Pub Date : 2025-07-01Epub Date: 2025-06-17DOI: 10.1016/j.probengmech.2025.103797
Salih Tatar , Mohamed BenSalah
In this paper, we address the simultaneous identification of the strain hardening exponent, the shear modulus, and the yield stress through an inverse problem formulation. We begin by analyzing both the direct and inverse problems, and subsequently reformulate the inverse problem within a Bayesian framework. The direct problem is solved using an iterative approach, followed by the development of a numerical method based on Bayesian inference to address the inverse problem. Numerical examples with noisy data are presented to demonstrate the applicability and the accuracy of the proposed method.
{"title":"Simultaneous identification of the parameters in the plasticity function for power hardening materials: A Bayesian approach","authors":"Salih Tatar , Mohamed BenSalah","doi":"10.1016/j.probengmech.2025.103797","DOIUrl":"10.1016/j.probengmech.2025.103797","url":null,"abstract":"<div><div>In this paper, we address the simultaneous identification of the strain hardening exponent, the shear modulus, and the yield stress through an inverse problem formulation. We begin by analyzing both the direct and inverse problems, and subsequently reformulate the inverse problem within a Bayesian framework. The direct problem is solved using an iterative approach, followed by the development of a numerical method based on Bayesian inference to address the inverse problem. Numerical examples with noisy data are presented to demonstrate the applicability and the accuracy of the proposed method.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103797"},"PeriodicalIF":3.0,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144313686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-07-01Epub Date: 2025-05-31DOI: 10.1016/j.probengmech.2025.103771
Cristóbal H. Acevedo , Xuan-Yi Zhang , Marcos A. Valdebenito , Matthias G.R. Faes
Estimating failure probabilities is a critical challenge in practice, due to high-dimensional parameter spaces and small failure probability levels. Existing sample-based methods are dimensionally robust but face efficiency challenges when estimating small failure probabilities. Approximate methods provide a balance between accuracy and computational efficiency; however, their performance is often sensitive to the dimensionality of the parameter spaces. Among existing approximate methods, Method of Moments (MoM) estimates failure probabilities by utilizing the higher-order moments of the performance function. While it provides analytical efficiency, it faces challenges in high-dimensional problems due to the difficulties in efficient moment estimation. Control Variates (CV), a variance reduction technique based on sampling, enhances moment estimation with efficiency independent of dimensionality by leveraging numerical models of different fidelities. However, it is rarely applied to the estimation of higher-order moments. This paper introduces an approach for reliability analysis that combines MoM with CV, proposing estimators for the third and fourth raw moments of the performance function based on CV. The approach achieves significant computational savings in small failure probability problems and demonstrates strong potential for high-dimensional applications. The effectiveness of the proposed approach is validated through three numerical examples, including non-Gaussian problems, computationally intensive finite element models, and nonlinear dynamic systems. The results highlight its accuracy and efficiency.
{"title":"Reliability analysis combining method of moments with control variates","authors":"Cristóbal H. Acevedo , Xuan-Yi Zhang , Marcos A. Valdebenito , Matthias G.R. Faes","doi":"10.1016/j.probengmech.2025.103771","DOIUrl":"10.1016/j.probengmech.2025.103771","url":null,"abstract":"<div><div>Estimating failure probabilities is a critical challenge in practice, due to high-dimensional parameter spaces and small failure probability levels. Existing sample-based methods are dimensionally robust but face efficiency challenges when estimating small failure probabilities. Approximate methods provide a balance between accuracy and computational efficiency; however, their performance is often sensitive to the dimensionality of the parameter spaces. Among existing approximate methods, Method of Moments (MoM) estimates failure probabilities by utilizing the higher-order moments of the performance function. While it provides analytical efficiency, it faces challenges in high-dimensional problems due to the difficulties in efficient moment estimation. Control Variates (CV), a variance reduction technique based on sampling, enhances moment estimation with efficiency independent of dimensionality by leveraging numerical models of different fidelities. However, it is rarely applied to the estimation of higher-order moments. This paper introduces an approach for reliability analysis that combines MoM with CV, proposing estimators for the third and fourth raw moments of the performance function based on CV. The approach achieves significant computational savings in small failure probability problems and demonstrates strong potential for high-dimensional applications. The effectiveness of the proposed approach is validated through three numerical examples, including non-Gaussian problems, computationally intensive finite element models, and nonlinear dynamic systems. The results highlight its accuracy and efficiency.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103771"},"PeriodicalIF":3.0,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144231762","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-07-01Epub Date: 2025-06-06DOI: 10.1016/j.probengmech.2025.103790
