基于物理信息神经网络的时变可靠性分析方法

doi:10.3901/JME.2024.13.141

机械工程学报 ›› 2024, Vol. 60 ›› Issue (13): 141-153.doi: 10.3901/JME.2024.13.141

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基于物理信息神经网络的时变可靠性分析方法

胡伟飞^1,2,3, 廖家乐¹, 郭云飞⁴, 鄢继铨¹, 李光⁴, 岳海峰⁴, 谭建荣^1,2

1. 浙江大学流体动力基础件与机电系统全国重点实验室杭州 310058;
2. 设计工程及数字孪生浙江省工程研究中心杭州 310058;
3. 浙江大学台州研究院台州 318000;
4. 智能采矿装备技术全国重点实验室太原 030024

收稿日期:2023-10-08 修回日期:2024-03-01 出版日期:2024-07-05 发布日期:2024-08-24
作者简介:胡伟飞(通信作者),男,1985年出生,研究员,博士研究生导师。主要研究方向为数字孪生、人工智能、不确定性优化设计、风能。E-mail:weifeihu@zju.edu.cn;廖家乐,男,2001年出生,博士研究生。主要研究方向为数字孪生、可靠性分析、不确定性优化设计。E-mail:jialeliao@zju.edu.cn;郭云飞,男,1987年出生,高级工程师。主要研究方向为智能装备设计及优化。E-mail:guoyunfei@tz.com.cn;鄢继铨,男,1999年出生,博士研究生。主要研究方向为数字孪生、可靠性分析、不确定性优化设计。E-mail:jiquanyan@zju.edu.cn;李光,男,1982年出生,高级工程师。主要研究方向:智能矿山装备设计与制造。E-mail:13513614486@163.com;岳海峰,男,1982年出生,高级工程师。主要研究方向:采矿装备智能控制。E-mail:yhf82524@163.com;谭建荣,男,1954年出生,教授,博士研究生导师,中国工程院院士。主要研究方向为机械设计及理论、计算机辅助设计与图形学、数字化设计与制造。E-mail:egi@zju.edu.cn
基金资助:
浙江省自然科学基金(LZ22E050006)、国家自然科学基金(52275275,52111540267)和浙江省‘尖兵'‘领雁'研发攻关计划(2023C01008)资助项目。

Time-dependent Reliability Analysis Based on Physics-Informed Neutral Network

HU Weifei^1,2,3, LIAO Jiale¹, GUO Yunfei⁴, YAN Jiquan¹, LI Guang⁴, YUE Haifeng⁴, TAN Jianrong^1,2

1. State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310058;
2. Engineering Research Center for Design Engineering and Digital Twin of Zhejiang Province, Hangzhou 310058;
3. Taizhou Institute of Zhejiang University, Taizhou 318000;
4. State Key Laboratory of Intelligent Mining Equipment Technology, Taiyuan 030024

Received:2023-10-08 Revised:2024-03-01 Online:2024-07-05 Published:2024-08-24

摘要/Abstract

摘要： 传统时变可靠性分析(Time-dependent reliability analysis, TRA)往往通过大量实验设计样本(Design of experiments, DoE)构建代理模型，从而实现时变可靠性分析计算。在这个过程中，随着性能方程的非线性程度、响应求解难度等增加，DoE的计算成本愈发高昂，使得可靠性分析耗时冗长。针对该问题，创新性地提出了一种基于物理信息神经网络(Physics-informed neural network，PINN)的时变可靠性分析方法(PINN-based TRA, PBTRA)。该方法在TRA过程中将约束系统响应的偏微分方程(Partial differential equation, PDE)融入PINN模型训练的损失函数，使用PINN模型预测系统的实际响应，并基于此构建性能方程，解决了传统时变可靠性分析依赖大量仿真计算获取实验样本的难题，有效降低了TRA计算成本。同时针对传统PINN训练过程出现的收敛缓慢和模型欠拟合等问题，根据训练过程中PINN模型在不同采样区域的响应情况，判断相关区域是否接近系统响应的极限状态，并据此划分敏感区域，动态调整训练点采样分布，进一步结合神经网络的重采样机制，提出了一种基于区域响应权重的PINN模型动态采样训练方法，并且将其应用于TRA中。相较于传统的PINN，所提方法具有更快的训练速度与更高的性能响应计算精度，进而能够提升TRA精度与效率。文章中针对两个案例测试了所提出的PBTRA方法，并与传统TRA方法进行了对比，验证了所提出方法的优越性。

