Yuhua Yan

Northwestern Polytechnical University

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Zhenzhou Lü

Northwestern Polytechnical University

Yunlong Li

North China Electric Power University

Xiaojun Wang

Harbin Engineering University

Kaixuan Feng

Tongji University

Yixin Yang

Northwestern Polytechnical University

Zhenzhou Lü

Northwestern Polytechnical University

Lei Wang

Changsha University of Science and Technology

Yifei Li

Guangzhou Medical University

Zhuangbo Chen

Northwestern Polytechnical University

Linxi Zeng

Shanghai Power Equipment Research Institute

Cooperative Institutions

Northwestern Polytechnical University

Beihang University

Ningbo University of Technology

Changsha University of Science and Technology

Tongji University

Fudan University

Huashan Hospital

North China Electric Power University

Tianjin Chengjian University

Beijing Institute of Petrochemical Technology

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Adaptive Physics-Informed Neural Network Based Directional Sampling Method for Efficient Reliability Analysis

AIAA Journal (2025)

Yuhua Yan Zhenzhou Lü

To efficiently estimate the failure probability for structures with performance function governed by the partial differential equation, this paper proposed an adaptive physics-informed neural network based directional sampling (A-PINN-DS) method. The proposed A-PINN-DS possesses both the low dependence on labeled data from PINN and the high failure domain exploring efficiency from DS. In the proposed method, DS is firstly employed to generate the random input target collocation sample pool (TCSP) with high failure domain exploring efficiency. Then in TCSP, the neural network is trained by the partial differential physics information governing the performance function, and the neural network trained to be convergent in TCSP is used to predict the performance function response of TCSP, on which the failure probability can be estimated by DS. Because the proposed method only uses partial differential physics information instead of finite element simulation to train neural network in the TCSP for predicting performance function, it remarkably reduces the computational cost for estimating failure probability. To improve the efficiency of training PINN in TCSP, this paper designs a strategy of adaptively updating loss weights and a convergence distinguishing strategy for training PINN. Finally, the feasibility and superiority of the proposed method are verified by several examples.

Adaptive sampling

10.2514/1.j064926

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Adaptive stratified mixture importance sampling for efficiently estimating extremely small failure probability with high-dimensional inputs and multiple failure domains

Multidiscipline Modeling in Materials and Structures (2025)

Yuhua Yan Zhenzhou Lü

Purpose This study aims to efficiently estimate the extremely small failure probability with high-dimensional inputs and multiple failure domains. Design/methodology/approach This paper proposed an adaptive stratified mixture importance sampling method. The proposed method first constructs an explicit and regular mixture importance sampling probability density function (M-IS-PDF) by taking the clustering centroids as the density centers. Then by the constructed M-IS-PDF, the proposed method explores the rare multiple failure domains by adaptively stratifying, thereby addressing the issue of estimating extremely small failure probability robustly and efficiently. Findings Compared with the existing cross-entropy based IS method, the constructed M-IS-PDF not only covers the domains significantly contributing to the failure probability through clustering centroids to reduce the variance of failure probability estimation, but also has no undetermined parameter set to optimize, enhancing the adaptability in high-dimensional problems. Compared with the subset simulation method, the adaptive stratified M-IS-PDF constructed is explicit, regular and easy sampling. It not only has high sampling efficiency but also avoids estimating conditional failure probabilities layer by layer, improving the algorithmic robustness for estimating extremely small failure probability. Originality/value Both numerical and engineering examples indicate that, under the similar failure probability estimation accuracy, the proposed method requires significantly smaller sample size and lower computational cost than subset simulation and cross-entropy based IS methods, demonstrating higher efficiency and robustness in addressing intractable reliability analysis problems with high-dimensional inputs, multiple failure domains and rare failure.

Stratified Sampling

10.1108/mmms-01-2025-0015

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Structural reliability with credibility based on the non-probabilistic set-theoretic analysis

Aerospace Science and Technology (2022)

Yuhua Yan Xiaojun Wang Yunlong Li

Probabilistic method

10.1016/j.ast.2022.107730

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A new learning strategy for analyzing multi-mode system reliability by considering the correlation effect of multiple Kriging models

International Journal of Mechanics and Materials in Design (2023)

Yixin Yang Zhenzhou Lü Kaixuan Feng Yuhua Yan

Mode (computer interface)

10.1007/s10999-023-09671-8

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Novel Bayesian updating based interpolation method for estimating failure probability function in the presence of random-interval uncertainty

Probabilistic Engineering Mechanics (2024)

Yuhua Yan Zhenzhou Lü

Interpolation

Uncertainty Quantification

Interval estimation

10.1016/j.probengmech.2024.103694

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A novel and efficient stochastic collocation method for estimating failure probability function in one-dimensional reduced space

Computers & Structures (2024)

Zhuangbo Chen Zhenzhou Lü Kaixuan Feng Heng-Chao Li Yuhua Yan

Collocation (remote sensing)

Realization (probability)

10.1016/j.compstruc.2024.107365

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Non-probabilistic credible set model for structural uncertainty quantification

Structures (2023)

Yuhua Yan Xiaojun Wang Yunlong Li

Uncertainty Quantification

Sensitivity Analysis

Probabilistic method

10.1016/j.istruc.2023.05.011

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Single-Loop Sampling for Estimating Failure-Probability Upper-Bound Function

AIAA Journal (2024)

Yuhua Yan Zhenzhou Lü Kaixuan Feng Yixin Yang

Under random-interval mixed uncertainties of structures, failure-probability upper-bound function (FPUBF), which varies with the distribution parameters of random inputs, can not only provide the influence of distribution parameters on the failure-probability upper bound (FPUB), but also contribute to decoupling a reliability-based design optimization model. Although FPUBF can be estimated by repeatedly evaluating FPUBs at different distribution parameter realizations, it suffers from unaffordable computational cost resulting from this double-loop framework. To address this issue, this paper proposes a single-loop sampling strategy (SL) to estimate FPUBF at arbitrary realizations in the interested distribution parameter region. Instead of the huge computational cost of a double-loop framework, the SL estimates the entire FPUBF only by one simulation analysis. Moreover, importance sampling (IS) variance reduction technique is introduced, and a single-loop IS probability density function (PDF), or SL-IS-PDF, is constructed to more efficiently estimate FPUBF by reducing the required size of the candidate sample pool. For approximating the optimal SL-IS-PDF and identifying the states of candidate samples efficiently, the double-loop adaptive Kriging model of performance function is introduced to further reduce the number of performance function evaluations. A numerical example and two composite structure examples are employed to verify the accuracy, efficiency, and feasibility of the proposed methods.

Variance reduction

10.2514/1.j063472

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Importance measure analysis of design variables and uncertain parameters in multidisciplinary systems

Applied Mathematical Modelling (2022)

Yuhua Yan Xiaojun Wang Yifei Li Linxi Zeng Yunlong Li

Multidisciplinary design optimization

10.1016/j.apm.2022.01.029

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Citations (4)