A Multi-Fidelity Successive Response Surface Method for Crashworthiness Optimization Problems

Abstract

Due to the high computational burden and the high non-linearity of the responses, crashworthiness optimizations are notoriously hard-to-solve challenges. Among various approaches, methods like the Successive Response Surface Method (SRSM) have stood out for their efficiency in enhancing baseline designs within a few iterations. However, these methods have limitations that restrict their application. Their minimum iterative resampling required is often computationally prohibitive. Furthermore, surrogate models are conventionally constructed using Polynomial Response Surface (PRS), a method that is poorly versatile, prone to overfitting, and incapable of quantifying uncertainty. Furthermore, the lack of continuity between successive response surfaces results in suboptimal predictions. This paper introduces the Multi-Fidelity Successive Response Surface (MF-SRS), a Gaussian process-based method, which leverages a non-linear multi-fidelity approach for more accurate and efficient predictions compared to SRSM. After initial testing on synthetic problems, this method is applied to a real-world crashworthiness task: optimizing a bumper cross member and crash box system. The results, benchmarked against SRSM and the Gaussian Process Successive Response Surface (GP-SRS)—a single-fidelity Gaussian process-driven extension of SRSM—show that MF-SRS offers distinct advantages. Specifically, it improves upon the specific energy absorbed optimum value achieved by SRSM by 14%, revealing its potential for future applications.