Hybrid structure reliability method combining optimized Kriging model and importance sampling

In structural reliability analysis, a polynomial function is usually used to approach the implicit limit state function. But the limit state function is likely to be implicit and highly nonlinear for complex aeronautic and astronautic structures. The calculation may not converge if the simulation of the polynomial function is not accurate enough. In order to improve the accuracy, efficiency, and convergency, a reliability method combining the approved Kriging model and importance sampling is proposed in this paper. Firstly, the parameter of Kriging model is optimized using the artificial bee colony algorithm. Then the implicit limit state function is fitted with the optimized Kriging model, and the sampling center is revised constantly by importance sampling to improve gradually the fitting accuracy. Finally, the reliability is solved combining the Kriging model and the parsing algorithm such as the first order reliability method (FORM) or second order reliability method (SORM). This method improves the accuracy and convergency of reliability calculations with highly nonlinear limit state functions, and has high computing efficiency.