This paper presents a unified framework for analyzing power systems subjected to both discrete and continuous random disturbances—a critical gap in existing literature that typically treats these disturbances separately. Unlike conventional approaches that focus on either continuous stochastic processes or discrete switching events in isolation, our novel methodology simultaneously captures both types of uncertainties within an integrated Markovian jump framework. The stochastic model of multi-machine power systems is formulated as a high-dimensional hybrid system and transformed into a quasi-Hamiltonian system with Markovian jump processes. A pioneering two-step approximation method is developed that first converts the hybrid system into a weighted-average model, then reduces it to a one-dimensional averaged Itô equation representing system energy dynamics. The approximate analytical solution of the corresponding Fokker-Planck-Kolmogorov (FPK) equation provides stationary response estimates for the original hybrid systems. A Lyapunov exponent approach is employed for asymptotic stability analysis with probability one. The methodology is validated through comprehensive analysis of Kundur's 4-machine 2-area system, demonstrating superior computational efficiency and analytical insights compared to traditional Monte Carlo simulations.
{"title":"Stochastic dynamics in power systems excited by discrete-continuous random disturbances","authors":"Rongchun Hu, Zheng Zeng, Sheng Zhou, Zhongliang Xie, Xudong Gu","doi":"10.1016/j.probengmech.2025.103858","DOIUrl":"10.1016/j.probengmech.2025.103858","url":null,"abstract":"<div><div>This paper presents a unified framework for analyzing power systems subjected to both discrete and continuous random disturbances—a critical gap in existing literature that typically treats these disturbances separately. Unlike conventional approaches that focus on either continuous stochastic processes or discrete switching events in isolation, our novel methodology simultaneously captures both types of uncertainties within an integrated Markovian jump framework. The stochastic model of multi-machine power systems is formulated as a high-dimensional hybrid system and transformed into a quasi-Hamiltonian system with Markovian jump processes. A pioneering two-step approximation method is developed that first converts the hybrid system into a weighted-average model, then reduces it to a one-dimensional averaged Itô equation representing system energy dynamics. The approximate analytical solution of the corresponding Fokker-Planck-Kolmogorov (FPK) equation provides stationary response estimates for the original hybrid systems. A Lyapunov exponent approach is employed for asymptotic stability analysis with probability one. The methodology is validated through comprehensive analysis of Kundur's 4-machine 2-area system, demonstrating superior computational efficiency and analytical insights compared to traditional Monte Carlo simulations.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103858"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416726","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 : 2025-10-01DOI: 10.1016/j.probengmech.2025.103869
Meng Wang , Xiangling Gao , Chao-Lie Ning
The probabilistic seismic hazard analysis (PSHA) is a widely used framework to assess seismic hazard of a given site. Despite its wide usage, there are some limitations, particularly in quantifying the epistemic uncertainty through the traditional methods, i.e., the logic tree method, the ensemble model and the Monte Carlo (MC) simulation. These methods cannot accurately or efficiently capture the probability density functions (PDFs) of earthquake intensity measures (IMs). To address this problem, a novel method was proposed in this study by introducing the probability density evolution method into the PSHA to quantify the epistemic uncertainty. Different from the traditional methods, the proposed method treats the epistemic uncertainty as basic random variables within a physical stochastic system. Then, the generalized F-Discrepancy method is adopted to select the representative samples from the complete probability space formed by the basic random variables. Each representative sample refers to an alternative model of the PSHA with an assigned probability, predicting earthquake IMs at a prescribed annual exceedance rate through the classical formula. Furthermore, the generalized density evolution equation (GDEE) is employed for all representative samples to compute the PDFs of earthquake IMs. To demonstrate the advantage of the proposed method, the PDF of peak ground acceleration (PGA) and elastic spectral acceleration at various vibration periods, i.e., Sa is computed for a hypothetical site in Shanghai, China. For comparison, the corresponding PGA and Sa predicted by the logic tree method, the ensemble model and the MC simulation are computed. The investigations indicated that the proposed method can estimate the PDF of earthquake IMs at each annual exceedance rate accurately and efficiently. The PDFs have multimodal distributions, which cannot be well captured by the logic tree method or the ensemble model. Despite the MC simulation being capable of describing multimodal distribution characteristics, the proposed method requires fewer alternative models, thus reducing the computational cost greatly. Therefore, quantifying the epistemic uncertainty of the PSHA by the PDEM facilitates the uncertainty quantification in regional seismic risk analysis.
