S.G. et al. (2022). High-dimensional Bayesian optimization of 23 hyperparameters using SAASBO. *Computational Materials Science* 211:111505. DOI: 10.1016/j.commatsci.2022.111505\n26. Tunçel, O. (2024). Influence of raster angle on dimensional accuracy of FDM-printed PLA, PETG, and ABS. *European Mechanical Science* 8:11–18. DOI: 10.26701/ems.1392387\n27. Maathuis, H.F. et al. (2025). Scaling Bayesian optimization for high-dimensional and large-scale constrained spaces. *AIAA Journal*. DOI: 10.2514/1.J065252\n28. Skelton, R.E. et al. (2014). Minimum mass design of tensegrity bridges. *Mechanics Research Communications* 58:124–132. DOI: 10.1016/j.mechrescom.2013.10.017\n", + "formatted_answer": "Question: Per-member (heterogeneous) design parameters in tensegrity / lattice BO campaigns — when to vary strut and cable diameters independently, and how to keep the resulting high-dimensional search space tractable.\n\nProject context (read in full before answering):\n\n* Hardware: multi-material 3D-printed tensegrity-inspired energy absorber.\n Strut material PETG (or PLA in the current PR #35 batch), tendon material\n TPU 85A (NinjaFlex-class, E ~12 MPa secant, sigma_break ~26 MPa, rho\n ~1200 kg/m^3, strain-at-break ~550-660%). Printed on a Bambu H2D\n dual-extrusion FFF system with manual-painted supports. Baseline topology\n is a T3-prism (3 struts, 9 cables = 3 saddle + 3 top + 3 bottom). Stretch\n goals: 6-bar SUPERball icosahedron, stacked / tiled prisms, Pajunen\n truncated-octa.\n* Existing BO setup (PR #30 + PR #33 + PR #35): an Ax / BoTorch qNEHVI\n multi-objective campaign. PR #35 specifically — `bo/t3_prism_sobol_batch.py`\n — currently sweeps FIVE T3-prism design variables as a single Sobol batch\n of 9 specimens on the H2D plate:\n - `R_mm` (cell radius)\n - `H_mm` (cell height)\n - `twist_deg` (rotation between top and bottom triangles)\n - `strut_d_mm` (ONE diameter — applies to all 3 struts)\n - `cable_d_mm` (ONE diameter — applies to all 9 cables)\n Frozen: topology=t3_prism, tiling=1x1x1, joint geometry (captive TPU core\n inside hollow PLA shell), build_orientation=vertical, tpu_shore=85A.\n* Proposal under discussion (PR #24 comment 4520542433): allow the diameter\n of every individual strut and every individual cable to vary independently\n (so a T3-prism specimen would have ~3 strut-diameter axes + 9 cable-\n diameter axes = 12 diameter axes, instead of 2). The user also asks\n \"similar for other parameters perhaps\" — i.e. per-member length,\n per-cable prestress, per-member material assignment, per-cable shore,\n per-strut layer-height, etc.\n* Companion PR #24 design-space docs already encode a hierarchical\n `topology_family` -> conditional child parameters search space (per\n facebook/Ax#140). The per-member proposal sits one level below that —\n inside any chosen topology family, expand selected scalar parameters into\n vector / per-member parameters.\n\nAnswer EVERY sub-question below with primary, peer-reviewed citations\n(DOIs where available). When recommending a numeric value or a default\nchoice, justify from a cited source rather than rule-of-thumb. Do not\nfabricate DOIs.\n\n(a) MOTIVATION / LITERATURE PRECEDENT. In peer-reviewed tensegrity, cable\n dome, deployable space-structure, lattice-metamaterial, and ground-\n structure topology optimization work, when have authors deliberately\n allowed individual struts and individual cables to have heterogeneous\n (per-member) cross-section, length, prestress, or material — vs.\n enforcing a uniform value across the cell? Identify the canonical\n references (e.g. Skelton & de Oliveira 2009 minimal-mass tensegrity\n sizing; Masic, Skelton & Gill 2006 form-finding with member-wise force\n densities; Adam & Smith active-tensegrity bridges; Pellegrino &\n Calladine self-stress; Tibert & Pellegrino reviews; Achtziger /\n Bendsoe / Sigmund ground-structure topology optimization; Zegard &\n Paulino GRAND/Polytop; Hanaor double-layer grids; Goyal & Skelton\n minimum-mass tensegrity dynamics; Bel Hadj Ali, Rhode-Barbarigos,\n Smith active control; Wang, Senatore, Marano 2021+ optimal tensegrity\n sizing under impact; Veuve, Safaei, Smith deployable tensegrity).\n For each, summarise: what was varied per-member, what objective was\n optimized, what variation actually emerged at the optimum (i.e. do\n the per-member sizes converge to a few discrete clusters, or do they\n populate a continuum?), and how the heterogeneity compared\n quantitatively against a uniform-member baseline.\n\n(b) MECHANICAL / FORM-FINDING IMPLICATIONS. For a class-1 prismatic\n tensegrity (T3-prism, T4-prism), what is the literature on the\n feasibility envelope of heterogeneous member properties?\n Specifically:\n - Form-finding & self-stress: does varying individual cable\n cross-sections break the symmetric self-stress state, force an\n unsymmetric prestress distribution, or shift the cell's\n equilibrium geometry (R, H, twist)? Cite force-density-method\n and dynamic-relaxation references.\n - Buckling: per-strut diameter governs Euler buckling at known\n slenderness; what is the published trade-off between SEA and\n peak-force when individual struts are deliberately under-sized\n to act as sacrificial buckling fuses?\n - Bistability / multistability (Schenk & Guest 2014; Defossez 2003;\n Sumi & Miyashita): does per-member heterogeneity unlock bistable\n modes not accessible to uniform cells?\n - Anisotropy: how much directional stiffness / energy-absorption\n tailoring can be achieved by per-cable cross-section selection\n in a single T-prism vs. by going to multi-cell tilings?\n - Cycle life / fatigue: per-tendon shore / cross-section\n heterogeneity in TPU-tendon tensegrities — any reuse-count\n data?\n Cite numbers (peak-force reduction %, SEA gain %, prestress shift\n in % of uniform self-stress) where available.\n\n(c) MANUFACTURABILITY ON FFF MULTI-MATERIAL FDM (BAMBU H2D / IDEX).\n The lab prints PETG struts + TPU 85A cables in a single multi-\n material job. Per the PR #35 captive-TPU-core-inside-PLA-shell\n joint design, every joint shell has a uniform bore size set by\n the (currently single) cable diameter. If individual cables get\n independent diameters, what manufacturability gotchas appear?\n Specifically:\n - Bore tolerance: how many distinct cable diameters can a single\n joint sphere accommodate before the PLA shell becomes\n impractically thick (cable_d + 0.8 mm bore clearance, then\n +3 mm core, then +3.2 mm PLA wall)?\n - TPU bridging: can a 1.5 mm cable transition mid-print into a\n 4.5 mm cable on the same TPU extruder pass, or does the\n extruder retraction / line-width mismatch force a layer\n boundary at the transition?\n - Strut diameter discretization: PETG FFF practical strut\n diameters quantize on the 0.4 mm nozzle line-width. Cite\n published recommendations (Khatri 2024; Yavas 2022; Lopes\n 2018; Ye 2023; Bambu Lab / Prusa application notes) for\n discrete-set vs. continuous treatment.\n - Print time: how does the H2D wipe-tower volume scale with\n N_distinct_filament_diameters?\n - Variability noise: if the BO can request 12 different cable\n diameters per specimen but FFF reliably resolves only 3-4\n bins, the additional \"axes\" are noise. Cite repeatability /\n CoV numbers (Khatri 2024; Yavas 2022 PLA+TPU FFF tensile;\n Intrigila 2022; Davami 2025 SLA Tough 2000 + double-T3).\n\n(d) HIGH-DIMENSIONAL BO METHODOLOGY. Once the per-member expansion is\n taken, the design vector becomes O(10) to O(30) dimensional for a\n single T3-prism cell, and O(100+) for a 3x3x2 tiling. Survey peer-\n reviewed and well-cited workshop / preprint methodology for high-\n dim BO over structured design vectors. Cover at minimum:\n - Random embeddings (REMBO — Wang et al. 2016; BOCK; ALEBO —\n Letham et al. 2020).\n - Sparse / SAASBO (Eriksson & Jankowiak 2021) — strong fit\n for \"most members do not matter, a few do\" sparse-effect\n regimes. Recommend specific Ax / BoTorch hooks.\n - Additive / decomposed GPs (Kandasamy 2015; Gardner 2017;\n Wang & Jegelka 2018) — natural fit when per-member effects\n are largely independent.\n - Trust-region BO (TuRBO — Eriksson 2019) and SCBO — strong\n empirical performance in O(100+) dims, especially on\n physically-constrained problems.\n - Hierarchical / conditional search spaces (Ax HierarchicalSearch\n Space, facebook/Ax#140; SMAC; Auto-WEKA; HyperBand) — the\n natural way to nest per-member parameters under a topology\n choice.\n - Latent / generative parameterizations (VAE-BO; LSO — Tripp 2020;\n Maus et al. 2022 LOL-BO; differentiable-CAD or differentiable\n physics priors). Particularly relevant when there are physically\n meaningful symmetries (the 3-fold T-prism is permutation-\n invariant; the 9 cables decompose into 3 saddle + 3 top + 3\n bottom orbits — encode that symmetry explicitly).\n - Symmetry-aware / permutation-invariant kernels (Cohen & Welling;\n Bronstein et al. geometric deep learning; cited in\n Bayesian-optimization-with-symmetry preprints if any).\n - Multi-fidelity / multi-task GPs (PR #33 sim ladder maps\n cleanly onto MTGP / MF-GP — Kandasamy 2017; Wu 2020; Astudillo &\n Frazier 2021) as a way to amortize the high-dim cost.\n - Constraint handling: heterogeneity often introduces feasibility\n constraints (TPU bore set must be ≤4, strut slenderness L/D ≤\n some max, mass ≤ 500 g). Cite NEI / SCBO / cNEHVI.\n For each method, recommend whether to adopt it as the primary BO\n engine for PR #35, as a fallback if dimensionality blows up, or as\n a wrong-fit. Give a concrete recommended progression starting from\n the current 5-D Sobol → next-step BO step.\n\n(e) SYMMETRY EXPLOITATION. The T3-prism has a natural C3 rotational\n symmetry (rotate by 120 deg). All 3 struts are in one orbit; the 9\n cables decompose into 3 orbits of 3 (saddle, top, bottom triangles).\n Under that symmetry, the \"12 diameter axes\" reduce to 4 orbit\n diameters (1 strut orbit + 3 cable orbits). What does the literature\n say about exploiting this symmetry in BO, in form-finding, and in\n optimal-control of tensegrity? Cite Sultan & Skelton symmetry-\n decomposed self-stress; group-theoretic stability (Kangwai & Guest);\n invariant / equivariant GPs (van der Wilk 2018; Holderrieth, Hutchinson\n & Teh 2021). Recommend whether to (i) hard-enforce orbit symmetry as\n the default search space (so the BO never sees a symmetry-broken\n design), (ii) use orbit symmetry only as a kernel prior so symmetry\n breaking can emerge when warranted, or (iii) ignore symmetry and\n let the per-member axes float independently. Justify quantitatively\n in terms of expected sample efficiency given the lab's 50-100\n specimen budget.\n\n(f) NUMERIC RECOMMENDATIONS for the lab's next BO batch (PR #35 follow-on).\n For a single T3-prism cell on the H2D, recommend:\n - Which scalar parameters to keep scalar (R, H, twist, infill %).\n - Which scalar parameters to expand to per-orbit (strut diameter,\n cable diameter — recommend per-orbit, not per-member, for the\n first heterogeneous batch).\n - Which scalar parameters to expand to fully per-member\n (per-cable prestress fraction is the strongest candidate —\n cite Skelton's minimum-mass prestress optimization).\n - Recommended bounds and discretization for each new axis\n (e.g. strut_orbit_d_mm ∈ [3.5, 9.0] continuous; cable_orbit_d_mm\n ∈ (1.2, 1.8, 2.4, 3.0, 4.5) categorical for FFF resolvability;\n per-cable prestress fraction simplex with sum = 1).\n - Recommended BO engine + acquisition + batch size for the\n 50-100 specimen total budget. Give a specific Ax / BoTorch\n configuration recipe (model_class, surrogate_spec,\n acquisition_function_class, batch_size, n_init_sobol).\n - Recommended sample-efficiency analytic: how many specimens does\n SAASBO / TuRBO / orbit-symmetric GP each need on a published\n problem of comparable dimension to reach within 10% of the\n Pareto-front hypervolume? Cite the benchmark.\n\n(g) FAILURE MODES AND OPEN QUESTIONS. Top 5-10 ranked gotchas /\n pitfalls of adopting per-member heterogeneous BO axes for the\n lab's PETG + TPU 85A tensegrity-on-H2D context. For each: cite\n the failure mode from peer-reviewed work and propose a mitigation.\n\n(h) NUMBERED REFERENCES section (DOI when available) supporting every\n quantitative claim in (a)-(g).\n\nCite only primary, peer-reviewed sources or established standards\n(ASTM, ISO, JEDEC, NASA / NIST technical reports, well-cited workshop\npapers at NeurIPS / ICML / AISTATS). Do NOT fabricate DOIs.\n\n\n\n# Per-Member Heterogeneous Design Parameters in Tensegrity/Lattice BO Campaigns\n\n## (a) Literature Precedent for Per-Member Heterogeneous Sizing\n\nThe canonical framework for per-member heterogeneous tensegrity sizing is the Skelton–de Oliveira minimal-mass formulation, where per-member force densities (γ_i for cables, λ_j for bars) and per-member cross-sectional areas (A_si, A_bj) serve as explicit optimization variables. The total mass is minimized subject to equilibrium and material-yield/buckling constraints, formulated as a linear program for single-load cases or a multi-load LP when areas are shared across load cases (nagase2014minimalmassdesign pages 1-3, nagase2014minimalmassdesign pages 5-7). Nagase & Skelton (2014) demonstrated this framework on 2D and 3D box tensegrities, reporting optimized per-member force densities that take distinct values (e.g., γ_i(1) = 0.00 N/m and γ_i(2) = 10.00 N/m in a 2D box) and per-member cross-sections on the order of 10⁻² mm² (nagase2014minimalmassdesign pages 10-12).\n\nGoyal, Skelton & Peraza Hernandez (2020) extended this to 3D T-bar (D-bar) tensegrity lattices, finding a global minimum mass ratio μ_3D = 0.2159 (≈78% mass reduction versus a monolithic column) at complexity q = 3 and aperture angle α = 31°. Critically, optimizing per-member string cross-section areas yielded lower mass than optimizing prestress distribution alone (goyal2020designofminimal pages 6-8). Chen et al. (2021) formulated minimal-mass deployable tensegrity towers where per-member areas A_si and A_bj appear explicitly in the mass and stiffness expressions, with prestress ε₀ as a lower bound on string force densities (chen2021deployabletensegritylunar pages 3-6).\n\nIn topology optimization, Xu et al. (2018) formulated tensegrity sizing using discrete candidate cross-section sets with binary selection variables per member. They introduced global indicators N_As and N_Ac to explicitly count and constrain the number of distinct cross-sectional sizes adopted, enabling manufacturing-aware clustering (xu2018topologyoptimizationof pages 3-4, xu2018topologyoptimizationof pages 2-3). In the ground-structure approach, Zegard & Paulino (2014, 2015) treat per-member areas as continuous LP variables; the optimal truss is statically determinate with at most N_dof nonzero members, implying natural sparsity/clustering (zegard2015grand3—ground pages 1-3, zegard2014grand—ground pages 3-4).\n\nZhang et al. (2021) optimized energy absorption of truncated-octahedral tensegrity lattices, treating per-member-type cross-sectional areas and overall prestress level as design variables, with bar post-buckling explicitly modeled for energy absorption (zhang2021optimizationforenergy pages 1-2). Pajunen et al. (2019) demonstrated 3D-printable tensegrity-inspired structures where adjusting strut and cable diameters independently (ds/dc ratios of 1.44–2.23) yielded a 3.1× increase in strain energy at 0.4 strain and ~1.5× higher normalized strain energy per mass (pajunen2019designandimpact pages 4-5, pajunen2019designandimpact pages 2-3).\n\n**Key finding:** In all per-member sizing studies, the optimized cross-sections cluster into a small number of discrete groups corresponding to member types (e.g., top cables, saddle cables, bottom cables, struts) rather than populating a continuum. This is a direct consequence of symmetry orbits and the structure of the equilibrium constraints.\n\n## (b) Mechanical and Form-Finding Implications\n\n### Form-Finding and Self-Stress\nFor class-1 prismatic tensegrities (T3, T4), group-theoretic analysis under D3 symmetry decomposes the equilibrium matrix into four irreducible blocks (A1, A2, E1, E2). The A1 block (full symmetry) yields the integral self-stress state in which all cables of the same orbit carry equal prestress and all struts carry equal compression (chen2018grouptheoreticexploitationsof pages 8-10, chen2012initialprestressdistribution pages 7-9). Varying individual cable cross-sections breaks this symmetric self-stress: members with different EA values will carry different forces under the same elongation, forcing an asymmetric prestress distribution. The equilibrium geometry (R, H, twist) shifts because the force-density method couples geometry to the self-stress coefficients (masic2005pathplanningand pages 2-2).\n\n### Bistability\nMicheletti (2013) showed that T3-prism bistability arises when geometry and prestrain exceed critical thresholds — specifically, at the equilibrium twist angle ϕ = π/6, high prestrain can destabilize the symmetric configuration, creating two low-symmetry stable equilibria (micheletti2013bistableregimesin pages 9-11, micheletti2013bistableregimesin pages 5-7). Crucially, per-member heterogeneity (different spring constants k_a ≠ k_b) produces asymmetric energy wells — the two bistable minima have different energy values, so heterogeneity in cable/strut diameters shifts bistability thresholds and relative well depths (micheletti2013bistableregimesin pages 13-14). Vangelatos et al. (2020) confirmed experimentally that fabrication heterogeneities localize or confine bistability to specific layers in multi-cell tensegrity lattices (vangelatos2020designandtesting pages 13-16).\n\n### Energy Absorption\nPajunen et al. (2019) demonstrated that modifying strut-to-cable diameter ratios (from ds/dc = 2.23 to 1.44) in a spherically-jointed tensegrity produced 3.1× higher strain energy absorption at 0.4 strain with only 3.6% mass increase (pajunen2019designandimpact pages 4-5). Repeated impact tests showed excellent resilience: average remaining strain of only ~2.28% after 24 impacts (~0.11% per impact) (pajunen2019designandimpact pages 5-7).\n\n### Stability\nPer-member heterogeneity modifies both material stiffness K_M and geometric stiffness K_G; a prestress-stable configuration for one set of member properties may become unstable for another. This is because K_T = K_M + K_G depends on per-member EA products and rest-length mismatches (micheletti2013bistableregimesin pages 2-4).\n\n## (c) Manufacturability on FFF Multi-Material (Bambu H2D)\n\n### Dimensional Accuracy\nFDM/FFF dimensional studies report width deviations averaging ~1.5% and thickness deviations averaging ~9.5% for PLA, PETG, and ABS with a 0.4 mm nozzle at 0.2 mm layer height (tuncel2024theinfluenceof pages 5-7, tuncel2024theinfluenceof pages 1-2). PETG shows higher dimensional deviations than PLA and ABS. Cross-sectional areas consistently exceed nominal values by ~11.5% (tuncel2024theinfluenceof pages 2-4).\n\n### Practical Constraints\n- **Nozzle quantization:** With a 0.4 mm nozzle, practical minimum wall/line width is ~0.4–0.5 mm. Circular strut/cable cross-sections are built from concentric perimeters; reliable diameter steps are approximately 0.8 mm (2 × line width). This means cable diameters below ~1.2 mm are unreliable, and the practical resolution for diameter variation is ~0.6 mm steps.\n- **Bore tolerance:** Each joint shell must accommodate the largest cable entering it. If independent cable diameters range from 1.2 to 4.5 mm, the bore must be sized to the maximum, wasting clearance for thinner cables. Practically, 3–4 distinct cable diameter bins suffice.\n- **TPU bridging:** TPU 85A has poor bridging and retraction performance. Mid-print diameter transitions (e.g., 1.5 mm to 4.5 mm) require significant flow-rate changes that produce inconsistent geometry at the transition. Layer boundaries at transitions are recommended.\n- **Wipe tower:** On the H2D, wipe-tower volume scales with the number of tool changes per layer, not directly with the number of distinct diameters. However, more diameter variation increases slicer complexity.\n- **Recommendation:** Treat cable diameters as categorical with 4–5 bins (e.g., 1.2, 1.8, 2.4, 3.0, 4.5 mm) rather than continuous, and strut diameters similarly discretized in ~1 mm steps.\n\n## (d) High-Dimensional BO Methodology\n\n### SAASBO (Primary Recommendation for 7–12D)\nEriksson & Jankowiak (2021) introduced the SAAS GP prior with half-Cauchy priors on inverse-squared lengthscales, enabling automatic identification of important dimensions. SAASBO uses fully Bayesian inference via NUTS with recommended settings: num_warmup = 256, num_samples = 256, thinning = 32, α = 0.1 (santoni2024comparisonofhighdimensional pages 21-23). On BBOB benchmarks at D=10, SAASBO achieves the highest fraction of solved targets throughout the budget range; at D=20 it remains competitive with TuRBO (santoni2024comparisonofhighdimensional pages 32-36). SAASBO is initialized with as few as m=10 Sobol points and shows strong performance within 50 evaluations (eriksson2021highdimensionalbayesianoptimization pages 14-16). **This is the recommended primary engine for the orbit-reduced 7D search space.**\n\n### TuRBO (Fallback for >20D or Tiled Designs)\nTuRBO maintains multiple local trust regions with adaptive sizing, using Thompson Sampling for batch selection (eriksson2019scalableglobaloptimization pages 2-4). On BBOB at D=40–60, TuRBO clearly surpasses SAASBO, becoming the most effective method for larger budgets (santoni2024comparisonofhighdimensional pages 32-36). TuRBO is designed for scenarios allowing tens to thousands of evaluations and scales well to 100+ dimensions (eriksson2019scalableglobaloptimization pages 8-10). **Recommended as the fallback for fully per-member parameterizations or multi-cell tilings.**\n\n### MORBO (Multi-Objective High-Dimensional)\nDaulton et al. (2022) developed MORBO for multi-objective BO in high-dimensional spaces (tested up to d=222). MORBO achieves best average rank across DTLZ benchmarks at d=100 with batch size q=50, and provides order-of-magnitude computational savings over global GP methods (daulton2022multiobjectivebayesianoptimization pages 22-24, daulton2022multiobjectivebayesianoptimization pages 9-10). **Recommended for multi-objective campaigns if dimensionality exceeds ~20D.**\n\n### SCBO (Constrained BO)\nSCBO extends TuRBO with per-constraint GP models and constrained Thompson Sampling, handling feasibility constraints scalably (maathuis2025scalingbayesianoptimization pages 4-6). **Recommended for enforcing slenderness, mass, and bore-clearance constraints.**\n\n### REMBO/ALEBO (Not Recommended)\nREMBO uses random projections but suffers from distorted objective values; ALEBO addresses some issues but both have high runtime and memory constraints at moderate dimensions (santoni2024comparisonofhighdimensional pages 32-36). **Not recommended** for this application.\n\n### Recommended Progression\n1. **Current (5D):** Continue qNEHVI with Sobol initialization (9 specimens).\n2. **Next batch (7D, orbit-reduced):** Switch to SAASBO surrogate with qNEHVI acquisition. Use `SaasFullyBayesianSingleTaskGP` in BoTorch with NUTS inference (256 warmup, 256 samples). Initialize with 14 Sobol points (2D rule of thumb), then run sequential/small-batch (q=3–5) BO for 36–50 additional specimens.\n3. **If expanding to fully per-member (12D):** Stay with SAASBO but increase Sobol init to 24 points; monitor for lengthscale collapse.\n4. **For multi-cell tilings (30D+):** Switch to TuRBO-based MORBO with local GPs.\n\n## (e) Symmetry Exploitation\n\nThe T3-prism has D3 (≅ C3 × C2) rotational symmetry. Under C3, the 3 struts form one orbit; the 9 cables decompose into 3 orbits of 3 (saddle, top, bottom) (chen2012initialprestressdistribution pages 3-5, chen2012initialprestressdistribution pages 1-3). Group-theoretic block-diagonalization reduces the equilibrium matrix to four independent blocks, with the integral self-stress residing in the fully symmetric A1 block (chen2018grouptheoreticexploitationsof pages 8-10, chen2012initialprestressdistribution pages 7-9). This reduces 12 diameter axes to 4 orbit diameters.\n\nBrown et al. (2024) proved that invariant GP kernels constructed via k_G(x,y) = (1/|G|) Σ_{σ∈G} k(σ(x), y) achieve provably lower maximum information gain, with sample-complexity improvement scaling linearly with group size |G| (brown2024sampleefficientbayesianoptimisation pages 4-6). For C3 (|G|=3), this translates to roughly a 3× reduction in required samples. Empirically, invariant kernels substantially outperform non-invariant baselines on synthetic tasks, and the gains grow with dimension and group size (brown2024sampleefficientbayesianoptimisation pages 6-8). In a nuclear fusion application (12D, permutation-invariant), invariant UCB found high-performance solutions that non-invariant methods missed entirely (brown2024sampleefficientbayesianoptimisation pages 9-11, brown2024sampleefficientbayesianoptimisation pages 27-28).\n\n**Recommendation:** Hard-enforce orbit symmetry as the default search space (option i). With a 50–100 specimen budget, reducing from 12D to 4D (via orbit enforcement) is critical — SAASBO at 4D orbit parameters needs ~30–50 evaluations to converge, well within budget. Allow symmetry-breaking exploration only as a stretch goal after the orbit-symmetric Pareto front is characterized, using an invariant kernel prior (option ii) rather than fully independent axes.\n\n## (f) Numeric Recommendations\n\n### Parameters to Keep Scalar\n- `R_mm` (cell radius): scalar, [15, 45] mm continuous\n- `H_mm` (cell height): scalar, [20, 70] mm continuous \n- `twist_deg`: scalar, [15, 45]° continuous\n- `infill_%`: scalar (if varied), [20, 100]% in 20% steps\n\n### Parameters to Expand to Per-Orbit\n- `strut_orbit_d_mm`: 1 orbit × 1 value, [3.5, 9.0] mm continuous (all 3 struts equal)\n- `cable_saddle_d_mm`: 1 orbit, categorical {1.2, 1.8, 2.4, 3.0, 4.5} mm\n- `cable_top_d_mm`: 1 orbit, categorical {1.2, 1.8, 2.4, 3.0, 4.5} mm\n- `cable_bottom_d_mm`: 1 orbit, categorical {1.2, 1.8, 2.4, 3.0, 4.5} mm\n\n**Total: 7D** (3 continuous + 1 continuous strut + 3 categorical cable orbits)\n\n### Candidates for Fully Per-Member Expansion (Future)\nPer-cable prestress fraction (as in Skelton's minimal-mass formulation where force densities γ_i are independent variables) is the strongest candidate for per-member treatment (nagase2014minimalmassdesign pages 5-7). This would add 3 independent prestress ratios (one per orbit, constrained to sum to 1 on a simplex).\n\n### BO Configuration Recipe\n```python\n# Ax/BoTorch configuration for 7D orbit-symmetric T3-prism\nfrom ax.models.torch.botorch_modular.surrogate import Surrogate\nfrom botorch.models.fully_bayesian import SaasFullyBayesianSingleTaskGP\n\nexperiment_config = {\n \"model_class\": SaasFullyBayesianSingleTaskGP,\n \"acquisition_function\": \"qNEHVI\", # multi-objective\n \"num_warmup\": 256, # NUTS warmup (per Santoni 2024)\n \"num_samples\": 256, # NUTS samples\n \"thinning\": 32,\n \"n_init_sobol\": 14, # 2 × D for 7D\n \"batch_size\": 5, # H2D plate fits ~9, use 5 for BO batches\n \"total_budget\": 50-100,\n \"objectives\": [\"SEA_J_per_g\", \"neg_peak_force_kN\"],\n \"constraints\": [\"mass_g <= 500\", \"strut_slenderness <= 40\"],\n}\n```\n\n### Sample-Efficiency Estimates\nBased on BBOB benchmarks (Santoni et al. 2024): SAASBO at D=10 achieves the highest target-hit rate within budgets of 10D+50 = 150 evaluations (santoni2024comparisonofhighdimensional pages 32-36). At the lab's 7D, convergence to within 10% of optimal is expected within 40–70 evaluations. TuRBO requires larger budgets (>100 evaluations) to outperform SAASBO at D≤20.\n\n## (g) Failure Modes and Pitfalls\n\n1. **Symmetry-breaking artifacts from printing:** FFF layer-by-layer construction inherently breaks the C3 rotational symmetry due to build orientation, seam placement, and support differences. Mitigation: vertical build orientation (already adopted); rotate seam positions; include build-orientation noise in the GP noise model.\n\n2. **Cable diameter below FFF resolution:** Requesting cable diameters finer than ~1.2 mm with a 0.4 mm nozzle produces unreliable geometry. Mitigation: enforce categorical cable diameters with a 1.2 mm lower bound (tuncel2024theinfluenceof pages 2-4).\n\n3. **Prestress-stability loss under heterogeneity:** Per-member cable heterogeneity can inadvertently destabilize the self-stress equilibrium, shifting the cell into an unintended bistable or collapsed configuration (micheletti2013bistableregimesin pages 13-14, micheletti2013bistableregimesin pages 2-4). Mitigation: include a self-stress feasibility check (eigenvalue of tangent stiffness > 0) as a BO constraint.\n\n4. **GP model misspecification in mixed continuous/categorical space:** SAASBO assumes continuous parameters; categorical cable diameters require probabilistic reparameterization or one-hot encoding. Mitigation: use Ax's mixed-parameter support with probabilistic reparameterization for discrete parameters.\n\n5. **NUTS computational cost:** Fully Bayesian inference scales as O(N³D) per sample. At 100 observations × 7D with 256 NUTS samples, wall-clock overhead is ~5–15 minutes per iteration. Mitigation: use MAP fallback if budget is time-constrained (eriksson2021highdimensionalbayesianoptimization pages 4-5).\n\n6. **Bore-tolerance feasibility:** If three cable orbits have three different diameters, each 6-way joint must accommodate multiple bore sizes. The PLA shell becomes impractically thick if the spread is large. Mitigation: constrain max(cable_d) - min(cable_d) ≤ 2.0 mm as a BO feasibility constraint.\n\n7. **Overfitting with small data:** With only 50–100 specimens, a 12D fully per-member space is severely undersampled (curse of dimensionality). Mitigation: use orbit-reduced 7D as default; SAASBO's sparsity prior provides natural regularization (eriksson2021highdimensionalbayesianoptimization pages 3-4).\n\n8. **Fatigue/cycle-life data gap:** No published reuse-count data exists for TPU 85A tendons in tensegrity configurations under cyclic loading. Mitigation: include 5-cycle repeated compression in the test protocol to capture degradation as an additional BO objective.\n\n9. **Wipe-tower waste scaling:** Each additional distinct filament diameter per layer increases purge volume on the H2D. With 4 cable bins + 1 strut, this is manageable; fully per-member treatment with 12 diameters would be wasteful. Mitigation: the orbit-reduced approach naturally limits distinct diameters.\n\n10. **Interaction effects between orbit diameters and global geometry:** Cable orbit diameters interact strongly with twist angle and cell radius (they jointly determine prestress and buckling modes). SAASBO may underestimate these interactions if the sparse prior suppresses cross-terms. Mitigation: monitor GP lengthscales; if multiple dimensions show short lengthscales, consider switching to a non-sparse GP or TuRBO.\n\n## (h) References\n\n1. Skelton, R.E. & de Oliveira, M.C. (2009). *Tensegrity Systems*. Springer. DOI: 10.1007/978-0-387-74242-7\n2. 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Scalable global optimization via local bayesian optimization. Text, Jan 2019. URL: https://doi.org/10.48550/arxiv.1910.01739, doi:10.48550/arxiv.1910.01739. This article has 930 citations and is from a peer-reviewed journal.\n\n30. (daulton2022multiobjectivebayesianoptimization pages 22-24): Samuel Daulton, David Eriksson, Maximilian Balandat, and Eytan Bakshy. Multi-objective bayesian optimization over high-dimensional search spaces. Preprint, Jan 2022. URL: https://doi.org/10.48550/arxiv.2109.10964, doi:10.48550/arxiv.2109.10964. This article has 244 citations.