A novel active learning method based on matrix-operation RBF model for high-dimensional reliability analysis

In order to deal with high dimensional reliability analysis, an active learning method based on matrix-operation radial basis function (RBF) model is proposed in this paper. To accomplish active learning, the predicted mean and standard deviation of the RBF model need to be obtained with the help of leave-one-out cross validation (LOOCV). When dealing with high dimensional problems, by LOOCV, the calculation of RBF matrix between candidate points and the training points, and the prediction of the sub-models at candidate points will be very time-consuming. Therefore, in this paper, we propose a matrix-operation method for RBF matrix calculation and a matrix-operation method for sub-model prediction. Such a matrix-operation RBF model significantly reduces the computation time of LOOCV and makes active learning mechanism possible. On this basis, we propose a novel learning function according to the prediction information of RBF model. In addition, the error-monitor mechanism is introduced to timely terminate the learning process. Four high-dimensional complex examples are investigated to verify the performance of the proposed method.