An improved response surface method based on the resonable subdomain

The concept of reasonable subdomain is defined based on the theory of structural reliability in the paper. The size of domain around the design point which gives the main contribution to the failure probability is well-defined by using the reasonable subdomain. The failure points can be distributed in the reasonable subdomain in terms of a given probability. The proposed reasonable subdomain can solve the problem that the size of main domain influencing failure probability is not given obviously. Then, an improved response surface method is also proposed based on the reasonable subdomain. The proposed method can ensure that there is no fitting error of the response function at the design point, and can better fit the limit state function in the reasonable subdomain. The failure probability is evaluated by using the importance sampling Monte Carlo simulation. In order to improve the evaluation accuracy of failure probability, the evaluation method of subdomain is applied according to the locations of sample points. Numerical examples are shown that the proposed method has high accuracy and efficiency for both explicit and implicit limit states.