Pub Date : 2025-10-01Epub 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":"2025-10-01","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 : 2025-10-01Epub Date: 2025-11-24DOI: 10.1016/j.probengmech.2025.103870
Giacomo Navarra, Francesco Lo Iacono, Maria Oliva
Building codes typically define earthquake load design values using Response Spectra, which depend on site seismicity, soil conditions, structure importance, assumed ductility and limit states. Despite its popularity among engineers for predicting peak displacements and internal forces without directly integrating motion, this method is strictly valid only for single Degrees Of Freedom (DOF) systems. For multi-degrees of freedom structures, approximations in the determination of the modal response correlation coefficients must be used. An alternative approach is to model earthquakes as Gaussian processes using a Power Spectral Density (PSD) function. This probabilistic approach defines seismic input for linear multi-degree of freedom systems based on random vibration theory. When dealing with systems that exhibit weak nonlinearities, statistical linearization technique is applied to refine the solution, enabling the generation of artificial ground motions that match the response spectra for use in Monte Carlo Simulations. However, the computational burden of the PSD approach, especially for large DOF or heavy problems, makes it less convenient than the traditional Response Spectrum method. This paper presents an efficient analytical method with validated closed-form expressions of spectral moments for large-DOF systems. This approach facilitates the analysis of structural response statistics under seismic loads and enables the efficient assessment of the probabilistic distribution of response maxima for large-DOF systems, minimizing the need for computationally intensive numerical evaluations. In order to assess the effectiveness of the proposed method, a practical application on a base-isolated building structure has been carried out by comparing it with the Response Spectrum Method (RSM) and the analytical approach proposed in a previous work, demonstrating that it yields the smallest error compared to Monte Carlo simulations.
{"title":"The Enhanced Analytical Spectral Moments method for probabilistic characterization of large DOF systems under seismic actions","authors":"Giacomo Navarra, Francesco Lo Iacono, Maria Oliva","doi":"10.1016/j.probengmech.2025.103870","DOIUrl":"10.1016/j.probengmech.2025.103870","url":null,"abstract":"<div><div>Building codes typically define earthquake load design values using Response Spectra, which depend on site seismicity, soil conditions, structure importance, assumed ductility and limit states. Despite its popularity among engineers for predicting peak displacements and internal forces without directly integrating motion, this method is strictly valid only for single Degrees Of Freedom (DOF) systems. For multi-degrees of freedom structures, approximations in the determination of the modal response correlation coefficients must be used. An alternative approach is to model earthquakes as Gaussian processes using a Power Spectral Density (PSD) function. This probabilistic approach defines seismic input for linear multi-degree of freedom systems based on random vibration theory. When dealing with systems that exhibit weak nonlinearities, statistical linearization technique is applied to refine the solution, enabling the generation of artificial ground motions that match the response spectra for use in Monte Carlo Simulations. However, the computational burden of the PSD approach, especially for large DOF or heavy problems, makes it less convenient than the traditional Response Spectrum method. This paper presents an efficient analytical method with validated closed-form expressions of spectral moments for large-DOF systems. This approach facilitates the analysis of structural response statistics under seismic loads and enables the efficient assessment of the probabilistic distribution of response maxima for large-DOF systems, minimizing the need for computationally intensive numerical evaluations. In order to assess the effectiveness of the proposed method, a practical application on a base-isolated building structure has been carried out by comparing it with the Response Spectrum Method (RSM) and the analytical approach proposed in a previous work, demonstrating that it yields the smallest error compared to Monte Carlo simulations.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103870"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145617946","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 : 2025-10-01Epub Date: 2025-09-09DOI: 10.1016/j.probengmech.2025.103841
Boqun Xie , Xin Liu , Kai Liu , Shaowei Wu , Jiachang Tang
Multimodal random variables are widely encountered in practical engineering problems, such as the structural fatigue stress of a steel bridge accommodating both highway and railway traffic and the vibratory load experienced by a blade under stochastic dynamic excitations. Because of the error amplification effect caused by nonlinear response function in uncertainty propagation, traditional uncertainty analysis methods may yield large computational errors when multimodal distributions are involved. Herein, an uncertainty propagation method for multimodal distributions is proposed. First, the probability density function of multimodal random variables is modelled using a Gaussian mixture model. Second, the higher-order statistical moments of the response function are calculated through a bivariate dimension reduction method. Finally, the probability density function of the response function is computed using the maximum entropy method, and the desired statistical moment orders are means of an adaptive convergence framework. The effectiveness of the proposed method is demonstrated through two numerical examples and one engineering application.
