Structural reliability analysis using gradient-enhanced physics-informed neural network and probability density evolution method

• Published in: Structural safety Vol. 116; p. 102604
• Main Authors: Xu, Zidong, Wang, Hao, Zhao, Kaiyong, Zhang, Han
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.09.2025
• Subjects: Gradient-enhanced physics-informed neural network; Mesh-free solving method; Partial differential equation; Probability density evolution method; Structural reliability analysis; Structural reliability analysis; Gradient-enhanced physics-informed neural network; Probability density evolution method; Mesh-free solving method; Partial differential equation
• ISSN: 0167-4730
• DOI: 10.1016/j.strusafe.2025.102604

•A novel EPD-gPINN model is established to conduct SRA of the dynamic systems.•Normalized GDEE and the corresponding gradient function are derived as the physical laws.•Proposed EPD-gPINN framework for SRA is verified by both static and dynamic examples. In past decade, probability density evolution method (PDEM) has become one of the most popular approaches to conduct overall structural reliability analysis (SRA). The main procedure of the PDEM-based SRA lies in solving the generalized probability density evolution equation (GDEE) related to virtual stochastic process (VSP). Common methods for GDEE solving are highly sensitive to the choice of solving parameters, which may affect the accuracy, efficiency and stability of the solution. Recently, physics-informed neural network (PINN) and its extended form have successfully utilized to solve differential equations in different fields. With this in view, the gradient-enhanced PINN (gPINN) are utilized to solve the GDEE of the VSP for SRA, which leads to an improved approach, termed as evolutionary probability density (EPD)-gPINN model. Specifically, the normalized GDEE and the additional gradient residual equations are derived as the physical loss. Meanwhile, to offer sufficient supervised training data, an easy-to-operate data augmentation procedure is established. Numerical examples are posed for validating the validity of the proposed framework. Parametric analysis is conducted to investigate the influence of the network parameters to the predictive performance. Results indicate that using proper weight of the gradient loss, the proposed framework can efficiently conduct the SRA, whose predictive performance outperforms PINN.