Yukuai Wan , Yuqi Zhou , Linlan Shao , Yuke Wang
Three-dimensional convex turning corner slopes are frequently encountered in complex geological environments. Their distinctive geometry and spatial effects present greater challenges for stability analysis compared to traditional slopes. Conventional two-dimensional analytical methods often fall short in accurately capturing the failure mechanisms and stability characteristics of such slopes. In this study, a three-dimensional reliability analysis approach is employed. Random fields of soil parameters are generated using the Karhunen–Loève expansion method, and the most critical slip surface is identified via the Bishop method in conjunction with the particle swarm optimization (PSO) algorithm. Monte Carlo (MC) simulation is utilized to evaluate the probability of slope failure. The effects of factors such as convex turning corner angle, variation coefficients of soil parameters, autocorrelation distances, and correlation coefficients on failure probability and safety factors are systematically analyzed. The results demonstrate that the PSO algorithm significantly enhances the computational efficiency of three-dimensional slope reliability analysis while maintaining high accuracy. The influence of convex corner angle on slope stability exhibits distinct patterns for steep and gentle slopes. For steep slopes, the failure probability initially decreases and then increases with increasing corner angle, whereas for gentle slopes, it rises monotonically. Additionally, the spatial variability of soil parameters is shown to have a substantial impact on the stability and reliability of corner slopes.
{"title":"Three-dimensional reliability analysis of convex turning corner slopes considering spatial variability of soil parameters","authors":"Yukuai Wan , Yuqi Zhou , Linlan Shao , Yuke Wang","doi":"10.1016/j.probengmech.2025.103790","DOIUrl":"10.1016/j.probengmech.2025.103790","url":null,"abstract":"<div><div>Three-dimensional convex turning corner slopes are frequently encountered in complex geological environments. Their distinctive geometry and spatial effects present greater challenges for stability analysis compared to traditional slopes. Conventional two-dimensional analytical methods often fall short in accurately capturing the failure mechanisms and stability characteristics of such slopes. In this study, a three-dimensional reliability analysis approach is employed. Random fields of soil parameters are generated using the Karhunen–Loève expansion method, and the most critical slip surface is identified via the Bishop method in conjunction with the particle swarm optimization (PSO) algorithm. Monte Carlo (MC) simulation is utilized to evaluate the probability of slope failure. The effects of factors such as convex turning corner angle, variation coefficients of soil parameters, autocorrelation distances, and correlation coefficients on failure probability and safety factors are systematically analyzed. The results demonstrate that the PSO algorithm significantly enhances the computational efficiency of three-dimensional slope reliability analysis while maintaining high accuracy. The influence of convex corner angle on slope stability exhibits distinct patterns for steep and gentle slopes. For steep slopes, the failure probability initially decreases and then increases with increasing corner angle, whereas for gentle slopes, it rises monotonically. Additionally, the spatial variability of soil parameters is shown to have a substantial impact on the stability and reliability of corner slopes.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103790"},"PeriodicalIF":3.0,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144270916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-07-01Epub Date: 2025-08-08DOI: 10.1016/j.probengmech.2025.103824
Maral Ghaedi, Jian Deng
The moment Lyapunov exponent (MLE) is a critical index for assessing the stochastic stability of structures and has been widely applied to linear systems. However, its application to strongly nonlinear systems remains limited due to the inadequacy of traditional methods, such as the method of stochastic averaging. This paper addresses this gap by analyzing the stochastic stability of strongly nonlinear structural systems subjected to parametric excitations modeled as white noise, using MLEs. The analysis begins with the formulation of a strongly nonlinear system. A stochastic averaging method based on a transformed energy envelope is developed to derive a system of Itô stochastic differential equations. Unlike conventional approaches that rely on the Euclidean norm of the state vector, a modified Khasminskii-type transformation is employed, using the square root of the system's Hamiltonian to study stability. To validate the analytical findings, Monte Carlo simulations are conducted to independently compute the MLE. Additionally, the largest Lyapunov exponents and a stability index are evaluated to further characterize the system's stochastic behavior. The effects of key parameters on stability are systematically investigated. This study offers novel insights into the stochastic dynamics of strongly nonlinear structural systems.
