A gradient-based polynomial chaos approach for risk and reliability-based design optimization

Abstract

This paper presents an approach for the solution of risk and reliability-based design optimization problems using gradient-based algorithms together with polynomial chaos expansions (PCE) for probability of failure evaluation and sensitivity analysis. The approach is intended to alleviate the computational burden required by such problems with accurate evaluation of probabilities of failure. Benchmark problems from the literature are solved to assess the effectiveness of the proposed approach and the results show that it is able to obtain accurate solutions with tractable computational effort. The main limitation of the proposed approach, inherited from the PCE, is that the computational effort grows very fast for an increasing number of random variables.