{"title":"Quantification of epistemic uncertainty for probabilistic seismic hazard analysis based on probability density evolution method","authors":"Meng Wang , Xiangling Gao , Chao-Lie Ning","doi":"10.1016/j.probengmech.2025.103869","DOIUrl":"10.1016/j.probengmech.2025.103869","url":null,"abstract":"<div><div>The probabilistic seismic hazard analysis (PSHA) is a widely used framework to assess seismic hazard of a given site. Despite its wide usage, there are some limitations, particularly in quantifying the epistemic uncertainty through the traditional methods, i.e., the logic tree method, the ensemble model and the Monte Carlo (MC) simulation. These methods cannot accurately or efficiently capture the probability density functions (PDFs) of earthquake intensity measures (IMs). To address this problem, a novel method was proposed in this study by introducing the probability density evolution method into the PSHA to quantify the epistemic uncertainty. Different from the traditional methods, the proposed method treats the epistemic uncertainty as basic random variables within a physical stochastic system. Then, the generalized F-Discrepancy method is adopted to select the representative samples from the complete probability space formed by the basic random variables. Each representative sample refers to an alternative model of the PSHA with an assigned probability, predicting earthquake IMs at a prescribed annual exceedance rate through the classical formula. Furthermore, the generalized density evolution equation (GDEE) is employed for all representative samples to compute the PDFs of earthquake IMs. To demonstrate the advantage of the proposed method, the PDF of peak ground acceleration (PGA) and elastic spectral acceleration at various vibration periods, i.e., Sa is computed for a hypothetical site in Shanghai, China. For comparison, the corresponding PGA and Sa predicted by the logic tree method, the ensemble model and the MC simulation are computed. The investigations indicated that the proposed method can estimate the PDF of earthquake IMs at each annual exceedance rate accurately and efficiently. The PDFs have multimodal distributions, which cannot be well captured by the logic tree method or the ensemble model. Despite the MC simulation <strong>being</strong> capable of describing multimodal distribution characteristics, the proposed method requires fewer alternative models, thus reducing the computational cost greatly. Therefore, quantifying the epistemic uncertainty of the PSHA by the PDEM facilitates the uncertainty quantification in regional seismic risk analysis.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103869"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145617878","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}
Fatigue scatter models allow the computation of uncertainties and confidence intervals linked to fatigue failure prediction. This phenomenon can be linked to a microscopic crack growth mechanism that is not modeled in S–N curves fatigue assessment approaches. The main fatigue scatter models found in the literature only allow the linear dependence of the cyclic load amplitudes to be modeled. The first contribution of this article is the development of a fatigue model that allows the prediction of nonlinear scatter dependence on load amplitude. More precisely, the proposed dependence structure is based on a partially affine function with a threshold effect, such that there is no dependence for load amplitudes sufficiently high. The model is successfully tested on a large fatigue database. A cumulative damage model is then obtained by adding two assumptions extracted from the literature. It is based on representing fatigue damage as the decrease in a structure’s fatigue health. The constructed model presents nonlinear cumulative damage properties and is successfully tested on two amplitude fatigue tests extracted from the literature. The whole fatigue failure prediction framework is finally applied to a real structure subjected to variable amplitude loadings.