\n\n31. (daulton2022multiobjectivebayesianoptimization pages 9-10): Samuel Daulton, David Eriksson, Maximilian Balandat, and Eytan Bakshy. Multi-objective bayesian optimization over high-dimensional search spaces. Preprint, Jan 2022. URL: https://doi.org/10.48550/arxiv.2109.10964, doi:10.48550/arxiv.2109.10964. This article has 244 citations.\n\n32. (maathuis2025scalingbayesianoptimization pages 4-6): Hauke F. Maathuis, Roeland De Breuker, and Saullo G. P. Castro. Scaling bayesian optimization for high-dimensional and large-scale constrained spaces. AIAA Journal, pages 1-11, Jul 2025. URL: https://doi.org/10.2514/1.j065252, doi:10.2514/1.j065252. This article has 5 citations and is from a peer-reviewed journal.\n\n33. (chen2012initialprestressdistribution pages 3-5): YAO CHEN and JIAN FENG. Initial prestress distribution and natural vibration analysis of tensegrity structures based on group theory. International Journal of Structural Stability and Dynamics, 12:213-231, Apr 2012. URL: https://doi.org/10.1142/s0219455412500010, doi:10.1142/s0219455412500010. This article has 17 citations and is from a peer-reviewed journal.\n\n34. (chen2012initialprestressdistribution pages 1-3): YAO CHEN and JIAN FENG. Initial prestress distribution and natural vibration analysis of tensegrity structures based on group theory. International Journal of Structural Stability and Dynamics, 12:213-231, Apr 2012. 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URL: https://doi.org/10.48550/arxiv.2410.16972, doi:10.48550/arxiv.2410.16972. This article has 9 citations.\n\n38. (brown2024sampleefficientbayesianoptimisation pages 27-28): Theodore Brown, Alexandru Cioba, and Ilija Bogunovic. Sample-efficient bayesian optimisation using known invariances. ArXiv, Oct 2024. URL: https://doi.org/10.48550/arxiv.2410.16972, doi:10.48550/arxiv.2410.16972. This article has 9 citations.\n\n39. (eriksson2021highdimensionalbayesianoptimization pages 4-5): David Eriksson and Martin Jankowiak. High-dimensional bayesian optimization with sparse axis-aligned subspaces. Preprint, Jan 2021. URL: https://doi.org/10.48550/arxiv.2103.00349, doi:10.48550/arxiv.2103.00349. This article has 297 citations.\n\n40. (eriksson2021highdimensionalbayesianoptimization pages 3-4): David Eriksson and Martin Jankowiak. High-dimensional bayesian optimization with sparse axis-aligned subspaces. Preprint, Jan 2021. URL: https://doi.org/10.48550/arxiv.2103.00349, doi:10.48550/arxiv.2103.00349. This article has 297 citations.", + "answer_reasoning": null, + "has_successful_answer": true, + "total_cost": null, + "total_queries": null +} diff --git a/edison-trajectories/heterogeneous-params/heterogeneous-params-5191cf4d-873a-4e3e-9077-9565a2602ba1.md b/edison-trajectories/heterogeneous-params/heterogeneous-params-5191cf4d-873a-4e3e-9077-9565a2602ba1.md new file mode 100644 index 00000000..0493d7eb --- /dev/null +++ b/edison-trajectories/heterogeneous-params/heterogeneous-params-5191cf4d-873a-4e3e-9077-9565a2602ba1.md @@ -0,0 +1,467 @@ +# Edison LITERATURE_HIGH — Per-member (heterogeneous) design parameters in tensegrity / lattice BO campaigns — when to vary strut and cable diameters independently, and how to keep the resulting high-dimensional search space tractable + +- task_id: `5191cf4d-873a-4e3e-9077-9565a2602ba1` +- slug: `heterogeneous-params` +- job: `LITERATURE_HIGH` +- status: `success` +- fetched_at: `2026-05-22T17:00:17Z` +- source PR comment: https://github.com/vertical-cloud-lab/tensegrity-optimization/pull/24#issuecomment-4520542433 + +--- + +Question: Per-member (heterogeneous) design parameters in tensegrity / lattice BO campaigns — when to vary strut and cable diameters independently, and how to keep the resulting high-dimensional search space tractable. + +Project context (read in full before answering): + +* Hardware: multi-material 3D-printed tensegrity-inspired energy absorber. + Strut material PETG (or PLA in the current PR #35 batch), tendon material + TPU 85A (NinjaFlex-class, E ~12 MPa secant, sigma_break ~26 MPa, rho + ~1200 kg/m^3, strain-at-break ~550-660%). Printed on a Bambu H2D + dual-extrusion FFF system with manual-painted supports. Baseline topology + is a T3-prism (3 struts, 9 cables = 3 saddle + 3 top + 3 bottom). Stretch + goals: 6-bar SUPERball icosahedron, stacked / tiled prisms, Pajunen + truncated-octa. +* Existing BO setup (PR #30 + PR #33 + PR #35): an Ax / BoTorch qNEHVI + multi-objective campaign. PR #35 specifically — `bo/t3_prism_sobol_batch.py` + — currently sweeps FIVE T3-prism design variables as a single Sobol batch + of 9 specimens on the H2D plate: + - `R_mm` (cell radius) + - `H_mm` (cell height) + - `twist_deg` (rotation between top and bottom triangles) + - `strut_d_mm` (ONE diameter — applies to all 3 struts) + - `cable_d_mm` (ONE diameter — applies to all 9 cables) + Frozen: topology=t3_prism, tiling=1x1x1, joint geometry (captive TPU core + inside hollow PLA shell), build_orientation=vertical, tpu_shore=85A. +* Proposal under discussion (PR #24 comment 4520542433): allow the diameter + of every individual strut and every individual cable to vary independently + (so a T3-prism specimen would have ~3 strut-diameter axes + 9 cable- + diameter axes = 12 diameter axes, instead of 2). The user also asks + "similar for other parameters perhaps" — i.e. per-member length, + per-cable prestress, per-member material assignment, per-cable shore, + per-strut layer-height, etc. +* Companion PR #24 design-space docs already encode a hierarchical + `topology_family` -> conditional child parameters search space (per + facebook/Ax#140). The per-member proposal sits one level below that — + inside any chosen topology family, expand selected scalar parameters into + vector / per-member parameters. + +Answer EVERY sub-question below with primary, peer-reviewed citations +(DOIs where available). When recommending a numeric value or a default +choice, justify from a cited source rather than rule-of-thumb. Do not +fabricate DOIs. + +(a) MOTIVATION / LITERATURE PRECEDENT. In peer-reviewed tensegrity, cable + dome, deployable space-structure, lattice-metamaterial, and ground- + structure topology optimization work, when have authors deliberately + allowed individual struts and individual cables to have heterogeneous + (per-member) cross-section, length, prestress, or material — vs. + enforcing a uniform value across the cell? Identify the canonical + references (e.g. Skelton & de Oliveira 2009 minimal-mass tensegrity + sizing; Masic, Skelton & Gill 2006 form-finding with member-wise force + densities; Adam & Smith active-tensegrity bridges; Pellegrino & + Calladine self-stress; Tibert & Pellegrino reviews; Achtziger / + Bendsoe / Sigmund ground-structure topology optimization; Zegard & + Paulino GRAND/Polytop; Hanaor double-layer grids; Goyal & Skelton + minimum-mass tensegrity dynamics; Bel Hadj Ali, Rhode-Barbarigos, + Smith active control; Wang, Senatore, Marano 2021+ optimal tensegrity + sizing under impact; Veuve, Safaei, Smith deployable tensegrity). + For each, summarise: what was varied per-member, what objective was + optimized, what variation actually emerged at the optimum (i.e. do + the per-member sizes converge to a few discrete clusters, or do they + populate a continuum?), and how the heterogeneity compared + quantitatively against a uniform-member baseline. + +(b) MECHANICAL / FORM-FINDING IMPLICATIONS. For a class-1 prismatic + tensegrity (T3-prism, T4-prism), what is the literature on the + feasibility envelope of heterogeneous member properties? + Specifically: + - Form-finding & self-stress: does varying individual cable + cross-sections break the symmetric self-stress state, force an + unsymmetric prestress distribution, or shift the cell's + equilibrium geometry (R, H, twist)? Cite force-density-method + and dynamic-relaxation references. + - Buckling: per-strut diameter governs Euler buckling at known + slenderness; what is the published trade-off between SEA and + peak-force when individual struts are deliberately under-sized + to act as sacrificial buckling fuses? + - Bistability / multistability (Schenk & Guest 2014; Defossez 2003; + Sumi & Miyashita): does per-member heterogeneity unlock bistable + modes not accessible to uniform cells? + - Anisotropy: how much directional stiffness / energy-absorption + tailoring can be achieved by per-cable cross-section selection + in a single T-prism vs. by going to multi-cell tilings? + - Cycle life / fatigue: per-tendon shore / cross-section + heterogeneity in TPU-tendon tensegrities — any reuse-count + data? + Cite numbers (peak-force reduction %, SEA gain %, prestress shift + in % of uniform self-stress) where available. + +(c) MANUFACTURABILITY ON FFF MULTI-MATERIAL FDM (BAMBU H2D / IDEX). + The lab prints PETG struts + TPU 85A cables in a single multi- + material job. Per the PR #35 captive-TPU-core-inside-PLA-shell + joint design, every joint shell has a uniform bore size set by + the (currently single) cable diameter. If individual cables get + independent diameters, what manufacturability gotchas appear? + Specifically: + - Bore tolerance: how many distinct cable diameters can a single + joint sphere accommodate before the PLA shell becomes + impractically thick (cable_d + 0.8 mm bore clearance, then + +3 mm core, then +3.2 mm PLA wall)? + - TPU bridging: can a 1.5 mm cable transition mid-print into a + 4.5 mm cable on the same TPU extruder pass, or does the + extruder retraction / line-width mismatch force a layer + boundary at the transition? + - Strut diameter discretization: PETG FFF practical strut + diameters quantize on the 0.4 mm nozzle line-width. Cite + published recommendations (Khatri 2024; Yavas 2022; Lopes + 2018; Ye 2023; Bambu Lab / Prusa application notes) for + discrete-set vs. continuous treatment. + - Print time: how does the H2D wipe-tower volume scale with + N_distinct_filament_diameters? + - Variability noise: if the BO can request 12 different cable + diameters per specimen but FFF reliably resolves only 3-4 + bins, the additional "axes" are noise. Cite repeatability / + CoV numbers (Khatri 2024; Yavas 2022 PLA+TPU FFF tensile; + Intrigila 2022; Davami 2025 SLA Tough 2000 + double-T3). + +(d) HIGH-DIMENSIONAL BO METHODOLOGY. Once the per-member expansion is + taken, the design vector becomes O(10) to O(30) dimensional for a + single T3-prism cell, and O(100+) for a 3x3x2 tiling. Survey peer- + reviewed and well-cited workshop / preprint methodology for high- + dim BO over structured design vectors. Cover at minimum: + - Random embeddings (REMBO — Wang et al. 2016; BOCK; ALEBO — + Letham et al. 2020). + - Sparse / SAASBO (Eriksson & Jankowiak 2021) — strong fit + for "most members do not matter, a few do" sparse-effect + regimes. Recommend specific Ax / BoTorch hooks. + - Additive / decomposed GPs (Kandasamy 2015; Gardner 2017; + Wang & Jegelka 2018) — natural fit when per-member effects + are largely independent. + - Trust-region BO (TuRBO — Eriksson 2019) and SCBO — strong + empirical performance in O(100+) dims, especially on + physically-constrained problems. + - Hierarchical / conditional search spaces (Ax HierarchicalSearch + Space, facebook/Ax#140; SMAC; Auto-WEKA; HyperBand) — the + natural way to nest per-member parameters under a topology + choice. + - Latent / generative parameterizations (VAE-BO; LSO — Tripp 2020; + Maus et al. 2022 LOL-BO; differentiable-CAD or differentiable + physics priors). Particularly relevant when there are physically + meaningful symmetries (the 3-fold T-prism is permutation- + invariant; the 9 cables decompose into 3 saddle + 3 top + 3 + bottom orbits — encode that symmetry explicitly). + - Symmetry-aware / permutation-invariant kernels (Cohen & Welling; + Bronstein et al. geometric deep learning; cited in + Bayesian-optimization-with-symmetry preprints if any). + - Multi-fidelity / multi-task GPs (PR #33 sim ladder maps + cleanly onto MTGP / MF-GP — Kandasamy 2017; Wu 2020; Astudillo & + Frazier 2021) as a way to amortize the high-dim cost. + - Constraint handling: heterogeneity often introduces feasibility + constraints (TPU bore set must be ≤4, strut slenderness L/D ≤ + some max, mass ≤ 500 g). Cite NEI / SCBO / cNEHVI. + For each method, recommend whether to adopt it as the primary BO + engine for PR #35, as a fallback if dimensionality blows up, or as + a wrong-fit. Give a concrete recommended progression starting from + the current 5-D Sobol → next-step BO step. + +(e) SYMMETRY EXPLOITATION. The T3-prism has a natural C3 rotational + symmetry (rotate by 120 deg). All 3 struts are in one orbit; the 9 + cables decompose into 3 orbits of 3 (saddle, top, bottom triangles). + Under that symmetry, the "12 diameter axes" reduce to 4 orbit + diameters (1 strut orbit + 3 cable orbits). What does the literature + say about exploiting this symmetry in BO, in form-finding, and in + optimal-control of tensegrity? Cite Sultan & Skelton symmetry- + decomposed self-stress; group-theoretic stability (Kangwai & Guest); + invariant / equivariant GPs (van der Wilk 2018; Holderrieth, Hutchinson + & Teh 2021). Recommend whether to (i) hard-enforce orbit symmetry as + the default search space (so the BO never sees a symmetry-broken + design), (ii) use orbit symmetry only as a kernel prior so symmetry + breaking can emerge when warranted, or (iii) ignore symmetry and + let the per-member axes float independently. Justify quantitatively + in terms of expected sample efficiency given the lab's 50-100 + specimen budget. + +(f) NUMERIC RECOMMENDATIONS for the lab's next BO batch (PR #35 follow-on). + For a single T3-prism cell on the H2D, recommend: + - Which scalar parameters to keep scalar (R, H, twist, infill %). + - Which scalar parameters to expand to per-orbit (strut diameter, + cable diameter — recommend per-orbit, not per-member, for the + first heterogeneous batch). + - Which scalar parameters to expand to fully per-member + (per-cable prestress fraction is the strongest candidate — + cite Skelton's minimum-mass prestress optimization). + - Recommended bounds and discretization for each new axis + (e.g. strut_orbit_d_mm ∈ [3.5, 9.0] continuous; cable_orbit_d_mm + ∈ (1.2, 1.8, 2.4, 3.0, 4.5) categorical for FFF resolvability; + per-cable prestress fraction simplex with sum = 1). + - Recommended BO engine + acquisition + batch size for the + 50-100 specimen total budget. Give a specific Ax / BoTorch + configuration recipe (model_class, surrogate_spec, + acquisition_function_class, batch_size, n_init_sobol). + - Recommended sample-efficiency analytic: how many specimens does + SAASBO / TuRBO / orbit-symmetric GP each need on a published + problem of comparable dimension to reach within 10% of the + Pareto-front hypervolume? Cite the benchmark. + +(g) FAILURE MODES AND OPEN QUESTIONS. Top 5-10 ranked gotchas / + pitfalls of adopting per-member heterogeneous BO axes for the + lab's PETG + TPU 85A tensegrity-on-H2D context. For each: cite + the failure mode from peer-reviewed work and propose a mitigation. + +(h) NUMBERED REFERENCES section (DOI when available) supporting every + quantitative claim in (a)-(g). + +Cite only primary, peer-reviewed sources or established standards +(ASTM, ISO, JEDEC, NASA / NIST technical reports, well-cited workshop +papers at NeurIPS / ICML / AISTATS). Do NOT fabricate DOIs. + + + +# Per-Member Heterogeneous Design Parameters in Tensegrity/Lattice BO Campaigns + +## (a) Literature Precedent for Per-Member Heterogeneous Sizing + +The canonical framework for per-member heterogeneous tensegrity sizing is the Skelton–de Oliveira minimal-mass formulation, where per-member force densities (γ_i for cables, λ_j for bars) and per-member cross-sectional areas (A_si, A_bj) serve as explicit optimization variables. The total mass is minimized subject to equilibrium and material-yield/buckling constraints, formulated as a linear program for single-load cases or a multi-load LP when areas are shared across load cases (nagase2014minimalmassdesign pages 1-3, nagase2014minimalmassdesign pages 5-7). Nagase & Skelton (2014) demonstrated this framework on 2D and 3D box tensegrities, reporting optimized per-member force densities that take distinct values (e.g., γ_i(1) = 0.00 N/m and γ_i(2) = 10.00 N/m in a 2D box) and per-member cross-sections on the order of 10⁻² mm² (nagase2014minimalmassdesign pages 10-12). + +Goyal, Skelton & Peraza Hernandez (2020) extended this to 3D T-bar (D-bar) tensegrity lattices, finding a global minimum mass ratio μ_3D = 0.2159 (≈78% mass reduction versus a monolithic column) at complexity q = 3 and aperture angle α = 31°. Critically, optimizing per-member string cross-section areas yielded lower mass than optimizing prestress distribution alone (goyal2020designofminimal pages 6-8). Chen et al. (2021) formulated minimal-mass deployable tensegrity towers where per-member areas A_si and A_bj appear explicitly in the mass and stiffness expressions, with prestress ε₀ as a lower bound on string force densities (chen2021deployabletensegritylunar pages 3-6). + +In topology optimization, Xu et al. (2018) formulated tensegrity sizing using discrete candidate cross-section sets with binary selection variables per member. They introduced global indicators N_As and N_Ac to explicitly count and constrain the number of distinct cross-sectional sizes adopted, enabling manufacturing-aware clustering (xu2018topologyoptimizationof pages 3-4, xu2018topologyoptimizationof pages 2-3). In the ground-structure approach, Zegard & Paulino (2014, 2015) treat per-member areas as continuous LP variables; the optimal truss is statically determinate with at most N_dof nonzero members, implying natural sparsity/clustering (zegard2015grand3—ground pages 1-3, zegard2014grand—ground pages 3-4). + +Zhang et al. (2021) optimized energy absorption of truncated-octahedral tensegrity lattices, treating per-member-type cross-sectional areas and overall prestress level as design variables, with bar post-buckling explicitly modeled for energy absorption (zhang2021optimizationforenergy pages 1-2). Pajunen et al. (2019) demonstrated 3D-printable tensegrity-inspired structures where adjusting strut and cable diameters independently (ds/dc ratios of 1.44–2.23) yielded a 3.1× increase in strain energy at 0.4 strain and ~1.5× higher normalized strain energy per mass (pajunen2019designandimpact pages 4-5, pajunen2019designandimpact pages 2-3). + +**Key finding:** In all per-member sizing studies, the optimized cross-sections cluster into a small number of discrete groups corresponding to member types (e.g., top cables, saddle cables, bottom cables, struts) rather than populating a continuum. This is a direct consequence of symmetry orbits and the structure of the equilibrium constraints. + +## (b) Mechanical and Form-Finding Implications + +### Form-Finding and Self-Stress +For class-1 prismatic tensegrities (T3, T4), group-theoretic analysis under D3 symmetry decomposes the equilibrium matrix into four irreducible blocks (A1, A2, E1, E2). The A1 block (full symmetry) yields the integral self-stress state in which all cables of the same orbit carry equal prestress and all struts carry equal compression (chen2018grouptheoreticexploitationsof pages 8-10, chen2012initialprestressdistribution pages 7-9). Varying individual cable cross-sections breaks this symmetric self-stress: members with different EA values will carry different forces under the same elongation, forcing an asymmetric prestress distribution. The equilibrium geometry (R, H, twist) shifts because the force-density method couples geometry to the self-stress coefficients (masic2005pathplanningand pages 2-2). + +### Bistability +Micheletti (2013) showed that T3-prism bistability arises when geometry and prestrain exceed critical thresholds — specifically, at the equilibrium twist angle ϕ = π/6, high prestrain can destabilize the symmetric configuration, creating two low-symmetry stable equilibria (micheletti2013bistableregimesin pages 9-11, micheletti2013bistableregimesin pages 5-7). Crucially, per-member heterogeneity (different spring constants k_a ≠ k_b) produces asymmetric energy wells — the two bistable minima have different energy values, so heterogeneity in cable/strut diameters shifts bistability thresholds and relative well depths (micheletti2013bistableregimesin pages 13-14). Vangelatos et al. (2020) confirmed experimentally that fabrication heterogeneities localize or confine bistability to specific layers in multi-cell tensegrity lattices (vangelatos2020designandtesting pages 13-16). + +### Energy Absorption +Pajunen et al. (2019) demonstrated that modifying strut-to-cable diameter ratios (from ds/dc = 2.23 to 1.44) in a spherically-jointed tensegrity produced 3.1× higher strain energy absorption at 0.4 strain with only 3.6% mass increase (pajunen2019designandimpact pages 4-5). Repeated impact tests showed excellent resilience: average remaining strain of only ~2.28% after 24 impacts (~0.11% per impact) (pajunen2019designandimpact pages 5-7). + +### Stability +Per-member heterogeneity modifies both material stiffness K_M and geometric stiffness K_G; a prestress-stable configuration for one set of member properties may become unstable for another. This is because K_T = K_M + K_G depends on per-member EA products and rest-length mismatches (micheletti2013bistableregimesin pages 2-4). + +## (c) Manufacturability on FFF Multi-Material (Bambu H2D) + +### Dimensional Accuracy +FDM/FFF dimensional studies report width deviations averaging ~1.5% and thickness deviations averaging ~9.5% for PLA, PETG, and ABS with a 0.4 mm nozzle at 0.2 mm layer height (tuncel2024theinfluenceof pages 5-7, tuncel2024theinfluenceof pages 1-2). PETG shows higher dimensional deviations than PLA and ABS. Cross-sectional areas consistently exceed nominal values by ~11.5% (tuncel2024theinfluenceof pages 2-4). + +### Practical Constraints +- **Nozzle quantization:** With a 0.4 mm nozzle, practical minimum wall/line width is ~0.4–0.5 mm. Circular strut/cable cross-sections are built from concentric perimeters; reliable diameter steps are approximately 0.8 mm (2 × line width). This means cable diameters below ~1.2 mm are unreliable, and the practical resolution for diameter variation is ~0.6 mm steps. +- **Bore tolerance:** Each joint shell must accommodate the largest cable entering it. If independent cable diameters range from 1.2 to 4.5 mm, the bore must be sized to the maximum, wasting clearance for thinner cables. Practically, 3–4 distinct cable diameter bins suffice. +- **TPU bridging:** TPU 85A has poor bridging and retraction performance. Mid-print diameter transitions (e.g., 1.5 mm to 4.5 mm) require significant flow-rate changes that produce inconsistent geometry at the transition. Layer boundaries at transitions are recommended. +- **Wipe tower:** On the H2D, wipe-tower volume scales with the number of tool changes per layer, not directly with the number of distinct diameters. However, more diameter variation increases slicer complexity. +- **Recommendation:** Treat cable diameters as categorical with 4–5 bins (e.g., 1.2, 1.8, 2.4, 3.0, 4.5 mm) rather than continuous, and strut diameters similarly discretized in ~1 mm steps. + +## (d) High-Dimensional BO Methodology + +### SAASBO (Primary Recommendation for 7–12D) +Eriksson & Jankowiak (2021) introduced the SAAS GP prior with half-Cauchy priors on inverse-squared lengthscales, enabling automatic identification of important dimensions. SAASBO uses fully Bayesian inference via NUTS with recommended settings: num_warmup = 256, num_samples = 256, thinning = 32, α = 0.1 (santoni2024comparisonofhighdimensional pages 21-23). On BBOB benchmarks at D=10, SAASBO achieves the highest fraction of solved targets throughout the budget range; at D=20 it remains competitive with TuRBO (santoni2024comparisonofhighdimensional pages 32-36). SAASBO is initialized with as few as m=10 Sobol points and shows strong performance within 50 evaluations (eriksson2021highdimensionalbayesianoptimization pages 14-16). **This is the recommended primary engine for the orbit-reduced 7D search space.** + +### TuRBO (Fallback for >20D or Tiled Designs) +TuRBO maintains multiple local trust regions with adaptive sizing, using Thompson Sampling for batch selection (eriksson2019scalableglobaloptimization pages 2-4). On BBOB at D=40–60, TuRBO clearly surpasses SAASBO, becoming the most effective method for larger budgets (santoni2024comparisonofhighdimensional pages 32-36). TuRBO is designed for scenarios allowing tens to thousands of evaluations and scales well to 100+ dimensions (eriksson2019scalableglobaloptimization pages 8-10). **Recommended as the fallback for fully per-member parameterizations or multi-cell tilings.** + +### MORBO (Multi-Objective High-Dimensional) +Daulton et al. (2022) developed MORBO for multi-objective BO in high-dimensional spaces (tested up to d=222). MORBO achieves best average rank across DTLZ benchmarks at d=100 with batch size q=50, and provides order-of-magnitude computational savings over global GP methods (daulton2022multiobjectivebayesianoptimization pages 22-24, daulton2022multiobjectivebayesianoptimization pages 9-10). **Recommended for multi-objective campaigns if dimensionality exceeds ~20D.** + +### SCBO (Constrained BO) +SCBO extends TuRBO with per-constraint GP models and constrained Thompson Sampling, handling feasibility constraints scalably (maathuis2025scalingbayesianoptimization pages 4-6). **Recommended for enforcing slenderness, mass, and bore-clearance constraints.** + +### REMBO/ALEBO (Not Recommended) +REMBO uses random projections but suffers from distorted objective values; ALEBO addresses some issues but both have high runtime and memory constraints at moderate dimensions (santoni2024comparisonofhighdimensional pages 32-36). **Not recommended** for this application. + +### Recommended Progression +1. **Current (5D):** Continue qNEHVI with Sobol initialization (9 specimens). +2. **Next batch (7D, orbit-reduced):** Switch to SAASBO surrogate with qNEHVI acquisition. Use `SaasFullyBayesianSingleTaskGP` in BoTorch with NUTS inference (256 warmup, 256 samples). Initialize with 14 Sobol points (2D rule of thumb), then run sequential/small-batch (q=3–5) BO for 36–50 additional specimens. +3. **If expanding to fully per-member (12D):** Stay with SAASBO but increase Sobol init to 24 points; monitor for lengthscale collapse. +4. **For multi-cell tilings (30D+):** Switch to TuRBO-based MORBO with local GPs. + +## (e) Symmetry Exploitation + +The T3-prism has D3 (≅ C3 × C2) rotational symmetry. Under C3, the 3 struts form one orbit; the 9 cables decompose into 3 orbits of 3 (saddle, top, bottom) (chen2012initialprestressdistribution pages 3-5, chen2012initialprestressdistribution pages 1-3). Group-theoretic block-diagonalization reduces the equilibrium matrix to four independent blocks, with the integral self-stress residing in the fully symmetric A1 block (chen2018grouptheoreticexploitationsof pages 8-10, chen2012initialprestressdistribution pages 7-9). This reduces 12 diameter axes to 4 orbit diameters. + +Brown et al. (2024) proved that invariant GP kernels constructed via k_G(x,y) = (1/|G|) Σ_{σ∈G} k(σ(x), y) achieve provably lower maximum information gain, with sample-complexity improvement scaling linearly with group size |G| (brown2024sampleefficientbayesianoptimisation pages 4-6). For C3 (|G|=3), this translates to roughly a 3× reduction in required samples. Empirically, invariant kernels substantially outperform non-invariant baselines on synthetic tasks, and the gains grow with dimension and group size (brown2024sampleefficientbayesianoptimisation pages 6-8). In a nuclear fusion application (12D, permutation-invariant), invariant UCB found high-performance solutions that non-invariant methods missed entirely (brown2024sampleefficientbayesianoptimisation pages 9-11, brown2024sampleefficientbayesianoptimisation pages 27-28). + +**Recommendation:** Hard-enforce orbit symmetry as the default search space (option i). With a 50–100 specimen budget, reducing from 12D to 4D (via orbit enforcement) is critical — SAASBO at 4D orbit parameters needs ~30–50 evaluations to converge, well within budget. Allow symmetry-breaking exploration only as a stretch goal after the orbit-symmetric Pareto front is characterized, using an invariant kernel prior (option ii) rather than fully independent axes. + +## (f) Numeric Recommendations + +### Parameters to Keep Scalar +- `R_mm` (cell radius): scalar, [15, 45] mm continuous +- `H_mm` (cell height): scalar, [20, 70] mm continuous +- `twist_deg`: scalar, [15, 45]° continuous +- `infill_%`: scalar (if varied), [20, 100]% in 20% steps + +### Parameters to Expand to Per-Orbit +- `strut_orbit_d_mm`: 1 orbit × 1 value, [3.5, 9.0] mm continuous (all 3 struts equal) +- `cable_saddle_d_mm`: 1 orbit, categorical {1.2, 1.8, 2.4, 3.0, 4.5} mm +- `cable_top_d_mm`: 1 orbit, categorical {1.2, 1.8, 2.4, 3.0, 4.5} mm +- `cable_bottom_d_mm`: 1 orbit, categorical {1.2, 1.8, 2.4, 3.0, 4.5} mm + +**Total: 7D** (3 continuous + 1 continuous strut + 3 categorical cable orbits) + +### Candidates for Fully Per-Member Expansion (Future) +Per-cable prestress fraction (as in Skelton's minimal-mass formulation where force densities γ_i are independent variables) is the strongest candidate for per-member treatment (nagase2014minimalmassdesign pages 5-7). This would add 3 independent prestress ratios (one per orbit, constrained to sum to 1 on a simplex). + +### BO Configuration Recipe +```python +# Ax/BoTorch configuration for 7D orbit-symmetric T3-prism +from ax.models.torch.botorch_modular.surrogate import Surrogate +from botorch.models.fully_bayesian import SaasFullyBayesianSingleTaskGP + +experiment_config = { + "model_class": SaasFullyBayesianSingleTaskGP, + "acquisition_function": "qNEHVI", # multi-objective + "num_warmup": 256, # NUTS warmup (per Santoni 2024) + "num_samples": 256, # NUTS samples + "thinning": 32, + "n_init_sobol": 14, # 2 × D for 7D + "batch_size": 5, # H2D plate fits ~9, use 5 for BO batches + "total_budget": 50-100, + "objectives": ["SEA_J_per_g", "neg_peak_force_kN"], + "constraints": ["mass_g <= 500", "strut_slenderness <= 40"], +} +``` + +### Sample-Efficiency Estimates +Based on BBOB benchmarks (Santoni et al. 2024): SAASBO at D=10 achieves the highest target-hit rate within budgets of 10D+50 = 150 evaluations (santoni2024comparisonofhighdimensional pages 32-36). At the lab's 7D, convergence to within 10% of optimal is expected within 40–70 evaluations. TuRBO requires larger budgets (>100 evaluations) to outperform SAASBO at D≤20. + +## (g) Failure Modes and Pitfalls + +1. **Symmetry-breaking artifacts from printing:** FFF layer-by-layer construction inherently breaks the C3 rotational symmetry due to build orientation, seam placement, and support differences. Mitigation: vertical build orientation (already adopted); rotate seam positions; include build-orientation noise in the GP noise model. + +2. **Cable diameter below FFF resolution:** Requesting cable diameters finer than ~1.2 mm with a 0.4 mm nozzle produces unreliable geometry. Mitigation: enforce categorical cable diameters with a 1.2 mm lower bound (tuncel2024theinfluenceof pages 2-4). + +3. **Prestress-stability loss under heterogeneity:** Per-member cable heterogeneity can inadvertently destabilize the self-stress equilibrium, shifting the cell into an unintended bistable or collapsed configuration (micheletti2013bistableregimesin pages 13-14, micheletti2013bistableregimesin pages 2-4). Mitigation: include a self-stress feasibility check (eigenvalue of tangent stiffness > 0) as a BO constraint. + +4. **GP model misspecification in mixed continuous/categorical space:** SAASBO assumes continuous parameters; categorical cable diameters require probabilistic reparameterization or one-hot encoding. Mitigation: use Ax's mixed-parameter support with probabilistic reparameterization for discrete parameters. + +5. **NUTS computational cost:** Fully Bayesian inference scales as O(N³D) per sample. At 100 observations × 7D with 256 NUTS samples, wall-clock overhead is ~5–15 minutes per iteration. Mitigation: use MAP fallback if budget is time-constrained (eriksson2021highdimensionalbayesianoptimization pages 4-5). + +6. **Bore-tolerance feasibility:** If three cable orbits have three different diameters, each 6-way joint must accommodate multiple bore sizes. The PLA shell becomes impractically thick if the spread is large. Mitigation: constrain max(cable_d) - min(cable_d) ≤ 2.0 mm as a BO feasibility constraint. + +7. **Overfitting with small data:** With only 50–100 specimens, a 12D fully per-member space is severely undersampled (curse of dimensionality). Mitigation: use orbit-reduced 7D as default; SAASBO's sparsity prior provides natural regularization (eriksson2021highdimensionalbayesianoptimization pages 3-4). + +8. **Fatigue/cycle-life data gap:** No published reuse-count data exists for TPU 85A tendons in tensegrity configurations under cyclic loading. Mitigation: include 5-cycle repeated compression in the test protocol to capture degradation as an additional BO objective. + +9. **Wipe-tower waste scaling:** Each additional distinct filament diameter per layer increases purge volume on the H2D. With 4 cable bins + 1 strut, this is manageable; fully per-member treatment with 12 diameters would be wasteful. Mitigation: the orbit-reduced approach naturally limits distinct diameters. + +10. **Interaction effects between orbit diameters and global geometry:** Cable orbit diameters interact strongly with twist angle and cell radius (they jointly determine prestress and buckling modes). SAASBO may underestimate these interactions if the sparse prior suppresses cross-terms. Mitigation: monitor GP lengthscales; if multiple dimensions show short lengthscales, consider switching to a non-sparse GP or TuRBO. + +## (h) References + +1. Skelton, R.E. & de Oliveira, M.C. (2009). *Tensegrity Systems*. Springer. DOI: 10.1007/978-0-387-74242-7 +2. 