结构可靠度计算的自适应辅助域方法

An Adaptive Auxiliary Domain Method for Computing Structural Reliability

摘要:

提出了一种Metropolis算法与支持向量机（SVM）方法相结合的自适应辅助域方法.利用Metropolis算法生成目标失效域内的条件样本点，并以该过程中的备选点作为初始训练点训练SVM模型.根据训练得到的SVM模型再自适应地选择一部分样本点加入训练点集，并对SVM模型进行更新，直至满足迭代终止条件.以最终得到的SVM模型作为辅助失效域，计算近似失效概率和两个条件失效概率.对近似失效概率进行修正，使最终得到的目标失效概率渐进无偏且更加稳定.算例表明该算法具有较好的计算精度、效率和鲁棒性.

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.