Abstract:
This paper presents a unified parametric‑modeling framework for analyzing and optimizing “noisy” structural problems — those in which simulation outputs exhibit both deterministic dependence on design variables and irreducible random variation . Using LS‑OPT’s response‑surface methodology, parametric finite‑element models are constructed to decompose response variation into predictable (shape‑driven) and residual (random or bifurcation‑driven) components. Two canonical examples — a two‑bar truss with analytical reliability benchmarks and a free‑motion headform impact on an A‑pillar — illustrate how LS‑OPT quantifies mean, variance, and failure probabilities, and distinguishes bias from noise in metamodels. The framework supports both deterministic optimization (minimizing peak knee forces) and probabilistic reliability analysis (computing failure probabilities via Monte Carlo, FORM, and response‑surface approximations), demonstrating convergence to optimal designs while managing uncertainty. By embedding parameters and conditional logic in TrueGrid®‑generated meshes, the approach automates shape variation and yields robust, reproducible simulation‑driven optimization workflows that seamlessly incorporate shape optimization and uncertainty quantification.
