Active learning for system reliability analysis using PC-Kriging, subset simulation and sensitivity analysis

Authors

P. Parisi, M. Moustapha, S. Marelli, B. Sudret

Abstract

Structural reliability analysis aims at assessing the safety of structures which often operate under uncertain conditions. Approximation-, simulation- or surrogate-based methods are used in this context to estimate the failure probability. Surrogate-based methods are the least computationally intensive and consist in building a cheaper proxy of the original limit-state function, which is calibrated using a limited set of samples known as the experimental design. The latter is sequentially enriched to increase the accuracy of the surrogate in areas of interest, hence allowing for an accurate estimation of the failure probability.

A large number of such techniques has been recently developed in the literature (e.g., active Kriging - Monte Carlo simulation). However most of these techniques consider a single limit-state function. These methods lose efficiency when used to solve system reliability problems, where failure is defined by a non-trivial combination of multiple limit-states. This is due to some peculiarities of the system problem such as the presence of disjoint failure domains or the uneven contribution of each limit-state to the overall failure.

In this work, we propose an efficient algorithm combining Kriging/PC-Kriging and subset simulation to solve system reliability problems in their most general setting, i.e., with an arbitrary combination of components. We devise a new learning function which first identifies candidate samples and then selects for enrichment the specific limit-state that contributes the most to system failure. The algorithm is validated on a set of analytical functions and compared with existing methods in the literature.