{"title":"An adaptive moment-based approach to uncertainty analysis considering multimodal random parameters","authors":"Boqun Xie , Xin Liu , Kai Liu , Shaowei Wu , Jiachang Tang","doi":"10.1016/j.probengmech.2025.103841","DOIUrl":"10.1016/j.probengmech.2025.103841","url":null,"abstract":"<div><div>Multimodal random variables are widely encountered in practical engineering problems, such as the structural fatigue stress of a steel bridge accommodating both highway and railway traffic and the vibratory load experienced by a blade under stochastic dynamic excitations. Because of the error amplification effect caused by nonlinear response function in uncertainty propagation, traditional uncertainty analysis methods may yield large computational errors when multimodal distributions are involved. Herein, an uncertainty propagation method for multimodal distributions is proposed. First, the probability density function of multimodal random variables is modelled using a Gaussian mixture model. Second, the higher-order statistical moments of the response function are calculated through a bivariate dimension reduction method. Finally, the probability density function of the response function is computed using the maximum entropy method, and the desired statistical moment orders are means of an adaptive convergence framework. The effectiveness of the proposed method is demonstrated through two numerical examples and one engineering application.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103841"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050189","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 : 2025-10-01Epub Date: 2025-11-21DOI: 10.1016/j.probengmech.2025.103868
Menghao Ping, Wenhua Zhang, Liang Tang
Using modal properties to identify mass and stiffness parameters leads to an underdetermined inverse problem, resulting in non-unique solutions, and consequently to unidentifiable Bayesian inference. Therefore, conventional Bayesian methods typically assume mass parameters to be known and focus only on stiffness parameter identification. However, inaccurate mass assumption may introduce significant errors in stiffness estimation. To circumvent mass assumptions, this study proposes a novel Bayesian method integrating a mass addition strategy for mass and stiffness parameter identification. We obtain two sets of modal properties: one from the original structure and the other from the structure with an added known mass. These datasets are then employed to construct a Bayesian modeling framework to infer the joint distribution of mass and stiffness parameters. Specifically, we modify the Metropolis–Hastings (MH) algorithm into a two-stage sampling scheme where each stage establishes the target distribution based on the likelihood function derived from one dataset independently, which ensures that the resulting samples satisfy both independent likelihood functions. We can consider the samples generated by the modified MH algorithm as approximate samples of the joint posterior distribution of mass and stiffness parameters by leveraging the equivalence between the joint likelihood and the combination of the two independent likelihoods. To further apply the proposed method to high-dimensional problems, we modify the Transitional Markov Chain Monte Carlo (TMCMC) to make it compatible with the two likelihood functions and then integrate it with the modified MH algorithm. The proposed Bayesian method with modified sampling algorithms is validated on dynamic models, demonstrating its effectiveness in mass and stiffness parameter identification. It is then applied to damage identification, where improved accuracy is realized in damage localization and damage extent estimation.
