Active Polynomial Chaos Expansion for Reliability-Based Design Optimization

Abstract

The aim of the present paper is to develop a strategy for solving reliability-based design optimization (RBDO) problems by sparse polynomial chaos expansion (PCE). Because classic sparse regression methods cannot provide the surrogate error measure that can be employed to improve the sampling performance for failure probability estimation in RBDO, Bayesian compressed sensing with state-of-the-art performance is employed to build sparse PCE in the paper. In the meanwhile, a new active learning function is proposed to adaptively select new training points. Two goals can be achieved using this criterion; that is, most of the selected training points are selected from the desired regions to approximate limit state surfaces, and these points tend to be far away from the existing points in the current design to avoid the clustering problem. Because the sparse PCEs are built in an augmented space, it is made numerically affordable to solve the RBDO problem with no extra computational cost. The computation capability of the proposed method is demonstrated by several analytical RBDO problems. Meanwhile, the design optimization of a stiffened rib of the wing edge in a certain aircraft also verifies its good engineering applicability.