{"title":"Development of a probabilistic health model representing variable amplitude fatigue loading damage in austenitic stainless steel nuclear components","authors":"Théo Lecleve , Stéphan Courtin , Fabien Szmytka , Chu Mai","doi":"10.1016/j.probengmech.2025.103851","DOIUrl":"10.1016/j.probengmech.2025.103851","url":null,"abstract":"<div><div>Fatigue scatter models allow the computation of uncertainties and confidence intervals linked to fatigue failure prediction. This phenomenon can be linked to a microscopic crack growth mechanism that is not modeled in S–N curves fatigue assessment approaches. The main fatigue scatter models found in the literature only allow the linear dependence of the cyclic load amplitudes to be modeled. The first contribution of this article is the development of a fatigue model that allows the prediction of nonlinear scatter dependence on load amplitude. More precisely, the proposed dependence structure is based on a partially affine function with a threshold effect, such that there is no dependence for load amplitudes sufficiently high. The model is successfully tested on a large fatigue database. A cumulative damage model is then obtained by adding two assumptions extracted from the literature. It is based on representing fatigue damage as the decrease in a structure’s fatigue health. The constructed model presents nonlinear cumulative damage properties and is successfully tested on two amplitude fatigue tests extracted from the literature. The whole fatigue failure prediction framework is finally applied to a real structure subjected to variable amplitude loadings.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103851"},"PeriodicalIF":3.5,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145158438","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 : 2025-09-17DOI: 10.1016/j.probengmech.2025.103847
Yan Zhang , Zhengyang Zhang , Guanlan Xu , Yunsen Ren , Xiaoxiao Bai , You Qin , Kai Zhao , Guoxing Chen , Zhenglong Zhou , Jiawei Jiang
The reasonable determination of correlation distances serves as the prerequisite for ensuring the accuracy of random field simulation results for geotechnical parameters, and also constitutes a critical challenge in random field simulations that remains difficult to resolve. The Bootstrap method was employed to perform resampling on correlation distances. Utilizing the sampling results, a weighted prior probability density function for correlation distances was constructed. By applying Bayesian principles in conjunction with Hoffman's conditional random field simulation method, the decoupling and simultaneous updating of correlation distance determinations and geotechnical parameter estimations in random field simulations were achieved. Taking a seabed site as an example, this study simulated the spatial variability of marine soil SPT-N values and their influence on seabed liquefaction probability. The research revealed the impacts of correlation distances, constraints from measured borehole data, and heterogeneity of original site stratigraphy on random field simulation outcomes and seabed liquefaction probability. The validity of the proposed methodology was confirmed through verification against reserved measurement results at actual borehole locations.
{"title":"Improved conditional random field simulation method based on bootstrap- Bayesian inference and its application in identification of seafloor liquefaction","authors":"Yan Zhang , Zhengyang Zhang , Guanlan Xu , Yunsen Ren , Xiaoxiao Bai , You Qin , Kai Zhao , Guoxing Chen , Zhenglong Zhou , Jiawei Jiang","doi":"10.1016/j.probengmech.2025.103847","DOIUrl":"10.1016/j.probengmech.2025.103847","url":null,"abstract":"<div><div>The reasonable determination of correlation distances serves as the prerequisite for ensuring the accuracy of random field simulation results for geotechnical parameters, and also constitutes a critical challenge in random field simulations that remains difficult to resolve. The Bootstrap method was employed to perform resampling on correlation distances. Utilizing the sampling results, a weighted prior probability density function for correlation distances was constructed. By applying Bayesian principles in conjunction with Hoffman's conditional random field simulation method, the decoupling and simultaneous updating of correlation distance determinations and geotechnical parameter estimations in random field simulations were achieved. Taking a seabed site as an example, this study simulated the spatial variability of marine soil SPT-<em>N</em> values and their influence on seabed liquefaction probability. The research revealed the impacts of correlation distances, constraints from measured borehole data, and heterogeneity of original site stratigraphy on random field simulation outcomes and seabed liquefaction probability. The validity of the proposed methodology was confirmed through verification against reserved measurement results at actual borehole locations.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103847"},"PeriodicalIF":3.5,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097515","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 : 2025-09-17DOI: 10.1016/j.probengmech.2025.103850
Zhengwei Li , Wenping Gong , Zilong Zhang , Tianzheng Li
This study proposes a novel active learning-based method for reliability analysis, termed AK-EIG-ESC. The method integrates the adaptive Kriging metamodel with Monte Carlo simulation to estimate the probability of failure and, most importantly, introduces a novel active learning strategy to guide the selection of training samples. To achieve this, a random variable associated with the probability of failure is introduced and demonstrated to follow a Gaussian distribution according to the Central Limit Theorem. Building on this formulation, a new learning strategy is designed by quantifying the expected information gain from a hypothetical experiment. The information gain is expressed as the Kullback-Leibler divergence between the prior and posterior distributions of the introduced random variable associated with the probability of failure. Following this active learning strategy, a sequential sampling scheme is used to actively select new training samples, and the Kriging model is adaptively updated after each new sample is acquired. An error-based stopping criterion is adopted to evaluate the convergence of the proposed algorithm. Several illustrative examples are then used to assess the proposed AK-EIG-ESC algorithm, and the results show that the proposed algorithm exhibits high accuracy and efficiency for reliability analysis.