{"title":"A novel Bayesian method for simultaneous identification of structural mass and stiffness parameters","authors":"Menghao Ping, Wenhua Zhang, Liang Tang","doi":"10.1016/j.probengmech.2025.103868","DOIUrl":"10.1016/j.probengmech.2025.103868","url":null,"abstract":"<div><div>Using modal properties to identify mass and stiffness parameters leads to an underdetermined inverse problem, resulting in non-unique solutions, and consequently to unidentifiable Bayesian inference. Therefore, conventional Bayesian methods typically assume mass parameters to be known and focus only on stiffness parameter identification. However, inaccurate mass assumption may introduce significant errors in stiffness estimation. To circumvent mass assumptions, this study proposes a novel Bayesian method integrating a mass addition strategy for mass and stiffness parameter identification. We obtain two sets of modal properties: one from the original structure and the other from the structure with an added known mass. These datasets are then employed to construct a Bayesian modeling framework to infer the joint distribution of mass and stiffness parameters. Specifically, we modify the Metropolis–Hastings (MH) algorithm into a two-stage sampling scheme where each stage establishes the target distribution based on the likelihood function derived from one dataset independently, which ensures that the resulting samples satisfy both independent likelihood functions. We can consider the samples generated by the modified MH algorithm as approximate samples of the joint posterior distribution of mass and stiffness parameters by leveraging the equivalence between the joint likelihood and the combination of the two independent likelihoods. To further apply the proposed method to high-dimensional problems, we modify the Transitional Markov Chain Monte Carlo (TMCMC) to make it compatible with the two likelihood functions and then integrate it with the modified MH algorithm. The proposed Bayesian method with modified sampling algorithms is validated on dynamic models, demonstrating its effectiveness in mass and stiffness parameter identification. It is then applied to damage identification, where improved accuracy is realized in damage localization and damage extent estimation.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103868"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145617949","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 : 2025-10-01Epub 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":"2025-10-01","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 : 2025-10-01Epub Date: 2025-11-12DOI: 10.1016/j.probengmech.2025.103863
Dimitra A. Karatzia , George C. Tsiatas , Panos Tsopelas
This paper investigates the vibration control performance of both linear and nonlinear mass damping system devices under stochastic excitation. These devices are installed atop a primary structure, modeled as a typical linearly elastic single-degree-of-freedom (SDOF) system, and subjected to Gaussian White Noise (GWN) ground acceleration. To estimate the stochastic response of the nonlinear system, the Statistical Linearization (SL) method is employed. This approach approximates the original nonlinear system with an equivalent linear one by minimizing the mean-square error between their respective statistical properties. As a result, it facilitates the application of linear stochastic system theory to analyze the complex dynamics of nonlinear systems under random excitation. The SL method proves particularly effective in estimating the mean and variance of system responses in nonlinear dynamic systems. Several case studies are presented to illustrate the method's application and to demonstrate its computational efficiency and accuracy in comparison with Monte Carlo (MC) simulations. Furthermore, the results provide valuable insights into the stochastic response characteristics of both linear and nonlinear mass damping systems. Notably, a key finding challenges the prevailing belief: stiffness nonlinearity does not improve the passive device's capacity to absorb and dissipate energy from the primary structure.
