Surrogate modeling immersed probability density evolution method for structural reliability analysis in high dimensions. (1st May 2021) - Peng, Yongbo; Zhou, Tong; Li, Jie
Highlights: An improved reliability method combining PDEM and surrogate modeling is presented. KPCA-based dimension reduction and GPR model are combined though joint training. KPCA-GPR model is constructed adaptively using AL-based sampling strategy. Massive computational savings and desirable accuracy are achieved by the method. Abstract: In conjunction with advanced surrogate modeling methods, an improved scheme of probability density evolution method (PDEM) is presented to tackle with the challenge inherent in high-dimensional structural reliability analysis. In this method, the KPCA-GPR model is developed, where the kernel principal component analysis (KPCA)-based nonlinear dimension reduction and the Gaussian process regression (GPR) surrogate model are combined via a joint-training scheme. In this regard, the identified KPCA-based subspace is optimal to the approximation accuracy of the resultant GPR model. Then, the KPCA-GPR model is constructed using the active learning (AL)-based sampling strategy, so as to accurately approximate the equivalent extreme-value (EEV) of structural responses at the whole representative point set involved in the PDEM with as fewer samples as possible. Finally, the reliability is readily evaluated by the one-dimensional integral of the EEVs' probability density function derived from the PDEM. To illustrate the effectiveness of the proposed AL-KPCA-GPR-PDEM, two numerical examples are studied, involving the reliability analysis of both nonlinear analytical functions with different dimensions and shear-frame structures under earthquake ground motions. Numerical results indicate that massive computational cost savings and desirable accuracy enhancement are achieved by the AL-KPCA-GPR-PDEM when dealing with the reliability problems in high dimensions.