A physics-informed neural network enhanced importance sampling (PINN-IS) for data-free reliability analysis无数据可靠性分析的物理信息神经网络增强重要性抽样
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Roy A, Chatterjee T, Adhikari S, 2024. A physics-informed neural network enhanced importance sampling (PINN-IS) for data-free reliability analysis. Probabilistic Engineering Mechanics, 78: 103701.DOI: 10.1016/j.probengmech.2024.103701
高敏感性结构的可靠性分析对防止灾难性失效和确保安全至关重要。因此，这些关键安全系统的设计应针对极罕遇失效事件。对这些极小发生概率事件进行精确统计量化需对极限状态函数 (limit state function, LSF) 进行数百万次评估，这需要进行计算量巨大的数值模拟。方差缩减技术 (如重要性抽样 (importance sampling, IS)) 可将此类重复次数减少至几千次。使用以数据为中心的元模型可进一步将其减少到几百次。在以数据为中心的元建模方法中，实际只在几个点处进行复杂数值分析，以训练元模型近似结构响应。另一方面，物理信息神经网络 (physics-informed neural network, PINN) 可根据描述问题物理性质的控制微分方程预测结构响应，而无需对复杂数值求解格式进行单次评估，即无数据。然而，现有可靠性分析的物理信息神经网络模型仅在估计较大范围失效概率 (1e-1~1e-3) 时才有效。为解决此问题，本研究提出了一类基于物理信息神经网络的小失效概率 (< 1e-5) 无数据可靠性分析。为此，提出了一类两阶段的重要性抽样物理信息神经网络 (PINN integrated with IS, PINN-IS)。第一阶段用于适当近似设计点 (most probable failure point, MPP)，而第二阶段用于提高以近似设计点为中心的重要性抽样群的极限状态函数预测精度。通过三个结构可靠性分析算例数值说明了所提方法的有效性。关键词: 结构可靠性, 物理信息神经网络, 无数据, 小失效概率, 重要性抽样Reliability analysis of highly sensitive structures is crucial to prevent catastrophic failures and ensure safety. Therefore, these safety-critical systems are to be designed for extremely rare failure events. Accurate statistical quantification of these events associated with a very low probability of occurrence requires millions of evaluations of the limit state function (LSF) involving computationally expensive numerical simulations. Variance reduction techniques like importance sampling (IS) reduce such repetitions to a few thousand. The use of a data-centric metamodel can further cut it down to a few hundred. In data-centric metamodeling approaches, the actual complex numerical analysis is performed at a few points to train the metamodel for approximating the structural response. On the other hand, a physics-informed neural network (PINN) can predict the structural response based on the governing differential equation describing the physics of the problem, without a single evaluation of the complex numerical solver, i.e., data-free. However, the existing PINN models for reliability analysis have been effective only in estimating a large range of failure probabilities (10−1∼10−3). To address this issue, the present study develops a PINN-based data-free reliability analysis for low failure probabilities (<10−5). In doing so, a two-stage PINN integrated with IS (PINN-IS) is proposed. The first stage is employed to approximate the most probable failure point (MPP) appropriately while the second stage enhances the accuracy of LSF predictions at the IS population centred on the approximated MPP. The effectiveness of the proposed approach is numerically illustrated by three structural reliability analysis examples.Keywords: Structural reliability; Physics-informed neural network; Data-free; Low failure probability; Importance sampling.Fig. 1. A straight bar subjected to an axial load
图 2: 不同可靠性分析方法重复获得结果的统计观测总结: (a) 最大容许位移 4.4e-3 m; (b) 最大容许位移 4.5e-3 m; (c) 最大容许位移 4.6e-3 mFig. 2. Summary of statistical observation on results obtained from repetitions of different reliability analysis approaches: (a) u_max = 4.4e-3 m; (b) u_max = 4.5e-3 m; (c) u_max = 4.6e-3 m
图 3: 直杆高维情形重复不同可靠性分析方法获得结果的统计观测总结Fig. 3. Summary of statistical observation on results obtained from repetitions of different reliability analysis approaches for the high-dimension case of the straight bar
Fig. 4. A cantilever beam under a uniform distributed load
图 5: 不同可靠性分析方法重复获得结果的统计观测总结: (a) 最大容许位移 3.9e-3 m; (b) 最大容许位移 4.0e-3 m; (c) 最大容许位移 4.2e-3 mFig. 5. Summary of statistical observation on results obtained from repetitions of different reliability analysis approaches: (a) u_max = 3.9e-3 m; (b) u_max = 4.0e-3 m; (c) u_max = 4.2e-3 m
Fig. 6. A thin square plate with a non-uniform loading
图 7: 不同可靠性分析方法重复获得结果的统计观测总结: (a) 最大容许位移 0.2 m; (b) 最大容许位移 0.21 m; (c) 最大容许位移 0.22 mFig. 7. Summary of statistical observation on results obtained from repetitions of different reliability analysis approaches: (a) u_max = 0.2 m; (b) u_max = 0.21 m; (c) u_max = 0.22 m
作者信息 | Authors
Atin Roy, 通讯作者 (Corresp.)英国格拉斯哥大学 (University of Glasgow) 瓦特工学院Email: atin.roy@glasgow.ac.uk
英国萨里大学 (University of Surrey) 机械工程科学学院
英国格拉斯哥大学 (University of Glasgow) 瓦特工学院
律梦泽 M.Z. Lyu | 编辑 (Ed)
P.D. Spanos | 审校 (Rev)
陈建兵 J.B. Chen | 审校 (Rev)
彭勇波 Y.B. Peng | 审校 (Rev)