关键词: 时变可靠性分析, 优化设计, 物理信息神经网络, 重要性采样, 代理模型

Abstract: Traditional time-dependent reliability analysis (TRA) often constructs a surrogate model through a large number of design of experiments (DoE) samples, thereby achieving the calculation of time-dependent reliability analysis. As the nonlinearity of the performance function and the difficulty of response solution increase, the calculation cost of DoE becomes increasingly expensive, making the reliability analysis time-consuming and cumbersome. To address this problem, a time-dependent reliability analysis method based on physics-informed neural network (PINN-Based TRA, PBTRA) is proposed in this paper. This method incorporates the partial differential equation that constrains the system response into the loss function of the PINN training process, which uses the PINN model to predict the system's response. Based on the PINN model, the system performance function is constructed to preform TRA, which can solve the problem that traditional TRA relies on a large number of simulation calculations to obtain DoE samples, effectively reducing the calculation cost. At the same time, for the problems of slow convergence and underfitting that occur in the traditional PINN training process, the proposed method judges whether the relevant region is close to the limit state of the system response according to the response of the PINN model in different sampling regions during the training process and divide the sensitive regions accordingly. The distribution of training point sampling is dynamically adjusted, and combined with the resampling method of neural network, a dynamic sampling training method based on regional reaction weight function that suitable for PINN model is proposed and applied to TRA. Compared with traditional PINN, this method has faster training speed and higher accuracy of performance response calculation, which can improve the accuracy and efficiency of TRA. Two cases are analyzed by PBTRA and compared with traditional TRA methods to verify the superiority of the method proposed in this paper.

Key words: time-dependent reliability analysis, optimal design, physics-informed neutral network, importance sampling, surrogate model

中图分类号:

TH114

胡伟飞, 廖家乐, 郭云飞, 鄢继铨, 李光, 岳海峰, 谭建荣. 基于物理信息神经网络的时变可靠性分析方法[J]. 机械工程学报, 2024, 60(13): 141-153.

HU Weifei, LIAO Jiale, GUO Yunfei, YAN Jiquan, LI Guang, YUE Haifeng, TAN Jianrong. Time-dependent Reliability Analysis Based on Physics-Informed Neutral Network[J]. Journal of Mechanical Engineering, 2024, 60(13): 141-153.