{"title":"Vibration control performance of linear and nonlinear mass damping systems under stochastic excitation","authors":"Dimitra A. Karatzia , George C. Tsiatas , Panos Tsopelas","doi":"10.1016/j.probengmech.2025.103863","DOIUrl":"10.1016/j.probengmech.2025.103863","url":null,"abstract":"<div><div>This paper investigates the vibration control performance of both linear and nonlinear mass damping system devices under stochastic excitation. These devices are installed atop a primary structure, modeled as a typical linearly elastic single-degree-of-freedom (SDOF) system, and subjected to Gaussian White Noise (GWN) ground acceleration. To estimate the stochastic response of the nonlinear system, the Statistical Linearization (SL) method is employed. This approach approximates the original nonlinear system with an equivalent linear one by minimizing the mean-square error between their respective statistical properties. As a result, it facilitates the application of linear stochastic system theory to analyze the complex dynamics of nonlinear systems under random excitation. The SL method proves particularly effective in estimating the mean and variance of system responses in nonlinear dynamic systems. Several case studies are presented to illustrate the method's application and to demonstrate its computational efficiency and accuracy in comparison with Monte Carlo (MC) simulations. Furthermore, the results provide valuable insights into the stochastic response characteristics of both linear and nonlinear mass damping systems. Notably, a key finding challenges the prevailing belief: stiffness nonlinearity does not improve the passive device's capacity to absorb and dissipate energy from the primary structure.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103863"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145571737","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 : 2025-10-01Epub 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":"2025-10-01","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}
Pub Date : 2025-10-01Epub Date: 2025-11-01DOI: 10.1016/j.probengmech.2025.103856
Lifang Feng , Bin Pei , Yong Xu
This paper aims to explore non-Markovian dynamics of nonlinear dynamical systems subjected to fractional Gaussian noise (FGN) and Gaussian white noise (GWN). A novel memory-dependent Fokker–Planck–Kolmogorov (memFPK) equation is developed to characterize the probability structure in such non-Markovian systems. The main challenge in this research comes from the long-memory characteristics of FGN. These features make it impossible to model the FGN-excited nonlinear dynamical systems as finite dimensional GWN-driven Markovian augmented filtering systems, so the classical FPK equation is no longer applicable. To solve this problem, based on fractional Wick–Itô–Skorohod integral theory, this study first derives the fractional Itô formula. Then, a memory kernel function is constructed to reflect the long-memory characteristics from FGN. By using fractional Itô formula and integration by parts, the memFPK equation is established. Importantly, the proposed memFPK equation is not limited to specific forms of drift and diffusion terms, making it broadly applicable to a wide class of nonlinear dynamical systems subjected to FGN and GWN. Due to the historical dependence of the memory kernel function, a Volterra adjustable decoupling approximation is used to reconstruct the memory kernel dependence term. This approximation method can effectively solve the memFPK equation, thereby obtaining probabilistic responses of nonlinear dynamical systems subjected to FGN and GWN excitations. Finally, some numerical examples verify the accuracy and effectiveness of the proposed method.
{"title":"The memory-dependent FPK equation for fractional Gaussian noise","authors":"Lifang Feng , Bin Pei , Yong Xu","doi":"10.1016/j.probengmech.2025.103856","DOIUrl":"10.1016/j.probengmech.2025.103856","url":null,"abstract":"<div><div>This paper aims to explore non-Markovian dynamics of nonlinear dynamical systems subjected to fractional Gaussian noise (FGN) and Gaussian white noise (GWN). A novel memory-dependent Fokker–Planck–Kolmogorov (memFPK) equation is developed to characterize the probability structure in such non-Markovian systems. The main challenge in this research comes from the long-memory characteristics of FGN. These features make it impossible to model the FGN-excited nonlinear dynamical systems as finite dimensional GWN-driven Markovian augmented filtering systems, so the classical FPK equation is no longer applicable. To solve this problem, based on fractional Wick–Itô–Skorohod integral theory, this study first derives the fractional Itô formula. Then, a memory kernel function is constructed to reflect the long-memory characteristics from FGN. By using fractional Itô formula and integration by parts, the memFPK equation is established. Importantly, the proposed memFPK equation is not limited to specific forms of drift and diffusion terms, making it broadly applicable to a wide class of nonlinear dynamical systems subjected to FGN and GWN. Due to the historical dependence of the memory kernel function, a Volterra adjustable decoupling approximation is used to reconstruct the memory kernel dependence term. This approximation method can effectively solve the memFPK equation, thereby obtaining probabilistic responses of nonlinear dynamical systems subjected to FGN and GWN excitations. Finally, some numerical examples verify the accuracy and effectiveness of the proposed method.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103856"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145465825","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 : 2025-10-01Epub Date: 2025-11-04DOI: 10.1016/j.probengmech.2025.103860
Ilias G. Mavromatis , Yuanjin Zhang , Ioannis A. Kougioumtzoglou
A technique is developed, based on an extrapolation approach within the Wiener path integral (WPI) methodology, for addressing the first-passage problem and for determining the time-dependent survival probability of stochastically excited nonlinear oscillators. The novelty and contributions of this paper are twofold. First, the nonlinear oscillator response transition probability density function (PDF) is determined in a computationally efficient manner. This is done, within the WPI framework, by solving numerically only a relatively small number of standard optimization problems, each yielding a corresponding most probable path. Next, the information embedded in the time histories of these most probable paths is exploited for extrapolating and for determining, at no additional cost, new paths to be used for evaluating the response transition PDF for any combination of initial and final states. Second, relying on the efficiently determined response transition PDF, an appropriate time-domain discretization is employed for evaluating the nonlinear oscillator survival probability in relatively short time steps. Two representative numerical examples are considered for demonstrating the high degree of accuracy exhibited by the developed technique. These pertain to a Duffing nonlinear oscillator and to a vibro-impact nonlinear oscillator with fractional derivative elements. Juxtapositions with pertinent Monte Carlo simulation data are included as well.