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ACM Transactions on Evolutionary Learning and Optimization, 4:1-33, Jul 2024. URL: https://doi.org/10.1145/3670683, doi:10.1145/3670683. This article has 54 citations. + +27. (eriksson2021highdimensionalbayesianoptimization pages 14-16): David Eriksson and Martin Jankowiak. High-dimensional bayesian optimization with sparse axis-aligned subspaces. Preprint, Jan 2021. URL: https://doi.org/10.48550/arxiv.2103.00349, doi:10.48550/arxiv.2103.00349. This article has 297 citations. + +28. (eriksson2019scalableglobaloptimization pages 2-4): David Eriksson, Michael Pearce, Jacob R Gardner, Ryan Turner, and Matthias Poloczek. Scalable global optimization via local bayesian optimization. Text, Jan 2019. URL: https://doi.org/10.48550/arxiv.1910.01739, doi:10.48550/arxiv.1910.01739. This article has 930 citations and is from a peer-reviewed journal. + +29. (eriksson2019scalableglobaloptimization pages 8-10): David Eriksson, Michael Pearce, Jacob R Gardner, Ryan Turner, and Matthias Poloczek. Scalable global optimization via local bayesian optimization. Text, Jan 2019. URL: https://doi.org/10.48550/arxiv.1910.01739, doi:10.48550/arxiv.1910.01739. This article has 930 citations and is from a peer-reviewed journal. + +30. (daulton2022multiobjectivebayesianoptimization pages 22-24): Samuel Daulton, David Eriksson, Maximilian Balandat, and Eytan Bakshy. Multi-objective bayesian optimization over high-dimensional search spaces. Preprint, Jan 2022. URL: https://doi.org/10.48550/arxiv.2109.10964, doi:10.48550/arxiv.2109.10964. This article has 244 citations. + +31. (daulton2022multiobjectivebayesianoptimization pages 9-10): Samuel Daulton, David Eriksson, Maximilian Balandat, and Eytan Bakshy. Multi-objective bayesian optimization over high-dimensional search spaces. Preprint, Jan 2022. URL: https://doi.org/10.48550/arxiv.2109.10964, doi:10.48550/arxiv.2109.10964. This article has 244 citations. + +32. (maathuis2025scalingbayesianoptimization pages 4-6): Hauke F. Maathuis, Roeland De Breuker, and Saullo G. P. Castro. Scaling bayesian optimization for high-dimensional and large-scale constrained spaces. AIAA Journal, pages 1-11, Jul 2025. URL: https://doi.org/10.2514/1.j065252, doi:10.2514/1.j065252. This article has 5 citations and is from a peer-reviewed journal. + +33. (chen2012initialprestressdistribution pages 3-5): YAO CHEN and JIAN FENG. Initial prestress distribution and natural vibration analysis of tensegrity structures based on group theory. International Journal of Structural Stability and Dynamics, 12:213-231, Apr 2012. URL: https://doi.org/10.1142/s0219455412500010, doi:10.1142/s0219455412500010. This article has 17 citations and is from a peer-reviewed journal. + +34. (chen2012initialprestressdistribution pages 1-3): YAO CHEN and JIAN FENG. Initial prestress distribution and natural vibration analysis of tensegrity structures based on group theory. International Journal of Structural Stability and Dynamics, 12:213-231, Apr 2012. URL: https://doi.org/10.1142/s0219455412500010, doi:10.1142/s0219455412500010. This article has 17 citations and is from a peer-reviewed journal. + +35. (brown2024sampleefficientbayesianoptimisation pages 4-6): Theodore Brown, Alexandru Cioba, and Ilija Bogunovic. Sample-efficient bayesian optimisation using known invariances. ArXiv, Oct 2024. URL: https://doi.org/10.48550/arxiv.2410.16972, doi:10.48550/arxiv.2410.16972. This article has 9 citations. + +36. (brown2024sampleefficientbayesianoptimisation pages 6-8): Theodore Brown, Alexandru Cioba, and Ilija Bogunovic. Sample-efficient bayesian optimisation using known invariances. ArXiv, Oct 2024. URL: https://doi.org/10.48550/arxiv.2410.16972, doi:10.48550/arxiv.2410.16972. This article has 9 citations. + +37. (brown2024sampleefficientbayesianoptimisation pages 9-11): Theodore Brown, Alexandru Cioba, and Ilija Bogunovic. Sample-efficient bayesian optimisation using known invariances. ArXiv, Oct 2024. URL: https://doi.org/10.48550/arxiv.2410.16972, doi:10.48550/arxiv.2410.16972. This article has 9 citations. + +38. (brown2024sampleefficientbayesianoptimisation pages 27-28): Theodore Brown, Alexandru Cioba, and Ilija Bogunovic. Sample-efficient bayesian optimisation using known invariances. ArXiv, Oct 2024. URL: https://doi.org/10.48550/arxiv.2410.16972, doi:10.48550/arxiv.2410.16972. This article has 9 citations. + +39. (eriksson2021highdimensionalbayesianoptimization pages 4-5): David Eriksson and Martin Jankowiak. High-dimensional bayesian optimization with sparse axis-aligned subspaces. Preprint, Jan 2021. URL: https://doi.org/10.48550/arxiv.2103.00349, doi:10.48550/arxiv.2103.00349. This article has 297 citations. + +40. (eriksson2021highdimensionalbayesianoptimization pages 3-4): David Eriksson and Martin Jankowiak. High-dimensional bayesian optimization with sparse axis-aligned subspaces. Preprint, Jan 2021. URL: https://doi.org/10.48550/arxiv.2103.00349, doi:10.48550/arxiv.2103.00349. This article has 297 citations. \ No newline at end of file diff --git a/edison-trajectories/tpu-petg-bo-variables-5ae24eaf-5b6e-45cf-9f6c-1c7fbd881738.json b/edison-trajectories/tpu-petg-bo-variables-5ae24eaf-5b6e-45cf-9f6c-1c7fbd881738.json new file mode 100644 index 00000000..f4170acf --- /dev/null +++ b/edison-trajectories/tpu-petg-bo-variables-5ae24eaf-5b6e-45cf-9f6c-1c7fbd881738.json @@ -0,0 +1,23 @@ +{ + "status": "success", + "query": "For a Bayesian-optimization-driven, multi-material FDM 3D-printed\ntensegrity-inspired energy-absorbing structure made from TPU (flexible tension\nelements) + PETG (rigid compression struts) -- NOT PLA -- enumerate and\nrecommend, with literature citations:\n\n(A) BASE / SEED UNIT-CELL TOPOLOGIES suitable as the starting design family\n (e.g., 3-bar / 4-bar prism, octahedron, icosahedron, expanded octahedron,\n truncated tetrahedron, \"tensegrity-inspired\" Pajunen-style cells, stacked\n prisms, lattice tilings of these). For each, note manufacturability with\n multi-material FDM and reported energy-absorption performance.\n\n(B) DESIGN VARIABLES that are normally swept in BO of these structures,\n grouped as:\n 1. Geometric/topological (strut length L, strut diameter D, slenderness\n L/D, cable/skin cross-section, prestress level, twist angle, cell\n tiling Nx*Ny*Nz, relative density, member connectivity).\n 2. Material/print-parameter (PETG vs TPU layer height, infill % and\n pattern for PETG struts, TPU shore hardness e.g. 85A/95A, TPU wall\n count / infill, print temperature, print speed, bed adhesion,\n interface wrapping thickness following Ye et al. 2023 /\n Khatri 2024).\n 3. Loading/test variables (drop height, impactor mass, quasi-static\n strain rate) -- treat as fixed conditions, not BO variables.\n\n(C) Specifically address PETG-vs-PLA differences relevant to BO bounds and\n constraints: PETG is tougher, less brittle, has lower stiffness and lower\n glass-transition temperature than PLA; how does this shift sensible\n variable ranges (e.g., strut slenderness, infill, layer adhesion, allowed\n impact energy before brittle fracture)?\n\n(D) Recommend reasonable numeric BOUNDS for each continuous variable and\n CATEGORIES for each categorical variable, suitable for a BoTorch/Ax\n search space for an undergraduate-led campaign of ~50-100 specimens.\n\n(E) Recommended PRIMARY OBJECTIVES (peak transmitted force, specific energy\n absorption SEA, compaction efficiency, plateau stress) and any\n constraints (max specimen mass, max print time, min cycle durability).\n\nReturn a structured answer with tables where helpful. Cite peer-reviewed\nsources for the structures, the PETG/TPU mechanical data, and prior BO\ncampaigns on architected/lattice/tensegrity energy absorbers.", + "user": null, + "created_at": "2026-05-08T17:02:43.640557Z", + "job_name": "job-futurehouse-paperqa3-high", + "share_status": "private", + "permitted_accessors": { + "users": [], + "organizations": [] + }, + "build_owner": "FutureHouse", + "environment_name": null, + "agent_name": null, + "task_id": "5ae24eaf-5b6e-45cf-9f6c-1c7fbd881738", + "project_id": null, + "answer": "# Bayesian-Optimization-Driven Multi-Material FDM Tensegrity-Inspired Energy Absorbers: Design Framework for PETG + TPU\n\n## (A) Base / Seed Unit-Cell Topologies\n\nThe following table enumerates candidate tensegrity and tensegrity-inspired unit-cell topologies suitable as starting design families, with assessment of manufacturability and energy-absorption evidence.\n\n| Topology Name | Members (bars/cables) | Key Reference | Reported EA Performance | Multi-Material FDM Manufacturability | Recommended Priority |\n|---|---:|---|---|---|---|\n| T3 / 3-bar prism | 3 / 9 (classical T3 prism) | Zhang et al. 2018; review coverage in Micheletti & Podio-Guidugli 2022 | T3 prism with metal-rubber insert showed increased energy absorption and tunable nonlinearity under static/dynamic loading versus prism alone; useful proof of concept, but not polymer FDM-specific (micheletti2022seventyyearsof pages 23-24) | Good for PETG struts + TPU tendons in principle; simple member count and clear load path, but needs careful joint design and twist-control during print/assembly | **Medium** |\n| 4-strut simplex | 4 / 12 (simplex-type tensegrity module) | Al Sabouni-Zawadzka et al. 2024 | Experimental uniaxial compression on printed modules showed tensegrity-like response, post-critical strut behavior, and strong dependence on parent-material elongation-at-break; useful as a mechanically validated seed cell, though published tests were not multi-material FDM (sabounizawadzka2024experimentalinvestigationson pages 1-3, sabounizawadzka2024experimentalinvestigationsona pages 6-11) | Moderate: topology is compact and experimentally validated, but printed rigid joints and manufacturing inaccuracies strongly affect behavior; FDM feasible if joints are thickened and TPU paths are simplified | **High** |\n| Truncated octahedron (Pajunen-style) | 12 / 36 in Pajunen-inspired printable cell; optimized lattice unit also treated as 12 bars + 36 cables equivalent | Pajunen et al. 2019; Zhang et al. 2021 | Best-supported option: high elastic strain-energy absorption, post-buckling stability, reusable impact response, low relative density, and optimized strain-energy storage under stress/volume constraints; specifically proposed as a tessellatable manufacturable unit cell (pajunen2019designandimpact pages 1-2, pajunen2019designandimpact pages 8-9, zhang2021optimizationforenergy pages 1-2) | **Excellent**: tessellation-friendly faces, strongest literature base, already adapted to printable tensegrity-inspired geometry; very suitable for dual-extrusion PETG+TPU and BO campaigns | **Very High / Best seed family** |\n| Truncated tetrahedron | Varies by formulation; regular tensegrity versions reported in the broader tensegrity literature | Zhang & Ohsaki / broader tensegrity topology literature cited in reviews | Strong theoretical/form-finding literature, but little direct polymer energy-absorption evidence found here relative to truncated octahedron; better treated as a secondary exploratory topology (micheletti2022seventyyearsof pages 20-21, liu2019tensegritytopologyoptimization pages 22-22) | Moderate-to-low: printable, but less experimentally validated for energy absorption and less straightforward as an undergrad BO baseline than truncated octahedra or simplex cells | **Low-Medium** |\n| Expanded / regular octahedron | Varies by realization; octahedral families common in lattice literature | General lattice/tensegrity review evidence; truncated-octahedral work is much better supported than regular octahedral tensegrity here | Octet/octahedral families are widely used in energy-absorbing lattices, but direct tensegrity-specific polymer EA evidence in the gathered set is sparse compared with Pajunen-style truncated octahedra (bustihan2026recentadvancesin pages 19-21, micheletti2022seventyyearsof pages 23-24) | Good geometric simplicity for FDM, but weaker direct evidence base for tensegrity-inspired PETG+TPU energy absorbers | **Medium** |\n| Icosahedron tensegrity | Varies by module; icosahedral and truncated-icosahedral modules appear in tensegrity form-finding/stability literature | Micheletti & Podio-Guidugli 2022 review and cited foundational studies | Attractive isotropic tensegrity family, but little direct reported 3D-printed polymer compression/impact EA evidence in the gathered sources; best regarded as a later-stage topology screen (micheletti2022seventyyearsof pages 20-21) | Fair in theory, but node complexity and support burden are higher for multi-material FDM; not ideal as first BO seed family | **Low** |\n| Stacked prism columns | Repeated T3/Tn prisms in columnar chains | Prism-chain and beam literature summarized in tensegrity review | Literature supports tunable softening–stiffening and wave/impact behavior in stacked prism systems; useful for 1D impact columns and sequential collapse studies, but less directly validated here as reusable polymer EA lattices than truncated octahedra (micheletti2022seventyyearsof pages 23-24, pajunen2019designandimpact pages 9-9) | Good for simple specimen fabrication and drop-tower testing; easier than full 3D lattices, though less space-filling and less scalable to panel cores | **High for pilot tests; Medium overall** |\n| 2D/3D lattice tilings of truncated octahedra | Repeated unit-cell assembly | Pajunen et al. 2019; Zhang et al. 2021 | Most promising system-level extension: Pajunen explicitly proposes tessellation into multidimensional lattices, and Zhang optimizes 3D lattices of truncated-octahedral units for stored strain energy/energy absorption (pajunen2019designandimpact pages 8-9, zhang2021optimizationforenergy pages 1-2) | **Excellent**: natural next step after single-cell screening; compatible with BO over tiling counts, relative density, and graded TPU/PETG layouts | **Very High** |\n\n\n*Table: This table compares candidate seed unit-cell families for tensegrity-inspired energy absorbers, emphasizing energy-absorption evidence and manufacturability for PETG+TPU multi-material FDM. It is useful for selecting a practical starting topology family before defining a Bayesian optimization search space.*\n\n**Recommended primary seed family:** The **truncated octahedron tensegrity** (Pajunen-style) is the strongest candidate. Pajunen et al. demonstrated a single-material, 3D-printable tensegrity-inspired structure based on a truncated octahedron (12 struts, 36 cables) that exhibited high elastic strain energy absorption, post-buckling stability, resilience under severe deformation, load-limitation, and reusability under repeated impacts (pajunen2019designandimpact pages 1-2). The spherically-jointed variant achieved the lowest energy absorption metric Wmin at ultra-low relative density, placing it in a favorable target region (Wmin < 0.21, ρ*/ρs < 0.1) (pajunen2019designandimpact pages 8-9). Zhang et al. subsequently formulated optimization of 3D tensegrity lattices with truncated octahedral units (24 nodes, 12 bars, 24 cutting cables, 12 edge cables per unit) to maximize stored strain energy, explicitly leveraging bar buckling (zhang2021optimizationforenergy pages 1-2).\n\nThe **4-strut simplex module** is the second-best-supported option, with Sabouni-Zawadzka et al. providing experimental uniaxial compression data on 3D-printed modules across multiple AM techniques, parent materials, and cell sizes (20–50 mm edge), using 3.0 mm strut diameter and 0.95 mm cable diameter (sabounizawadzka2024experimentalinvestigationson pages 1-3, sabounizawadzka2024experimentalinvestigationsona pages 6-11). Key findings: elongation at break of the parent material strongly governs module ductility, and post-critical buckling behavior of struts was clearly observed (sabounizawadzka2024experimentalinvestigationsona pages 1-3).\n\nThe **T3 (3-bar) prism** has been studied as a metamaterial building block with metal rubber inserts, demonstrating increased energy absorption and tunable nonlinearity under quasi-static, vibration, and impact loading (micheletti2022seventyyearsof pages 23-24). **Stacked prism columns** are practical for pilot drop-tower testing, and **2D/3D lattice tilings** of truncated octahedra represent the natural system-level extension (pajunen2019designandimpact pages 8-9, zhang2021optimizationforenergy pages 1-2).\n\nFor **multi-material FDM manufacturability** with PETG (rigid struts) + TPU (flexible tension elements), the truncated octahedron is especially suitable because its tessellation-friendly faces enable systematic tiling, and the distinct compression/tension member roles map naturally to a dual-extrusion PETG/TPU workflow (pajunen2019designandimpact pages 1-2).\n\n---\n\n## (B) Design Variables for BO\n\nThe following table provides a comprehensive enumeration of design variables grouped into geometric/topological, material/print-parameter, and loading/test categories, with recommended bounds suitable for a BoTorch/Ax search space.\n\n| Variable | Group | Type | Recommended Bounds/Categories | Rationale/Source |\n|---|---|---|---|---|\n| Strut diameter `D_PETG` | Geometric/Topological | Continuous | 1.5–5.0 mm | Conservative FDM range for 0.4 mm nozzle and undergraduate campaign; Pajunen’s tensegrity-inspired truncated-octahedron used strut diameters around 3.05 mm, with later geometry variants down to 2.6 mm; strut diameter is a standard lattice/EA optimization variable (pajunen2019designandimpact pages 3-4, pajunen2019designandimpact pages 2-3, bustihan2026recentadvancesin pages 6-7) |\n| Cable/skin diameter `D_TPU` | Geometric/Topological | Continuous | 1.0–3.0 mm | Pajunen-style cable diameters were ~1.37–1.8 mm; lower bound keeps TPU roads manufacturable and bonded, upper bound avoids over-stiffening tension network (pajunen2019designandimpact pages 3-4, pajunen2019designandimpact pages 2-3) |\n| Slenderness `L/D` | Geometric/Topological | Continuous | 8–25 | Captures elastic buckling-to-crushing transition while avoiding extremely fragile PETG struts; informed by Pajunen member lengths/diameters and PETG’s lower modulus than PLA (pajunen2019designandimpact pages 2-3, martins2024mechanicalpropertiesof pages 4-6, bustihan2026recentadvancesin pages 6-7) |\n| Twist angle `α` | Geometric/Topological | Continuous | 10°–45° | Meaningful for prism/stacked-prism families and twisted energy absorbers; broad enough to capture stiffness-collapse mode shifts without self-intersection (micheletti2022seventyyearsof pages 23-24, bustihan2025reusable3dprintedthermoplastic pages 7-9) |\n| Prestress level | Geometric/Topological | Continuous | 0–5% tensile prestrain | Pajunen reported 2% prestress as an effective tuning level; Zhang/Ohsaki-type tensegrity optimization treats prestress as a key design variable, but 0–5% is safer for PETG/TPU undergraduate fabrication than higher values (pajunen2019designandimpact pages 3-4, zhang2021optimizationforenergy pages 1-2) |\n| Cell tiling `N_x × N_y × N_z` | Geometric/Topological | Categorical/Ordinal | {1×1×1, 1×1×2, 2×2×1, 2×2×2, 3×3×2, 3×3×3} | Keeps specimen count and print time manageable while allowing single-cell vs lattice effects; BO on architected materials often includes discrete topological layout variables (vangelatos2021strengththroughdefects pages 1-2, vangelatos2021strengththroughdefects pages 2-3) |\n| Relative density `ρ*/ρ_s` | Geometric/Topological | Continuous/Derived | 0.05–0.30 | Covers ultralight to moderately dense polymer lattices; Pajunen targets low relative density, while stochastic lattice studies report useful SEA around 10–25% density (pajunen2019designandimpact pages 8-9, cronau2025energyabsorptionof pages 1-2, cronau2025energyabsorptionof pages 11-11) |\n| Unit-cell topology | Geometric/Topological | Categorical | {Truncated octahedron, 4-strut simplex, T3 prism, Stacked prism} | These are the most defensible seed families for BO: strongest support for truncated octahedron; experimental support for 4-strut simplex; T3 prism established in tensegrity metamaterials; stacked prisms are practical for columnar absorbers (pajunen2019designandimpact pages 1-2, zhang2021optimizationforenergy pages 1-2, sabounizawadzka2024experimentalinvestigationson pages 1-3, micheletti2022seventyyearsof pages 23-24) |\n| PETG layer height | Material/Print | Continuous | 0.15–0.30 mm | Lies inside reported FDM range where layer height strongly affects strength and print time; 0.15–0.30 mm is realistic for PETG campaign printing (bustihan2026recentadvancesin pages 6-7, hsueh2021effectofprinting pages 2-3) |\n| PETG infill % | Material/Print | Continuous | 40–100% | Infill percentage is among the most influential FDM parameters; lower bound avoids overly weak PETG struts, upper bound allows near-solid compression members (hsueh2021effectofprinting pages 2-3, bembenek2022researchonthe pages 2-3) |\n| PETG infill pattern | Material/Print | Categorical | {Rectilinear, Grid, Gyroid} | Common slicer choices with distinct anisotropy and crush behavior; pattern is a standard AM variable in lattice/property studies (bustihan2026recentadvancesin pages 6-7, hsueh2021effectofprinting pages 2-3) |\n| PETG print temperature | Material/Print | Continuous | 230–250 °C | PETG typically requires >230 °C for good fusion; higher temperatures reduce porosity but too high can degrade dimensional fidelity; this range is well-supported for mechanical optimization (hsueh2021effectofprinting pages 2-3, hsueh2021effectofprinting pages 6-8) |\n| PETG print speed | Material/Print | Continuous | 30–60 mm/s | Reflects common PETG processing window and tradeoff between bonding and throughput; slower speeds often improve PETG bonding (hsueh2021effectofprinting pages 6-8, bustihan2026recentadvancesin pages 6-7) |\n| TPU Shore hardness | Material/Print | Categorical | {85A, 95A} | These grades are directly supported in energy-absorbing TPU studies; 95A gives higher stress/plateau stability, 85A offers a softer compromise (bustihan2025reusable3dprintedthermoplastic pages 7-9, bustihan2025reusable3dprintedthermoplastic pages 2-4) |\n| TPU layer height | Material/Print | Continuous | 0.15–0.25 mm | Matches practical TPU FDM windows and avoids overly tall layers that can impair bead fusion in flexible members (khatri2024energyabsorptionof pages 3-5, leoncalero20213dprintingof pages 10-12) |\n| TPU wall count | Material/Print | Ordinal | 2–5 | Wall count materially changes effective stiffness and durability of flexible tendons/skins; compatible with common slicers and small DOE/BO budgets (bustihan2026recentadvancesin pages 6-7, khatri2024energyabsorptionof pages 3-5) |\n| TPU infill % | Material/Print | Continuous | 50–100% | TPU energy-absorption studies found strong dependence on infill density, with many optima near 50%; full infill remains useful for durable tendons/skins (leoncalero20213dprintingof pages 1-2, leoncalero20213dprintingof pages 10-12) |\n| TPU infill pattern | Material/Print | Categorical | {Honeycomb, Gyroid, Grid} | Honeycomb at ~50% gave optimal SEA/SDC in León-Calero et al.; gyroid/grid are natural comparators with different damping/compliance (leoncalero20213dprintingof pages 1-2, leoncalero20213dprintingof pages 4-5) |\n| TPU print temperature | Material/Print | Continuous | 215–235 °C | Supported by TPU 70A/85A/95A studies and technical ranges; upper limit stays below degradation concerns while covering good interlayer adhesion (bustihan2025reusable3dprintedthermoplastic pages 7-9, leoncalero20213dprintingof pages 10-12, leoncalero20213dprintingof pages 8-10) |\n| TPU print speed | Material/Print | Continuous | 15–30 mm/s | Flexible filaments generally require lower speed; Khatri used ~25 mm/s for TPU, and softer TPUs may need still slower extrusion (khatri2024energyabsorptionof pages 3-5, leoncalero20213dprintingof pages 10-12) |\n| Interface wrapping thickness | Material/Print | Continuous | 0.4–2.0 mm | Practical one-to-five-road overlap/interlock thickness for multimaterial joints; motivated by need to strengthen rigid/flexible interfaces in multimaterial FDM, even though direct PETG/TPU tensegrity data are sparse (khatri2024energyabsorptionof pages 1-3, khatri2024energyabsorptionof pages 3-5, bustihan2025reusable3dprintedthermoplastic pages 24-25) |\n| Build orientation | Material/Print | Categorical | {Vertical axis aligned with load, Horizontal, 45°} | Orientation strongly affects anisotropy, porosity, and interlayer failure in PETG/PLA and lattice performance; should be categorical if specimen count permits (martins2024mechanicalpropertiesof pages 4-6, bembenek2022researchonthe pages 2-3, martins2024mechanicalpropertiesof pages 9-14) |\n| Drop height | Loading/Test | Fixed | Fixed per campaign, e.g. 0.25–1.0 m equivalent | Treat as a controlled condition, not a BO variable, to keep comparisons meaningful; impact studies in tensegrity/lattice structures use fixed impact energy conditions (pajunen2019designandimpact pages 7-8, khatri2024energyabsorptionof pages 1-3) |\n| Impactor mass | Loading/Test | Fixed | Fixed per campaign, e.g. 2–10 kg equivalent | Must remain fixed so transmitted-force and SEA comparisons are interpretable across BO trials (pajunen2019designandimpact pages 7-8, khatri2024energyabsorptionof pages 1-3) |\n| Quasi-static strain rate | Loading/Test | Fixed | 0.001–0.01 s⁻¹ | Appropriate laboratory compression window; Khatri used ~0.13 s⁻¹ engineering strain rate for honeycombs, but a lower quasi-static range is preferable for controlled BO screening (khatri2024energyabsorptionof pages 3-5, gorguluarslan2022multiobjectivedesignoptimization pages 5-6) |\n\n\n*Table: This table summarizes a practical BoTorch/Ax search space for a multi-material PETG+TPU tensegrity-inspired energy-absorbing campaign. It groups recommended variables, bounds, and categories by geometry, material/print settings, and fixed test conditions, with literature-based rationale.*\n\n### B1. Geometric/Topological Variables\n\nKey geometric variables identified from the tensegrity and lattice energy-absorption literature include strut diameter, cable/skin cross-section, slenderness ratio L/D, twist angle, prestress level, cell tiling array, relative density, and unit-cell topology. Pajunen et al. used strut diameters of 2.6–3.32 mm, cable diameters of 1.37–1.8 mm, and 2% prestress as design knobs, noting that member diameter ratios (ds/dc = 1.44–2.23) control stiffness and buckling onset (pajunen2019designandimpact pages 3-4, pajunen2019designandimpact pages 2-3). Zhang et al. treated cross-sectional areas of cables and bars and prestress levels (force density parameters) as explicit optimization variables (zhang2021optimizationforenergy pages 1-2, ohsaki2019optimizationoftensegrity pages 1-3). Cronau & Engstler found that strut diameter and seed-point density (controlling relative density, tested at 10–25%) were primary drivers of specific energy absorption in lattice structures, with 25% density yielding highest SEA (cronau2025energyabsorptionof pages 1-2).\n\n### B2. Material/Print-Parameter Variables\n\nFor **PETG struts**: layer height (0.15–0.30 mm), infill percentage (40–100%), infill pattern (rectilinear/grid/gyroid), and print temperature (230–250°C) are the most influential FDM parameters (bustihan2026recentadvancesin pages 4-6, bustihan2026recentadvancesin pages 6-7, hsueh2021effectofprinting pages 6-8). PETG requires temperatures above ~230°C for adequate fusion, with porosity decreasing at higher temperatures (hsueh2021effectofprinting pages 2-3). Print speed for PETG (30–60 mm/s) trades off bonding quality against throughput (hsueh2021effectofprinting pages 6-8).\n\nFor **TPU tension elements**: shore hardness (85A vs 95A) is a key categorical variable. TPU 95A provides higher modulus (~39 MPa) and stress resistance with optimal breaking force at 215°C print temperature, while TPU 85A (NinjaFlex) is intermediate in stiffness with a recommended range of 220–225°C (bustihan2025reusable3dprintedthermoplastic pages 7-9, bustihan2025reusable3dprintedthermoplastic pages 2-4). Lower-hardness TPUs require significantly slower print speeds (as low as 8–15 mm/s for 82A–85A grades) (leoncalero20213dprintingof pages 10-12). Infill density and pattern strongly affect TPU energy absorption; León-Calero et al. found that honeycomb pattern at 50% infill produced optimal specific energy absorption (SEA) and specific damping capacity (SDC) (leoncalero20213dprintingof pages 1-2). Wall count (2–5 perimeters) affects effective stiffness and durability of flexible elements.\n\nFor **multi-material interfaces**: Khatri & Egan demonstrated that TPU band height (0–12 mm, in 3 mm increments) in rigid/flexible honeycomb structures strongly controls energy absorption and failure mode, with hexagonal honeycombs showing 66% higher energy absorption than square ones at matched band thickness (khatri2024energyabsorptionof pages 1-3, khatri2024energyabsorptionof pages 3-5, khatri2024energyabsorptionof pages 10-11). Interface wrapping thickness (0.4–2.0 mm) should be included as a continuous BO variable to strengthen PETG/TPU joints.\n\n### B3. Loading/Test Variables (Fixed Conditions)\n\nDrop height, impactor mass, and quasi-static strain rate should be treated as fixed experimental conditions, not BO variables, to maintain comparability across the campaign (pajunen2019designandimpact pages 7-8, khatri2024energyabsorptionof pages 3-5).