New neural network response surface methods for reliability analysis

This article presents two new kinds of artificial neural network (ANN) response surface methods (RSMs): the ANN RSM based on early stopping technique (ANNRSM-1), and the ANN RSM based on regularization theory (ANNRSM-2). The following improvements are made to the conventional ANN RSM (ANNRSM-0): 1) by monitoring the validation error during the training process, ANNRSM-1 determines the early stopping point and the training stopping point, and the weight vector at the early stopping point, which corresponds to the ANN model with the optimal generalization, is finally returned as the training result; 2) according to the regularization theory, ANNRSM-2 modifies the conventional training performance function by adding to it the sum of squares of the network weights, so the network weights are forced to have smaller values while the training error decreases. Tests show that the performance of ANN RSM becomes much better due to the above-mentioned improvements: first, ANNRSM-1 and ANNRSM-2 approximate to the limit state function (LSF) more accurately than ANNRSM-0; second, the estimated failure probabilities given by ANNRSM-1 and ANNRSM-2 have smaller errors than that obtained by ANNRSM-0; third, compared with ANNRSM-0, ANNRSM-1 and ANNRSM-2 require much fewer data samples to achieve stable failure probability results.