An efficient method for reliability-based design optimization of structures under random excitation by mapping between reliability and operator norm

Reliability-based design optimization (RBDO) can fulfill both reliability and economic requirements by considering the stochastic properties of structure and excitation. However, the computational efficiency of this optimization is hindered by the nested loops involved in reliability analysis and optimization processes. In order to overcome this limitation, a novel method is proposed for structures subjected to random excitation, which is based on the mapping between operator norm and reliability index. This approach necessitates effectuating the transformation of the optimization objective from reliability indexes to operator norms with a small number of samples, thereby eliminating the laborious process of nested loops. It can effectively solve design optimization problems with reliability constraints, particularly for structures with explicit structural response under random excitation. Four examples are presented to demonstrate the effectiveness and applicability of the proposed method.