Structural reliability analysis based on neural networks with physics-informed training samples

Abstract

In order to develop high-fidelity and high-efficiency machine learning (ML) models in reliability engineering, a novel ML approach based on Neural Networks (NN) with Physics-Informed Training Samples (PITS) is established, which is abbreviated as NN-PITS. The proposed NN-PITS framework uses data augmentation techniques to improve the training samples based on the properties of the failure surface, so that the physical information is embedded into the NN. Two approaches for embedding physical information are introduced. When the limit state equation (LSE) can be solved analytically, the training samples are extended to the failure surface based on the LSE, and then the physics-informed loss function is constructed. When the LSE is implicit or unsolvable analytically, a novel sampling method based on pseudo-probability distribution to generate the samples of required distribution is proposed, so as to obtain the PITS that are near the failure surface. Compared with the common data-driven NN model, the proposed NN-PITS framework can effectively utilize the physical information in reliability problem, so as to reduce the dependence on label samples. The proposed NN-PITS can be combined with finite element analysis (FEA) and applied to reliability engineering problems. Three engineering examples, including two static problems and one time-varying problem, are given to illustrate the good applicability and capability of the proposed methods for structural reliability analysis.