A Surrogate Approach for Stochastic Modeling of a Crash Box Under Impact Loading in the Time Domain

Abstract

A time-dependent stochastic modeling of a crash box was performed considering the material property, the impactor mass, and the thickness of the crash box as the uncertain parameters. To study such problem, a surrogate model has been developed combining a proper orthogonal decomposition (POD) and a polynomial chaos expansion (PCE) approach. The stochastic response was projected on some POD vectors. The coefficient corresponding to a POD vector was then uncertain and was predicted using a PCE approach. Uncertainty quantification was performed for the impactor displacement, impactor velocity, and contact force by the POD-PCE model and leave-one-out (LOO) errors were computed. With the POD approach, it was possible to obtain very good results, whereas the number of PCE coefficients is quite low. It was also possible to achieve a low LOO error for the stochastic responses with very few model evaluations and with low degree polynomial.