\n\n---\n\n## (C) PETG-vs-PLA Differences Relevant to BO Bounds\n\nThe following table summarizes key property differences and their implications for search-space design.\n\n| Property | PLA (FDM printed) | PETG (FDM printed) | Shift Direction for PETG | Implication for BO Variable Ranges |\n|---|---|---|---|---|\n| Tensile strength | ~55 MPa | ~37 MPa | Lower | PETG compression struts should be allowed to be somewhat stockier than PLA for equal load capacity; cap slenderness more conservatively and avoid very low PETG infill when screening impact specimens (martins2024mechanicalpropertiesof pages 4-6) |\n| Young's modulus | ~2350 MPa | ~1200 MPa | ~50% lower | Euler buckling load is lower for the same geometry, so reduce practical upper bound on `L/D` from roughly PLA-like ~30 to ~25 for PETG, and raise PETG infill/perimeter lower bounds to recover stiffness (martins2024mechanicalpropertiesof pages 4-6) |\n| Elongation at break | ~4.3% | ~6.5% | Higher | PETG can tolerate more deformation before fracture, so strain-to-failure and allowable crush stroke can be set less conservatively than for PLA; this supports modestly broader deformation-space exploration before catastrophic breakage (martins2024mechanicalpropertiesof pages 4-6) |\n| Glass transition `T_g` | ~69.3 °C | ~73.5 °C | Slightly higher | PETG is somewhat safer for warm-service testing, but still needs elevated bed temperatures for reliable printing; set bed-temperature/process windows higher than PLA and avoid long dwell times near `T_g` in environmental tests (martins2024mechanicalpropertiesof pages 8-9) |\n| Thermal decomposition `T_d` | ~357.6 °C | ~419.3 °C | Higher | PETG has a wider thermal processing safety margin; BO bounds for nozzle temperature can safely shift upward relative to PLA, though adhesion/oozing tradeoffs still constrain the upper end (martins2024mechanicalpropertiesof pages 8-9) |\n| Impact toughness / fracture mode | More brittle; lower ductility | More ductile; better damage tolerance in practice | Higher toughness / ductility | PETG allows a less restrictive upper bound on impact energy before brittle fracture than PLA, but because modulus and strength are lower, peak-energy limits should still scale with strut geometry and relative density rather than be relaxed unconditionally (martins2024mechanicalpropertiesof pages 4-6, hsueh2021effectofprinting pages 2-3) |\n| Layer adhesion / print temperature | Good fusion commonly around ~190–220 °C | Typically needs ~230–250 °C; slower printing often helps | Requires higher temperature | Shift PETG print-temperature BO bounds upward and PETG speed bounds downward/moderate versus PLA; include temperature-speed interaction because PETG benefits more from slower deposition for better fusion and lower porosity (hsueh2021effectofprinting pages 6-8, hsueh2021effectofprinting pages 2-3) |\n| Porosity at nominal 100% infill | ~9.3% total porosity | ~12% total porosity | Higher | Since PETG prints can retain more voidage, use a higher PETG infill lower bound (about 40% rather than a PLA-like 20%), and consider wall count / orientation as active BO variables because effective cross-section is reduced by voids (martins2024mechanicalpropertiesof pages 9-14) |\n| Infill sensitivity | Strong dependence of strength on infill | Also strong; PETG specific tensile strength can deteriorate more with mass increase | Different tradeoff | For PETG, BO should optimize strength-to-weight or SEA rather than absolute load alone; avoid assuming that higher infill is always better, and search infill jointly with wall count and topology (bembenek2022researchonthe pages 2-3) |\n| Anisotropy / build-orientation sensitivity | Anisotropic | Anisotropic, with notable sensitivity to orientation and air-gap effects | Slightly higher practical sensitivity | Build orientation should be explicitly included as a categorical BO variable for PETG tensegrity struts; orientation-dependent porosity and bead geometry can materially alter failure mode and effective stiffness (bembenek2022researchonthe pages 2-3, martins2024mechanicalpropertiesof pages 9-14) |\n\n\n*Table: This table compares FDM-printed PLA and PETG properties most relevant to Bayesian optimization bounds for PETG+TPU tensegrity absorbers. It translates literature property differences into practical search-space implications for slenderness, infill, temperature, impact limits, and orientation.*\n\n**Quantitative summary:** FDM-printed PLA exhibits tensile strength ~55 MPa, Young's modulus ~2350 MPa, and elongation at break ~4.3%, while PETG shows ~37 MPa, ~1200 MPa, and ~6.5% respectively (martins2024mechanicalpropertiesof pages 4-6). Thermal analysis reveals PLA Tg ≈ 69.3°C and PETG Tg ≈ 73.5°C, with PETG showing higher thermal decomposition temperature (~419°C vs ~358°C for PLA) (martins2024mechanicalpropertiesof pages 8-9).\n\n**Critical implications for BO bounds:**\n\n1. **Strut slenderness (L/D):** PETG's ~50% lower Young's modulus means Euler buckling loads are substantially reduced for the same geometry. The practical upper bound on L/D should be reduced from ~30 (appropriate for PLA) to ~25 for PETG struts to avoid premature elastic buckling (martins2024mechanicalpropertiesof pages 4-6, pajunen2019designandimpact pages 2-3).\n\n2. **Infill percentage:** PETG prints retain more porosity (~12% vs ~9.3% for PLA at nominal 100% infill) (martins2024mechanicalpropertiesof pages 9-14), so the infill lower bound should be set higher (~40% vs ~20% for PLA) to ensure adequate effective cross-section in compression struts.\n\n3. **Layer adhesion and print temperature:** PETG requires 230–250°C for adequate fusion versus 190–220°C for PLA. Slower print speeds improve PETG bonding, and the interaction between temperature and speed is more critical than for PLA (hsueh2021effectofprinting pages 6-8, hsueh2021effectofprinting pages 2-3).\n\n4. **Impact energy before brittle fracture:** PETG's higher elongation at break (~6.5% vs ~4.3%) and greater ductility mean the allowable impact energy before catastrophic brittle fracture can be somewhat relaxed compared to PLA, but the lower modulus and strength mean this advantage is geometry-dependent (martins2024mechanicalpropertiesof pages 4-6).\n\n5. **Build orientation sensitivity:** PETG shows notable anisotropy and air-gap effects that reduce effective modulus and strength depending on orientation. Build orientation should be explicitly included as a categorical BO variable (bembenek2022researchonthe pages 2-3, martins2024mechanicalpropertiesof pages 9-14).\n\n---\n\n## (D) Recommended Numeric Bounds for BoTorch/Ax Search Space\n\nBased on the evidence, for a campaign of ~50–100 specimens:\n\n**Continuous variables:**\n- PETG strut diameter D_PETG: [1.5, 5.0] mm\n- TPU cable/skin diameter D_TPU: [1.0, 3.0] mm\n- Slenderness L/D: [8, 25]\n- Twist angle α: [10°, 45°]\n- Prestress level: [0%, 5%] tensile prestrain\n- Relative density ρ*/ρs: [0.05, 0.30] (derived)\n- PETG layer height: [0.15, 0.30] mm\n- PETG infill: [40%, 100%]\n- PETG print temperature: [230, 250] °C\n- PETG print speed: [30, 60] mm/s\n- TPU layer height: [0.15, 0.25] mm\n- TPU infill: [50%, 100%]\n- TPU print temperature: [215, 235] °C\n- TPU print speed: [15, 30] mm/s\n- Interface wrapping thickness: [0.4, 2.0] mm\n\n**Categorical variables:**\n- Unit-cell topology: {Truncated octahedron, 4-strut simplex, T3 prism, Stacked prism}\n- TPU shore hardness: {85A, 95A}\n- PETG infill pattern: {Rectilinear, Grid, Gyroid}\n- TPU infill pattern: {Honeycomb, Gyroid, Grid}\n- Cell tiling Nx×Ny×Nz: {1×1×1, 1×1×2, 2×2×1, 2×2×2, 3×3×2}\n- Build orientation: {Vertical (load-aligned), Horizontal, 45°}\n\n**Practical BO guidance:** Vangelatos et al. demonstrated that BO on architected lattices with 17 categorical design variables can find optima within ~250 evaluations starting from 50 random initial samples, using an EMCS framework with GP surrogate models (vangelatos2021strengththroughdefects pages 2-3, vangelatos2021strengththroughdefects pages 5-6, vangelatos2021strengththroughdefects pages 7-9). For a physically-tested campaign of 50–100 specimens, a Sobol/LHS initial batch of ~15–25 specimens followed by sequential BO iterations is recommended. The mixed continuous+categorical search space is well-handled by BoTorch's Mixed Optimization (SAASBO or multi-task GP with categorical kernels).\n\n---\n\n## (E) Recommended Primary Objectives and Constraints\n\n| Metric | Role (Objective/Constraint) | Definition | Target Direction | Rationale/Source |\n|---|---|---|---|---|\n| Specific Energy Absorption (SEA) | Primary objective | Total absorbed energy divided by specimen mass (J/g) | Maximize | Most common crashworthiness metric for lattices and cellular absorbers; normalizes for mass and allows fair comparison across relative densities and topologies (cronau2025energyabsorptionof pages 11-11, leoncalero20213dprintingof pages 1-2, gorguluarslan2022multiobjectivedesignoptimization pages 5-6) |\n| Peak Transmitted Force ($F_{peak}$) | Primary objective or hard constraint | Maximum force measured at the support/base plate during impact or compression | Minimize | Critical for protection applications because lower peak force corresponds to better load limitation and lower injury/equipment risk; also complements SEA when highly absorptive designs still spike early load (pajunen2019designandimpact pages 7-8, khatri2024energyabsorptionof pages 1-3, khatri2024energyabsorptionof pages 10-11) |\n| Energy Absorption Efficiency (EAE, or EAEm) | Secondary objective | Ratio of absorbed energy to the energy/stroke available before densification; often interpreted as how efficiently the crush plateau is used | Maximize | Captures whether the structure absorbs energy progressively rather than through a sharp initial peak; used explicitly in additively manufactured lattice optimization studies (bates20163dprintedpolyurethane pages 16-18, gorguluarslan2022multiobjectivedesignoptimization pages 5-6) |\n| Crush Stress Efficiency (CSE) | Secondary objective | Plateau stress divided by peak stress | Maximize | High CSE indicates a flatter, more useful stress plateau and more uniform dissipation; Gorguluarslan uses CSE jointly with energy-absorption efficiency in multi-objective optimization (gorguluarslan2022multiobjectivedesignoptimization pages 5-6) |\n| Plateau Stress ($\\sigma_{pl}$) | Informational metric or application-tuned objective | Mean stress over the post-yield/pre-densification plateau region | Application-dependent; often target a band | Determines force-transmission level during sustained crushing; should be high enough to absorb energy but not so high that transmitted loads become unacceptable (gorguluarslan2022multiobjectivedesignoptimization pages 5-6, khatri2024energyabsorptionof pages 10-11) |\n| Compaction strain ($\\varepsilon_d$) | Informational metric or secondary objective | Strain at onset of densification/compaction | Generally maximize | Higher compaction strain gives more usable stroke before densification, improving practical absorber stroke utilization (gorguluarslan2022multiobjectivedesignoptimization pages 5-6, bates20163dprintedpolyurethane pages 16-18) |\n| Specimen mass | Constraint | Total printed mass of one specimen | Keep below threshold, e.g. $\\leq$ 50 g | Keeps the campaign practical, preserves fair specific-property comparisons, and limits the optimizer from trivially improving absolute energy absorption by adding material (cronau2025energyabsorptionof pages 11-11, gorguluarslan2022multiobjectivedesignoptimization pages 5-6) |\n| Print time | Constraint | Total print duration per specimen | Keep below threshold, e.g. $\\leq$ 4 h | Essential for a 50-100 specimen undergraduate BO campaign; printability/time are standard AM-side constraints in design-of-experiments and optimization workflows (bustihan2026recentadvancesin pages 6-7, vangelatos2021strengththroughdefects pages 2-3) |\n| Cycle durability | Constraint | Number of compression/impact cycles before a chosen degradation limit, e.g. 10% strength-loss or SEA-loss threshold | Keep above threshold, e.g. $\\geq$ 3 cycles | Important for reusable absorbers; TPU-based absorbers show recoverability while cyclic softening and PETG strut damage can limit reuse (pajunen2019designandimpact pages 7-8, bates20163dprintedpolyurethane pages 16-18, bustihan2025reusable3dprintedthermoplastic pages 7-9) |\n| $W_{min}$ (cushion factor $\\times$ relative density) | Alternative primary objective | Pajunen-style efficiency metric combining cushion factor and relative density | Minimize | Useful for benchmarking against foams and other polymer absorbers; Pajunen identifies favorable designs in the region $W_{min} < 0.21$ and $\\rho^*/\\rho_s < 0.1$ (pajunen2019designandimpact pages 8-9) |\n\n\n*Table: This table summarizes recommended primary objectives, secondary metrics, and practical constraints for a Bayesian-optimization campaign on PETG+TPU tensegrity-inspired energy absorbers. It is useful for turning the literature into a measurable Ax/BoTorch optimization problem.*\n\n**Primary objectives (multi-objective BO):**\n\n1. **Maximize Specific Energy Absorption (SEA):** The most widely used crashworthiness metric, computed as total absorbed energy divided by specimen mass (J/g). This normalizes for mass and allows fair comparison across relative densities and topologies (leoncalero20213dprintingof pages 1-2, gorguluarslan2022multiobjectivedesignoptimization pages 5-6).\n\n2. **Minimize Peak Transmitted Force (F_peak):** Critical for protective applications; lower peak force corresponds to better load limitation. Alternatively, this can be treated as a hard constraint (F_peak ≤ threshold) (pajunen2019designandimpact pages 7-8, khatri2024energyabsorptionof pages 1-3).\n\n**Secondary objectives:**\n\n3. **Maximize Energy Absorption Efficiency (EAE):** Captures how efficiently the crush plateau is exploited before densification. Gorguluarslan used EAEm jointly with CSE in multi-objective lattice optimization (gorguluarslan2022multiobjectivedesignoptimization pages 5-6). Pajunen used Wmin = cushion factor × relative density, targeting Wmin < 0.21 at ρ*/ρs < 0.1 (pajunen2019designandimpact pages 8-9).\n\n4. **Maximize Crush Stress Efficiency (CSE):** Plateau stress / peak stress; higher CSE indicates a flatter, more uniform stress plateau (gorguluarslan2022multiobjectivedesignoptimization pages 5-6).\n\n**Constraints:**\n\n- **Maximum specimen mass:** ≤ 50 g (keeps campaign practical and enables specific-property comparisons)\n- **Maximum print time:** ≤ 4 hours per specimen (ensures 50–100 specimens fit an undergraduate semester timeline) (bustihan2026recentadvancesin pages 6-7)\n- **Minimum cycle durability:** ≥ 3 compression cycles to <10% SEA loss (important for reusable absorbers; TPU enables elastic recovery with ~24.5% energy drop from cycle 1→2 then convergence, while PETG strut fracture limits reuse) (bates20163dprintedpolyurethane pages 16-18, bustihan2025reusable3dprintedthermoplastic pages 7-9)\n- **Minimum printability:** no print failures (enforced by excluding non-manufacturable designs via geometry constraints on minimum overhang angle, minimum feature size ≥ 1.0 mm, and bridging distance limits)\n\n**Recommended BO formulation:** A multi-objective formulation maximizing SEA while minimizing F_peak, subject to mass, print-time, and durability constraints, is the most practical starting point. This can be implemented in BoTorch using `qNoisyExpectedHypervolumeImprovement` (qNEHVI) as the acquisition function for Pareto-optimal design discovery with noisy experimental observations.", + "formatted_answer": "Question: For a Bayesian-optimization-driven, multi-material FDM 3D-printed\ntensegrity-inspired energy-absorbing structure made from TPU (flexible tension\nelements) + PETG (rigid compression struts) -- NOT PLA -- enumerate and\nrecommend, with literature citations:\n\n(A) BASE / SEED UNIT-CELL TOPOLOGIES suitable as the starting design family\n (e.g., 3-bar / 4-bar prism, octahedron, icosahedron, expanded octahedron,\n truncated tetrahedron, \"tensegrity-inspired\" Pajunen-style cells, stacked\n prisms, lattice tilings of these). For each, note manufacturability with\n multi-material FDM and reported energy-absorption performance.\n\n(B) DESIGN VARIABLES that are normally swept in BO of these structures,\n grouped as:\n 1. Geometric/topological (strut length L, strut diameter D, slenderness\n L/D, cable/skin cross-section, prestress level, twist angle, cell\n tiling Nx*Ny*Nz, relative density, member connectivity).\n 2. Material/print-parameter (PETG vs TPU layer height, infill % and\n pattern for PETG struts, TPU shore hardness e.g. 85A/95A, TPU wall\n count / infill, print temperature, print speed, bed adhesion,\n interface wrapping thickness following Ye et al. 2023 /\n Khatri 2024).\n 3. Loading/test variables (drop height, impactor mass, quasi-static\n strain rate) -- treat as fixed conditions, not BO variables.\n\n(C) Specifically address PETG-vs-PLA differences relevant to BO bounds and\n constraints: PETG is tougher, less brittle, has lower stiffness and lower\n glass-transition temperature than PLA; how does this shift sensible\n variable ranges (e.g., strut slenderness, infill, layer adhesion, allowed\n impact energy before brittle fracture)?\n\n(D) Recommend reasonable numeric BOUNDS for each continuous variable and\n CATEGORIES for each categorical variable, suitable for a BoTorch/Ax\n search space for an undergraduate-led campaign of ~50-100 specimens.\n\n(E) Recommended PRIMARY OBJECTIVES (peak transmitted force, specific energy\n absorption SEA, compaction efficiency, plateau stress) and any\n constraints (max specimen mass, max print time, min cycle durability).\n\nReturn a structured answer with tables where helpful. Cite peer-reviewed\nsources for the structures, the PETG/TPU mechanical data, and prior BO\ncampaigns on architected/lattice/tensegrity energy absorbers.\n\n# Bayesian-Optimization-Driven Multi-Material FDM Tensegrity-Inspired Energy Absorbers: Design Framework for PETG + TPU\n\n## (A) Base / Seed Unit-Cell Topologies\n\nThe following table enumerates candidate tensegrity and tensegrity-inspired unit-cell topologies suitable as starting design families, with assessment of manufacturability and energy-absorption evidence.\n\n| Topology Name | Members (bars/cables) | Key Reference | Reported EA Performance | Multi-Material FDM Manufacturability | Recommended Priority |\n|---|---:|---|---|---|---|\n| T3 / 3-bar prism | 3 / 9 (classical T3 prism) | Zhang et al. 2018; review coverage in Micheletti & Podio-Guidugli 2022 | T3 prism with metal-rubber insert showed increased energy absorption and tunable nonlinearity under static/dynamic loading versus prism alone; useful proof of concept, but not polymer FDM-specific (micheletti2022seventyyearsof pages 23-24) | Good for PETG struts + TPU tendons in principle; simple member count and clear load path, but needs careful joint design and twist-control during print/assembly | **Medium** |\n| 4-strut simplex | 4 / 12 (simplex-type tensegrity module) | Al Sabouni-Zawadzka et al. 2024 | Experimental uniaxial compression on printed modules showed tensegrity-like response, post-critical strut behavior, and strong dependence on parent-material elongation-at-break; useful as a mechanically validated seed cell, though published tests were not multi-material FDM (sabounizawadzka2024experimentalinvestigationson pages 1-3, sabounizawadzka2024experimentalinvestigationsona pages 6-11) | Moderate: topology is compact and experimentally validated, but printed rigid joints and manufacturing inaccuracies strongly affect behavior; FDM feasible if joints are thickened and TPU paths are simplified | **High** |\n| Truncated octahedron (Pajunen-style) | 12 / 36 in Pajunen-inspired printable cell; optimized lattice unit also treated as 12 bars + 36 cables equivalent | Pajunen et al. 2019; Zhang et al. 2021 | Best-supported option: high elastic strain-energy absorption, post-buckling stability, reusable impact response, low relative density, and optimized strain-energy storage under stress/volume constraints; specifically proposed as a tessellatable manufacturable unit cell (pajunen2019designandimpact pages 1-2, pajunen2019designandimpact pages 8-9, zhang2021optimizationforenergy pages 1-2) | **Excellent**: tessellation-friendly faces, strongest literature base, already adapted to printable tensegrity-inspired geometry; very suitable for dual-extrusion PETG+TPU and BO campaigns | **Very High / Best seed family** |\n| Truncated tetrahedron | Varies by formulation; regular tensegrity versions reported in the broader tensegrity literature | Zhang & Ohsaki / broader tensegrity topology literature cited in reviews | Strong theoretical/form-finding literature, but little direct polymer energy-absorption evidence found here relative to truncated octahedron; better treated as a secondary exploratory topology (micheletti2022seventyyearsof pages 20-21, liu2019tensegritytopologyoptimization pages 22-22) | Moderate-to-low: printable, but less experimentally validated for energy absorption and less straightforward as an undergrad BO baseline than truncated octahedra or simplex cells | **Low-Medium** |\n| Expanded / regular octahedron | Varies by realization; octahedral families common in lattice literature | General lattice/tensegrity review evidence; truncated-octahedral work is much better supported than regular octahedral tensegrity here | Octet/octahedral families are widely used in energy-absorbing lattices, but direct tensegrity-specific polymer EA evidence in the gathered set is sparse compared with Pajunen-style truncated octahedra (bustihan2026recentadvancesin pages 19-21, micheletti2022seventyyearsof pages 23-24) | Good geometric simplicity for FDM, but weaker direct evidence base for tensegrity-inspired PETG+TPU energy absorbers | **Medium** |\n| Icosahedron tensegrity | Varies by module; icosahedral and truncated-icosahedral modules appear in tensegrity form-finding/stability literature | Micheletti & Podio-Guidugli 2022 review and cited foundational studies | Attractive isotropic tensegrity family, but little direct reported 3D-printed polymer compression/impact EA evidence in the gathered sources; best regarded as a later-stage topology screen (micheletti2022seventyyearsof pages 20-21) | Fair in theory, but node complexity and support burden are higher for multi-material FDM; not ideal as first BO seed family | **Low** |\n| Stacked prism columns | Repeated T3/Tn prisms in columnar chains | Prism-chain and beam literature summarized in tensegrity review | Literature supports tunable softening–stiffening and wave/impact behavior in stacked prism systems; useful for 1D impact columns and sequential collapse studies, but less directly validated here as reusable polymer EA lattices than truncated octahedra (micheletti2022seventyyearsof pages 23-24, pajunen2019designandimpact pages 9-9) | Good for simple specimen fabrication and drop-tower testing; easier than full 3D lattices, though less space-filling and less scalable to panel cores | **High for pilot tests; Medium overall** |\n| 2D/3D lattice tilings of truncated octahedra | Repeated unit-cell assembly | Pajunen et al. 2019; Zhang et al. 2021 | Most promising system-level extension: Pajunen explicitly proposes tessellation into multidimensional lattices, and Zhang optimizes 3D lattices of truncated-octahedral units for stored strain energy/energy absorption (pajunen2019designandimpact pages 8-9, zhang2021optimizationforenergy pages 1-2) | **Excellent**: natural next step after single-cell screening; compatible with BO over tiling counts, relative density, and graded TPU/PETG layouts | **Very High** |\n\n\n*Table: This table compares candidate seed unit-cell families for tensegrity-inspired energy absorbers, emphasizing energy-absorption evidence and manufacturability for PETG+TPU multi-material FDM. It is useful for selecting a practical starting topology family before defining a Bayesian optimization search space.*\n\n**Recommended primary seed family:** The **truncated octahedron tensegrity** (Pajunen-style) is the strongest candidate. Pajunen et al. demonstrated a single-material, 3D-printable tensegrity-inspired structure based on a truncated octahedron (12 struts, 36 cables) that exhibited high elastic strain energy absorption, post-buckling stability, resilience under severe deformation, load-limitation, and reusability under repeated impacts (pajunen2019designandimpact pages 1-2). The spherically-jointed variant achieved the lowest energy absorption metric Wmin at ultra-low relative density, placing it in a favorable target region (Wmin < 0.21, ρ*/ρs < 0.1) (pajunen2019designandimpact pages 8-9). Zhang et al. subsequently formulated optimization of 3D tensegrity lattices with truncated octahedral units (24 nodes, 12 bars, 24 cutting cables, 12 edge cables per unit) to maximize stored strain energy, explicitly leveraging bar buckling (zhang2021optimizationforenergy pages 1-2).\n\nThe **4-strut simplex module** is the second-best-supported option, with Sabouni-Zawadzka et al. providing experimental uniaxial compression data on 3D-printed modules across multiple AM techniques, parent materials, and cell sizes (20–50 mm edge), using 3.0 mm strut diameter and 0.95 mm cable diameter (sabounizawadzka2024experimentalinvestigationson pages 1-3, sabounizawadzka2024experimentalinvestigationsona pages 6-11). Key findings: elongation at break of the parent material strongly governs module ductility, and post-critical buckling behavior of struts was clearly observed (sabounizawadzka2024experimentalinvestigationsona pages 1-3).\n\nThe **T3 (3-bar) prism** has been studied as a metamaterial building block with metal rubber inserts, demonstrating increased energy absorption and tunable nonlinearity under quasi-static, vibration, and impact loading (micheletti2022seventyyearsof pages 23-24). **Stacked prism columns** are practical for pilot drop-tower testing, and **2D/3D lattice tilings** of truncated octahedra represent the natural system-level extension (pajunen2019designandimpact pages 8-9, zhang2021optimizationforenergy pages 1-2).\n\nFor **multi-material FDM manufacturability** with PETG (rigid struts) + TPU (flexible tension elements), the truncated octahedron is especially suitable because its tessellation-friendly faces enable systematic tiling, and the distinct compression/tension member roles map naturally to a dual-extrusion PETG/TPU workflow (pajunen2019designandimpact pages 1-2).\n\n---\n\n## (B) Design Variables for BO\n\nThe following table provides a comprehensive enumeration of design variables grouped into geometric/topological, material/print-parameter, and loading/test categories, with recommended bounds suitable for a BoTorch/Ax search space.\n\n| Variable | Group | Type | Recommended Bounds/Categories | Rationale/Source |\n|---|---|---|---|---|\n| Strut diameter `D_PETG` | Geometric/Topological | Continuous | 1.5–5.0 mm | Conservative FDM range for 0.4 mm nozzle and undergraduate campaign; Pajunen’s tensegrity-inspired truncated-octahedron used strut diameters around 3.05 mm, with later geometry variants down to 2.6 mm; strut diameter is a standard lattice/EA optimization variable (pajunen2019designandimpact pages 3-4, pajunen2019designandimpact pages 2-3, bustihan2026recentadvancesin pages 6-7) |\n| Cable/skin diameter `D_TPU` | Geometric/Topological | Continuous | 1.0–3.0 mm | Pajunen-style cable diameters were ~1.37–1.8 mm; lower bound keeps TPU roads manufacturable and bonded, upper bound avoids over-stiffening tension network (pajunen2019designandimpact pages 3-4, pajunen2019designandimpact pages 2-3) |\n| Slenderness `L/D` | Geometric/Topological | Continuous | 8–25 | Captures elastic buckling-to-crushing transition while avoiding extremely fragile PETG struts; informed by Pajunen member lengths/diameters and PETG’s lower modulus than PLA (pajunen2019designandimpact pages 2-3, martins2024mechanicalpropertiesof pages 4-6, bustihan2026recentadvancesin pages 6-7) |\n| Twist angle `α` | Geometric/Topological | Continuous | 10°–45° | Meaningful for prism/stacked-prism families and twisted energy absorbers; broad enough to capture stiffness-collapse mode shifts without self-intersection (micheletti2022seventyyearsof pages 23-24, bustihan2025reusable3dprintedthermoplastic pages 7-9) |\n| Prestress level | Geometric/Topological | Continuous | 0–5% tensile prestrain | Pajunen reported 2% prestress as an effective tuning level; Zhang/Ohsaki-type tensegrity optimization treats prestress as a key design variable, but 0–5% is safer for PETG/TPU undergraduate fabrication than higher values (pajunen2019designandimpact pages 3-4, zhang2021optimizationforenergy pages 1-2) |\n| Cell tiling `N_x × N_y × N_z` | Geometric/Topological | Categorical/Ordinal | {1×1×1, 1×1×2, 2×2×1, 2×2×2, 3×3×2, 3×3×3} | Keeps specimen count and print time manageable while allowing single-cell vs lattice effects; BO on architected materials often includes discrete topological layout variables (vangelatos2021strengththroughdefects pages 1-2, vangelatos2021strengththroughdefects pages 2-3) |\n| Relative density `ρ*/ρ_s` | Geometric/Topological | Continuous/Derived | 0.05–0.30 | Covers ultralight to moderately dense polymer lattices; Pajunen targets low relative density, while stochastic lattice studies report useful SEA around 10–25% density (pajunen2019designandimpact pages 8-9, cronau2025energyabsorptionof pages 1-2, cronau2025energyabsorptionof pages 11-11) |\n| Unit-cell topology | Geometric/Topological | Categorical | {Truncated octahedron, 4-strut simplex, T3 prism, Stacked prism} | These are the most defensible seed families for BO: strongest support for truncated octahedron; experimental support for 4-strut simplex; T3 prism established in tensegrity metamaterials; stacked prisms are practical for columnar absorbers (pajunen2019designandimpact pages 1-2, zhang2021optimizationforenergy pages 1-2, sabounizawadzka2024experimentalinvestigationson pages 1-3, micheletti2022seventyyearsof pages 23-24) |\n| PETG layer height | Material/Print | Continuous | 0.15–0.30 mm | Lies inside reported FDM range where layer height strongly affects strength and print time; 0.15–0.30 mm is realistic for PETG campaign printing (bustihan2026recentadvancesin pages 6-7, hsueh2021effectofprinting pages 2-3) |\n| PETG infill % | Material/Print | Continuous | 40–100% | Infill percentage is among the most influential FDM parameters; lower bound avoids overly weak PETG struts, upper bound allows near-solid compression members (hsueh2021effectofprinting pages 2-3, bembenek2022researchonthe pages 2-3) |\n| PETG infill pattern | Material/Print | Categorical | {Rectilinear, Grid, Gyroid} | Common slicer choices with distinct anisotropy and crush behavior; pattern is a standard AM variable in lattice/property studies (bustihan2026recentadvancesin pages 6-7, hsueh2021effectofprinting pages 2-3) |\n| PETG print temperature | Material/Print | Continuous | 230–250 °C | PETG typically requires >230 °C for good fusion; higher temperatures reduce porosity but too high can degrade dimensional fidelity; this range is well-supported for mechanical optimization (hsueh2021effectofprinting pages 2-3, hsueh2021effectofprinting pages 6-8) |\n| PETG print speed | Material/Print | Continuous | 30–60 mm/s | Reflects common PETG processing window and tradeoff between bonding and throughput; slower speeds often improve PETG bonding (hsueh2021effectofprinting pages 6-8, bustihan2026recentadvancesin pages 6-7) |\n| TPU Shore hardness | Material/Print | Categorical | {85A, 95A} | These grades are directly supported in energy-absorbing TPU studies; 95A gives higher stress/plateau stability, 85A offers a softer compromise (bustihan2025reusable3dprintedthermoplastic pages 7-9, bustihan2025reusable3dprintedthermoplastic pages 2-4) |\n| TPU layer height | Material/Print | Continuous | 0.15–0.25 mm | Matches practical TPU FDM windows and avoids overly tall layers that can impair bead fusion in flexible members (khatri2024energyabsorptionof pages 3-5, leoncalero20213dprintingof pages 10-12) |\n| TPU wall count | Material/Print | Ordinal | 2–5 | Wall count materially changes effective stiffness and durability of flexible tendons/skins; compatible with common slicers and small DOE/BO budgets (bustihan2026recentadvancesin pages 6-7, khatri2024energyabsorptionof pages 3-5) |\n| TPU infill % | Material/Print | Continuous | 50–100% | TPU energy-absorption studies found strong dependence on infill density, with many optima near 50%; full infill remains useful for durable tendons/skins (leoncalero20213dprintingof pages 1-2, leoncalero20213dprintingof pages 10-12) |\n| TPU infill pattern | Material/Print | Categorical | {Honeycomb, Gyroid, Grid} | Honeycomb at ~50% gave optimal SEA/SDC in León-Calero et al.; gyroid/grid are natural comparators with different damping/compliance (leoncalero20213dprintingof pages 1-2, leoncalero20213dprintingof pages 4-5) |\n| TPU print temperature | Material/Print | Continuous | 215–235 °C | Supported by TPU 70A/85A/95A studies and technical ranges; upper limit stays below degradation concerns while covering good interlayer adhesion (bustihan2025reusable3dprintedthermoplastic pages 7-9, leoncalero20213dprintingof pages 10-12, leoncalero20213dprintingof pages 8-10) |\n| TPU print speed | Material/Print | Continuous | 15–30 mm/s | Flexible filaments generally require lower speed; Khatri used ~25 mm/s for TPU, and softer TPUs may need still slower extrusion (khatri2024energyabsorptionof pages 3-5, leoncalero20213dprintingof pages 10-12) |\n| Interface wrapping thickness | Material/Print | Continuous | 0.4–2.0 mm | Practical one-to-five-road overlap/interlock thickness for multimaterial joints; motivated by need to strengthen rigid/flexible interfaces in multimaterial FDM, even though direct PETG/TPU tensegrity data are sparse (khatri2024energyabsorptionof pages 1-3, khatri2024energyabsorptionof pages 3-5, bustihan2025reusable3dprintedthermoplastic pages 24-25) |\n| Build orientation | Material/Print | Categorical | {Vertical axis aligned with load, Horizontal, 45°} | Orientation strongly affects anisotropy, porosity, and interlayer failure in PETG/PLA and lattice performance; should be categorical if specimen count permits (martins2024mechanicalpropertiesof pages 4-6, bembenek2022researchonthe pages 2-3, martins2024mechanicalpropertiesof pages 9-14) |\n| Drop height | Loading/Test | Fixed | Fixed per campaign, e.g. 0.25–1.0 m equivalent | Treat as a controlled condition, not a BO variable, to keep comparisons meaningful; impact studies in tensegrity/lattice structures use fixed impact energy conditions (pajunen2019designandimpact pages 7-8, khatri2024energyabsorptionof pages 1-3) |\n| Impactor mass | Loading/Test | Fixed | Fixed per campaign, e.g. 2–10 kg equivalent | Must remain fixed so transmitted-force and SEA comparisons are interpretable across BO trials (pajunen2019designandimpact pages 7-8, khatri2024energyabsorptionof pages 1-3) |\n| Quasi-static strain rate | Loading/Test | Fixed | 0.001–0.01 s⁻¹ | Appropriate laboratory compression window; Khatri used ~0.13 s⁻¹ engineering strain rate for honeycombs, but a lower quasi-static range is preferable for controlled BO screening (khatri2024energyabsorptionof pages 3-5, gorguluarslan2022multiobjectivedesignoptimization pages 5-6) |\n\n\n*Table: This table summarizes a practical BoTorch/Ax search space for a multi-material PETG+TPU tensegrity-inspired energy-absorbing campaign. It groups recommended variables, bounds, and categories by geometry, material/print settings, and fixed test conditions, with literature-based rationale.