{"title":"基于梯度增强物理信息神经网络和概率密度演化方法的结构可靠性分析","authors":"Zidong Xu, Hao Wang, Kaiyong Zhao, Han Zhang","doi":"10.1016/j.strusafe.2025.102604","DOIUrl":null,"url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"116 ","pages":"Article 102604"},"PeriodicalIF":6.3000,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Structural reliability analysis using gradient-enhanced physics-informed neural network and probability density evolution method\",\"authors\":\"Zidong Xu, Hao Wang, Kaiyong Zhao, Han Zhang\",\"doi\":\"10.1016/j.strusafe.2025.102604\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>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.</div></div>\",\"PeriodicalId\":21978,\"journal\":{\"name\":\"Structural Safety\",\"volume\":\"116 \",\"pages\":\"Article 102604\"},\"PeriodicalIF\":6.3000,\"publicationDate\":\"2025-04-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Structural Safety\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0167473025000323\",\"RegionNum\":1,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, CIVIL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Structural Safety","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167473025000323","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, CIVIL","Score":null,"Total":0}
Structural reliability analysis using gradient-enhanced physics-informed neural network and probability density evolution method
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.
期刊介绍:
Structural Safety is an international journal devoted to integrated risk assessment for a wide range of constructed facilities such as buildings, bridges, earth structures, offshore facilities, dams, lifelines and nuclear structural systems. Its purpose is to foster communication about risk and reliability among technical disciplines involved in design and construction, and to enhance the use of risk management in the constructed environment