{"title":"An adaptive Kriging-based method for reliability analysis with a new learning strategy","authors":"Zhengwei Li , Wenping Gong , Zilong Zhang , Tianzheng Li","doi":"10.1016/j.probengmech.2025.103850","DOIUrl":"10.1016/j.probengmech.2025.103850","url":null,"abstract":"<div><div>This study proposes a novel active learning-based method for reliability analysis, termed AK-EIG-ESC. The method integrates the adaptive Kriging metamodel with Monte Carlo simulation to estimate the probability of failure and, most importantly, introduces a novel active learning strategy to guide the selection of training samples. To achieve this, a random variable associated with the probability of failure is introduced and demonstrated to follow a Gaussian distribution according to the Central Limit Theorem. Building on this formulation, a new learning strategy is designed by quantifying the expected information gain from a hypothetical experiment. The information gain is expressed as the Kullback-Leibler divergence between the prior and posterior distributions of the introduced random variable associated with the probability of failure. Following this active learning strategy, a sequential sampling scheme is used to actively select new training samples, and the Kriging model is adaptively updated after each new sample is acquired. An error-based stopping criterion is adopted to evaluate the convergence of the proposed algorithm. Several illustrative examples are then used to assess the proposed AK-EIG-ESC algorithm, and the results show that the proposed algorithm exhibits high accuracy and efficiency for reliability analysis.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103850"},"PeriodicalIF":3.5,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097513","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 : 2025-09-17DOI: 10.1016/j.probengmech.2025.103848
Wanying Yun , Fengyuan Li , Yue Pan , Hongfeng Zhang
Global reliability sensitivity analysis plays a critical role in identifying both important and unimportant variables affecting reliability, thus providing guidance for the simplification of reliability-based design optimization. Developing an efficient algorithm for estimating global reliability sensitivity indices is essential for the practical application of this theory in engineering contexts. This paper proposes an effective algorithm leveraging a metamodel-based importance sampling method combined with an adaptive Kriging model and a new single-loop estimation formula. Firstly, global reliability sensitivity analysis is equivalently transformed into an unconditional failure probability analysis and a two failure modes-based parallel failure probability analysis, utilizing the new single-loop estimation formula. Secondly, by sequentially constructing the importance sampling probability density functions for the variables within the global reliability sensitivity indices, both the unconditional failure probability and the two failure modes-based parallel failure probability can be efficiently estimated through the integrated metamodel-based importance sampling approach with the adaptive Kriging method. Finally, the efficiency and accuracy of the proposed method are methodically validated through analyzing a numerical analysis of a roof truss structure and a finite element model-based turbine shaft engineering structure.
