Surrogate Based Method for Evaluation of Failure Probability under Multiple Constraints

In this paper we study the problem of computing failure probability subject to multiple constraints. In particular, we consider the case of surrogate models, also known as response surfaces, for the available constraints. An important feature is that the surrogates are not required to have high accuracy. An efficient numerical algorithm based on Monte Carlo sampling is presented, where a large portion of the samples is evaluated using the surrogates and only a small portion using the underlying stochastic system. By doing so, the proposed algorithm can be much more efficient than the brute force Monte Carlo sampling and also achieve high accuracy even when the surrogates are not highly accurate. The consideration of multiple constraints is a notable extension of the earlier studies, which mostly considered failure probability defined by a single constraint. Here we establish rigorous convergence analysis of the algorithm for multiple constraints and demonstrate its efficiency via several numerical examples.

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