A semi-single-loop method using approximation of most probable point for reliability-based design optimization

Abstract

A semi-single-loop structure for an efficient reliability-based design optimization (RBDO) is proposed in this study. This structure makes up for the weaknesses of the double-loop method and the single-loop method. In the double-loop method, a heavy computational cost could be required due to an inherent nature of a nested structure. The single-loop method lacks robustness, which means its performance is sensitively affected by several factors. A decoupled method has also been developed in an effort to improve the efficiency of RBDO. Although it separates the nested structure, it retains a double-loop structure. In the semi-single-loop method, a sensitivity analysis of the reliability analysis result is performed in order to approximate a most probable point (MPP). According to the validity of the approximation, the approximated MPP is used for the evaluation of probabilistic constraints. As long as the approximation of MPP is valid, the proposed method has a complete single-loop structure with great efficiency and assured accuracy. If the approximation of MPP loses its validity, a fast reliability analysis is carried out by selecting the approximated MPP as a starting point. The robustness and accuracy of the proposed method are fully ensured due to the concept of checking the validity of the approximated MPP. Numerical examples are tested to verify these advantages of the proposed method and to compare the results here to those of existing RBDO methods