{"title":"A sequential metamodel-based importance sampling coupled with adaptive Kriging model method for efficiently estimating the global reliability sensitivity indices","authors":"Wanying Yun , Fengyuan Li , Yue Pan , Hongfeng Zhang","doi":"10.1016/j.probengmech.2025.103848","DOIUrl":"10.1016/j.probengmech.2025.103848","url":null,"abstract":"<div><div>Global reliability sensitivity analysis plays a critical role in identifying both important and unimportant variables affecting reliability, thus providing guidance for the simplification of reliability-based design optimization. Developing an efficient algorithm for estimating global reliability sensitivity indices is essential for the practical application of this theory in engineering contexts. This paper proposes an effective algorithm leveraging a metamodel-based importance sampling method combined with an adaptive Kriging model and a new single-loop estimation formula. Firstly, global reliability sensitivity analysis is equivalently transformed into an unconditional failure probability analysis and a two failure modes-based parallel failure probability analysis, utilizing the new single-loop estimation formula. Secondly, by sequentially constructing the importance sampling probability density functions for the variables within the global reliability sensitivity indices, both the unconditional failure probability and the two failure modes-based parallel failure probability can be efficiently estimated through the integrated metamodel-based importance sampling approach with the adaptive Kriging method. Finally, the efficiency and accuracy of the proposed method are methodically validated through analyzing a numerical analysis of a roof truss structure and a finite element model-based turbine shaft engineering structure.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103848"},"PeriodicalIF":3.5,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145109617","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 : 2025-09-16DOI: 10.1016/j.probengmech.2025.103849
Wenxuan Han , Qinghua Zeng , Tingting Lu , Xinchen Zhuang , Tianxiang Yu
Time-dependent reliability analysis evaluates the probability that a structural system will perform its intended function throughout its service life. However, for large-scale complex structures, particularly those with implicit performance functions, the computational cost of numerical simulation methods in time-dependent reliability analysis can be substantial. Therefore, developing an effective surrogate model for time-dependent reliability analysis can significantly reduce computational demands. To assess time-dependent reliability accurately and efficiently, a method combining principal component analysis (PCA) with an adaptive ensemble of surrogate models is proposed. In this approach, the time interval is discretized, associating instantaneous performance functions with each time node. PCA is then applied to retain a reduced set of principal components (PCs) that capture nearly all the uncertainty in the outputs. Multiple Kriging models are subsequently built based on these PCs to maximize modeling accuracy in representing the relationships between each PC and the input variables. Finally, a hybrid weighting scheme is applied to each surrogate model, balancing global and local accuracy, to compute the time-dependent failure probability of the system via weighted integration. The proposed method is validated through engineering case studies.
{"title":"A time-dependent reliability analysis method based on principal component analysis and an ensemble of surrogate models","authors":"Wenxuan Han , Qinghua Zeng , Tingting Lu , Xinchen Zhuang , Tianxiang Yu","doi":"10.1016/j.probengmech.2025.103849","DOIUrl":"10.1016/j.probengmech.2025.103849","url":null,"abstract":"<div><div>Time-dependent reliability analysis evaluates the probability that a structural system will perform its intended function throughout its service life. However, for large-scale complex structures, particularly those with implicit performance functions, the computational cost of numerical simulation methods in time-dependent reliability analysis can be substantial. Therefore, developing an effective surrogate model for time-dependent reliability analysis can significantly reduce computational demands. To assess time-dependent reliability accurately and efficiently, a method combining principal component analysis (PCA) with an adaptive ensemble of surrogate models is proposed. In this approach, the time interval is discretized, associating instantaneous performance functions with each time node. PCA is then applied to retain a reduced set of principal components (PCs) that capture nearly all the uncertainty in the outputs. Multiple Kriging models are subsequently built based on these PCs to maximize modeling accuracy in representing the relationships between each PC and the input variables. Finally, a hybrid weighting scheme is applied to each surrogate model, balancing global and local accuracy, to compute the time-dependent failure probability of the system <em>via</em> weighted integration. The proposed method is validated through engineering case studies.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103849"},"PeriodicalIF":3.5,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097514","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 : 2025-09-11DOI: 10.1016/j.probengmech.2025.103842
Shuai Zhu , Jiaquan Xie , Wei Shi , Zhikuan Xie , Jialin Si , Jiani Ren
This paper focuses on the resonance and safety basin erosion of the fractional-order delayed asymmetric Duffing-Mathieu system. Its innovation compared with existing studies lies in: for the first time, integrating fractional calculus, time-delay effect and asymmetric stiffness characteristics into a coupled analysis framework, and introducing a memory characteristic correction term of fractional operators when deriving the amplitude-frequency relationship, which improves the accuracy of analytical modeling for non-integer order vibration systems. In the research, the improved averaging method is used to approximate the amplitude-frequency relationship and verify its accuracy, combined with the Jacobian matrix for stability analysis; the cell mapping method is adopted to capture the boundary of fractal attractive basins of coexisting attractors, and the potential function theory is used to quantify the erosion process of the safety basin, which is better than traditional methods in revealing the intrinsic mechanism. This system can simulate the dynamic response of asymmetric vibration structures containing viscoelastic materials under time-delay feedback control, and the research results can provide a theoretical basis for parameter design and safety early warning of related systems.
