An Adaptive Auxiliary Domain Method for Computing Structural Reliability

Abstract:

An adaptive auxiliary domain method that combines the Metropolis algorithm and the support vector machine (SVM) method is proposed in this paper. First, conditional sample points were generated in the target failure domain by using the Metropolis algorithm and then an SVM model with the candidate points produced in this process was trained. Secondly, according to the SVM model obtained, a number of extra sample points were adaptively added into the training set and the SVM model was updated until the stopping criterion was reached. Then, the final SVM model was taken as an auxiliary failure domain and the corresponding approximate failure probability and two conditional failure probabilities were calculated respectively. Finally, the approximate failure probability was corrected with the two conditional failure probabilities to make the final target failure probability asymptotically unbiased and more stable. The examples given in this paper demonstrate the satisfactory accuracy, efficiency and robustness of the proposed method.