{"title":"First-passage analysis of nonlinear oscillators by leveraging information in the Wiener path integral most probable path","authors":"Ilias G. Mavromatis , Yuanjin Zhang , Ioannis A. Kougioumtzoglou","doi":"10.1016/j.probengmech.2025.103860","DOIUrl":"10.1016/j.probengmech.2025.103860","url":null,"abstract":"<div><div>A technique is developed, based on an extrapolation approach within the Wiener path integral (WPI) methodology, for addressing the first-passage problem and for determining the time-dependent survival probability of stochastically excited nonlinear oscillators. The novelty and contributions of this paper are twofold. First, the nonlinear oscillator response transition probability density function (PDF) is determined in a computationally efficient manner. This is done, within the WPI framework, by solving numerically only a relatively small number of standard optimization problems, each yielding a corresponding most probable path. Next, the information embedded in the time histories of these most probable paths is exploited for extrapolating and for determining, at no additional cost, new paths to be used for evaluating the response transition PDF for any combination of initial and final states. Second, relying on the efficiently determined response transition PDF, an appropriate time-domain discretization is employed for evaluating the nonlinear oscillator survival probability in relatively short time steps. Two representative numerical examples are considered for demonstrating the high degree of accuracy exhibited by the developed technique. These pertain to a Duffing nonlinear oscillator and to a vibro-impact nonlinear oscillator with fractional derivative elements. Juxtapositions with pertinent Monte Carlo simulation data are included as well.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103860"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145465824","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 : 2025-10-01Epub Date: 2025-11-24DOI: 10.1016/j.probengmech.2025.103866
Wantao Jia , Zhengrong Jin , Fei Ni , Weiqiu Zhu
In electromagnetic suspension (EMS) maglev trains, maintaining the suspension gap within a set range is crucial for levitation control. Research often addresses deterministic systems or those disturbed by Gaussian white noise, overlooking stochastic jump noise from factors like railway track joint offset. This study introduces a probabilistic tracking control approach in which a single-point electromagnet levitation system subject to Gaussian and Poisson white noise is modeled using Physics-Informed Neural Networks (PINNs). By constructing two deep neural networks to respectively approximate the system response probability density function (PDF) and control input, the forward Kolmogorov equation constraints and target PDF tracking task are unified into an optimization problem. The Monte Carlo integration manages Poisson white noise integrals, and an adaptive sampling strategy based on the target PDF improves training efficiency. The control problems involving two pre-specified PDFs in practical scenarios are addressed using the proposed approach. The results indicate that this method is capable of designing feedback control forces for both linearized and nonlinear systems. Validity is also tested on linearized and nonlinear levitation systems subjected to Gaussian white noise under exact control conditions. The close match between the proposed control and the exact solution confirms the effectiveness of the method.
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