Probability and interval hybrid reliability analysis based on adaptive local approximation of projection outlines using support vector machine

This paper investigates structural reliability analysis with both random and interval variables, which is defined as a three-classification problem and handled by support vector machine (SVM). First, it is determined that projection outlines on the limit-state surface are crucial for describing separating hyperplanes of the three-classification problem. Compared with the whole limit-state surface, the region of projection outlines are much smaller. It will be beneficial to reduce the number of update points and the computational cost if SVM update concentrates on refining the approximate projection outlines. An adaptive local approximation method is developed to realize that the initial built SVM model is sequentially updated by adding new training samples located around the projection outlines. Using this method, the separating hyperplanes can be accurately and efficiently approximated by SVM. Finally, a new method is proposed to evaluate the failure probability interval based on Monte Carlo simulation and the refined SVM.