*\n\n### B1. Geometric/Topological Variables\n\nKey geometric variables identified from the tensegrity and lattice energy-absorption literature include strut diameter, cable/skin cross-section, slenderness ratio L/D, twist angle, prestress level, cell tiling array, relative density, and unit-cell topology. Pajunen et al. used strut diameters of 2.6–3.32 mm, cable diameters of 1.37–1.8 mm, and 2% prestress as design knobs, noting that member diameter ratios (ds/dc = 1.44–2.23) control stiffness and buckling onset (pajunen2019designandimpact pages 3-4, pajunen2019designandimpact pages 2-3). Zhang et al. treated cross-sectional areas of cables and bars and prestress levels (force density parameters) as explicit optimization variables (zhang2021optimizationforenergy pages 1-2, ohsaki2019optimizationoftensegrity pages 1-3). Cronau & Engstler found that strut diameter and seed-point density (controlling relative density, tested at 10–25%) were primary drivers of specific energy absorption in lattice structures, with 25% density yielding highest SEA (cronau2025energyabsorptionof pages 1-2).\n\n### B2. Material/Print-Parameter Variables\n\nFor **PETG struts**: layer height (0.15–0.30 mm), infill percentage (40–100%), infill pattern (rectilinear/grid/gyroid), and print temperature (230–250°C) are the most influential FDM parameters (bustihan2026recentadvancesin pages 4-6, bustihan2026recentadvancesin pages 6-7, hsueh2021effectofprinting pages 6-8). PETG requires temperatures above ~230°C for adequate fusion, with porosity decreasing at higher temperatures (hsueh2021effectofprinting pages 2-3). Print speed for PETG (30–60 mm/s) trades off bonding quality against throughput (hsueh2021effectofprinting pages 6-8).\n\nFor **TPU tension elements**: shore hardness (85A vs 95A) is a key categorical variable. TPU 95A provides higher modulus (~39 MPa) and stress resistance with optimal breaking force at 215°C print temperature, while TPU 85A (NinjaFlex) is intermediate in stiffness with a recommended range of 220–225°C (bustihan2025reusable3dprintedthermoplastic pages 7-9, bustihan2025reusable3dprintedthermoplastic pages 2-4). Lower-hardness TPUs require significantly slower print speeds (as low as 8–15 mm/s for 82A–85A grades) (leoncalero20213dprintingof pages 10-12). Infill density and pattern strongly affect TPU energy absorption; León-Calero et al. found that honeycomb pattern at 50% infill produced optimal specific energy absorption (SEA) and specific damping capacity (SDC) (leoncalero20213dprintingof pages 1-2). Wall count (2–5 perimeters) affects effective stiffness and durability of flexible elements.\n\nFor **multi-material interfaces**: Khatri & Egan demonstrated that TPU band height (0–12 mm, in 3 mm increments) in rigid/flexible honeycomb structures strongly controls energy absorption and failure mode, with hexagonal honeycombs showing 66% higher energy absorption than square ones at matched band thickness (khatri2024energyabsorptionof pages 1-3, khatri2024energyabsorptionof pages 3-5, khatri2024energyabsorptionof pages 10-11). Interface wrapping thickness (0.4–2.0 mm) should be included as a continuous BO variable to strengthen PETG/TPU joints.\n\n### B3. Loading/Test Variables (Fixed Conditions)\n\nDrop height, impactor mass, and quasi-static strain rate should be treated as fixed experimental conditions, not BO variables, to maintain comparability across the campaign (pajunen2019designandimpact pages 7-8, khatri2024energyabsorptionof pages 3-5).\n\n---\n\n## (C) PETG-vs-PLA Differences Relevant to BO Bounds\n\nThe following table summarizes key property differences and their implications for search-space design.\n\n| Property | PLA (FDM printed) | PETG (FDM printed) | Shift Direction for PETG | Implication for BO Variable Ranges |\n|---|---|---|---|---|\n| Tensile strength | ~55 MPa | ~37 MPa | Lower | PETG compression struts should be allowed to be somewhat stockier than PLA for equal load capacity; cap slenderness more conservatively and avoid very low PETG infill when screening impact specimens (martins2024mechanicalpropertiesof pages 4-6) |\n| Young's modulus | ~2350 MPa | ~1200 MPa | ~50% lower | Euler buckling load is lower for the same geometry, so reduce practical upper bound on `L/D` from roughly PLA-like ~30 to ~25 for PETG, and raise PETG infill/perimeter lower bounds to recover stiffness (martins2024mechanicalpropertiesof pages 4-6) |\n| Elongation at break | ~4.3% | ~6.5% | Higher | PETG can tolerate more deformation before fracture, so strain-to-failure and allowable crush stroke can be set less conservatively than for PLA; this supports modestly broader deformation-space exploration before catastrophic breakage (martins2024mechanicalpropertiesof pages 4-6) |\n| Glass transition `T_g` | ~69.3 °C | ~73.5 °C | Slightly higher | PETG is somewhat safer for warm-service testing, but still needs elevated bed temperatures for reliable printing; set bed-temperature/process windows higher than PLA and avoid long dwell times near `T_g` in environmental tests (martins2024mechanicalpropertiesof pages 8-9) |\n| Thermal decomposition `T_d` | ~357.6 °C | ~419.3 °C | Higher | PETG has a wider thermal processing safety margin; BO bounds for nozzle temperature can safely shift upward relative to PLA, though adhesion/oozing tradeoffs still constrain the upper end (martins2024mechanicalpropertiesof pages 8-9) |\n| Impact toughness / fracture mode | More brittle; lower ductility | More ductile; better damage tolerance in practice | Higher toughness / ductility | PETG allows a less restrictive upper bound on impact energy before brittle fracture than PLA, but because modulus and strength are lower, peak-energy limits should still scale with strut geometry and relative density rather than be relaxed unconditionally (martins2024mechanicalpropertiesof pages 4-6, hsueh2021effectofprinting pages 2-3) |\n| Layer adhesion / print temperature | Good fusion commonly around ~190–220 °C | Typically needs ~230–250 °C; slower printing often helps | Requires higher temperature | Shift PETG print-temperature BO bounds upward and PETG speed bounds downward/moderate versus PLA; include temperature-speed interaction because PETG benefits more from slower deposition for better fusion and lower porosity (hsueh2021effectofprinting pages 6-8, hsueh2021effectofprinting pages 2-3) |\n| Porosity at nominal 100% infill | ~9.3% total porosity | ~12% total porosity | Higher | Since PETG prints can retain more voidage, use a higher PETG infill lower bound (about 40% rather than a PLA-like 20%), and consider wall count / orientation as active BO variables because effective cross-section is reduced by voids (martins2024mechanicalpropertiesof pages 9-14) |\n| Infill sensitivity | Strong dependence of strength on infill | Also strong; PETG specific tensile strength can deteriorate more with mass increase | Different tradeoff | For PETG, BO should optimize strength-to-weight or SEA rather than absolute load alone; avoid assuming that higher infill is always better, and search infill jointly with wall count and topology (bembenek2022researchonthe pages 2-3) |\n| Anisotropy / build-orientation sensitivity | Anisotropic | Anisotropic, with notable sensitivity to orientation and air-gap effects | Slightly higher practical sensitivity | Build orientation should be explicitly included as a categorical BO variable for PETG tensegrity struts; orientation-dependent porosity and bead geometry can materially alter failure mode and effective stiffness (bembenek2022researchonthe pages 2-3, martins2024mechanicalpropertiesof pages 9-14) |\n\n\n*Table: This table compares FDM-printed PLA and PETG properties most relevant to Bayesian optimization bounds for PETG+TPU tensegrity absorbers. It translates literature property differences into practical search-space implications for slenderness, infill, temperature, impact limits, and orientation.*\n\n**Quantitative summary:** FDM-printed PLA exhibits tensile strength ~55 MPa, Young's modulus ~2350 MPa, and elongation at break ~4.3%, while PETG shows ~37 MPa, ~1200 MPa, and ~6.5% respectively (martins2024mechanicalpropertiesof pages 4-6). Thermal analysis reveals PLA Tg ≈ 69.3°C and PETG Tg ≈ 73.5°C, with PETG showing higher thermal decomposition temperature (~419°C vs ~358°C for PLA) (martins2024mechanicalpropertiesof pages 8-9).\n\n**Critical implications for BO bounds:**\n\n1. **Strut slenderness (L/D):** PETG's ~50% lower Young's modulus means Euler buckling loads are substantially reduced for the same geometry. The practical upper bound on L/D should be reduced from ~30 (appropriate for PLA) to ~25 for PETG struts to avoid premature elastic buckling (martins2024mechanicalpropertiesof pages 4-6, pajunen2019designandimpact pages 2-3).\n\n2. **Infill percentage:** PETG prints retain more porosity (~12% vs ~9.3% for PLA at nominal 100% infill) (martins2024mechanicalpropertiesof pages 9-14), so the infill lower bound should be set higher (~40% vs ~20% for PLA) to ensure adequate effective cross-section in compression struts.\n\n3. **Layer adhesion and print temperature:** PETG requires 230–250°C for adequate fusion versus 190–220°C for PLA. Slower print speeds improve PETG bonding, and the interaction between temperature and speed is more critical than for PLA (hsueh2021effectofprinting pages 6-8, hsueh2021effectofprinting pages 2-3).\n\n4. **Impact energy before brittle fracture:** PETG's higher elongation at break (~6.5% vs ~4.3%) and greater ductility mean the allowable impact energy before catastrophic brittle fracture can be somewhat relaxed compared to PLA, but the lower modulus and strength mean this advantage is geometry-dependent (martins2024mechanicalpropertiesof pages 4-6).\n\n5. **Build orientation sensitivity:** PETG shows notable anisotropy and air-gap effects that reduce effective modulus and strength depending on orientation. Build orientation should be explicitly included as a categorical BO variable (bembenek2022researchonthe pages 2-3, martins2024mechanicalpropertiesof pages 9-14).\n\n---\n\n## (D) Recommended Numeric Bounds for BoTorch/Ax Search Space\n\nBased on the evidence, for a campaign of ~50–100 specimens:\n\n**Continuous variables:**\n- PETG strut diameter D_PETG: [1.5, 5.0] mm\n- TPU cable/skin diameter D_TPU: [1.0, 3.0] mm\n- Slenderness L/D: [8, 25]\n- Twist angle α: [10°, 45°]\n- Prestress level: [0%, 5%] tensile prestrain\n- Relative density ρ*/ρs: [0.05, 0.30] (derived)\n- PETG layer height: [0.15, 0.30] mm\n- PETG infill: [40%, 100%]\n- PETG print temperature: [230, 250] °C\n- PETG print speed: [30, 60] mm/s\n- TPU layer height: [0.15, 0.25] mm\n- TPU infill: [50%, 100%]\n- TPU print temperature: [215, 235] °C\n- TPU print speed: [15, 30] mm/s\n- Interface wrapping thickness: [0.4, 2.0] mm\n\n**Categorical variables:**\n- Unit-cell topology: {Truncated octahedron, 4-strut simplex, T3 prism, Stacked prism}\n- TPU shore hardness: {85A, 95A}\n- PETG infill pattern: {Rectilinear, Grid, Gyroid}\n- TPU infill pattern: {Honeycomb, Gyroid, Grid}\n- Cell tiling Nx×Ny×Nz: {1×1×1, 1×1×2, 2×2×1, 2×2×2, 3×3×2}\n- Build orientation: {Vertical (load-aligned), Horizontal, 45°}\n\n**Practical BO guidance:** Vangelatos et al. demonstrated that BO on architected lattices with 17 categorical design variables can find optima within ~250 evaluations starting from 50 random initial samples, using an EMCS framework with GP surrogate models (vangelatos2021strengththroughdefects pages 2-3, vangelatos2021strengththroughdefects pages 5-6, vangelatos2021strengththroughdefects pages 7-9). For a physically-tested campaign of 50–100 specimens, a Sobol/LHS initial batch of ~15–25 specimens followed by sequential BO iterations is recommended. The mixed continuous+categorical search space is well-handled by BoTorch's Mixed Optimization (SAASBO or multi-task GP with categorical kernels).\n\n---\n\n## (E) Recommended Primary Objectives and Constraints\n\n| Metric | Role (Objective/Constraint) | Definition | Target Direction | Rationale/Source |\n|---|---|---|---|---|\n| Specific Energy Absorption (SEA) | Primary objective | Total absorbed energy divided by specimen mass (J/g) | Maximize | Most common crashworthiness metric for lattices and cellular absorbers; normalizes for mass and allows fair comparison across relative densities and topologies (cronau2025energyabsorptionof pages 11-11, leoncalero20213dprintingof pages 1-2, gorguluarslan2022multiobjectivedesignoptimization pages 5-6) |\n| Peak Transmitted Force ($F_{peak}$) | Primary objective or hard constraint | Maximum force measured at the support/base plate during impact or compression | Minimize | Critical for protection applications because lower peak force corresponds to better load limitation and lower injury/equipment risk; also complements SEA when highly absorptive designs still spike early load (pajunen2019designandimpact pages 7-8, khatri2024energyabsorptionof pages 1-3, khatri2024energyabsorptionof pages 10-11) |\n| Energy Absorption Efficiency (EAE, or EAEm) | Secondary objective | Ratio of absorbed energy to the energy/stroke available before densification; often interpreted as how efficiently the crush plateau is used | Maximize | Captures whether the structure absorbs energy progressively rather than through a sharp initial peak; used explicitly in additively manufactured lattice optimization studies (bates20163dprintedpolyurethane pages 16-18, gorguluarslan2022multiobjectivedesignoptimization pages 5-6) |\n| Crush Stress Efficiency (CSE) | Secondary objective | Plateau stress divided by peak stress | Maximize | High CSE indicates a flatter, more useful stress plateau and more uniform dissipation; Gorguluarslan uses CSE jointly with energy-absorption efficiency in multi-objective optimization (gorguluarslan2022multiobjectivedesignoptimization pages 5-6) |\n| Plateau Stress ($\\sigma_{pl}$) | Informational metric or application-tuned objective | Mean stress over the post-yield/pre-densification plateau region | Application-dependent; often target a band | Determines force-transmission level during sustained crushing; should be high enough to absorb energy but not so high that transmitted loads become unacceptable (gorguluarslan2022multiobjectivedesignoptimization pages 5-6, khatri2024energyabsorptionof pages 10-11) |\n| Compaction strain ($\\varepsilon_d$) | Informational metric or secondary objective | Strain at onset of densification/compaction | Generally maximize | Higher compaction strain gives more usable stroke before densification, improving practical absorber stroke utilization (gorguluarslan2022multiobjectivedesignoptimization pages 5-6, bates20163dprintedpolyurethane pages 16-18) |\n| Specimen mass | Constraint | Total printed mass of one specimen | Keep below threshold, e.g. $\\leq$ 50 g | Keeps the campaign practical, preserves fair specific-property comparisons, and limits the optimizer from trivially improving absolute energy absorption by adding material (cronau2025energyabsorptionof pages 11-11, gorguluarslan2022multiobjectivedesignoptimization pages 5-6) |\n| Print time | Constraint | Total print duration per specimen | Keep below threshold, e.g. $\\leq$ 4 h | Essential for a 50-100 specimen undergraduate BO campaign; printability/time are standard AM-side constraints in design-of-experiments and optimization workflows (bustihan2026recentadvancesin pages 6-7, vangelatos2021strengththroughdefects pages 2-3) |\n| Cycle durability | Constraint | Number of compression/impact cycles before a chosen degradation limit, e.g. 10% strength-loss or SEA-loss threshold | Keep above threshold, e.g. $\\geq$ 3 cycles | Important for reusable absorbers; TPU-based absorbers show recoverability while cyclic softening and PETG strut damage can limit reuse (pajunen2019designandimpact pages 7-8, bates20163dprintedpolyurethane pages 16-18, bustihan2025reusable3dprintedthermoplastic pages 7-9) |\n| $W_{min}$ (cushion factor $\\times$ relative density) | Alternative primary objective | Pajunen-style efficiency metric combining cushion factor and relative density | Minimize | Useful for benchmarking against foams and other polymer absorbers; Pajunen identifies favorable designs in the region $W_{min} < 0.21$ and $\\rho^*/\\rho_s < 0.1$ (pajunen2019designandimpact pages 8-9) |\n\n\n*Table: This table summarizes recommended primary objectives, secondary metrics, and practical constraints for a Bayesian-optimization campaign on PETG+TPU tensegrity-inspired energy absorbers. It is useful for turning the literature into a measurable Ax/BoTorch optimization problem.*\n\n**Primary objectives (multi-objective BO):**\n\n1. **Maximize Specific Energy Absorption (SEA):** The most widely used crashworthiness metric, computed as total absorbed energy divided by specimen mass (J/g). This normalizes for mass and allows fair comparison across relative densities and topologies (leoncalero20213dprintingof pages 1-2, gorguluarslan2022multiobjectivedesignoptimization pages 5-6).\n\n2. **Minimize Peak Transmitted Force (F_peak):** Critical for protective applications; lower peak force corresponds to better load limitation. Alternatively, this can be treated as a hard constraint (F_peak ≤ threshold) (pajunen2019designandimpact pages 7-8, khatri2024energyabsorptionof pages 1-3).\n\n**Secondary objectives:**\n\n3. **Maximize Energy Absorption Efficiency (EAE):** Captures how efficiently the crush plateau is exploited before densification. Gorguluarslan used EAEm jointly with CSE in multi-objective lattice optimization (gorguluarslan2022multiobjectivedesignoptimization pages 5-6). Pajunen used Wmin = cushion factor × relative density, targeting Wmin < 0.21 at ρ*/ρs < 0.1 (pajunen2019designandimpact pages 8-9).\n\n4. **Maximize Crush Stress Efficiency (CSE):** Plateau stress / peak stress; higher CSE indicates a flatter, more uniform stress plateau (gorguluarslan2022multiobjectivedesignoptimization pages 5-6).\n\n**Constraints:**\n\n- **Maximum specimen mass:** ≤ 50 g (keeps campaign practical and enables specific-property comparisons)\n- **Maximum print time:** ≤ 4 hours per specimen (ensures 50–100 specimens fit an undergraduate semester timeline) (bustihan2026recentadvancesin pages 6-7)\n- **Minimum cycle durability:** ≥ 3 compression cycles to <10% SEA loss (important for reusable absorbers; TPU enables elastic recovery with ~24.5% energy drop from cycle 1→2 then convergence, while PETG strut fracture limits reuse) (bates20163dprintedpolyurethane pages 16-18, bustihan2025reusable3dprintedthermoplastic pages 7-9)\n- **Minimum printability:** no print failures (enforced by excluding non-manufacturable designs via geometry constraints on minimum overhang angle, minimum feature size ≥ 1.0 mm, and bridging distance limits)\n\n**Recommended BO formulation:** A multi-objective formulation maximizing SEA while minimizing F_peak, subject to mass, print-time, and durability constraints, is the most practical starting point. This can be implemented in BoTorch using `qNoisyExpectedHypervolumeImprovement` (qNEHVI) as the acquisition function for Pareto-optimal design discovery with noisy experimental observations.\n\nReferences\n\n1. (micheletti2022seventyyearsof pages 23-24): Andrea Micheletti and Paolo Podio-Guidugli. Seventy years of tensegrities (and counting). Archive of Applied Mechanics, 92:2525-2548, Jul 2022. URL: https://doi.org/10.1007/s00419-022-02192-4, doi:10.1007/s00419-022-02192-4. This article has 75 citations and is from a peer-reviewed journal.\n\n2. (sabounizawadzka2024experimentalinvestigationson pages 1-3): Anna Al Sabouni-Zawadzka, Wojciech Gilewski, and Adam Zawadzki. Experimental investigations on mechanical propertiesof 3d-printed tensegrity-inspired metamaterialsbased on 4-strut simplex module. Archives of Civil Engineering, pages 343-357, Jun 2024. URL: https://doi.org/10.24425/ace.2024.150987, doi:10.24425/ace.2024.150987. This article has 0 citations.\n\n3. (sabounizawadzka2024experimentalinvestigationsona pages 6-11): A Al Sabouni-Zawadzka and W Gilewski. Experimental investigations on mechanical properties of 3d-printed tensegrity-inspired metamaterials based on 4-strut simplex module. Unknown journal, 2024.\n\n4. (pajunen2019designandimpact pages 1-2): Kirsti Pajunen, Paul Johanns, Raj Kumar Pal, Julian J. Rimoli, and Chiara Daraio. Design and impact response of 3d-printable tensegrity-inspired structures. Materials & Design, 182:107966, Nov 2019. URL: https://doi.org/10.1016/j.matdes.2019.107966, doi:10.1016/j.matdes.2019.107966. This article has 98 citations and is from a highest quality peer-reviewed journal.\n\n5. (pajunen2019designandimpact pages 8-9): Kirsti Pajunen, Paul Johanns, Raj Kumar Pal, Julian J. Rimoli, and Chiara Daraio. Design and impact response of 3d-printable tensegrity-inspired structures. Materials & Design, 182:107966, Nov 2019. URL: https://doi.org/10.1016/j.matdes.2019.107966, doi:10.1016/j.matdes.2019.107966. This article has 98 citations and is from a highest quality peer-reviewed journal.\n\n6. (zhang2021optimizationforenergy pages 1-2): Jingyao Zhang, Makoto Ohsaki, Julian J. Rimoli, and Kosuke Kogiso. Optimization for energy absorption of 3-dimensional tensegrity lattice with truncated octahedral units. Composite Structures, 267:113903, Jul 2021. URL: https://doi.org/10.1016/j.compstruct.2021.113903, doi:10.1016/j.compstruct.2021.113903. This article has 33 citations and is from a domain leading peer-reviewed journal.\n\n7. (micheletti2022seventyyearsof pages 20-21): Andrea Micheletti and Paolo Podio-Guidugli. Seventy years of tensegrities (and counting). Archive of Applied Mechanics, 92:2525-2548, Jul 2022. URL: https://doi.org/10.1007/s00419-022-02192-4, doi:10.1007/s00419-022-02192-4. This article has 75 citations and is from a peer-reviewed journal.\n\n8. (liu2019tensegritytopologyoptimization pages 22-22): Ke Liu and Glaucio H. Paulino. Tensegrity topology optimization by force maximization on arbitrary ground structures. Structural and Multidisciplinary Optimization, 59:2041-2062, Jan 2019. URL: https://doi.org/10.1007/s00158-018-2172-3, doi:10.1007/s00158-018-2172-3. This article has 65 citations and is from a domain leading peer-reviewed journal.\n\n9. (bustihan2026recentadvancesin pages 19-21): Alin Bustihan and Ioan Botiz. Recent advances in additively manufactured polymeric structures for mechanical energy absorption. Polymers, 18:1019, Apr 2026. URL: https://doi.org/10.3390/polym18091019, doi:10.3390/polym18091019. This article has 0 citations.\n\n10. (pajunen2019designandimpact pages 9-9): Kirsti Pajunen, Paul Johanns, Raj Kumar Pal, Julian J. Rimoli, and Chiara Daraio. Design and impact response of 3d-printable tensegrity-inspired structures. Materials & Design, 182:107966, Nov 2019. URL: https://doi.org/10.1016/j.matdes.2019.107966, doi:10.1016/j.matdes.2019.107966. This article has 98 citations and is from a highest quality peer-reviewed journal.\n\n11. (sabounizawadzka2024experimentalinvestigationsona pages 1-3): A Al Sabouni-Zawadzka and W Gilewski. Experimental investigations on mechanical properties of 3d-printed tensegrity-inspired metamaterials based on 4-strut simplex module. Unknown journal, 2024.\n\n12. (pajunen2019designandimpact pages 3-4): Kirsti Pajunen, Paul Johanns, Raj Kumar Pal, Julian J. Rimoli, and Chiara Daraio. Design and impact response of 3d-printable tensegrity-inspired structures. Materials & Design, 182:107966, Nov 2019. URL: https://doi.org/10.1016/j.matdes.2019.107966, doi:10.1016/j.matdes.2019.107966. This article has 98 citations and is from a highest quality peer-reviewed journal.\n\n13. (pajunen2019designandimpact pages 2-3): Kirsti Pajunen, Paul Johanns, Raj Kumar Pal, Julian J. Rimoli, and Chiara Daraio. Design and impact response of 3d-printable tensegrity-inspired structures. Materials & Design, 182:107966, Nov 2019. URL: https://doi.org/10.1016/j.matdes.2019.107966, doi:10.1016/j.matdes.2019.107966. This article has 98 citations and is from a highest quality peer-reviewed journal.\n\n14. (bustihan2026recentadvancesin pages 6-7): Alin Bustihan and Ioan Botiz. Recent advances in additively manufactured polymeric structures for mechanical energy absorption. Polymers, 18:1019, Apr 2026. URL: https://doi.org/10.3390/polym18091019, doi:10.3390/polym18091019. This article has 0 citations.\n\n15. (martins2024mechanicalpropertiesof pages 4-6): Rui F. Martins, Ricardo Branco, Miguel Martins, Wojciech Macek, Zbigniew Marciniak, Rui Silva, Daniela Trindade, Carla Moura, Margarida Franco, and Cândida Malça. Mechanical properties of additively manufactured polymeric materials—pla and petg—for biomechanical applications. Polymers, 16:1868, Jun 2024. URL: https://doi.org/10.3390/polym16131868, doi:10.3390/polym16131868. This article has 36 citations.\n\n16. (bustihan2025reusable3dprintedthermoplastic pages 7-9): Alin Bustihan, Razvan Hirian, and Ioan Botiz. Reusable 3d-printed thermoplastic polyurethane honeycombs for mechanical energy absorption. Polymers, 17:3035, Nov 2025. URL: https://doi.org/10.3390/polym17223035, doi:10.3390/polym17223035. This article has 3 citations.\n\n17. (vangelatos2021strengththroughdefects pages 1-2): Zacharias Vangelatos, Haris Moazam Sheikh, Philip S. Marcus, Costas P. Grigoropoulos, Victor Z. Lopez, George Flamourakis, and Maria Farsari. Strength through defects: a novel bayesian approach for the optimization of architected materials. Science Advances, Oct 2021. URL: https://doi.org/10.1126/sciadv.abk2218, doi:10.1126/sciadv.abk2218. This article has 124 citations and is from a highest quality peer-reviewed journal.\n\n18. (vangelatos2021strengththroughdefects pages 2-3): Zacharias Vangelatos, Haris Moazam Sheikh, Philip S. Marcus, Costas P. Grigoropoulos, Victor Z. Lopez, George Flamourakis, and Maria Farsari. Strength through defects: a novel bayesian approach for the optimization of architected materials. Science Advances, Oct 2021. URL: https://doi.org/10.1126/sciadv.abk2218, doi:10.1126/sciadv.abk2218. This article has 124 citations and is from a highest quality peer-reviewed journal.\n\n19. (cronau2025energyabsorptionof pages 1-2): J. Cronau and F. Engstler. Energy absorption of 3d printed stochastic lattice structures under impact loading – design parameters, manufacturing, and testing. Progress in Additive Manufacturing, 10:3145-3156, Apr 2025. URL: https://doi.org/10.1007/s40964-025-01094-5, doi:10.1007/s40964-025-01094-5. This article has 16 citations and is from a peer-reviewed journal.\n\n20. (cronau2025energyabsorptionof pages 11-11): J. Cronau and F. Engstler. Energy absorption of 3d printed stochastic lattice structures under impact loading – design parameters, manufacturing, and testing. Progress in Additive Manufacturing, 10:3145-3156, Apr 2025. URL: https://doi.org/10.1007/s40964-025-01094-5, doi:10.1007/s40964-025-01094-5. This article has 16 citations and is from a peer-reviewed journal.\n\n21. (hsueh2021effectofprinting pages 2-3): Ming-Hsien Hsueh, Chao-Jung Lai, Shi-Hao Wang, Yu-Shan Zeng, Chia-Hsin Hsieh, Chieh-Yu Pan, and Wen-Chen Huang. Effect of printing parameters on the thermal and mechanical properties of 3d-printed pla and petg, using fused deposition modeling. Polymers, 13:1758, May 2021. URL: https://doi.org/10.3390/polym13111758, doi:10.3390/polym13111758. This article has 407 citations.\n\n22. (bembenek2022researchonthe pages 2-3): Michał Bembenek, Łukasz Kowalski, and Agnieszka Kosoń-Schab. Research on the influence of processing parameters on the specific tensile strength of fdm additive manufactured pet-g and pla materials. Polymers, 14:2446, Jun 2022. URL: https://doi.org/10.3390/polym14122446, doi:10.3390/polym14122446. This article has 69 citations.