Stochastic Crashworthiness Optimization Accounting for Simulation Noise

Finite element-based crashworthiness optimization is extensively used to improve the safety of motor vehicles. However, the responses of crash simulations are characterized by a high level of numerical noise, which can hamper the blind use of surrogate-based design optimization methods. It is therefore essential to account for the noise-induced uncertainty when performing optimization. For this purpose, a surrogate, referred to as non-deterministic kriging (NDK), can be used. It models the noise as a non-stationary stochastic process, which is added to a traditional deterministic kriging surrogate. Based on the NDK surrogate, this study proposes an optimization algorithm tailored to account for both epistemic uncertainty, due to the lack of data, and irreducible aleatory uncertainty, due to the simulation noise. The variances are included within an extension of the well-known expected improvement infill criterion referred to as modified augmented expected improvement (MAEI). Because the proposed optimization scheme requires an estimate of the aleatory variance, it is approximated through a regression kriging, referred to as variance kriging, which is iteratively refined. The proposed algorithm is tested on a set of analytical functions and applied to the optimization of an occupant restraint system (ORS) during a crash.

Automated summary

Finite element-based crashworthiness optimization is widely used to improve the safety of motor vehicles. However, the high numerical noise in crash simulations poses challenges for surrogate-based design optimization. In this study, a non-deterministic kriging surrogate, called NDK, is proposed to model the noise-induced uncertainty. An optimization algorithm, incorporating both epistemic and irreducible aleatory uncertainty, is developed based on the NDK surrogate. The algorithm estimates the aleatory variance through variance kriging and iteratively refines the estimate.