{"title":"Moment Lyapunov exponents and stochastic stability of non-linear systems under white-noise excitation","authors":"Maral Ghaedi, Jian Deng","doi":"10.1016/j.probengmech.2025.103824","DOIUrl":"10.1016/j.probengmech.2025.103824","url":null,"abstract":"<div><div>The moment Lyapunov exponent (MLE) is a critical index for assessing the stochastic stability of structures and has been widely applied to linear systems. However, its application to strongly nonlinear systems remains limited due to the inadequacy of traditional methods, such as the method of stochastic averaging. This paper addresses this gap by analyzing the stochastic stability of strongly nonlinear structural systems subjected to parametric excitations modeled as white noise, using MLEs. The analysis begins with the formulation of a strongly nonlinear system. A stochastic averaging method based on a transformed energy envelope is developed to derive a system of Itô stochastic differential equations. Unlike conventional approaches that rely on the Euclidean norm of the state vector, a modified Khasminskii-type transformation is employed, using the square root of the system's Hamiltonian to study stability. To validate the analytical findings, Monte Carlo simulations are conducted to independently compute the MLE. Additionally, the largest Lyapunov exponents and a stability index are evaluated to further characterize the system's stochastic behavior. The effects of key parameters on stability are systematically investigated. This study offers novel insights into the stochastic dynamics of strongly nonlinear structural systems.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103824"},"PeriodicalIF":3.5,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144813864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-07-01Epub Date: 2025-07-20DOI: 10.1016/j.probengmech.2025.103807
Navaneeth N. , Tushar , Souvik Chakraborty
Quantifying the reliability of complex engineering systems under uncertainty is a computationally demanding task, particularly when the system response depends on a large number of stochastic parameters. Traditional reliability analysis techniques, anchored in repeated high-fidelity simulations or experimental evaluations, become prohibitively expensive in high-dimensional settings, especially for systems governed by partial differential equations (PDEs) that require discretization-based solvers such as the finite element or finite volume methods. Surrogate modeling offers a viable alternative by approximating the input–output mapping of such systems with reduced computational overhead. Among these, neural operators have recently gained attention for their ability to learn solution operators of PDEs from limited data. In this work, we investigate the utility of the physics-informed wavelet neural operator (PI-WNO) for high-dimensional reliability analysis. We demonstrate that PI-WNO can accurately learn the stochastic input-to-solution map without resorting to repeated numerical simulations, thereby enabling efficient and scalable reliability estimation. Through benchmark problems, we illustrate the effectiveness of the proposed framework in handling high-dimensional uncertainty while preserving accuracy. Furthermore, we extend this approach to systems governed by coupled PDEs, highlighting the broad applicability and potential of physics-informed neural operators for reliability analysis in complex physical systems.
{"title":"Harnessing physics-informed operators for high-dimensional reliability analysis problems","authors":"Navaneeth N. , Tushar , Souvik Chakraborty","doi":"10.1016/j.probengmech.2025.103807","DOIUrl":"10.1016/j.probengmech.2025.103807","url":null,"abstract":"<div><div>Quantifying the reliability of complex engineering systems under uncertainty is a computationally demanding task, particularly when the system response depends on a large number of stochastic parameters. Traditional reliability analysis techniques, anchored in repeated high-fidelity simulations or experimental evaluations, become prohibitively expensive in high-dimensional settings, especially for systems governed by partial differential equations (PDEs) that require discretization-based solvers such as the finite element or finite volume methods. Surrogate modeling offers a viable alternative by approximating the input–output mapping of such systems with reduced computational overhead. Among these, neural operators have recently gained attention for their ability to learn solution operators of PDEs from limited data. In this work, we investigate the utility of the physics-informed wavelet neural operator (PI-WNO) for high-dimensional reliability analysis. We demonstrate that PI-WNO can accurately learn the stochastic input-to-solution map without resorting to repeated numerical simulations, thereby enabling efficient and scalable reliability estimation. Through benchmark problems, we illustrate the effectiveness of the proposed framework in handling high-dimensional uncertainty while preserving accuracy. Furthermore, we extend this approach to systems governed by coupled PDEs, highlighting the broad applicability and potential of physics-informed neural operators for reliability analysis in complex physical systems.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103807"},"PeriodicalIF":3.0,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144702606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-07-01Epub Date: 2025-06-07DOI: 10.1016/j.probengmech.2025.103788
Kaiyong Zhao, Hao Wang, Zidong Xu, Yuxuan Lin
The energy reckoning-based method (ERM) offers a physically interpretable approach to estimating the evolutionary power spectrum (EPS) of nonstationary stochastic processes. However, estimation errors may arise from pronounced oscillations exist in the numerically computed system energy. Additionally, the method's efficiency in estimating the ensemble-averaged EPS of numerous samples requires enhancement. This study proposes an interpolation enhanced ERM for estimating the EPS of multi-variate nonstationary processes. The time-varying energy calculated in the ERM is reconstructed and smoothed via piecewise temporal interpolation. Frequency-domain interpolation is simultaneously utilized to reduce the number of the dynamic equations solved in ERM, thereby accelerating the estimating procedure. Numerical examples demonstrate the piecewise interpolation effectively smooths the estimated EPS and produces more reliable results. Comparative analyses reveal the IERM's superior accuracy and computational efficiency relative to the other classical methods. The method's feasibility is eventually validated through the EPS estimation of measured typhoon data.
