Adaptive surrogates of crashworthiness models for multi-purpose engineering analyses accounting for uncertainty

TL;DR

This paper introduces an adaptive surrogate modeling approach using kernel PCA to efficiently perform uncertainty quantification in complex crashworthiness models with high-dimensional outputs, reducing computational costs.

Contribution

It proposes a novel methodology combining kernel PCA with surrogate models to handle high-dimensional, nonlinear crash models efficiently, requiring fewer full-order simulations.

Findings

Kernel PCA improves surrogate model efficiency in high-dimensional problems.

The methodology reduces computational time significantly.

Validated on an automotive crashworthiness case study.

Abstract

Uncertainty Quantification (UQ) is a booming discipline for complex computational models based on the analysis of robustness, reliability and credibility. UQ analysis for nonlinear crash models with high dimensional outputs presents important challenges. In crashworthiness, nonlinear structural behaviours with multiple hidden modes require expensive models (18 hours for a single run). Surrogate models (metamodels) allow substituting the full order model, introducing a response surface for a reduced training set of numerical experiments. Moreover, uncertain input and large number of degrees of freedom result in high dimensional problems, which derives to a bottle neck that blocks the computational efficiency of the metamodels. Kernel Principal Component Analysis (kPCA) is a multidimensionality reduction technique for non-linear problems, with the advantage of capturing the most relevant information from the response and improving the efficiency of the metamodel. Aiming to compute the minimum number of samples with the full order model. The proposed methodology is tested with a practical industrial problem that arises from the automotive industry.