A decoupled double-loop method with the adaptive allowable limits for probabilistic performance-based design optimization

•A decoupled double-loop method for probabilistic PBDO has been proposed.•In each cycle, deterministic PBDO and reliability assessment are performed.•The allowable limit of the violated probabilistic constraints is shifted.•The proposed method leads the search path to a reliable space. In this study, inspired by the idea of the sequential optimization and reliability assessment (SORA) method, a new decoupled double-loop method for probabilistic performance-based design optimization (PPBDO) has been proposed. The highlight of the proposed method is the independence of this method from the type of problem and the limit state function; in such a way that it can be used in non-linear problems with multiple probabilistic constraints with the implicit form of the limit state function. However, it requires less computational effort than conventional double-loop methods. In each cycle of this method, deterministic performance-based design optimization was performed and then the reliability of the optimal design was evaluated. If the results of the reliability assessment are not desirable, the allowable limit of the constraints in the deterministic optimization problem will be changed based on the results of the reliability assessment. This process repeats until the results of the reliability assessment become desirable. The metaheuristic enhanced vibrating particle system algorithm and the Monte Carlo simulation method were used for optimization process and reliability analysis, respectively. To evaluate the efficiency of the proposed method, the optimization problem was defined so as to reduce the structural weight while meeting the acceptance criteria for performance-based design of steel moment frames according to ASCE 41-13. The PPBDO of three- and nine-story steel moment frames were investigated and the results showed that the proposed method was able to reduce the volume of calculations and direct the search path toward a reliable space.