{"title":"Evolutionary power spectrum estimation of multi-variate nonstationary stochastic processes based on interpolation enhanced energy reckoning-based method","authors":"Kaiyong Zhao, Hao Wang, Zidong Xu, Yuxuan Lin","doi":"10.1016/j.probengmech.2025.103788","DOIUrl":"10.1016/j.probengmech.2025.103788","url":null,"abstract":"<div><div>The energy reckoning-based method (ERM) offers a physically interpretable approach to estimating the evolutionary power spectrum (EPS) of nonstationary stochastic processes. However, estimation errors may arise from pronounced oscillations exist in the numerically computed system energy. Additionally, the method's efficiency in estimating the ensemble-averaged EPS of numerous samples requires enhancement. This study proposes an interpolation enhanced ERM for estimating the EPS of multi-variate nonstationary processes. The time-varying energy calculated in the ERM is reconstructed and smoothed via piecewise temporal interpolation. Frequency-domain interpolation is simultaneously utilized to reduce the number of the dynamic equations solved in ERM, thereby accelerating the estimating procedure. Numerical examples demonstrate the piecewise interpolation effectively smooths the estimated EPS and produces more reliable results. Comparative analyses reveal the IERM's superior accuracy and computational efficiency relative to the other classical methods. The method's feasibility is eventually validated through the EPS estimation of measured typhoon data.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103788"},"PeriodicalIF":3.0,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144254320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-07-01Epub Date: 2025-08-05DOI: 10.1016/j.probengmech.2025.103810
Darwish Alzeort , Anas Batou , Rubens Sampaio , Thiago G. Ritto
This paper is concerned with the identification of the hyperparameters of probabilistic computational models using experimental data collected on a family of structures nominally identical but exhibiting some variability in its parameters (mechanical properties, geometry, …) resulting in random fluctuations in the observed responses. Such a problem generally yields a challenging multivariate probabilistic inverse problems to be solved in high dimensions. High dimensionality requires the use of a global optimisation algorithm to efficiently explore the input parameter space. In this paper, we propose an alternative algorithm that allows each random variable of the stochastic model to be identified separately and sequentially by solving a set of low-dimension probabilistic inverse problems. For each parameter, a devoted stochastic inverse problem is introduced by identifying a random output, which is sensitive to this parameter only, the sensitivity being quantified using Sobol indices. The proposed method is illustrated through two numerical examples: the first one concerns the frequency analysis of a clamped beam, and the second one is related to the vibration of a bridge.
