Structural design optimization under stochastic excitations considering first-passage probability constraint based on dimension-reduced probability density evolution equation

In this paper, a new method for dynamic-reliability-based design optimization (DRBDO) of structures under stochastic excitations is proposed. In DRBDO, the first-passage probability (FPP) is involved in the reliability constraint functions, and thereby, has to be iteratively calculated with varying values of design variables. This can result in high computational costs, especially when dynamical systems under stochastic excitations are considered. Consequently, an efficient and accurate dynamic reliability analysis method is of fundamental significance for DRBDO. The recently developed dimension-reduced probability density evolution equation (DR-PDEE) has shown its potential in analyzing high-dimensional dynamical systems subject to stochastic excitations. In the proposed method, the DR-PDEE of the absorbing boundary process is adopted for efficient dynamic reliability analysis such that its feasibility in DRBDO is further explored. Several tailored techniques are devised to further enhance the efficiency and robustness of the repeated reliability analyses. Noting that the analytical solution of the reliability sensitivity is intractable, a surrogate-based optimization scheme is employed to solve the DRBDO problem. In particular, a constrained Bayesian optimization method is customized according to the unique characteristics of the considered DRBDO problem to address the constraint on the FPP. Finally, the efficiency and effectiveness of the proposed method is verified through numerical examples involving linear and nonlinear structures under nonstationary stochastic seismic excitations.