Kernel principal component analysis-based Gaussian process regression modelling for high-dimensional reliability analysis

Abstract

An efficient reliability method is presented to address the challenge inherent in the high-dimensional reliability analysis. The critical contribution is an elegant implementation of combining the kernel principal component analysis (KPCA)-based nonlinear dimension reduction and the Gaussian process regression (GPR) surrogate model by introducing a nonintrusive, joint-training scheme. This treatment leads to an optimal KPCA-based subspace in which an accurate low-dimensional GPR model, denoted as the KPCA-GPR model, can be readily achieved. Then, the KPCA-GPR model is combined with the active learning (AL) -based sampling strategy and the Monte Carlo simulation (MCS). In this regard, the newly-added sample at each iteration can be employed simultaneously to both update the estimated KPCA-based subspace and refine the GPR model built on that subspace, which alleviates the 'curse of dimensionality' to some extent and improves progressively the failure probability estimation provided by the low-dimensional GPR model. In order to demonstrate the effectiveness of the proposed method, two numerical examples are investigated, involving both the analysis of high-dimensional, nonlinear, explicit performance functions and the static/dynamic reliability analysis of a truss structure with implicit performance functions. Numerical results indicate that the proposed method is of both accuracy and efficiency for high-dimensional reliability problems.