{"title":"A sensitivity-based separation approach for the experimental calibration of probabilistic computational models","authors":"Darwish Alzeort , Anas Batou , Rubens Sampaio , Thiago G. Ritto","doi":"10.1016/j.probengmech.2025.103810","DOIUrl":"10.1016/j.probengmech.2025.103810","url":null,"abstract":"<div><div>This paper is concerned with the identification of the hyperparameters of probabilistic computational models using experimental data collected on a family of structures nominally identical but exhibiting some variability in its parameters (mechanical properties, geometry, …) resulting in random fluctuations in the observed responses. Such a problem generally yields a challenging multivariate probabilistic inverse problems to be solved in high dimensions. High dimensionality requires the use of a global optimisation algorithm to efficiently explore the input parameter space. In this paper, we propose an alternative algorithm that allows each random variable of the stochastic model to be identified separately and sequentially by solving a set of low-dimension probabilistic inverse problems. For each parameter, a devoted stochastic inverse problem is introduced by identifying a random output, which is sensitive to this parameter only, the sensitivity being quantified using Sobol indices. The proposed method is illustrated through two numerical examples: the first one concerns the frequency analysis of a clamped beam, and the second one is related to the vibration of a bridge.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103810"},"PeriodicalIF":3.5,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144781325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-07-01Epub Date: 2025-07-02DOI: 10.1016/j.probengmech.2025.103805
K. Wen , W. Zeng , S.Y. Zeng
Various system reliability analysis methods based on surrogate models have recently been developed for problems reliant on costly performance function (PF) evaluation. Existing surrogate-based methods approximate the system performance function (SPF) using the max/min of component performance functions (CPFs), which may introduce errors in failure probability estimation. Through SPF analysis across diverse scenarios, we demonstrate that substituting a certain CPF for SPF may introduce significant errors. Furthermore, SPF distributions exhibit non-Gaussian characteristics in specific contexts. According to these cases, we propose the AGP-SYS method. This approach employs Gaussian process modeling to predict CPFs, then rigorously derives the mean and variance of SPF using all CPF predictions—thereby avoiding errors induced by maximum/minimum approximations. Given that the SPF distribution is non-Gaussian, the probability of misclassification (PMC) is used as the learning function instead of the conventional U-function, whose physical significance is strictly confined to Gaussian-distributed SPF. Furthermore, an adaptive shrinking distance criterion preventing training-point clustering is introduced for enhancing model-updating efficiency. The effectiveness of AGP-SYS is demonstrated through three case studies: a series system, a parallel system, and a column-based independent foundation in civil engineering.
基于代理模型的各种系统可靠性分析方法最近被开发出来用于依赖于昂贵性能函数（PF）评估的问题。现有的基于代理的方法使用部件性能函数（cpf）的最大/最小值来近似系统性能函数（SPF），这可能会在故障概率估计中引入错误。通过不同场景下的SPF分析，我们证明用特定的CPF代替SPF可能会引入显著的误差。此外，SPF分布在特定环境中表现出非高斯特征。针对这些情况，我们提出了AGP-SYS方法。该方法采用高斯过程建模来预测CPF，然后使用所有CPF预测严格推导SPF的均值和方差，从而避免了由最大/最小近似引起的误差。考虑到SPF的非高斯分布，采用误分类概率（probability of misclassification， PMC）代替传统的u函数作为学习函数，其物理意义严格局限于高斯分布的SPF。此外，为了提高模型更新效率，引入了防止训练点聚类的自适应距离缩小准则。通过串联系统、并联系统和柱式独立基础在土木工程中的应用，验证了AGP-SYS的有效性。
{"title":"AGP-SYS: An adaptive learning and Gaussian process modeling-based system reliability method","authors":"K. Wen , W. Zeng , S.Y. Zeng","doi":"10.1016/j.probengmech.2025.103805","DOIUrl":"10.1016/j.probengmech.2025.103805","url":null,"abstract":"<div><div>Various system reliability analysis methods based on surrogate models have recently been developed for problems reliant on costly performance function (PF) evaluation. Existing surrogate-based methods approximate the system performance function (SPF) using the max/min of component performance functions (CPFs), which may introduce errors in failure probability estimation. Through SPF analysis across diverse scenarios, we demonstrate that substituting a certain CPF for SPF may introduce significant errors. Furthermore, SPF distributions exhibit non-Gaussian characteristics in specific contexts. According to these cases, we propose the AGP-SYS method. This approach employs Gaussian process modeling to predict CPFs, then rigorously derives the mean and variance of SPF using all CPF predictions—thereby avoiding errors induced by maximum/minimum approximations. Given that the SPF distribution is non-Gaussian, the probability of misclassification (PMC) is used as the learning function instead of the conventional U-function, whose physical significance is strictly confined to Gaussian-distributed SPF. Furthermore, an adaptive shrinking distance criterion preventing training-point clustering is introduced for enhancing model-updating efficiency. The effectiveness of AGP-SYS is demonstrated through three case studies: a series system, a parallel system, and a column-based independent foundation in civil engineering.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103805"},"PeriodicalIF":3.0,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144579300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-07-01Epub Date: 2025-07-19DOI: 10.1016/j.probengmech.2025.103812
Nan Ye , Zhenzhou Lu