{"title":"Resonance and safety basin erosion of fractional order delay asymmetric Duffing-Mathieu system","authors":"Shuai Zhu , Jiaquan Xie , Wei Shi , Zhikuan Xie , Jialin Si , Jiani Ren","doi":"10.1016/j.probengmech.2025.103842","DOIUrl":"10.1016/j.probengmech.2025.103842","url":null,"abstract":"<div><div>This paper focuses on the resonance and safety basin erosion of the fractional-order delayed asymmetric Duffing-Mathieu system. Its innovation compared with existing studies lies in: for the first time, integrating fractional calculus, time-delay effect and asymmetric stiffness characteristics into a coupled analysis framework, and introducing a memory characteristic correction term of fractional operators when deriving the amplitude-frequency relationship, which improves the accuracy of analytical modeling for non-integer order vibration systems. In the research, the improved averaging method is used to approximate the amplitude-frequency relationship and verify its accuracy, combined with the Jacobian matrix for stability analysis; the cell mapping method is adopted to capture the boundary of fractal attractive basins of coexisting attractors, and the potential function theory is used to quantify the erosion process of the safety basin, which is better than traditional methods in revealing the intrinsic mechanism. This system can simulate the dynamic response of asymmetric vibration structures containing viscoelastic materials under time-delay feedback control, and the research results can provide a theoretical basis for parameter design and safety early warning of related systems.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103842"},"PeriodicalIF":3.5,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097512","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 : 2025-09-10DOI: 10.1016/j.probengmech.2025.103839
Haoyu Yao , Rui Pang , Bin Xu , Mingyang Xu , Jun Liu
With respect to evolutionary non-stationary processes, the underlying evolutionary power spectral density (EPSD) cannot be accurately calculated from the autocorrelation function (ACF). Efficient and accurate characterization of the non-Gaussianity and fully non-stationarity of ground motions is a difficult problem to be solved, and the stochastic response analysis of strongly nonlinear structures such as slopes under non-stationary non-Gaussian earthquakes does not provide clarity. In this paper, an efficient non-iterative approach for estimating the EPSD of the underlying Gaussian process built upon the unified Hermite polynomial Model (UHPM) is proposed. The proposed method eliminates the need for iterative procedures and avoids the need to solve integral equations, thereby improving computational efficiency, and the accuracy is validated through a typical case study. Proper orthogonal decomposition (POD) and Fast Fourier Transform (FFT) techniques are introduced, and efficient and accurate modelling of fully non-stationary and non-Gaussian random earthquakes is achieved. The Congress Street cut slope is employed as a numerical illustration and the slope stochastic dynamic stability assessment is conducted via the direct probability integral method (DPIM). The impact of the non-Gaussianity and non-stationarity of earthquakes on slope dynamic stability is studied for the first time. The analysis indicates that neglecting the non-Gaussian characteristics of earthquakes can cause an undervaluation of seismic slope stability, whereas the non-stationary characteristics can reduce seismic slope stability.
