High-Dimensional Reliability Analysis with Error-Guided Active-Learning Probabilistic Support Vector Machine: Application to Wind-Reliability Analysis of Transmission Towers

Adaptive reliability analysis methods based on surrogate models, especially kriging, have been successfully implemented in many problems. However, the application of kriging is limited to low-dimensional problems with noncategorical performance data. Support vector machine (SVM), by contrast, addresses these limitations, but its application in reliability analysis faces several challenges with regard to robustness, accuracy, and efficiency. This study proposed a new adaptive approach based on probabilistic support vector machine for reliability analysis (PSVM-RA). Different from existing methods that only select training points in the margin of the SVM, the proposed method adopts a new learning function that considers the wrong classification probability for each realization and maximizes the potential for new information offered by a candidate sample for the training set. Moreover, the upper bound of the error that is introduced by the SVM in estimating the failure probability is derived based on a Poisson binomial distribution model considering the likelihood of wrong classification for all the points in the margin of the SVM. This upper bound of error was used in the proposed framework as a stopping criterion to guarantee the desired accuracy. Three numerical examples and an engineering application regarding the wind-reliability analysis of transmission towers were investigated to demonstrate the performance of the proposed method. It was demonstrated that PSVM-RA can provide robust estimates of failure probability when other state-of-the-art methods fail. Moreover, it offers a balance between efficiency and accuracy.