\n\n23. (hsueh2021effectofprinting pages 6-8): Ming-Hsien Hsueh, Chao-Jung Lai, Shi-Hao Wang, Yu-Shan Zeng, Chia-Hsin Hsieh, Chieh-Yu Pan, and Wen-Chen Huang. Effect of printing parameters on the thermal and mechanical properties of 3d-printed pla and petg, using fused deposition modeling. Polymers, 13:1758, May 2021. URL: https://doi.org/10.3390/polym13111758, doi:10.3390/polym13111758. This article has 407 citations.\n\n24. (bustihan2025reusable3dprintedthermoplastic pages 2-4): Alin Bustihan, Razvan Hirian, and Ioan Botiz. Reusable 3d-printed thermoplastic polyurethane honeycombs for mechanical energy absorption. Polymers, 17:3035, Nov 2025. URL: https://doi.org/10.3390/polym17223035, doi:10.3390/polym17223035. This article has 3 citations.\n\n25. (khatri2024energyabsorptionof pages 3-5): Nava Raj Khatri and Paul F. Egan. Energy absorption of 3d printed abs and tpu multimaterial honeycomb structures. 3D Printing and Additive Manufacturing, 11:e840-e850, Apr 2024. URL: https://doi.org/10.1089/3dp.2022.0196, doi:10.1089/3dp.2022.0196. This article has 29 citations and is from a peer-reviewed journal.\n\n26. (leoncalero20213dprintingof pages 10-12): Marina León-Calero, Sara Catherine Reyburn Valés, Ángel Marcos-Fernández, and Juan Rodríguez-Hernandez. 3d printing of thermoplastic elastomers: role of the chemical composition and printing parameters in the production of parts with controlled energy absorption and damping capacity. Polymers, 13:3551, Oct 2021. URL: https://doi.org/10.3390/polym13203551, doi:10.3390/polym13203551. This article has 110 citations.\n\n27. (leoncalero20213dprintingof pages 1-2): Marina León-Calero, Sara Catherine Reyburn Valés, Ángel Marcos-Fernández, and Juan Rodríguez-Hernandez. 3d printing of thermoplastic elastomers: role of the chemical composition and printing parameters in the production of parts with controlled energy absorption and damping capacity. Polymers, 13:3551, Oct 2021. URL: https://doi.org/10.3390/polym13203551, doi:10.3390/polym13203551. This article has 110 citations.\n\n28. (leoncalero20213dprintingof pages 4-5): Marina León-Calero, Sara Catherine Reyburn Valés, Ángel Marcos-Fernández, and Juan Rodríguez-Hernandez. 3d printing of thermoplastic elastomers: role of the chemical composition and printing parameters in the production of parts with controlled energy absorption and damping capacity. Polymers, 13:3551, Oct 2021. URL: https://doi.org/10.3390/polym13203551, doi:10.3390/polym13203551. This article has 110 citations.\n\n29. (leoncalero20213dprintingof pages 8-10): Marina León-Calero, Sara Catherine Reyburn Valés, Ángel Marcos-Fernández, and Juan Rodríguez-Hernandez. 3d printing of thermoplastic elastomers: role of the chemical composition and printing parameters in the production of parts with controlled energy absorption and damping capacity. Polymers, 13:3551, Oct 2021. URL: https://doi.org/10.3390/polym13203551, doi:10.3390/polym13203551. This article has 110 citations.\n\n30. (khatri2024energyabsorptionof pages 1-3): Nava Raj Khatri and Paul F. Egan. Energy absorption of 3d printed abs and tpu multimaterial honeycomb structures. 3D Printing and Additive Manufacturing, 11:e840-e850, Apr 2024. URL: https://doi.org/10.1089/3dp.2022.0196, doi:10.1089/3dp.2022.0196. This article has 29 citations and is from a peer-reviewed journal.\n\n31. (bustihan2025reusable3dprintedthermoplastic pages 24-25): Alin Bustihan, Razvan Hirian, and Ioan Botiz. Reusable 3d-printed thermoplastic polyurethane honeycombs for mechanical energy absorption. Polymers, 17:3035, Nov 2025. URL: https://doi.org/10.3390/polym17223035, doi:10.3390/polym17223035. This article has 3 citations.\n\n32. (martins2024mechanicalpropertiesof pages 9-14): Rui F. Martins, Ricardo Branco, Miguel Martins, Wojciech Macek, Zbigniew Marciniak, Rui Silva, Daniela Trindade, Carla Moura, Margarida Franco, and Cândida Malça. Mechanical properties of additively manufactured polymeric materials—pla and petg—for biomechanical applications. Polymers, 16:1868, Jun 2024. URL: https://doi.org/10.3390/polym16131868, doi:10.3390/polym16131868. This article has 36 citations.\n\n33. (pajunen2019designandimpact pages 7-8): Kirsti Pajunen, Paul Johanns, Raj Kumar Pal, Julian J. Rimoli, and Chiara Daraio. Design and impact response of 3d-printable tensegrity-inspired structures. Materials & Design, 182:107966, Nov 2019. URL: https://doi.org/10.1016/j.matdes.2019.107966, doi:10.1016/j.matdes.2019.107966. This article has 98 citations and is from a highest quality peer-reviewed journal.\n\n34. (gorguluarslan2022multiobjectivedesignoptimization pages 5-6): Recep M Gorguluarslan. Multi-objective design optimization of additively manufactured lattice structures for improved energy absorption performance. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 236:3-15, May 2022. URL: https://doi.org/10.1177/0954406221995542, doi:10.1177/0954406221995542. This article has 18 citations.\n\n35. (ohsaki2019optimizationoftensegrity pages 1-3): M Ohsaki, J Zhang, and K Kogiso. Optimization of tensegrity lattice with truncated octahedral units. Unknown journal, 2019.\n\n36. (bustihan2026recentadvancesin pages 4-6): Alin Bustihan and Ioan Botiz. Recent advances in additively manufactured polymeric structures for mechanical energy absorption. Polymers, 18:1019, Apr 2026. URL: https://doi.org/10.3390/polym18091019, doi:10.3390/polym18091019. This article has 0 citations.\n\n37. (khatri2024energyabsorptionof pages 10-11): Nava Raj Khatri and Paul F. Egan. Energy absorption of 3d printed abs and tpu multimaterial honeycomb structures. 3D Printing and Additive Manufacturing, 11:e840-e850, Apr 2024. URL: https://doi.org/10.1089/3dp.2022.0196, doi:10.1089/3dp.2022.0196. This article has 29 citations and is from a peer-reviewed journal.\n\n38. (martins2024mechanicalpropertiesof pages 8-9): Rui F. Martins, Ricardo Branco, Miguel Martins, Wojciech Macek, Zbigniew Marciniak, Rui Silva, Daniela Trindade, Carla Moura, Margarida Franco, and Cândida Malça. Mechanical properties of additively manufactured polymeric materials—pla and petg—for biomechanical applications. Polymers, 16:1868, Jun 2024. URL: https://doi.org/10.3390/polym16131868, doi:10.3390/polym16131868. This article has 36 citations.\n\n39. (vangelatos2021strengththroughdefects pages 5-6): Zacharias Vangelatos, Haris Moazam Sheikh, Philip S. Marcus, Costas P. Grigoropoulos, Victor Z. Lopez, George Flamourakis, and Maria Farsari. Strength through defects: a novel bayesian approach for the optimization of architected materials. Science Advances, Oct 2021. URL: https://doi.org/10.1126/sciadv.abk2218, doi:10.1126/sciadv.abk2218. This article has 124 citations and is from a highest quality peer-reviewed journal.\n\n40. (vangelatos2021strengththroughdefects pages 7-9): Zacharias Vangelatos, Haris Moazam Sheikh, Philip S. Marcus, Costas P. Grigoropoulos, Victor Z. Lopez, George Flamourakis, and Maria Farsari. Strength through defects: a novel bayesian approach for the optimization of architected materials. Science Advances, Oct 2021. URL: https://doi.org/10.1126/sciadv.abk2218, doi:10.1126/sciadv.abk2218. This article has 124 citations and is from a highest quality peer-reviewed journal.\n\n41. (bates20163dprintedpolyurethane pages 16-18): Simon R.G. Bates, Ian R. Farrow, and Richard S. Trask. 3d printed polyurethane honeycombs for repeated tailored energy absorption. Materials & Design, 112:172-183, Dec 2016. URL: https://doi.org/10.1016/j.matdes.2016.08.062, doi:10.1016/j.matdes.2016.08.062. This article has 388 citations and is from a highest quality peer-reviewed journal.", + "answer_reasoning": null, + "has_successful_answer": true, + "total_cost": null, + "total_queries": null +} \ No newline at end of file diff --git a/edison-trajectories/tpu-petg-bo-variables-5ae24eaf-5b6e-45cf-9f6c-1c7fbd881738.md b/edison-trajectories/tpu-petg-bo-variables-5ae24eaf-5b6e-45cf-9f6c-1c7fbd881738.md new file mode 100644 index 00000000..81a330a7 --- /dev/null +++ b/edison-trajectories/tpu-petg-bo-variables-5ae24eaf-5b6e-45cf-9f6c-1c7fbd881738.md @@ -0,0 +1,316 @@ +Question: For a Bayesian-optimization-driven, multi-material FDM 3D-printed +tensegrity-inspired energy-absorbing structure made from TPU (flexible tension +elements) + PETG (rigid compression struts) -- NOT PLA -- enumerate and +recommend, with literature citations: + +(A) BASE / SEED UNIT-CELL TOPOLOGIES suitable as the starting design family + (e.g., 3-bar / 4-bar prism, octahedron, icosahedron, expanded octahedron, + truncated tetrahedron, "tensegrity-inspired" Pajunen-style cells, stacked + prisms, lattice tilings of these). For each, note manufacturability with + multi-material FDM and reported energy-absorption performance. + +(B) DESIGN VARIABLES that are normally swept in BO of these structures, + grouped as: + 1. Geometric/topological (strut length L, strut diameter D, slenderness + L/D, cable/skin cross-section, prestress level, twist angle, cell + tiling Nx*Ny*Nz, relative density, member connectivity). + 2. Material/print-parameter (PETG vs TPU layer height, infill % and + pattern for PETG struts, TPU shore hardness e.g. 85A/95A, TPU wall + count / infill, print temperature, print speed, bed adhesion, + interface wrapping thickness following Ye et al. 2023 / + Khatri 2024). + 3. Loading/test variables (drop height, impactor mass, quasi-static + strain rate) -- treat as fixed conditions, not BO variables. + +(C) Specifically address PETG-vs-PLA differences relevant to BO bounds and + constraints: PETG is tougher, less brittle, has lower stiffness and lower + glass-transition temperature than PLA; how does this shift sensible + variable ranges (e.g., strut slenderness, infill, layer adhesion, allowed + impact energy before brittle fracture)? + +(D) Recommend reasonable numeric BOUNDS for each continuous variable and + CATEGORIES for each categorical variable, suitable for a BoTorch/Ax + search space for an undergraduate-led campaign of ~50-100 specimens. + +(E) Recommended PRIMARY OBJECTIVES (peak transmitted force, specific energy + absorption SEA, compaction efficiency, plateau stress) and any + constraints (max specimen mass, max print time, min cycle durability). + +Return a structured answer with tables where helpful. Cite peer-reviewed +sources for the structures, the PETG/TPU mechanical data, and prior BO +campaigns on architected/lattice/tensegrity energy absorbers. + +# Bayesian-Optimization-Driven Multi-Material FDM Tensegrity-Inspired Energy Absorbers: Design Framework for PETG + TPU + +## (A) Base / Seed Unit-Cell Topologies + +The following table enumerates candidate tensegrity and tensegrity-inspired unit-cell topologies suitable as starting design families, with assessment of manufacturability and energy-absorption evidence. + +| Topology Name | Members (bars/cables) | Key Reference | Reported EA Performance | Multi-Material FDM Manufacturability | Recommended Priority | +|---|---:|---|---|---|---| +| T3 / 3-bar prism | 3 / 9 (classical T3 prism) | Zhang et al. 2018; review coverage in Micheletti & Podio-Guidugli 2022 | T3 prism with metal-rubber insert showed increased energy absorption and tunable nonlinearity under static/dynamic loading versus prism alone; useful proof of concept, but not polymer FDM-specific (micheletti2022seventyyearsof pages 23-24) | Good for PETG struts + TPU tendons in principle; simple member count and clear load path, but needs careful joint design and twist-control during print/assembly | **Medium** | +| 4-strut simplex | 4 / 12 (simplex-type tensegrity module) | Al Sabouni-Zawadzka et al. 2024 | Experimental uniaxial compression on printed modules showed tensegrity-like response, post-critical strut behavior, and strong dependence on parent-material elongation-at-break; useful as a mechanically validated seed cell, though published tests were not multi-material FDM (sabounizawadzka2024experimentalinvestigationson pages 1-3, sabounizawadzka2024experimentalinvestigationsona pages 6-11) | Moderate: topology is compact and experimentally validated, but printed rigid joints and manufacturing inaccuracies strongly affect behavior; FDM feasible if joints are thickened and TPU paths are simplified | **High** | +| Truncated octahedron (Pajunen-style) | 12 / 36 in Pajunen-inspired printable cell; optimized lattice unit also treated as 12 bars + 36 cables equivalent | Pajunen et al. 2019; Zhang et al. 2021 | Best-supported option: high elastic strain-energy absorption, post-buckling stability, reusable impact response, low relative density, and optimized strain-energy storage under stress/volume constraints; specifically proposed as a tessellatable manufacturable unit cell (pajunen2019designandimpact pages 1-2, pajunen2019designandimpact pages 8-9, zhang2021optimizationforenergy pages 1-2) | **Excellent**: tessellation-friendly faces, strongest literature base, already adapted to printable tensegrity-inspired geometry; very suitable for dual-extrusion PETG+TPU and BO campaigns | **Very High / Best seed family** | +| Truncated tetrahedron | Varies by formulation; regular tensegrity versions reported in the broader tensegrity literature | Zhang & Ohsaki / broader tensegrity topology literature cited in reviews | Strong theoretical/form-finding literature, but little direct polymer energy-absorption evidence found here relative to truncated octahedron; better treated as a secondary exploratory topology (micheletti2022seventyyearsof pages 20-21, liu2019tensegritytopologyoptimization pages 22-22) | Moderate-to-low: printable, but less experimentally validated for energy absorption and less straightforward as an undergrad BO baseline than truncated octahedra or simplex cells | **Low-Medium** | +| Expanded / regular octahedron | Varies by realization; octahedral families common in lattice literature | General lattice/tensegrity review evidence; truncated-octahedral work is much better supported than regular octahedral tensegrity here | Octet/octahedral families are widely used in energy-absorbing lattices, but direct tensegrity-specific polymer EA evidence in the gathered set is sparse compared with Pajunen-style truncated octahedra (bustihan2026recentadvancesin pages 19-21, micheletti2022seventyyearsof pages 23-24) | Good geometric simplicity for FDM, but weaker direct evidence base for tensegrity-inspired PETG+TPU energy absorbers | **Medium** | +| Icosahedron tensegrity | Varies by module; icosahedral and truncated-icosahedral modules appear in tensegrity form-finding/stability literature | Micheletti & Podio-Guidugli 2022 review and cited foundational studies | Attractive isotropic tensegrity family, but little direct reported 3D-printed polymer compression/impact EA evidence in the gathered sources; best regarded as a later-stage topology screen (micheletti2022seventyyearsof pages 20-21) | Fair in theory, but node complexity and support burden are higher for multi-material FDM; not ideal as first BO seed family | **Low** | +| Stacked prism columns | Repeated T3/Tn prisms in columnar chains | Prism-chain and beam literature summarized in tensegrity review | Literature supports tunable softening–stiffening and wave/impact behavior in stacked prism systems; useful for 1D impact columns and sequential collapse studies, but less directly validated here as reusable polymer EA lattices than truncated octahedra (micheletti2022seventyyearsof pages 23-24, pajunen2019designandimpact pages 9-9) | Good for simple specimen fabrication and drop-tower testing; easier than full 3D lattices, though less space-filling and less scalable to panel cores | **High for pilot tests; Medium overall** | +| 2D/3D lattice tilings of truncated octahedra | Repeated unit-cell assembly | Pajunen et al. 2019; Zhang et al. 2021 | Most promising system-level extension: Pajunen explicitly proposes tessellation into multidimensional lattices, and Zhang optimizes 3D lattices of truncated-octahedral units for stored strain energy/energy absorption (pajunen2019designandimpact pages 8-9, zhang2021optimizationforenergy pages 1-2) | **Excellent**: natural next step after single-cell screening; compatible with BO over tiling counts, relative density, and graded TPU/PETG layouts | **Very High** | + + +*Table: This table compares candidate seed unit-cell families for tensegrity-inspired energy absorbers, emphasizing energy-absorption evidence and manufacturability for PETG+TPU multi-material FDM. It is useful for selecting a practical starting topology family before defining a Bayesian optimization search space.* + +**Recommended primary seed family:** The **truncated octahedron tensegrity** (Pajunen-style) is the strongest candidate. Pajunen et al. demonstrated a single-material, 3D-printable tensegrity-inspired structure based on a truncated octahedron (12 struts, 36 cables) that exhibited high elastic strain energy absorption, post-buckling stability, resilience under severe deformation, load-limitation, and reusability under repeated impacts (pajunen2019designandimpact pages 1-2). The spherically-jointed variant achieved the lowest energy absorption metric Wmin at ultra-low relative density, placing it in a favorable target region (Wmin < 0.21, ρ*/ρs < 0.1) (pajunen2019designandimpact pages 8-9). Zhang et al. subsequently formulated optimization of 3D tensegrity lattices with truncated octahedral units (24 nodes, 12 bars, 24 cutting cables, 12 edge cables per unit) to maximize stored strain energy, explicitly leveraging bar buckling (zhang2021optimizationforenergy pages 1-2). + +The **4-strut simplex module** is the second-best-supported option, with Sabouni-Zawadzka et al. providing experimental uniaxial compression data on 3D-printed modules across multiple AM techniques, parent materials, and cell sizes (20–50 mm edge), using 3.0 mm strut diameter and 0.95 mm cable diameter (sabounizawadzka2024experimentalinvestigationson pages 1-3, sabounizawadzka2024experimentalinvestigationsona pages 6-11). Key findings: elongation at break of the parent material strongly governs module ductility, and post-critical buckling behavior of struts was clearly observed (sabounizawadzka2024experimentalinvestigationsona pages 1-3). + +The **T3 (3-bar) prism** has been studied as a metamaterial building block with metal rubber inserts, demonstrating increased energy absorption and tunable nonlinearity under quasi-static, vibration, and impact loading (micheletti2022seventyyearsof pages 23-24). **Stacked prism columns** are practical for pilot drop-tower testing, and **2D/3D lattice tilings** of truncated octahedra represent the natural system-level extension (pajunen2019designandimpact pages 8-9, zhang2021optimizationforenergy pages 1-2). + +For **multi-material FDM manufacturability** with PETG (rigid struts) + TPU (flexible tension elements), the truncated octahedron is especially suitable because its tessellation-friendly faces enable systematic tiling, and the distinct compression/tension member roles map naturally to a dual-extrusion PETG/TPU workflow (pajunen2019designandimpact pages 1-2). + +--- + +## (B) Design Variables for BO + +The following table provides a comprehensive enumeration of design variables grouped into geometric/topological, material/print-parameter, and loading/test categories, with recommended bounds suitable for a BoTorch/Ax search space. + +| Variable | Group | Type | Recommended Bounds/Categories | Rationale/Source | +|---|---|---|---|---| +| Strut diameter `D_PETG` | Geometric/Topological | Continuous | 1.5–5.0 mm | Conservative FDM range for 0.4 mm nozzle and undergraduate campaign; Pajunen’s tensegrity-inspired truncated-octahedron used strut diameters around 3.05 mm, with later geometry variants down to 2.6 mm; strut diameter is a standard lattice/EA optimization variable (pajunen2019designandimpact pages 3-4, pajunen2019designandimpact pages 2-3, bustihan2026recentadvancesin pages 6-7) | +| Cable/skin diameter `D_TPU` | Geometric/Topological | Continuous | 1.0–3.0 mm | Pajunen-style cable diameters were ~1.37–1.8 mm; lower bound keeps TPU roads manufacturable and bonded, upper bound avoids over-stiffening tension network (pajunen2019designandimpact pages 3-4, pajunen2019designandimpact pages 2-3) | +| Slenderness `L/D` | Geometric/Topological | Continuous | 8–25 | Captures elastic buckling-to-crushing transition while avoiding extremely fragile PETG struts; informed by Pajunen member lengths/diameters and PETG’s lower modulus than PLA (pajunen2019designandimpact pages 2-3, martins2024mechanicalpropertiesof pages 4-6, bustihan2026recentadvancesin pages 6-7) | +| Twist angle `α` | Geometric/Topological | Continuous | 10°–45° | Meaningful for prism/stacked-prism families and twisted energy absorbers; broad enough to capture stiffness-collapse mode shifts without self-intersection (micheletti2022seventyyearsof pages 23-24, bustihan2025reusable3dprintedthermoplastic pages 7-9) | +| Prestress level | Geometric/Topological | Continuous | 0–5% tensile prestrain | Pajunen reported 2% prestress as an effective tuning level; Zhang/Ohsaki-type tensegrity optimization treats prestress as a key design variable, but 0–5% is safer for PETG/TPU undergraduate fabrication than higher values (pajunen2019designandimpact pages 3-4, zhang2021optimizationforenergy pages 1-2) | +| Cell tiling `N_x × N_y × N_z` | Geometric/Topological | Categorical/Ordinal | {1×1×1, 1×1×2, 2×2×1, 2×2×2, 3×3×2, 3×3×3} | Keeps specimen count and print time manageable while allowing single-cell vs lattice effects; BO on architected materials often includes discrete topological layout variables (vangelatos2021strengththroughdefects pages 1-2, vangelatos2021strengththroughdefects pages 2-3) | +| Relative density `ρ*/ρ_s` | Geometric/Topological | Continuous/Derived | 0.05–0.30 | Covers ultralight to moderately dense polymer lattices; Pajunen targets low relative density, while stochastic lattice studies report useful SEA around 10–25% density (pajunen2019designandimpact pages 8-9, cronau2025energyabsorptionof pages 1-2, cronau2025energyabsorptionof pages 11-11) | +| Unit-cell topology | Geometric/Topological | Categorical | {Truncated octahedron, 4-strut simplex, T3 prism, Stacked prism} | These are the most defensible seed families for BO: strongest support for truncated octahedron; experimental support for 4-strut simplex; T3 prism established in tensegrity metamaterials; stacked prisms are practical for columnar absorbers (pajunen2019designandimpact pages 1-2, zhang2021optimizationforenergy pages 1-2, sabounizawadzka2024experimentalinvestigationson pages 1-3, micheletti2022seventyyearsof pages 23-24) | +| PETG layer height | Material/Print | Continuous | 0.15–0.30 mm | Lies inside reported FDM range where layer height strongly affects strength and print time; 0.15–0.30 mm is realistic for PETG campaign printing (bustihan2026recentadvancesin pages 6-7, hsueh2021effectofprinting pages 2-3) | +| PETG infill % | Material/Print | Continuous | 40–100% | Infill percentage is among the most influential FDM parameters; lower bound avoids overly weak PETG struts, upper bound allows near-solid compression members (hsueh2021effectofprinting pages 2-3, bembenek2022researchonthe pages 2-3) | +| PETG infill pattern | Material/Print | Categorical | {Rectilinear, Grid, Gyroid} | Common slicer choices with distinct anisotropy and crush behavior; pattern is a standard AM variable in lattice/property studies (bustihan2026recentadvancesin pages 6-7, hsueh2021effectofprinting pages 2-3) | +| PETG print temperature | Material/Print | Continuous | 230–250 °C | PETG typically requires >230 °C for good fusion; higher temperatures reduce porosity but too high can degrade dimensional fidelity; this range is well-supported for mechanical optimization (hsueh2021effectofprinting pages 2-3, hsueh2021effectofprinting pages 6-8) | +| PETG print speed | Material/Print | Continuous | 30–60 mm/s | Reflects common PETG processing window and tradeoff between bonding and throughput; slower speeds often improve PETG bonding (hsueh2021effectofprinting pages 6-8, bustihan2026recentadvancesin pages 6-7) | +| TPU Shore hardness | Material/Print | Categorical | {85A, 95A} | These grades are directly supported in energy-absorbing TPU studies; 95A gives higher stress/plateau stability, 85A offers a softer compromise (bustihan2025reusable3dprintedthermoplastic pages 7-9, bustihan2025reusable3dprintedthermoplastic pages 2-4) | +| TPU layer height | Material/Print | Continuous | 0.15–0.25 mm | Matches practical TPU FDM windows and avoids overly tall layers that can impair bead fusion in flexible members (khatri2024energyabsorptionof pages 3-5, leoncalero20213dprintingof pages 10-12) | +| TPU wall count | Material/Print | Ordinal | 2–5 | Wall count materially changes effective stiffness and durability of flexible tendons/skins; compatible with common slicers and small DOE/BO budgets (bustihan2026recentadvancesin pages 6-7, khatri2024energyabsorptionof pages 3-5) | +| TPU infill % | Material/Print | Continuous | 50–100% | TPU energy-absorption studies found strong dependence on infill density, with many optima near 50%; full infill remains useful for durable tendons/skins (leoncalero20213dprintingof pages 1-2, leoncalero20213dprintingof pages 10-12) | +| TPU infill pattern | Material/Print | Categorical | {Honeycomb, Gyroid, Grid} | Honeycomb at ~50% gave optimal SEA/SDC in León-Calero et al.; gyroid/grid are natural comparators with different damping/compliance (leoncalero20213dprintingof pages 1-2, leoncalero20213dprintingof pages 4-5) | +| TPU print temperature | Material/Print | Continuous | 215–235 °C | Supported by TPU 70A/85A/95A studies and technical ranges; upper limit stays below degradation concerns while covering good interlayer adhesion (bustihan2025reusable3dprintedthermoplastic pages 7-9, leoncalero20213dprintingof pages 10-12, leoncalero20213dprintingof pages 8-10) | +| TPU print speed | Material/Print | Continuous | 15–30 mm/s | Flexible filaments generally require lower speed; Khatri used ~25 mm/s for TPU, and softer TPUs may need still slower extrusion (khatri2024energyabsorptionof pages 3-5, leoncalero20213dprintingof pages 10-12) | +| Interface wrapping thickness | Material/Print | Continuous | 0.4–2.0 mm | Practical one-to-five-road overlap/interlock thickness for multimaterial joints; motivated by need to strengthen rigid/flexible interfaces in multimaterial FDM, even though direct PETG/TPU tensegrity data are sparse (khatri2024energyabsorptionof pages 1-3, khatri2024energyabsorptionof pages 3-5, bustihan2025reusable3dprintedthermoplastic pages 24-25) | +| Build orientation | Material/Print | Categorical | {Vertical axis aligned with load, Horizontal, 45°} | Orientation strongly affects anisotropy, porosity, and interlayer failure in PETG/PLA and lattice performance; should be categorical if specimen count permits (martins2024mechanicalpropertiesof pages 4-6, bembenek2022researchonthe pages 2-3, martins2024mechanicalpropertiesof pages 9-14) | +| Drop height | Loading/Test | Fixed | Fixed per campaign, e.g. 0.25–1.0 m equivalent | Treat as a controlled condition, not a BO variable, to keep comparisons meaningful; impact studies in tensegrity/lattice structures use fixed impact energy conditions (pajunen2019designandimpact pages 7-8, khatri2024energyabsorptionof pages 1-3) | +| Impactor mass | Loading/Test | Fixed | Fixed per campaign, e.g. 2–10 kg equivalent | Must remain fixed so transmitted-force and SEA comparisons are interpretable across BO trials (pajunen2019designandimpact pages 7-8, khatri2024energyabsorptionof pages 1-3) | +| Quasi-static strain rate | Loading/Test | Fixed | 0.001–0.01 s⁻¹ | Appropriate laboratory compression window; Khatri used ~0.13 s⁻¹ engineering strain rate for honeycombs, but a lower quasi-static range is preferable for controlled BO screening (khatri2024energyabsorptionof pages 3-5, gorguluarslan2022multiobjectivedesignoptimization pages 5-6) | + + +*Table: This table summarizes a practical BoTorch/Ax search space for a multi-material PETG+TPU tensegrity-inspired energy-absorbing campaign. It groups recommended variables, bounds, and categories by geometry, material/print settings, and fixed test conditions, with literature-based rationale.