New structural reliability method with focus on important region and based on adaptive support vector machines

Support vector machine has been shown to be an effective classification tool for reliability analysis. Its training set governs the computational cost of the whole reliability analysis. To reduce this training set, researchers focus on important region to decrease samples and refine support vector machine adaptively. In accordance with this methodology, this article presents a more efficient algorithm from the aspect of sampling strategy and that of adaptive manner. To reduce simulated samples, only the important region is considered using Monte Carlo samples in only that region. Moreover, Hasofer-Lind reliability index and the physical meanings of random variables are utilized to identify samples. To speed up convergence of the adaptive procedure, it is proposed to add the most likely support vector to the training set at each step. The illustrative examples show that the proposed sampling strategy largely reduces the classification burden of support vector machine, and the new adaptive procedure converges quickly. The results of the examples demonstrate the proposed method to be accurate and efficient.