In the surrogate model-based time-dependent reliability analysis, the discretization of stochastic process may lead to a great increase of input dimensionality, which poses challenges to the construction and training of surrogate model. To address this issue, a novel Double-Layer Kriging model-based Reliability Analysis Framework (nDLK-RAF) is proposed for time-dependent structural system with stochastic process in this paper. The random vector and stochastic process are treated separately in nDLK-RAF. Specifically, the Kriging model of time-dependent performance function under given random vector realization is established in the inner layer of nDLK-RAF, thus the conditional time-dependent failure probability (TDFP) corresponding to given random vector realization can be estimated by the inner convergent Kriging model. On this basis, the relationship between conditional TDFP and random vector is further surrogated by the Kriging model of outer-layer, and the final TDFP can be estimated by the outer convergent Kriging model. Further, aiming at the rare failure problem in engineering, this paper designs the variance reduction strategies of embedding directional sampling and importance sampling in the inner and outer layers, respectively, which improves the training efficiency of double-layer Kriging models in nDLK-RAF. Compared with the existing methods that simultaneously consider random vector and stochastic process, the nDLK-RAF reasonably balances the input dimensionalities of inner and outer Kriging models, which avoids the construction of high-dimensional surrogate models. Meanwhile, the two combined variance reduction sampling methods reduce the required candidate sample pool size for updating Kriging model, ultimately achieving efficient time-dependent reliability analysis. The superiority of nDLK-RAF over existing Kriging model-based methods is demonstrated by the example analysis.
{"title":"A novel double-layer kriging model-based reliability analysis framework for time-dependent structural system with stochastic process","authors":"Nan Ye , Zhenzhou Lu","doi":"10.1016/j.probengmech.2025.103812","DOIUrl":"10.1016/j.probengmech.2025.103812","url":null,"abstract":"<div><div>In the surrogate model-based time-dependent reliability analysis, the discretization of stochastic process may lead to a great increase of input dimensionality, which poses challenges to the construction and training of surrogate model. To address this issue, a novel Double-Layer Kriging model-based Reliability Analysis Framework (nDLK-RAF) is proposed for time-dependent structural system with stochastic process in this paper. The random vector and stochastic process are treated separately in nDLK-RAF. Specifically, the Kriging model of time-dependent performance function under given random vector realization is established in the inner layer of nDLK-RAF, thus the conditional time-dependent failure probability (TDFP) corresponding to given random vector realization can be estimated by the inner convergent Kriging model. On this basis, the relationship between conditional TDFP and random vector is further surrogated by the Kriging model of outer-layer, and the final TDFP can be estimated by the outer convergent Kriging model. Further, aiming at the rare failure problem in engineering, this paper designs the variance reduction strategies of embedding directional sampling and importance sampling in the inner and outer layers, respectively, which improves the training efficiency of double-layer Kriging models in nDLK-RAF. Compared with the existing methods that simultaneously consider random vector and stochastic process, the nDLK-RAF reasonably balances the input dimensionalities of inner and outer Kriging models, which avoids the construction of high-dimensional surrogate models. Meanwhile, the two combined variance reduction sampling methods reduce the required candidate sample pool size for updating Kriging model, ultimately achieving efficient time-dependent reliability analysis. The superiority of nDLK-RAF over existing Kriging model-based methods is demonstrated by the example analysis.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103812"},"PeriodicalIF":3.0,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144680404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-07-01Epub Date: 2025-06-06DOI: 10.1016/j.probengmech.2025.103796
Bin Wang , Helu Yu , Zewen Wang , Huiding Wang , Yongle Li
The random vibration analysis of beams subjected to train loads is an interesting research subject in the field of civil engineering. Two critical problems in this subject deserving further study are how to reasonably model the random wheel-rail forces and efficiently evaluate the response statistics of beams. This paper aims to contribute to addressing these two problems. First, an appropriate wheel-rail force model that can accurately represent the statistical characteristics of train loads is established, where the wheel-rail forces are modelled as a series of stationary stochastic processes with fixed time delays, and their inherent relation with the track irregularity is established based on the frequency-domain random vibration theory. Next, an approach combining the spectral decomposition and modal superposition techniques is proposed to derive a closed-form response expression for the Euler beams with general boundary conditions, which can be further used to accurately and efficiently evaluate the time-frequency response statistics of beams. In the numerical examples, the evolutionary spectral method and Monte Carlo simulation are used to demonstrate the performance of the proposed method, and the effects of several parameters of the wheel-rail force model on the stochastic responses of the beams are investigated.
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