Robust Level-Set-Based Topology Optimization Under Uncertainties Using Anchored ANOVA Petrov–Galerkin Method
Bibliographic record
Abstract
Abstract. We present a nonintrusive approach to robust structural topology optimization. Specifically, we consider optimization of mean- and variance-based robustness metrics of a linear functional output associated with the linear elasticity equation in the presence of probabilistic uncertainties in the loading and material properties. To provide an efficient approximation of higher-dimensional problems, we approximate the solution to the governing stochastic partial differential equations using the anchored ANOVA Petrov–Galerkin projection scheme. We then develop a nonintrusive quadrature-based formulation to evaluate the robustness metric and the associated shape derivative. The formulation is nonintrusive in the sense that it works with any level-set-based topology optimization code that can provide deterministic displacements, outputs, and shape derivatives for selected stochastic parameter values. We demonstrate the effectiveness of the proposed approach on various problems under loading and material uncertainties.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".