* + +### B1. Geometric/Topological Variables + +Key geometric variables identified from the tensegrity and lattice energy-absorption literature include strut diameter, cable/skin cross-section, slenderness ratio L/D, twist angle, prestress level, cell tiling array, relative density, and unit-cell topology. Pajunen et al. used strut diameters of 2.6–3.32 mm, cable diameters of 1.37–1.8 mm, and 2% prestress as design knobs, noting that member diameter ratios (ds/dc = 1.44–2.23) control stiffness and buckling onset (pajunen2019designandimpact pages 3-4, pajunen2019designandimpact pages 2-3). Zhang et al. treated cross-sectional areas of cables and bars and prestress levels (force density parameters) as explicit optimization variables (zhang2021optimizationforenergy pages 1-2, ohsaki2019optimizationoftensegrity pages 1-3). Cronau & Engstler found that strut diameter and seed-point density (controlling relative density, tested at 10–25%) were primary drivers of specific energy absorption in lattice structures, with 25% density yielding highest SEA (cronau2025energyabsorptionof pages 1-2). + +### B2. Material/Print-Parameter Variables + +For **PETG struts**: layer height (0.15–0.30 mm), infill percentage (40–100%), infill pattern (rectilinear/grid/gyroid), and print temperature (230–250°C) are the most influential FDM parameters (bustihan2026recentadvancesin pages 4-6, bustihan2026recentadvancesin pages 6-7, hsueh2021effectofprinting pages 6-8). PETG requires temperatures above ~230°C for adequate fusion, with porosity decreasing at higher temperatures (hsueh2021effectofprinting pages 2-3). Print speed for PETG (30–60 mm/s) trades off bonding quality against throughput (hsueh2021effectofprinting pages 6-8). + +For **TPU tension elements**: shore hardness (85A vs 95A) is a key categorical variable. TPU 95A provides higher modulus (~39 MPa) and stress resistance with optimal breaking force at 215°C print temperature, while TPU 85A (NinjaFlex) is intermediate in stiffness with a recommended range of 220–225°C (bustihan2025reusable3dprintedthermoplastic pages 7-9, bustihan2025reusable3dprintedthermoplastic pages 2-4). Lower-hardness TPUs require significantly slower print speeds (as low as 8–15 mm/s for 82A–85A grades) (leoncalero20213dprintingof pages 10-12). Infill density and pattern strongly affect TPU energy absorption; León-Calero et al. found that honeycomb pattern at 50% infill produced optimal specific energy absorption (SEA) and specific damping capacity (SDC) (leoncalero20213dprintingof pages 1-2). Wall count (2–5 perimeters) affects effective stiffness and durability of flexible elements. + +For **multi-material interfaces**: Khatri & Egan demonstrated that TPU band height (0–12 mm, in 3 mm increments) in rigid/flexible honeycomb structures strongly controls energy absorption and failure mode, with hexagonal honeycombs showing 66% higher energy absorption than square ones at matched band thickness (khatri2024energyabsorptionof pages 1-3, khatri2024energyabsorptionof pages 3-5, khatri2024energyabsorptionof pages 10-11). Interface wrapping thickness (0.4–2.0 mm) should be included as a continuous BO variable to strengthen PETG/TPU joints. + +### B3. Loading/Test Variables (Fixed Conditions) + +Drop height, impactor mass, and quasi-static strain rate should be treated as fixed experimental conditions, not BO variables, to maintain comparability across the campaign (pajunen2019designandimpact pages 7-8, khatri2024energyabsorptionof pages 3-5). + +--- + +## (C) PETG-vs-PLA Differences Relevant to BO Bounds + +The following table summarizes key property differences and their implications for search-space design. + +| Property | PLA (FDM printed) | PETG (FDM printed) | Shift Direction for PETG | Implication for BO Variable Ranges | +|---|---|---|---|---| +| Tensile strength | ~55 MPa | ~37 MPa | Lower | PETG compression struts should be allowed to be somewhat stockier than PLA for equal load capacity; cap slenderness more conservatively and avoid very low PETG infill when screening impact specimens (martins2024mechanicalpropertiesof pages 4-6) | +| Young's modulus | ~2350 MPa | ~1200 MPa | ~50% lower | Euler buckling load is lower for the same geometry, so reduce practical upper bound on `L/D` from roughly PLA-like ~30 to ~25 for PETG, and raise PETG infill/perimeter lower bounds to recover stiffness (martins2024mechanicalpropertiesof pages 4-6) | +| Elongation at break | ~4.3% | ~6.5% | Higher | PETG can tolerate more deformation before fracture, so strain-to-failure and allowable crush stroke can be set less conservatively than for PLA; this supports modestly broader deformation-space exploration before catastrophic breakage (martins2024mechanicalpropertiesof pages 4-6) | +| Glass transition `T_g` | ~69.3 °C | ~73.5 °C | Slightly higher | PETG is somewhat safer for warm-service testing, but still needs elevated bed temperatures for reliable printing; set bed-temperature/process windows higher than PLA and avoid long dwell times near `T_g` in environmental tests (martins2024mechanicalpropertiesof pages 8-9) | +| Thermal decomposition `T_d` | ~357.6 °C | ~419.3 °C | Higher | PETG has a wider thermal processing safety margin; BO bounds for nozzle temperature can safely shift upward relative to PLA, though adhesion/oozing tradeoffs still constrain the upper end (martins2024mechanicalpropertiesof pages 8-9) | +| Impact toughness / fracture mode | More brittle; lower ductility | More ductile; better damage tolerance in practice | Higher toughness / ductility | PETG allows a less restrictive upper bound on impact energy before brittle fracture than PLA, but because modulus and strength are lower, peak-energy limits should still scale with strut geometry and relative density rather than be relaxed unconditionally (martins2024mechanicalpropertiesof pages 4-6, hsueh2021effectofprinting pages 2-3) | +| Layer adhesion / print temperature | Good fusion commonly around ~190–220 °C | Typically needs ~230–250 °C; slower printing often helps | Requires higher temperature | Shift PETG print-temperature BO bounds upward and PETG speed bounds downward/moderate versus PLA; include temperature-speed interaction because PETG benefits more from slower deposition for better fusion and lower porosity (hsueh2021effectofprinting pages 6-8, hsueh2021effectofprinting pages 2-3) | +| Porosity at nominal 100% infill | ~9.3% total porosity | ~12% total porosity | Higher | Since PETG prints can retain more voidage, use a higher PETG infill lower bound (about 40% rather than a PLA-like 20%), and consider wall count / orientation as active BO variables because effective cross-section is reduced by voids (martins2024mechanicalpropertiesof pages 9-14) | +| Infill sensitivity | Strong dependence of strength on infill | Also strong; PETG specific tensile strength can deteriorate more with mass increase | Different tradeoff | For PETG, BO should optimize strength-to-weight or SEA rather than absolute load alone; avoid assuming that higher infill is always better, and search infill jointly with wall count and topology (bembenek2022researchonthe pages 2-3) | +| Anisotropy / build-orientation sensitivity | Anisotropic | Anisotropic, with notable sensitivity to orientation and air-gap effects | Slightly higher practical sensitivity | Build orientation should be explicitly included as a categorical BO variable for PETG tensegrity struts; orientation-dependent porosity and bead geometry can materially alter failure mode and effective stiffness (bembenek2022researchonthe pages 2-3, martins2024mechanicalpropertiesof pages 9-14) | + + +*Table: This table compares FDM-printed PLA and PETG properties most relevant to Bayesian optimization bounds for PETG+TPU tensegrity absorbers. It translates literature property differences into practical search-space implications for slenderness, infill, temperature, impact limits, and orientation.* + +**Quantitative summary:** FDM-printed PLA exhibits tensile strength ~55 MPa, Young's modulus ~2350 MPa, and elongation at break ~4.3%, while PETG shows ~37 MPa, ~1200 MPa, and ~6.5% respectively (martins2024mechanicalpropertiesof pages 4-6). Thermal analysis reveals PLA Tg ≈ 69.3°C and PETG Tg ≈ 73.5°C, with PETG showing higher thermal decomposition temperature (~419°C vs ~358°C for PLA) (martins2024mechanicalpropertiesof pages 8-9). + +**Critical implications for BO bounds:** + +1. **Strut slenderness (L/D):** PETG's ~50% lower Young's modulus means Euler buckling loads are substantially reduced for the same geometry. The practical upper bound on L/D should be reduced from ~30 (appropriate for PLA) to ~25 for PETG struts to avoid premature elastic buckling (martins2024mechanicalpropertiesof pages 4-6, pajunen2019designandimpact pages 2-3). + +2. **Infill percentage:** PETG prints retain more porosity (~12% vs ~9.3% for PLA at nominal 100% infill) (martins2024mechanicalpropertiesof pages 9-14), so the infill lower bound should be set higher (~40% vs ~20% for PLA) to ensure adequate effective cross-section in compression struts. + +3. **Layer adhesion and print temperature:** PETG requires 230–250°C for adequate fusion versus 190–220°C for PLA. Slower print speeds improve PETG bonding, and the interaction between temperature and speed is more critical than for PLA (hsueh2021effectofprinting pages 6-8, hsueh2021effectofprinting pages 2-3). + +4. **Impact energy before brittle fracture:** PETG's higher elongation at break (~6.5% vs ~4.3%) and greater ductility mean the allowable impact energy before catastrophic brittle fracture can be somewhat relaxed compared to PLA, but the lower modulus and strength mean this advantage is geometry-dependent (martins2024mechanicalpropertiesof pages 4-6). + +5. **Build orientation sensitivity:** PETG shows notable anisotropy and air-gap effects that reduce effective modulus and strength depending on orientation. Build orientation should be explicitly included as a categorical BO variable (bembenek2022researchonthe pages 2-3, martins2024mechanicalpropertiesof pages 9-14). + +--- + +## (D) Recommended Numeric Bounds for BoTorch/Ax Search Space + +Based on the evidence, for a campaign of ~50–100 specimens: + +**Continuous variables:** +- PETG strut diameter D_PETG: [1.5, 5.0] mm +- TPU cable/skin diameter D_TPU: [1.0, 3.0] mm +- Slenderness L/D: [8, 25] +- Twist angle α: [10°, 45°] +- Prestress level: [0%, 5%] tensile prestrain +- Relative density ρ*/ρs: [0.05, 0.30] (derived) +- PETG layer height: [0.15, 0.30] mm +- PETG infill: [40%, 100%] +- PETG print temperature: [230, 250] °C +- PETG print speed: [30, 60] mm/s +- TPU layer height: [0.15, 0.25] mm +- TPU infill: [50%, 100%] +- TPU print temperature: [215, 235] °C +- TPU print speed: [15, 30] mm/s +- Interface wrapping thickness: [0.4, 2.0] mm + +**Categorical variables:** +- Unit-cell topology: {Truncated octahedron, 4-strut simplex, T3 prism, Stacked prism} +- TPU shore hardness: {85A, 95A} +- PETG infill pattern: {Rectilinear, Grid, Gyroid} +- TPU infill pattern: {Honeycomb, Gyroid, Grid} +- Cell tiling Nx×Ny×Nz: {1×1×1, 1×1×2, 2×2×1, 2×2×2, 3×3×2} +- Build orientation: {Vertical (load-aligned), Horizontal, 45°} + +**Practical BO guidance:** Vangelatos et al. demonstrated that BO on architected lattices with 17 categorical design variables can find optima within ~250 evaluations starting from 50 random initial samples, using an EMCS framework with GP surrogate models (vangelatos2021strengththroughdefects pages 2-3, vangelatos2021strengththroughdefects pages 5-6, vangelatos2021strengththroughdefects pages 7-9). For a physically-tested campaign of 50–100 specimens, a Sobol/LHS initial batch of ~15–25 specimens followed by sequential BO iterations is recommended. The mixed continuous+categorical search space is well-handled by BoTorch's Mixed Optimization (SAASBO or multi-task GP with categorical kernels). + +--- + +## (E) Recommended Primary Objectives and Constraints + +| Metric | Role (Objective/Constraint) | Definition | Target Direction | Rationale/Source | +|---|---|---|---|---| +| Specific Energy Absorption (SEA) | Primary objective | Total absorbed energy divided by specimen mass (J/g) | Maximize | Most common crashworthiness metric for lattices and cellular absorbers; normalizes for mass and allows fair comparison across relative densities and topologies (cronau2025energyabsorptionof pages 11-11, leoncalero20213dprintingof pages 1-2, gorguluarslan2022multiobjectivedesignoptimization pages 5-6) | +| Peak Transmitted Force ($F_{peak}$) | Primary objective or hard constraint | Maximum force measured at the support/base plate during impact or compression | Minimize | Critical for protection applications because lower peak force corresponds to better load limitation and lower injury/equipment risk; also complements SEA when highly absorptive designs still spike early load (pajunen2019designandimpact pages 7-8, khatri2024energyabsorptionof pages 1-3, khatri2024energyabsorptionof pages 10-11) | +| Energy Absorption Efficiency (EAE, or EAEm) | Secondary objective | Ratio of absorbed energy to the energy/stroke available before densification; often interpreted as how efficiently the crush plateau is used | Maximize | Captures whether the structure absorbs energy progressively rather than through a sharp initial peak; used explicitly in additively manufactured lattice optimization studies (bates20163dprintedpolyurethane pages 16-18, gorguluarslan2022multiobjectivedesignoptimization pages 5-6) | +| Crush Stress Efficiency (CSE) | Secondary objective | Plateau stress divided by peak stress | Maximize | High CSE indicates a flatter, more useful stress plateau and more uniform dissipation; Gorguluarslan uses CSE jointly with energy-absorption efficiency in multi-objective optimization (gorguluarslan2022multiobjectivedesignoptimization pages 5-6) | +| Plateau Stress ($\sigma_{pl}$) | Informational metric or application-tuned objective | Mean stress over the post-yield/pre-densification plateau region | Application-dependent; often target a band | Determines force-transmission level during sustained crushing; should be high enough to absorb energy but not so high that transmitted loads become unacceptable (gorguluarslan2022multiobjectivedesignoptimization pages 5-6, khatri2024energyabsorptionof pages 10-11) | +| Compaction strain ($\varepsilon_d$) | Informational metric or secondary objective | Strain at onset of densification/compaction | Generally maximize | Higher compaction strain gives more usable stroke before densification, improving practical absorber stroke utilization (gorguluarslan2022multiobjectivedesignoptimization pages 5-6, bates20163dprintedpolyurethane pages 16-18) | +| Specimen mass | Constraint | Total printed mass of one specimen | Keep below threshold, e.g. $\leq$ 50 g | Keeps the campaign practical, preserves fair specific-property comparisons, and limits the optimizer from trivially improving absolute energy absorption by adding material (cronau2025energyabsorptionof pages 11-11, gorguluarslan2022multiobjectivedesignoptimization pages 5-6) | +| Print time | Constraint | Total print duration per specimen | Keep below threshold, e.g. $\leq$ 4 h | Essential for a 50-100 specimen undergraduate BO campaign; printability/time are standard AM-side constraints in design-of-experiments and optimization workflows (bustihan2026recentadvancesin pages 6-7, vangelatos2021strengththroughdefects pages 2-3) | +| Cycle durability | Constraint | Number of compression/impact cycles before a chosen degradation limit, e.g. 10% strength-loss or SEA-loss threshold | Keep above threshold, e.g. $\geq$ 3 cycles | Important for reusable absorbers; TPU-based absorbers show recoverability while cyclic softening and PETG strut damage can limit reuse (pajunen2019designandimpact pages 7-8, bates20163dprintedpolyurethane pages 16-18, bustihan2025reusable3dprintedthermoplastic pages 7-9) | +| $W_{min}$ (cushion factor $\times$ relative density) | Alternative primary objective | Pajunen-style efficiency metric combining cushion factor and relative density | Minimize | Useful for benchmarking against foams and other polymer absorbers; Pajunen identifies favorable designs in the region $W_{min} < 0.21$ and $\rho^*/\rho_s < 0.1$ (pajunen2019designandimpact pages 8-9) | + + +*Table: This table summarizes recommended primary objectives, secondary metrics, and practical constraints for a Bayesian-optimization campaign on PETG+TPU tensegrity-inspired energy absorbers. It is useful for turning the literature into a measurable Ax/BoTorch optimization problem.* + +**Primary objectives (multi-objective BO):** + +1. **Maximize Specific Energy Absorption (SEA):** The most widely used crashworthiness metric, computed as total absorbed energy divided by specimen mass (J/g). This normalizes for mass and allows fair comparison across relative densities and topologies (leoncalero20213dprintingof pages 1-2, gorguluarslan2022multiobjectivedesignoptimization pages 5-6). + +2. **Minimize Peak Transmitted Force (F_peak):** Critical for protective applications; lower peak force corresponds to better load limitation. Alternatively, this can be treated as a hard constraint (F_peak ≤ threshold) (pajunen2019designandimpact pages 7-8, khatri2024energyabsorptionof pages 1-3). + +**Secondary objectives:** + +3. **Maximize Energy Absorption Efficiency (EAE):** Captures how efficiently the crush plateau is exploited before densification. Gorguluarslan used EAEm jointly with CSE in multi-objective lattice optimization (gorguluarslan2022multiobjectivedesignoptimization pages 5-6). Pajunen used Wmin = cushion factor × relative density, targeting Wmin < 0.21 at ρ*/ρs < 0.1 (pajunen2019designandimpact pages 8-9). + +4. **Maximize Crush Stress Efficiency (CSE):** Plateau stress / peak stress; higher CSE indicates a flatter, more uniform stress plateau (gorguluarslan2022multiobjectivedesignoptimization pages 5-6). + +**Constraints:** + +- **Maximum specimen mass:** ≤ 50 g (keeps campaign practical and enables specific-property comparisons) +- **Maximum print time:** ≤ 4 hours per specimen (ensures 50–100 specimens fit an undergraduate semester timeline) (bustihan2026recentadvancesin pages 6-7) +- **Minimum cycle durability:** ≥ 3 compression cycles to <10% SEA loss (important for reusable absorbers; TPU enables elastic recovery with ~24.5% energy drop from cycle 1→2 then convergence, while PETG strut fracture limits reuse) (bates20163dprintedpolyurethane pages 16-18, bustihan2025reusable3dprintedthermoplastic pages 7-9) +- **Minimum printability:** no print failures (enforced by excluding non-manufacturable designs via geometry constraints on minimum overhang angle, minimum feature size ≥ 1.0 mm, and bridging distance limits) + +**Recommended BO formulation:** A multi-objective formulation maximizing SEA while minimizing F_peak, subject to mass, print-time, and durability constraints, is the most practical starting point. This can be implemented in BoTorch using `qNoisyExpectedHypervolumeImprovement` (qNEHVI) as the acquisition function for Pareto-optimal design discovery with noisy experimental observations. + +References + +1. (micheletti2022seventyyearsof pages 23-24): Andrea Micheletti and Paolo Podio-Guidugli. Seventy years of tensegrities (and counting). Archive of Applied Mechanics, 92:2525-2548, Jul 2022. URL: https://doi.org/10.1007/s00419-022-02192-4, doi:10.1007/s00419-022-02192-4. This article has 75 citations and is from a peer-reviewed journal. + +2. (sabounizawadzka2024experimentalinvestigationson pages 1-3): Anna Al Sabouni-Zawadzka, Wojciech Gilewski, and Adam Zawadzki. Experimental investigations on mechanical propertiesof 3d-printed tensegrity-inspired metamaterialsbased on 4-strut simplex module. Archives of Civil Engineering, pages 343-357, Jun 2024. URL: https://doi.org/10.24425/ace.2024.150987, doi:10.24425/ace.2024.150987. This article has 0 citations. + +3. (sabounizawadzka2024experimentalinvestigationsona pages 6-11): A Al Sabouni-Zawadzka and W Gilewski. Experimental investigations on mechanical properties of 3d-printed tensegrity-inspired metamaterials based on 4-strut simplex module. Unknown journal, 2024. + +4. (pajunen2019designandimpact pages 1-2): Kirsti Pajunen, Paul Johanns, Raj Kumar Pal, Julian J. Rimoli, and Chiara Daraio. Design and impact response of 3d-printable tensegrity-inspired structures. Materials & Design, 182:107966, Nov 2019. URL: https://doi.org/10.1016/j.matdes.2019.107966, doi:10.1016/j.matdes.2019.107966. This article has 98 citations and is from a highest quality peer-reviewed journal. + +5. (pajunen2019designandimpact pages 8-9): Kirsti Pajunen, Paul Johanns, Raj Kumar Pal, Julian J. Rimoli, and Chiara Daraio. Design and impact response of 3d-printable tensegrity-inspired structures. Materials & Design, 182:107966, Nov 2019. URL: https://doi.org/10.1016/j.matdes.2019.107966, doi:10.1016/j.matdes.2019.107966. This article has 98 citations and is from a highest quality peer-reviewed journal. + +6. (zhang2021optimizationforenergy pages 1-2): Jingyao Zhang, Makoto Ohsaki, Julian J. Rimoli, and Kosuke Kogiso. Optimization for energy absorption of 3-dimensional tensegrity lattice with truncated octahedral units. Composite Structures, 267:113903, Jul 2021. URL: https://doi.org/10.1016/j.compstruct.2021.113903, doi:10.1016/j.compstruct.2021.113903. This article has 33 citations and is from a domain leading peer-reviewed journal. + +7. (micheletti2022seventyyearsof pages 20-21): Andrea Micheletti and Paolo Podio-Guidugli. Seventy years of tensegrities (and counting). Archive of Applied Mechanics, 92:2525-2548, Jul 2022. URL: https://doi.org/10.1007/s00419-022-02192-4, doi:10.1007/s00419-022-02192-4. This article has 75 citations and is from a peer-reviewed journal. + +8. (liu2019tensegritytopologyoptimization pages 22-22): Ke Liu and Glaucio H. Paulino. Tensegrity topology optimization by force maximization on arbitrary ground structures. Structural and Multidisciplinary Optimization, 59:2041-2062, Jan 2019. URL: https://doi.org/10.1007/s00158-018-2172-3, doi:10.1007/s00158-018-2172-3. This article has 65 citations and is from a domain leading peer-reviewed journal. + +9. (bustihan2026recentadvancesin pages 19-21): Alin Bustihan and Ioan Botiz. Recent advances in additively manufactured polymeric structures for mechanical energy absorption. Polymers, 18:1019, Apr 2026. URL: https://doi.org/10.3390/polym18091019, doi:10.3390/polym18091019. This article has 0 citations. + +10. (pajunen2019designandimpact pages 9-9): Kirsti Pajunen, Paul Johanns, Raj Kumar Pal, Julian J. Rimoli, and Chiara Daraio. Design and impact response of 3d-printable tensegrity-inspired structures. Materials & Design, 182:107966, Nov 2019. URL: https://doi.org/10.1016/j.matdes.2019.107966, doi:10.1016/j.matdes.2019.107966. This article has 98 citations and is from a highest quality peer-reviewed journal. + +11. (sabounizawadzka2024experimentalinvestigationsona pages 1-3): A Al Sabouni-Zawadzka and W Gilewski. Experimental investigations on mechanical properties of 3d-printed tensegrity-inspired metamaterials based on 4-strut simplex module. Unknown journal, 2024. + +12. (pajunen2019designandimpact pages 3-4): Kirsti Pajunen, Paul Johanns, Raj Kumar Pal, Julian J. Rimoli, and Chiara Daraio. Design and impact response of 3d-printable tensegrity-inspired structures. Materials & Design, 182:107966, Nov 2019. URL: https://doi.org/10.1016/j.matdes.2019.107966, doi:10.1016/j.matdes.2019.107966. This article has 98 citations and is from a highest quality peer-reviewed journal. + +13. (pajunen2019designandimpact pages 2-3): Kirsti Pajunen, Paul Johanns, Raj Kumar Pal, Julian J. Rimoli, and Chiara Daraio. Design and impact response of 3d-printable tensegrity-inspired structures. Materials & Design, 182:107966, Nov 2019. URL: https://doi.org/10.1016/j.matdes.2019.107966, doi:10.1016/j.matdes.2019.107966. This article has 98 citations and is from a highest quality peer-reviewed journal. + +14. (bustihan2026recentadvancesin pages 6-7): Alin Bustihan and Ioan Botiz. Recent advances in additively manufactured polymeric structures for mechanical energy absorption. Polymers, 18:1019, Apr 2026. URL: https://doi.org/10.3390/polym18091019, doi:10.3390/polym18091019. This article has 0 citations. + +15. (martins2024mechanicalpropertiesof pages 4-6): Rui F. Martins, Ricardo Branco, Miguel Martins, Wojciech Macek, Zbigniew Marciniak, Rui Silva, Daniela Trindade, Carla Moura, Margarida Franco, and Cândida Malça. Mechanical properties of additively manufactured polymeric materials—pla and petg—for biomechanical applications. Polymers, 16:1868, Jun 2024. URL: https://doi.org/10.3390/polym16131868, doi:10.3390/polym16131868. This article has 36 citations. + +16. (bustihan2025reusable3dprintedthermoplastic pages 7-9): Alin Bustihan, Razvan Hirian, and Ioan Botiz. Reusable 3d-printed thermoplastic polyurethane honeycombs for mechanical energy absorption. Polymers, 17:3035, Nov 2025. URL: https://doi.org/10.3390/polym17223035, doi:10.3390/polym17223035. This article has 3 citations. + +17. (vangelatos2021strengththroughdefects pages 1-2): Zacharias Vangelatos, Haris Moazam Sheikh, Philip S. Marcus, Costas P. Grigoropoulos, Victor Z. Lopez, George Flamourakis, and Maria Farsari. Strength through defects: a novel bayesian approach for the optimization of architected materials. Science Advances, Oct 2021. URL: https://doi.org/10.1126/sciadv.abk2218, doi:10.1126/sciadv.abk2218. This article has 124 citations and is from a highest quality peer-reviewed journal. + +18. (vangelatos2021strengththroughdefects pages 2-3): Zacharias Vangelatos, Haris Moazam Sheikh, Philip S. Marcus, Costas P. Grigoropoulos, Victor Z. Lopez, George Flamourakis, and Maria Farsari. Strength through defects: a novel bayesian approach for the optimization of architected materials. Science Advances, Oct 2021. URL: https://doi.org/10.1126/sciadv.abk2218, doi:10.1126/sciadv.abk2218. This article has 124 citations and is from a highest quality peer-reviewed journal. + +19. (cronau2025energyabsorptionof pages 1-2): J. Cronau and F. Engstler. Energy absorption of 3d printed stochastic lattice structures under impact loading – design parameters, manufacturing, and testing. Progress in Additive Manufacturing, 10:3145-3156, Apr 2025. URL: https://doi.org/10.1007/s40964-025-01094-5, doi:10.1007/s40964-025-01094-5. This article has 16 citations and is from a peer-reviewed journal. + +20. (cronau2025energyabsorptionof pages 11-11): J. Cronau and F. Engstler. Energy absorption of 3d printed stochastic lattice structures under impact loading – design parameters, manufacturing, and testing. Progress in Additive Manufacturing, 10:3145-3156, Apr 2025. URL: https://doi.org/10.1007/s40964-025-01094-5, doi:10.1007/s40964-025-01094-5. This article has 16 citations and is from a peer-reviewed journal. + +21. (hsueh2021effectofprinting pages 2-3): Ming-Hsien Hsueh, Chao-Jung Lai, Shi-Hao Wang, Yu-Shan Zeng, Chia-Hsin Hsieh, Chieh-Yu Pan, and Wen-Chen Huang. Effect of printing parameters on the thermal and mechanical properties of 3d-printed pla and petg, using fused deposition modeling. Polymers, 13:1758, May 2021. URL: https://doi.org/10.3390/polym13111758, doi:10.3390/polym13111758. This article has 407 citations. + +22. (bembenek2022researchonthe pages 2-3): Michał Bembenek, Łukasz Kowalski, and Agnieszka Kosoń-Schab. Research on the influence of processing parameters on the specific tensile strength of fdm additive manufactured pet-g and pla materials. Polymers, 14:2446, Jun 2022. URL: https://doi.org/10.3390/polym14122446, doi:10.3390/polym14122446. This article has 69 citations. + +23. (hsueh2021effectofprinting pages 6-8): Ming-Hsien Hsueh, Chao-Jung Lai, Shi-Hao Wang, Yu-Shan Zeng, Chia-Hsin Hsieh, Chieh-Yu Pan, and Wen-Chen Huang. Effect of printing parameters on the thermal and mechanical properties of 3d-printed pla and petg, using fused deposition modeling. Polymers, 13:1758, May 2021. URL: https://doi.org/10.3390/polym13111758, doi:10.3390/polym13111758. This article has 407 citations. + +24. (bustihan2025reusable3dprintedthermoplastic pages 2-4): Alin Bustihan, Razvan Hirian, and Ioan Botiz. Reusable 3d-printed thermoplastic polyurethane honeycombs for mechanical energy absorption. Polymers, 17:3035, Nov 2025. URL: https://doi.org/10.3390/polym17223035, doi:10.3390/polym17223035. This article has 3 citations. + +25. (khatri2024energyabsorptionof pages 3-5): Nava Raj Khatri and Paul F. Egan. Energy absorption of 3d printed abs and tpu multimaterial honeycomb structures. 3D Printing and Additive Manufacturing, 11:e840-e850, Apr 2024. URL: https://doi.org/10.1089/3dp.2022.0196, doi:10.1089/3dp.2022.0196. This article has 29 citations and is from a peer-reviewed journal. + +26. (leoncalero20213dprintingof pages 10-12): Marina León-Calero, Sara Catherine Reyburn Valés, Ángel Marcos-Fernández, and Juan Rodríguez-Hernandez. 3d printing of thermoplastic elastomers: role of the chemical composition and printing parameters in the production of parts with controlled energy absorption and damping capacity. Polymers, 13:3551, Oct 2021. URL: https://doi.org/10.3390/polym13203551, doi:10.3390/polym13203551. This article has 110 citations. + +27. (leoncalero20213dprintingof pages 1-2): Marina León-Calero, Sara Catherine Reyburn Valés, Ángel Marcos-Fernández, and Juan Rodríguez-Hernandez. 3d printing of thermoplastic elastomers: role of the chemical composition and printing parameters in the production of parts with controlled energy absorption and damping capacity. Polymers, 13:3551, Oct 2021. URL: https://doi.org/10.3390/polym13203551, doi:10.3390/polym13203551. This article has 110 citations. + +28. (leoncalero20213dprintingof pages 4-5): Marina León-Calero, Sara Catherine Reyburn Valés, Ángel Marcos-Fernández, and Juan Rodríguez-Hernandez. 3d printing of thermoplastic elastomers: role of the chemical composition and printing parameters in the production of parts with controlled energy absorption and damping capacity. Polymers, 13:3551, Oct 2021. URL: https://doi.org/10.3390/polym13203551, doi:10.3390/polym13203551. This article has 110 citations. + +29. (leoncalero20213dprintingof pages 8-10): Marina León-Calero, Sara Catherine Reyburn Valés, Ángel Marcos-Fernández, and Juan Rodríguez-Hernandez. 3d printing of thermoplastic elastomers: role of the chemical composition and printing parameters in the production of parts with controlled energy absorption and damping capacity. Polymers, 13:3551, Oct 2021. URL: https://doi.org/10.3390/polym13203551, doi:10.3390/polym13203551. This article has 110 citations. + +30. (khatri2024energyabsorptionof pages 1-3): Nava Raj Khatri and Paul F. Egan. Energy absorption of 3d printed abs and tpu multimaterial honeycomb structures. 3D Printing and Additive Manufacturing, 11:e840-e850, Apr 2024. URL: https://doi.org/10.1089/3dp.2022.0196, doi:10.1089/3dp.2022.0196. This article has 29 citations and is from a peer-reviewed journal. + +31. (bustihan2025reusable3dprintedthermoplastic pages 24-25): Alin Bustihan, Razvan Hirian, and Ioan Botiz. Reusable 3d-printed thermoplastic polyurethane honeycombs for mechanical energy absorption. Polymers, 17:3035, Nov 2025. URL: https://doi.org/10.3390/polym17223035, doi:10.3390/polym17223035. This article has 3 citations. + +32. (martins2024mechanicalpropertiesof pages 9-14): Rui F. Martins, Ricardo Branco, Miguel Martins, Wojciech Macek, Zbigniew Marciniak, Rui Silva, Daniela Trindade, Carla Moura, Margarida Franco, and Cândida Malça. Mechanical properties of additively manufactured polymeric materials—pla and petg—for biomechanical applications. Polymers, 16:1868, Jun 2024. URL: https://doi.org/10.3390/polym16131868, doi:10.3390/polym16131868. This article has 36 citations. + +33. (pajunen2019designandimpact pages 7-8): Kirsti Pajunen, Paul Johanns, Raj Kumar Pal, Julian J. Rimoli, and Chiara Daraio. Design and impact response of 3d-printable tensegrity-inspired structures. Materials & Design, 182:107966, Nov 2019. URL: https://doi.org/10.1016/j.matdes.2019.107966, doi:10.1016/j.matdes.2019.107966. This article has 98 citations and is from a highest quality peer-reviewed journal. + +34. (gorguluarslan2022multiobjectivedesignoptimization pages 5-6): Recep M Gorguluarslan. Multi-objective design optimization of additively manufactured lattice structures for improved energy absorption performance. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 236:3-15, May 2022. URL: https://doi.org/10.1177/0954406221995542, doi:10.1177/0954406221995542. This article has 18 citations. + +35. (ohsaki2019optimizationoftensegrity pages 1-3): M Ohsaki, J Zhang, and K Kogiso. Optimization of tensegrity lattice with truncated octahedral units. Unknown journal, 2019. + +36. (bustihan2026recentadvancesin pages 4-6): Alin Bustihan and Ioan Botiz. Recent advances in additively manufactured polymeric structures for mechanical energy absorption. Polymers, 18:1019, Apr 2026. URL: https://doi.org/10.3390/polym18091019, doi:10.3390/polym18091019. This article has 0 citations. + +37. (khatri2024energyabsorptionof pages 10-11): Nava Raj Khatri and Paul F. Egan. Energy absorption of 3d printed abs and tpu multimaterial honeycomb structures. 3D Printing and Additive Manufacturing, 11:e840-e850, Apr 2024. URL: https://doi.org/10.1089/3dp.2022.0196, doi:10.1089/3dp.2022.0196. This article has 29 citations and is from a peer-reviewed journal. + +38. (martins2024mechanicalpropertiesof pages 8-9): Rui F. Martins, Ricardo Branco, Miguel Martins, Wojciech Macek, Zbigniew Marciniak, Rui Silva, Daniela Trindade, Carla Moura, Margarida Franco, and Cândida Malça. Mechanical properties of additively manufactured polymeric materials—pla and petg—for biomechanical applications. Polymers, 16:1868, Jun 2024. URL: https://doi.org/10.3390/polym16131868, doi:10.3390/polym16131868. This article has 36 citations. + +39. (vangelatos2021strengththroughdefects pages 5-6): Zacharias Vangelatos, Haris Moazam Sheikh, Philip S. Marcus, Costas P. Grigoropoulos, Victor Z. Lopez, George Flamourakis, and Maria Farsari. Strength through defects: a novel bayesian approach for the optimization of architected materials. Science Advances, Oct 2021. URL: https://doi.org/10.1126/sciadv.abk2218, doi:10.1126/sciadv.abk2218. This article has 124 citations and is from a highest quality peer-reviewed journal. + +40. (vangelatos2021strengththroughdefects pages 7-9): Zacharias Vangelatos, Haris Moazam Sheikh, Philip S. Marcus, Costas P. Grigoropoulos, Victor Z. Lopez, George Flamourakis, and Maria Farsari. Strength through defects: a novel bayesian approach for the optimization of architected materials. Science Advances, Oct 2021. URL: https://doi.org/10.1126/sciadv.abk2218, doi:10.1126/sciadv.abk2218. This article has 124 citations and is from a highest quality peer-reviewed journal. + +41. (bates20163dprintedpolyurethane pages 16-18): Simon R.G. Bates, Ian R. Farrow, and Richard S. Trask. 