Intelligent initial point selection for MPP search in reliability-based design optimization

Abstract

In this paper, intelligent initial point selection for performance measure approach (PMA) of reliability-based design optimization (RBDO) is proposed to improve computational efficiency of the most probable point (MPP) search. Unlike existing PMA algorithms concentrating on enhancement of the optimization algorithm for MPP search, the proposed method focuses on how to intelligently select an initial point which is close to the true MPP so that fast convergence can be achieved. Since the proposed method provides a new initial point for MPP search, it can be combined with any existing PMA algorithms. To obtain the initial point, the first-order Taylor series expansion with respect to a design vector is applied to MPP in U-space obtained from the previous RBDO iteration. Thus, the Jacobian matrix of the MPP vector with respect to the design vector is derived in an analytical way with no additional function evaluation. The derived Jacobian matrix is validated through numerical study. Comparative study with two existing initial point strategies for MPP search—the origin in U-space and the previous MPP in U-space under the condition of design closeness—shows that the proposed initial point significantly improves efficiency of MPP search in any PMA algorithm with various types of performance functions and input distributions.