参考文献

[1] HU Zhen, DU Xiaoping. A sampling approach to extreme value distribution for time-dependent reliability analysis[J]. Journal of Mechanical Design, 2013, 135(7)：071003.
[2] ZHANG Dequan, HAN Xu, JIANG Chao, et al. Time-dependent reliability analysis through response surface method[J]. Journal of Mechanical Design, 2017, 139(4)：041404.
[3] 王丕东, 张建国, 阚琳洁, 等. 基于时变区间和穿阈模型的机械时变可靠性分析方法[J]. 机械工程学报, 2017, 53(11)：1-9. WANG Pidong, ZHANG Jianguo, KAN Linjie, et. al. Time variant reliability approach with time-variant interval and upcrossing model[J]. Journal of Mechanical Engineering, 2017, 53(11)：1-9.
[4] SUDRET B. Analytical derivation of the outcrossing rate in time-variant reliability problems[J]. Structure and Infrastructure Engineering, 2008, 4(5)：353-362.
[5] ANDRIEU-RENAUD C, SUDRET B, LEMAIRE M. The PHI2 method：a way to compute time-variant reliability[J]. Reliability Engineering & System Safety, 2004, 84(1)：75-86.
[6] 袁修开, 郑振轩, 罗冬秀. 加权随机模拟的时变可靠性分析方法[J]. 国防科技大学学报, 2021, 43(2)：125-131. YUAN Xiukai, ZHENG Zhenxuan, LUO Dongxiu. Weighted stochastic simulation for time-variant reliability analysis[J]. Journal of National University of Defense Technology, 2021, 43(2)：125-131
[7] LI Junxian, CHEN Jianqiao, WEI Junhong, et al. Developing an instantaneous response surface method t-IRS for time-dependent reliability analysis[J]. Acta Mechanica Solida Sinica, 2019, 32：446-462.
[8] HU Zhen, MAHADEVAN S. A single-loop kriging surrogate modeling for time-dependent reliability analysis[J]. Journal of Mechanical Design, 2016, 138(6)：061406.
[9] 彭磊, 刘莉, 龙腾. 基于动态径向基函数代理模型的优化策略[J]. 机械工程学报, 2011, 47(7)：164-170. PENG Lei, LIU Li, LONG Teng. Optimization strategy using dynamic radial basis function metamodel[J]. Journal of Mechanical Engineering, 2011, 47(7)：164-170.
[10] 陈霞, 李磊, 岳珠峰, 等. Kriging代理模型下基于垂距的多点取样算法[J]. 机械工程学报, 2015, 51(9)：153-158. CHEN Xia, LI Lei, YUE Zhufeng, et. al. Sampling method with multi-point sampling algorithm based on vertical distance in kriging model[J]. Journal of Mechanical Engineering, 2015, 51(9)：153-158.
[11] HU Weifei, YAN Jiquan, ZHAO Feng, et al. Surrogate-based time-dependent reliability analysis for a digital twin[J]. Journal of Mechanical Design, 2023, 145(9)：091708.
[12] SUN Zhili, WANG Jian, LI Rui, et al. LIF：A new Kriging based learning function and its application to structural reliability analysis[J]. Reliability Engineering & System Safety, 2017, 157：152-165.
[13] RAISSI M, PERDIKARIS P, KARNIADAKIS G E. Physics-informed neural networks：A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations[J]. Journal of Computational Physics, 2019, 378：686-707.
[14] LI Jing, XIU Dongbin. Evaluation of failure probability via surrogate models[J]. Journal of Computational Physics, 2010, 229(23)：8966-8980.
[15] NABIAN M A, GLADSTONE R J, MEIDANI H. Efficient training of physics‐informed neural networks via importance sampling [J]. Computer‐Aided Civil Infrastructure Engineering, 2021, 36(8)：962-77.
[16] WU Chenxi, ZHU Min, TAN Qinyang, et al. A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks[J]. Computer Methods in Applied Mechanics and Engineering, 2023, 403：115671.
[17] NABIAN M A, GLADSTONE R J, MEIDANI H. Efficient training of physics‐informed neural networks via importance sampling[J]. Computer‐Aided Civil and Infrastructure Engineering, 2021, 36(8)：962-977.
[18] CAI Shengze, MAO Zhiping, WANG Zhicheng, et al. Physics-informed neural networks (PINNs) for fluid mechanics：A review[J]. Acta Mechanica Sinica, 2021, 37(12)：1727-1738.
[19] CUOMO S, DI COLA V S, GIAMPAOLO F, et al. Scientific machine learning through physics–informed neural networks：Where we are and what’s next[J]. Journal of Scientific Computing,2022, 92(3)：88.
[20] ZHANG Chi, SHAFIEEZADEH A. Simulation-free reliability analysis with active learning and physics-informed neural network[J]. Reliability Engineering & System Safety, 2022, 226：108716.
[21] LI Chun-Ching, DER KIUREGHIAN A. Optimal discretization of random fields[J]. Journal of Engineering Mechanics, 1993, 119(6)：1136-1154.
[22] ZWICKER D. py-pde：A python package for solving partial differential equations[J]. Journal of Open Source Software, 2020, 5(48)：2158.
[23] XIU Dongbin, KARNIADAKIS G E. Supersensitivity due to uncertain boundary conditions[J]. International Journal for Numerical Methods in Engineering, 2004, 61(12)：2114-2138.
[24] CHIKAZAWA Y, KOSHIZUKA S, OKA Y. A particle method for elastic and visco-plastic structures and fluid-structure interactions[J]. Computational Mechanics, 2001, 27(2)：97-106.

基于物理信息神经网络的时变可靠性分析方法

Time-dependent Reliability Analysis Based on Physics-Informed Neutral Network

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