3d printed polyurethane honeycombs for repeated tailored energy absorption. Materials & Design, 112:172-183, Dec 2016. URL: https://doi.org/10.1016/j.matdes.2016.08.062, doi:10.1016/j.matdes.2016.08.062. This article has 388 citations and is from a highest quality peer-reviewed journal. \ No newline at end of file diff --git a/edison-trajectories/tpu-petg-bo-variables-additions-from-pr22.md b/edison-trajectories/tpu-petg-bo-variables-additions-from-pr22.md new file mode 100644 index 00000000..b52aa8ee --- /dev/null +++ b/edison-trajectories/tpu-petg-bo-variables-additions-from-pr22.md @@ -0,0 +1,202 @@ +# Additional BO design variables prompted by the PR #22 design-gaps survey + +Companion to: +- `tpu-petg-bo-variables-5ae24eaf-5b6e-45cf-9f6c-1c7fbd881738.md` — original + TPU+PETG variables / bounds / objectives (this PR #24). +- `2026-05-12-tensegrity-design-gaps-6226a551-b46a-49b4-936a-bca600cd8d30.md` + — design-gap survey on PR #22 ranking 18 missing tensegrity families + (Snelson X-module, Pajunen truncated-octa, Oster reentrant auxetic, + Rhode-Barbarigos pentagonal ring, Pugh diamond / zig-zag, tensegrity torus, + Hanaor double-layer grid, Levy / Suspen-dome, 6-bar wheel patent + US20240351370A1, Schenk & Guest bistable, D-bar / Sabouni-Zawadzka / + Hao auxetic + multistable AM lattices, etc.). +- Lab constraints: TPU **85A** (not 95A) tendons, PETG struts on Bambu H2D, + printable tendon Ø ∈ [1.2, 6.0] mm, strut Ø ≥ 2.0 mm + (`simulations/printable_design.py`, copilot-instructions.md). + +The original 5ae24eaf table treated topology as the categorical +{T3, T4, simplex, expanded-octa, truncated-octa, …}. The PR #22 catalog +surfaces several **new** axes that are worth exposing to the BO search +space (or pinning as fixed-but-explicit conditions) before launching a +~50–100-specimen campaign. + +## A. New / expanded categorical search axes + +| New axis | Domain | Why it matters | Source family | +|---|---|---|---| +| **`unit_cell` (extend list)** | add `snelson_x_module`, `pentagonal_ring_RB`, `pugh_diamond`, `pugh_zigzag`, `tensegrity_torus`, `oster_reentrant_auxetic`, `bistable_double_prism`, `superball_with_payload`, `hanaor_DLTG_square` | The 5ae24eaf list omitted X-module and the 2D weave / planar families that are the most "flat-printable" candidates on H2D, and omitted the auxetic / multistable cells most relevant to crutch-tip impact attenuation. | gaps survey items #1, #3, #4, #5–6, #7, #8, Pajunen #2 | +| **`chirality_pattern`** | {`left`, `right`, `alternating`, `mirrored_pair`} | Stacked T3 masts (Snelson Needle Tower, Tibert & Pellegrino) and ring modules show qualitatively different load paths and twist-coupling under alternating vs same-handed stacking. | gaps survey #4 (Tibert), #1 (X-module weaves) | +| **`cable_routing`** | {`prism_basic`, `diamond` (Pugh), `zig_zag` (Pugh), `circuit` (class-2)} | Pugh's three canonical tendon patterns sit on the *same* node set as a prism but yield distinct anisotropic crush responses — a free knob that costs nothing in print envelope. | gaps survey #5–6 | +| **`tensegrity_class`** | {1, 2, k} | Class-2 ring modules (Rhode-Barbarigos pentagon) and Skelton compound-bar (D-bar / T-bar) cells become eligible once joint design supports strut-to-strut contacts (issue #38 joint-design Phase-3 / Phase-4 work). Lets BO trade off class-1 manufacturability against class-k specific energy absorption. | gaps survey #4, #15 (Ding 2025 D-bar) | +| **`tendon_clustering`** | {`independent`, `clustered_axial`, `clustered_radial`} | Clustered (sliding) tendons (Hao 2026) enable programmable multistability and stiffness reuse — a TPU-printable analog of pulleyed cables. | gaps survey #17 | +| **`bistable_mode`** | {`monostable`, `bistable`, `multistable`} | Intrigila double-prism (already in #22) and Schenk & Guest mechanisms are the path to *load-limiting* impact attenuation (snap-through caps peak F). Trivial to expose as a discrete switch coupled to prestress level. | gaps survey #14, original #22 catalog item 11 | +| **`payload_carrier`** | {`none`, `inner_icosa_cradle`, `axial_hub`} | SUPERball-with-payload (in #22 STL set) and the 6-bar wheel patent (US20240351370A1) both attach a hub/cradle that *changes the boundary conditions* seen by the tendon network — needs to be a controlled categorical, not a hidden geometry choice. | gaps survey #13; #22 STL `superball_with_payload.stl` | +| **`tessellation_pattern`** | {`single_cell`, `1D_stack`, `2D_grid`, `3D_lattice`, `toroidal_ring`, `double_layer_grid`} | Original list only had `Nx·Ny·Nz`. Hanaor DLTGs and the tensegrity torus require *non-orthogonal* tilings; need an explicit tessellation type before tile counts make sense. | gaps survey #7, #8, #9 | + +## B. New continuous variables (or refined bounds) + +| Variable | Suggested bound | Reason | +|---|---|---| +| **Per-tendon prestress group fraction** `f_pre,i ∈ [0, 1]` for i ∈ {axial, hoop, diagonal} (sums to 1, scales the global 0–5 % prestress already in 5ae24eaf) | simplex on 3 groups | Pajunen reported 2 % prestress is the sweet spot, but only as a scalar. The auxetic (Oster) and ring (Rhode-Barbarigos) families need *non-uniform* prestress to even be stable — splitting the budget by tendon role lets BO rediscover those stability windows. | +| **Number of bays / stacked cells** `N_bay` ∈ {1, 2, 3, 4, 6} | discrete | Was implicit in `Nz`; calling it out separately matters because alternating-chirality stacks (axis "chirality_pattern") only make sense for `N_bay ≥ 2`. | +| **Re-entrancy angle** `θ_re ∈ [-30°, +30°]` (auxetic family only) | continuous, conditional | Drives Poisson's ratio sign in Oster-type cells; was not in 5ae24eaf because no auxetic family was in the original topology list. | +| **Ring radius / strut-circuit count** `(R_ring, N_circuit)` for ring/torus families | continuous + discrete, conditional | Defines the donut envelope when `unit_cell ∈ {pentagonal_ring_RB, tensegrity_torus}`; needed before tile counts are meaningful. | +| **Hub / cradle mass fraction** `m_hub / m_total ∈ [0, 0.5]` (when `payload_carrier ≠ none`) | continuous, conditional | Couples to the *fixed* test impactor mass (still a fixed loading parameter, per 5ae24eaf), so it needs its own BO axis. | + +## C. Refined PETG vs PLA scope notes (no change to bounds, but new caveats) + +- The auxetic Oster cell uses *rubber-like* prototypes; on PETG struts the + re-entrant geometry tends to fail by hinge-yield rather than buckling, so + **strut slenderness L/D should be revisited** for that family + (5ae24eaf already gave L/D ∈ [4, 30] which is wide enough — keep but log + failure mode). +- Bistable / clustered families need TPU 85A, not 95A, to keep the + snap-through energy barrier within hand-deployable range (lab uses 85A + per memory; 5ae24eaf had 85A/95A as a categorical — keep both). +- Class-2 contacts (Pugh `circuit`, ring modules, Skelton compound bars) + require validated PETG–PETG sliding/abrasion at the strut-end joint; not + yet experimentally characterised in this lab — flag as **constraint**, + not search axis, until issue #38 Phase-4 returns joint designs that + actually support strut-to-strut contact. + +## D. Hierarchical search space (per @sgbaird-alt, ref. Ax issue #140) + +Many of the §A/§B axes are **conditional** — they are only meaningful +when the parent categorical takes a specific value (e.g. `re_entrancy_angle` +is meaningless unless `unit_cell == oster_reentrant_auxetic`). Encoding +those as flat, always-active parameters wastes BO budget exploring +invalid combinations and fools the GP with phantom correlations. The +correct encoding is Ax's `HierarchicalSearchSpace` (parameter with +`dependents={value: [child_param_names]}`), introduced after +[facebook/Ax#140](https://github.com/facebook/Ax/issues/140) and +documented at + (`ax.core.search_space.HierarchicalSearchSpace`, +`ChoiceParameter(dependents=...)`). + +### D.1 Parameter tree + +``` +ROOT +├── topology_family [choice; ROOT categorical, drives everything below] +│ values = { +│ "prism_stack", # T3 / T4 / stacked-prism / Snelson mast / Pugh patterns +│ "icosa_class", # 6-bar icosa / expanded-octa / SUPERball / Jessen +│ "trunc_octa", # Pajunen 2019 + Zhang 2021 tessellations +│ "ring_torus", # Rhode-Barbarigos pentagonal ring, tensegrity torus +│ "auxetic_periodic", # Oster 2021 reentrant chiral +│ "double_layer_grid",# Hanaor DLTG / Charalambides square-base +│ "bistable_cell", # Intrigila double-prism, Schenk–Guest snap-through +│ "x_module_weave", # Snelson X-module planar weaves +│ } +│ +├── [always-on] shared continuous axes from 5ae24eaf +│ strut_D, cable_D, L_over_D, prestress_global, +│ PETG_layer_h, PETG_infill_pct, TPU_shore (categorical 85A/95A), +│ TPU_wall_count, nozzle_T, bed_T, print_speed, wrap_thickness, +│ relative_density +│ +├── dependents of topology_family +│ ├── "prism_stack" → +│ │ unit_cell ∈ {T3, T4, T6, simplex, snelson_needle_tower, +│ │ pugh_diamond, pugh_zigzag} +│ │ N_bay ∈ {1, 2, 3, 4, 6} +│ │ twist_angle ∈ [10°, 45°] +│ │ cable_routing ∈ {prism_basic, diamond, zig_zag, circuit} +│ │ chirality_pattern ∈ {left, right, alternating, mirrored_pair} +│ │ └── only active when N_bay ≥ 2 +│ │ +│ ├── "icosa_class" → +│ │ unit_cell ∈ {icosahedron_6bar, jessen_expanded_octa, superball} +│ │ payload_carrier ∈ {none, inner_icosa_cradle, axial_hub} +│ │ └── hub_mass_fraction ∈ [0, 0.5] (active iff != none) +│ │ +│ ├── "trunc_octa" → +│ │ tessellation_pattern ∈ {single_cell, 1D_stack, 2D_grid, 3D_lattice} +│ │ Nx, Ny, Nz ∈ {1..6} (Nz=1 unless tessellation_pattern≠single_cell) +│ │ pre_axial_frac, pre_hoop_frac, pre_diag_frac (simplex, sum=1) +│ │ +│ ├── "ring_torus" → +│ │ unit_cell ∈ {pentagonal_ring_RB, tensegrity_torus} +│ │ ring_radius_mm ∈ [20, 120] +│ │ N_circuit ∈ {5, 6, 8, 10, 12} +│ │ tensegrity_class ∈ {2, k} # class-2 implies strut-to-strut contact; +│ │ # GATED on issue #38 Phase-4 joint validation +│ │ +│ ├── "auxetic_periodic" → +│ │ re_entrancy_angle_deg ∈ [-30, +30] +│ │ pre_axial_frac, pre_hoop_frac, pre_diag_frac (simplex) +│ │ +│ ├── "double_layer_grid" → +│ │ dltg_module ∈ {square_base, x_trihex_class_II} +│ │ Nx, Ny ∈ {1..6}; Nz = 1 (single double-layer) +│ │ +│ ├── "bistable_cell" → +│ │ unit_cell ∈ {intrigila_double_prism, schenk_snap_arch} +│ │ bistable_mode ∈ {monostable, bistable, multistable} +│ │ tendon_clustering ∈ {independent, clustered_axial, clustered_radial} +│ │ +│ └── "x_module_weave" → +│ weave_dim ∈ {1D, 2D} +│ tile_count ∈ {1..36} +│ (twist_angle, chirality_pattern as in prism_stack) +``` + +### D.2 Constraint encoding + +- `tensegrity_class` is **not** a free top-level axis; it is implied by + `topology_family` (mostly class-1) and only escapes class-1 inside + `ring_torus` (class-2) or `bistable_cell.tendon_clustering=clustered_*` + (class-k). This avoids the §A row that previously listed it as + unconditional. +- `chirality_pattern`, `cable_routing`, `payload_carrier`, + `tessellation_pattern` and `bistable_mode` from §A all become **child** + parameters of `topology_family` (not free axes), eliminating ~70 % of + the otherwise-invalid combinations a flat Cartesian space would + generate. +- The Phase-4 joint-design gate (issue #38) stays as a **fixed feature** + on the Ax `Experiment` (e.g. `joint_validated_class2 ∈ {False, True}`), + forcing the `ring_torus` branch out of the search space until the gate + flips. +- Per-tendon prestress group fractions are encoded as a 3-element simplex + child of any `topology_family` that has distinct tendon roles + (`trunc_octa`, `auxetic_periodic`); families without role-separable + tendons (`prism_stack` with a single tendon set) keep the original + scalar `prestress_global` from 5ae24eaf. + +### D.3 BO surrogate / acquisition implications + +- Use Ax's flat-encoded surrogate over the hierarchical space + (Ax injects `__INACTIVE__` for inactive child params and the default + GP / SAASBO model handles it). No custom kernel required for ≲50 BO + iters per branch. +- The 8 top-level `topology_family` values are most cheaply screened + with an initial Sobol budget *stratified by family* (≥3 specimens + per family) before turning on Bayesian optimisation, so the GP sees + at least one within-family pair per child sub-space. +- If a single contextual GP across families is desired, + consider Ax's `MultiTaskGP` with `topology_family` as the task + feature (cheaper than HSS for the project's ~50–100-specimen budget). + +## E. Suggested next action + +No source-of-truth file (`proposal.tex`, an `Ax` search-space JSON, etc.) +yet exists in the repo to encode these axes against; this document is the +synthesis the user asked for in PR comment 4411373088 ("Worth seeing if +there are additional parameters to consider based on new results in #22"). +When the BO search space is first encoded (Ax / BoTorch JSON, or a LaTeX +table in `proposal.tex` / `manuscript-body.tex`), it should consume: + +1. The original 5ae24eaf table (continuous strut/cable diameters, L/D, + prestress, twist, infill %, layer height, TPU shore, wrap thickness, + nozzle/bed temps, speed, plus the topology categorical). +2. The eight new categorical axes in §A above, **demoted to children of + `topology_family`** as shown in §D.1. +3. The five new (or conditional) continuous axes in §B above, attached + to the matching branch in §D.1. +4. Constraints in §C (especially: defer class-2 / class-k topologies until + Phase-4 joint designs are validated — encoded as the + `joint_validated_class2` fixed feature in §D.2). +5. The hierarchical encoding in §D, using + `ax.core.search_space.HierarchicalSearchSpace` with + `ChoiceParameter(dependents=...)` per + [facebook/Ax#140](https://github.com/facebook/Ax/issues/140). diff --git a/scripts/edison/submit_heterogeneous_params.py b/scripts/edison/submit_heterogeneous_params.py new file mode 100644 index 00000000..8ad4ea2b --- /dev/null +++ b/scripts/edison/submit_heterogeneous_params.py @@ -0,0 +1,384 @@ +"""Submit + fetch one Edison LITERATURE_HIGH query — per-member (heterogeneous) BO parameters. + +Context: PR #24 comment 4520542433 (sgbaird relaying @me-madsen): + + "noting that we could also allow for diameters of individual + struts/cables to vary, rather than assuming a fixed diameter. + Similar for other parameters perhaps. Mostly thinking in context + of #35 right now" + +PR #35 currently sweeps a *single* ``strut_d_mm`` and a single +``cable_d_mm`` per T3-prism specimen (i.e. all 3 struts share one diameter +and all 9 cables share one diameter). The proposal here is to expose +per-member diameters (and possibly per-member length, prestress, twist, +material, etc.) as independent BO axes, taking the dimensionality of the +search space from O(5) per specimen to O(N_members) per specimen for a +T3-prism (3 struts, 9 cables = 12 members → ~12 diameter axes alone). + +This script asks Edison for a peer-reviewed literature synthesis on: +(i) when and why peer-reviewed tensegrity / lattice / truss work allows +heterogeneous (per-member) parameters, (ii) what the manufacturing / +mechanical / form-finding / prestress-feasibility consequences are, and +(iii) how high-dimensional BO campaigns over per-member design vectors +have been structured in published work (random embeddings, sparse / SAAS +GPs, additive / decomposition kernels, latent / generative parameterizations, +trust-region / TuRBO, symmetry / permutation-invariance priors, hierarchical +search spaces a la Ax #140, etc.). + +Per repo convention: + +* edison-client reads ``EDISON_PLATFORM_API_KEY``; we mirror the documented + ``EDISON_API_KEY`` into that variable so the script runs unmodified in CI. +* Submit non-blocking (``create_task``), then poll ``get_task`` until terminal. + ``run_tasks_until_done()`` rebuilds + resubmits TaskRequests rather than + fetching by task_id, so we cannot reuse it here. +* Commit verbatim under + ``edison-trajectories/heterogeneous-params/heterogeneous-params-.{md,json}``. +* If the task is still in progress when the wall-clock budget expires, a + ``-SUBMITTED.json`` placeholder records the task_id so a follow-up session + can resume with ``client.get_task``. +""" + +from __future__ import annotations + +import json +import os +import sys +import time +from pathlib import Path + +# edison-client >= 0.12 reads EDISON_PLATFORM_API_KEY; copilot env exposes +# EDISON_API_KEY. Mirror so EdisonClient() picks it up. +if os.environ.get("EDISON_API_KEY") and not os.environ.get("EDISON_PLATFORM_API_KEY"): + os.environ["EDISON_PLATFORM_API_KEY"] = os.environ["EDISON_API_KEY"] + +from edison_client import EdisonClient, JobNames # noqa: E402 + +REPO_ROOT = Path(__file__).resolve().parents[2] +OUT_DIR = REPO_ROOT / "edison-trajectories" / "heterogeneous-params" +OUT_DIR.mkdir(parents=True, exist_ok=True) + +SLUG = "heterogeneous-params" +HEADLINE = ( + "Per-member (heterogeneous) design parameters in tensegrity / lattice BO " + "campaigns — when to vary strut and cable diameters independently, and " + "how to keep the resulting high-dimensional search space tractable" +) + +QUERY = f"""\ +{HEADLINE}. + +Project context (read in full before answering): + +* Hardware: multi-material 3D-printed tensegrity-inspired energy absorber. + Strut material PETG (or PLA in the current PR #35 batch), tendon material + TPU 85A (NinjaFlex-class, E ~12 MPa secant, sigma_break ~26 MPa, rho + ~1200 kg/m^3, strain-at-break ~550-660%). Printed on a Bambu H2D + dual-extrusion FFF system with manual-painted supports. Baseline topology + is a T3-prism (3 struts, 9 cables = 3 saddle + 3 top + 3 bottom). Stretch + goals: 6-bar SUPERball icosahedron, stacked / tiled prisms, Pajunen + truncated-octa. +* Existing BO setup (PR #30 + PR #33 + PR #35): an Ax / BoTorch qNEHVI + multi-objective campaign. PR #35 specifically — `bo/t3_prism_sobol_batch.py` + — currently sweeps FIVE T3-prism design variables as a single Sobol batch + of 9 specimens on the H2D plate: + - `R_mm` (cell radius) + - `H_mm` (cell height) + - `twist_deg` (rotation between top and bottom triangles) + - `strut_d_mm` (ONE diameter — applies to all 3 struts) + - `cable_d_mm` (ONE diameter — applies to all 9 cables) + Frozen: topology=t3_prism, tiling=1x1x1, joint geometry (captive TPU core + inside hollow PLA shell), build_orientation=vertical, tpu_shore=85A. +* Proposal under discussion (PR #24 comment 4520542433): allow the diameter + of every individual strut and every individual cable to vary independently + (so a T3-prism specimen would have ~3 strut-diameter axes + 9 cable- + diameter axes = 12 diameter axes, instead of 2). The user also asks + "similar for other parameters perhaps" — i.e. per-member length, + per-cable prestress, per-member material assignment, per-cable shore, + per-strut layer-height, etc. +* Companion PR #24 design-space docs already encode a hierarchical + `topology_family` -> conditional child parameters search space (per + facebook/Ax#140). The per-member proposal sits one level below that — + inside any chosen topology family, expand selected scalar parameters into + vector / per-member parameters. + +Answer EVERY sub-question below with primary, peer-reviewed citations +(DOIs where available). When recommending a numeric value or a default +choice, justify from a cited source rather than rule-of-thumb. Do not +fabricate DOIs. + +(a) MOTIVATION / LITERATURE PRECEDENT. In peer-reviewed tensegrity, cable + dome, deployable space-structure, lattice-metamaterial, and ground- + structure topology optimization work, when have authors deliberately + allowed individual struts and individual cables to have heterogeneous + (per-member) cross-section, length, prestress, or material — vs. + enforcing a uniform value across the cell? Identify the canonical + references (e.g. Skelton & de Oliveira 2009 minimal-mass tensegrity + sizing; Masic, Skelton & Gill 2006 form-finding with member-wise force + densities; Adam & Smith active-tensegrity bridges; Pellegrino & + Calladine self-stress; Tibert & Pellegrino reviews; Achtziger / + Bendsoe / Sigmund ground-structure topology optimization; Zegard & + Paulino GRAND/Polytop; Hanaor double-layer grids; Goyal & Skelton + minimum-mass tensegrity dynamics; Bel Hadj Ali, Rhode-Barbarigos, + Smith active control; Wang, Senatore, Marano 2021+ optimal tensegrity + sizing under impact; Veuve, Safaei, Smith deployable tensegrity). + For each, summarise: what was varied per-member, what objective was + optimized, what variation actually emerged at the optimum (i.e. do + the per-member sizes converge to a few discrete clusters, or do they + populate a continuum?), and how the heterogeneity compared + quantitatively against a uniform-member baseline. + +(b) MECHANICAL / FORM-FINDING IMPLICATIONS. For a class-1 prismatic + tensegrity (T3-prism, T4-prism), what is the literature on the + feasibility envelope of heterogeneous member properties? + Specifically: + - Form-finding & self-stress: does varying individual cable + cross-sections break the symmetric self-stress state, force an + unsymmetric prestress distribution, or shift the cell's + equilibrium geometry (R, H, twist)? Cite force-density-method + and dynamic-relaxation references. + - Buckling: per-strut diameter governs Euler buckling at known + slenderness; what is the published trade-off between SEA and + peak-force when individual struts are deliberately under-sized + to act as sacrificial buckling fuses? + - Bistability / multistability (Schenk & Guest 2014; Defossez 2003; + Sumi & Miyashita): does per-member heterogeneity unlock bistable + modes not accessible to uniform cells? + - Anisotropy: how much directional stiffness / energy-absorption + tailoring can be achieved by per-cable cross-section selection + in a single T-prism vs. by going to multi-cell tilings? + - Cycle life / fatigue: per-tendon shore / cross-section + heterogeneity in TPU-tendon tensegrities — any reuse-count + data? + Cite numbers (peak-force reduction %, SEA gain %, prestress shift + in % of uniform self-stress) where available. + +(c) MANUFACTURABILITY ON FFF MULTI-MATERIAL FDM (BAMBU H2D / IDEX). + The lab prints PETG struts + TPU 85A cables in a single multi- + material job. Per the PR #35 captive-TPU-core-inside-PLA-shell + joint design, every joint shell has a uniform bore size set by + the (currently single) cable diameter. If individual cables get + independent diameters, what manufacturability gotchas appear? + Specifically: + - Bore tolerance: how many distinct cable diameters can a single + joint sphere accommodate before the PLA shell becomes + impractically thick (cable_d + 0.8 mm bore clearance, then + +3 mm core, then +3.2 mm PLA wall)? + - TPU bridging: can a 1.5 mm cable transition mid-print into a + 4.5 mm cable on the same TPU extruder pass, or does the + extruder retraction / line-width mismatch force a layer + boundary at the transition? + - Strut diameter discretization: PETG FFF practical strut + diameters quantize on the 0.4 mm nozzle line-width. Cite + published recommendations (Khatri 2024; Yavas 2022; Lopes + 2018; Ye 2023; Bambu Lab / Prusa application notes) for + discrete-set vs. continuous treatment. + - Print time: how does the H2D wipe-tower volume scale with + N_distinct_filament_diameters? + - Variability noise: if the BO can request 12 different cable + diameters per specimen but FFF reliably resolves only 3-4 + bins, the additional "axes" are noise. Cite repeatability / + CoV numbers (Khatri 2024; Yavas 2022 PLA+TPU FFF tensile; + Intrigila 2022; Davami 2025 SLA Tough 2000 + double-T3). + +(d) HIGH-DIMENSIONAL BO METHODOLOGY. Once the per-member expansion is + taken, the design vector becomes O(10) to O(30) dimensional for a + single T3-prism cell, and O(100+) for a 3x3x2 tiling. Survey peer- + reviewed and well-cited workshop / preprint methodology for high- + dim BO over structured design vectors. Cover at minimum: + - Random embeddings (REMBO — Wang et al. 2016; BOCK; ALEBO — + Letham et al. 2020). + - Sparse / SAASBO (Eriksson & Jankowiak 2021) — strong fit + for "most members do not matter, a few do" sparse-effect + regimes. Recommend specific Ax / BoTorch hooks. + - Additive / decomposed GPs (Kandasamy 2015; Gardner 2017; + Wang & Jegelka 2018) — natural fit when per-member effects + are largely independent. + - Trust-region BO (TuRBO — Eriksson 2019) and SCBO — strong + empirical performance in O(100+) dims, especially on + physically-constrained problems. + - Hierarchical / conditional search spaces (Ax HierarchicalSearch + Space, facebook/Ax#140; SMAC; Auto-WEKA; HyperBand) — the + natural way to nest per-member parameters under a topology + choice. + - Latent / generative parameterizations (VAE-BO; LSO — Tripp 2020; + Maus et al. 2022 LOL-BO; differentiable-CAD or differentiable + physics priors). Particularly relevant when there are physically + meaningful symmetries (the 3-fold T-prism is permutation- + invariant; the 9 cables decompose into 3 saddle + 3 top + 3 + bottom orbits — encode that symmetry explicitly). + - Symmetry-aware / permutation-invariant kernels (Cohen & Welling; + Bronstein et al. geometric deep learning; cited in + Bayesian-optimization-with-symmetry preprints if any). + - Multi-fidelity / multi-task GPs (PR #33 sim ladder maps + cleanly onto MTGP / MF-GP — Kandasamy 2017; Wu 2020; Astudillo & + Frazier 2021) as a way to amortize the high-dim cost. + - Constraint handling: heterogeneity often introduces feasibility + constraints (TPU bore set must be ≤4, strut slenderness L/D ≤ + some max, mass ≤ 500 g). Cite NEI / SCBO / cNEHVI. + For each method, recommend whether to adopt it as the primary BO + engine for PR #35, as a fallback if dimensionality blows up, or as + a wrong-fit. Give a concrete recommended progression starting from + the current 5-D Sobol → next-step BO step. + +(e) SYMMETRY EXPLOITATION. The T3-prism has a natural C3 rotational + symmetry (rotate by 120 deg). All 3 struts are in one orbit; the 9 + cables decompose into 3 orbits of 3 (saddle, top, bottom triangles). + Under that symmetry, the "12 diameter axes" reduce to 4 orbit + diameters (1 strut orbit + 3 cable orbits). What does the literature + say about exploiting this symmetry in BO, in form-finding, and in + optimal-control of tensegrity? Cite Sultan & Skelton symmetry- + decomposed self-stress; group-theoretic stability (Kangwai & Guest); + invariant / equivariant GPs (van der Wilk 2018; Holderrieth, Hutchinson + & Teh 2021). Recommend whether to (i) hard-enforce orbit symmetry as + the default search space (so the BO never sees a symmetry-broken + design), (ii) use orbit symmetry only as a kernel prior so symmetry + breaking can emerge when warranted, or (iii) ignore symmetry and + let the per-member axes float independently. Justify quantitatively + in terms of expected sample efficiency given the lab's 50-100 + specimen budget. + +(f) NUMERIC RECOMMENDATIONS for the lab's next BO batch (PR #35 follow-on). + For a single T3-prism cell on the H2D, recommend: + - Which scalar parameters to keep scalar (R, H, twist, infill %). + - Which scalar parameters to expand to per-orbit (strut diameter, + cable diameter — recommend per-orbit, not per-member, for the + first heterogeneous batch). + - Which scalar parameters to expand to fully per-member + (per-cable prestress fraction is the strongest candidate — + cite Skelton's minimum-mass prestress optimization). + - Recommended bounds and discretization for each new axis + (e.g. strut_orbit_d_mm ∈ [3.5, 9.0] continuous; cable_orbit_d_mm + ∈ {1.2, 1.8, 2.4, 3.0, 4.5} categorical for FFF resolvability; + per-cable prestress fraction simplex with sum = 1). + - Recommended BO engine + acquisition + batch size for the + 50-100 specimen total budget. Give a specific Ax / BoTorch + configuration recipe (model_class, surrogate_spec, + acquisition_function_class, batch_size, n_init_sobol). + - Recommended sample-efficiency analytic: how many specimens does + SAASBO / TuRBO / orbit-symmetric GP each need on a published + problem of comparable dimension to reach within 10% of the + Pareto-front hypervolume? Cite the benchmark. + +(g) FAILURE MODES AND OPEN QUESTIONS. Top 5-10 ranked gotchas / + pitfalls of adopting per-member heterogeneous BO axes for the + lab's PETG + TPU 85A tensegrity-on-H2D context. For each: cite + the failure mode from peer-reviewed work and propose a mitigation. + +(h) NUMBERED REFERENCES section (DOI when available) supporting every + quantitative claim in (a)-(g). + +Cite only primary, peer-reviewed sources or established standards +(ASTM, ISO, JEDEC, NASA / NIST technical reports, well-cited workshop +papers at NeurIPS / ICML / AISTATS). Do NOT fabricate DOIs. +""" + + +def main() -> int: + client = EdisonClient( + api_key=os.environ.get("EDISON_PLATFORM_API_KEY") + or os.environ.get("EDISON_API_KEY") + ) + + placeholder = OUT_DIR / f"{SLUG}-SUBMITTED.json" + if placeholder.exists(): + existing = json.loads(placeholder.read_text()) + task_id = existing.get("task_id") + print(f"[submit] reusing prior task_id={task_id}", flush=True) + else: + task = {"name": JobNames.LITERATURE_HIGH, "query": QUERY} + print("[submit] creating LITERATURE_HIGH task...", flush=True) + resp = client.create_task(task) + # create_task returns trajectory_id as plain string (per repo memory) + task_id = resp if isinstance(resp, str) else ( + getattr(resp, "task_id", None) + or getattr(resp, "trajectory_id", None) + or str(resp) + ) + print(f"[submit] task_id={task_id}", flush=True) + placeholder.write_text( + json.dumps( + { + "slug": SLUG, + "headline": HEADLINE, + "task_id": task_id, + "job": "LITERATURE_HIGH", + "status": "submitted", + "submitted_at": time.strftime( + "%Y-%m-%dT%H:%M:%SZ", time.gmtime() + ), + "source_pr_comment": ( + "https://github.com/vertical-cloud-lab/" + "tensegrity-optimization/pull/24#issuecomment-4520542433" + ), + }, + indent=2, + ) + + "\n" + ) + + # Poll with get_task(task_id) until terminal. + TERMINAL = {"success", "failed", "cancelled", "error", "crashed"} + POLL_INTERVAL_S = 30 + BUDGET_S = 60 * 60 # 60 min budget for a single LITERATURE_HIGH task + + print(f"[fetch] polling {task_id}", flush=True) + deadline = time.time() + BUDGET_S + res = None + last_status = None + while time.time() < deadline: + try: + res = client.get_task(task_id=task_id) + except Exception as exc: + print(f" ! get_task raised: {exc!r}; retrying", flush=True) + time.sleep(POLL_INTERVAL_S) + continue + status = (getattr(res, "status", "") or "").lower() + if status != last_status: + print(f" - status={status}", flush=True) + last_status = status + if status in TERMINAL: + break + time.sleep(POLL_INTERVAL_S) + + if res is None: + print(f"[fetch] no response within budget for {task_id}", flush=True) + return 0 + + status = getattr(res, "status", None) or "unknown" + formatted = getattr(res, "formatted_answer", None) or "" + md_path = OUT_DIR / f"{SLUG}-{task_id}.md" + json_path = OUT_DIR / f"{SLUG}-{task_id}.json" + + header = ( + f"# Edison LITERATURE_HIGH — {HEADLINE}\n\n" + f"- task_id: `{task_id}`\n" + f"- slug: `{SLUG}`\n" + f"- job: `LITERATURE_HIGH`\n" + f"- status: `{status}`\n" + f"- fetched_at: `{time.strftime('%Y-%m-%dT%H:%M:%SZ', time.gmtime())}`\n" + f"- source PR comment: " + f"https://github.com/vertical-cloud-lab/tensegrity-optimization/" + f"pull/24#issuecomment-4520542433\n\n" + f"---\n\n" + ) + md_path.write_text(header + (formatted or "(empty formatted_answer)\n")) + + try: + dumped = res.model_dump_json(indent=2) + except Exception: + try: + dumped = json.dumps(res.model_dump(), indent=2, default=str) + except Exception: + dumped = json.dumps({"task_id": task_id, "status": status}, indent=2) + json_path.write_text(dumped + "\n") + + if placeholder.exists() and status in TERMINAL: + placeholder.unlink() + print(f"[fetch] wrote {md_path.name} + {json_path.name} (status={status})", + flush=True) + return 0 + + +if __name__ == "__main__": + sys.exit(main())