Polynomial chaos Kriging-based structural reliability analysis via the expected margin volume reduction

Abstract

Integral learning functions are theoretically sound but suffer from intensive computational complexity induced by the associated double integral. Based on a new notation of limit-state margin volume, a computationally-cheap integral learning function called Expected margin volume reduction (EMVR) is proposed for structural reliability analysis. EMVR has two key contributions. First, closed-form expression for the inner integral is well derived based on Kriging update formulas, due to tractable definition of the margin volume. This gets rid of cumbersome numerical quadrature or drawing massive realizations of Gaussian process. Second, a confined integral domain is rationally defined for the outer integral, by virtue of exploring the locality of its integrand. This bypasses annoying computer memory issue. Moreover, a hybrid stopping condition coupled with two different settings of the associated parameters is deployed, accommodating to reliability problems with different features. Then, the performance of EMVR-based reliability algorithm is illustrated on four numerical examples. The results show that the evaluation time of EMVR is reduced to a level comparable to pointwise learning functions. Moreover, it outperforms those existing learning functions in terms of both computational accuracy and efficiency.