A novel first–order reliability method based on performance measure approach for highly nonlinear problems

The first–order reliability method (FORM) is widely used in structural reliability analysis for its simplicity and efficiency. It can be solved by gradient–based algorithms, on which the nonlinear degree of performance functions may have a great influence. On the other hand, evolutionary algorithms could achieve convergence solutions even for highly nonlinear performance function, usually with expensive computational cost. To overcome their drawbacks, we propose a new reliability analysis method called PMA–IACC to search the most probable failure point (MPP). As the inverse reliability analysis and reliability analysis are reversible each other, the performance measure approach (PMA) of the inverse reliability analysis could be used for the reliability analysis based on the multi–objective optimization theory. To enhance the efficiency and robustness of the inverse reliability, the improved adaptive chaos control (IACC) method is proposed and then it is integrated into the PMA reliability analysis strategy. Five illustrative examples, including three two–dimensional problems and two multi–dimensional problems, demonstrate the outstanding efficiency and robustness of the PMA–IACC over other prevalent approaches.