Reliability based design optimization with approximate failure probability function in partitioned design space

This paper presents an efficient method for reliability-based design optimization (RBDO), which is robust to complex systems involving computationally expensive numerical models and/or a large number of random variables. This novel method belongs to a type of decoupling approaches in which the failure probability function (FPF) is approximated in the partitioned design space. In the setting of augmented reliability formulation, for a specific design configuration, the failure probability of a system is proportional to the probability density value of design variables conditioned on the failure event, thus transforming FPF approximation into a problem of density estimation. In this paper, we partition the design space into several subspaces and then estimate the density of failure samples in each subspace by binning and constructing regression functions. Sufficient failure samples are efficiently generated in each subspace using Markov Chain Monte Carlo method, which guarantees the accuracy of FPF approximation over there and ultimately over the entire design space. Three illustrative examples involving structural systems subjected to static or dynamic loadings are discussed to demonstrate the efficiency and accuracy of the proposed method.