Structural design optimization under dynamic reliability constraints based on the probability density evolution method and highly-efficient sensitivity analysis

The present contribution investigates the feasibility of solving a class of dynamic-reliability-based design optimization problems in the framework of the probability density evolution method (PDEM). The PDEM combined with the extreme value distribution strategy is employed for the dynamic reliability assessment. Based on this information, a small set of important representative points (IRPs) that have a relatively large impact on the dynamic reliability is identified. Then, the sensitivity of the dynamic reliability constraints with respect to the design variables is estimated with the set of IRPs. Since the number of IRPs is usually small, the numerical effort associated with the sensitivity analysis is considerably reduced without compromising the accuracy of the results. By embedding the PDEM-based dynamic reliability assessment and sensitivity analysis into a class of first-order optimization algorithms, the design optimization problem under dynamic reliability constraints is efficiently solved. Two numerical examples involving nonlinear structures are presented to demonstrate the effectiveness and efficiency of the proposed method.