{"title":"Stochastic ground motion simulation considering fully non-stationary non-Gaussian characteristics and its applications in slope reliability assessment","authors":"Haoyu Yao , Rui Pang , Bin Xu , Mingyang Xu , Jun Liu","doi":"10.1016/j.probengmech.2025.103839","DOIUrl":"10.1016/j.probengmech.2025.103839","url":null,"abstract":"<div><div>With respect to evolutionary non-stationary processes, the underlying evolutionary power spectral density (EPSD) cannot be accurately calculated from the autocorrelation function (ACF). Efficient and accurate characterization of the non-Gaussianity and fully non-stationarity of ground motions is a difficult problem to be solved, and the stochastic response analysis of strongly nonlinear structures such as slopes under non-stationary non-Gaussian earthquakes does not provide clarity. In this paper, an efficient non-iterative approach for estimating the EPSD of the underlying Gaussian process built upon the unified Hermite polynomial Model (UHPM) is proposed. The proposed method eliminates the need for iterative procedures and avoids the need to solve integral equations, thereby improving computational efficiency, and the accuracy is validated through a typical case study. Proper orthogonal decomposition (POD) and Fast Fourier Transform (FFT) techniques are introduced, and efficient and accurate modelling of fully non-stationary and non-Gaussian random earthquakes is achieved. The Congress Street cut slope is employed as a numerical illustration and the slope stochastic dynamic stability assessment is conducted via the direct probability integral method (DPIM). The impact of the non-Gaussianity and non-stationarity of earthquakes on slope dynamic stability is studied for the first time. The analysis indicates that neglecting the non-Gaussian characteristics of earthquakes can cause an undervaluation of seismic slope stability, whereas the non-stationary characteristics can reduce seismic slope stability.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103839"},"PeriodicalIF":3.5,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050188","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}
In practical engineering problems, scenarios frequently emerge where random parameters follow multimodal probability distributions. Traditional time-variant uncertainty propagation methods, originally designed for unimodal distributions, risk incurring significant inaccuracies when applied to such multimodal cases. To address this challenge this paper introduces a time-variant uncertainty propagation analysis framework tailored for multimodal probability distributions. Initially, the time-variant response function is discretized into a series of instantaneous response functions. Subsequently, an improved point estimation method is employed to compute high-order statistical moments and correlation coefficients of these instantaneous responses. Following this, the maximum entropy method is used to reconstruct the probability density function of each instantaneous response function from its derived statistical moments. The highest order of statistical moments is adaptively determined through entropy-based criteria to balance computational efficiency and accuracy. Ultimately, the validity and effectiveness of the proposed framework are demonstrated through three examples.
{"title":"A time-variant uncertainty propagation analysis method for multimodal probability distributions","authors":"Boqun Xie , Xinpeng Wei , Qiang Gu , Chao Jiang , Jinwu Li","doi":"10.1016/j.probengmech.2025.103840","DOIUrl":"10.1016/j.probengmech.2025.103840","url":null,"abstract":"<div><div>In practical engineering problems, scenarios frequently emerge where random parameters follow multimodal probability distributions. Traditional time-variant uncertainty propagation methods, originally designed for unimodal distributions, risk incurring significant inaccuracies when applied to such multimodal cases. To address this challenge this paper introduces a time-variant uncertainty propagation analysis framework tailored for multimodal probability distributions. Initially, the time-variant response function is discretized into a series of instantaneous response functions. Subsequently, an improved point estimation method is employed to compute high-order statistical moments and correlation coefficients of these instantaneous responses. Following this, the maximum entropy method is used to reconstruct the probability density function of each instantaneous response function from its derived statistical moments. The highest order of statistical moments is adaptively determined through entropy-based criteria to balance computational efficiency and accuracy. Ultimately, the validity and effectiveness of the proposed framework are demonstrated through three examples.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103840"},"PeriodicalIF":3.5,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050190","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}
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