Advanced response surface method for the failure probability of complex structure with multiple implicit limit state equations

An advanced response surface method is presented for implicit limit state equation. Based on the conventional response surface method, the higher order correction and equivalent probability transform are considered in the advanced response surface method. The equivalent explicit limit state equation can be established by the advanced response surface method so that the available reliability analysis method for explicit limit state can be used. The advanced surface response method can be extended to the complex structure with multiple implicit limit state equations. After the equivalent explicit limit state is established for every implicit limit state equation in the complex structure, Monte Carlo method and the extended importance sampling method can be employed to calculate the structure system failure probability. Illustrative examples show that the gradient is avoided in the presented method, and the higher accuracy is attained by taking the correlation of the failure modes into consideration.