Sequential most probable point update combining Gaussian process and comprehensive learning PSO for structural reliability-based design optimization

Abstract

This paper proposes an efficient reliability-based design optimization (RBDO) method that advantageously decouples comprehensive learning particle swarm optimization (CLPSO) algorithm with Gaussian process regression (GPR) model, termed as GPR-CLPSO. The method iteratively performs the CLPSO with deterministic parameters based on the most probable point (MPP) underpinning limit-state functions (LSFs) iteratively updated by the active learning reliability evaluation process. The GPR model approximates, from the design data given by CLPSO, the spectrum of LSFs under random parameters, and hence enables a significant computational reduction of Monte-Carlo simulations (MCSs) for failure probability approximation. The expected feasibility function is maximized using the CLPSO code to systematically refine the GPR model by adaptively adding new (intelligent) learning points in the region with high-reliability sensitivity leading to the more accurate prediction of failure probability. A novel inverse MCS constraint boundary method is developed to redefine the MPP assigned for the CLPSO algorithm in determining the new optimal design. The method efficiently leverages the decoupling approach, whilst significantly alleviating computing efforts, to quickly and accurately capture the optimal RBDO design. The resulting failure probability well satisfies the allowable limit. Four RBDO examples are provided to illustrate applications and robustness of the proposed decoupling GPR-CLPSO approach.