Active sparse polynomial chaos expansion for system reliability analysis

Surrogate model techniques have been widely used for structural systems with expensively evaluated simulations. However, their application to system reliability problems meets the challenge since approximating multiple implicit performance functions is required to estimate small failure probabilities. In this paper, we demonstrate the potential of a newly active learning method based on polynomial chaos expansion (PCE) to alleviate the problem. The method employs Bayesian compressed sensing (BCS) technique which incorporates a parameterized prior to establish the PCE with a sparse structure. Then, a new composite learning function is developed to update sparse PCEs adaptively by iteratively selecting new training points near the system failure surface until the preset target accuracy is satisfied. This criterion can identify important failure modes and thus guarantee that computation cost will be spent only on areas with a significant probability content. Three examples including a parallel and two series systems are used to demonstrate the effectiveness of the proposed method.