Pub 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":"2025-06-07","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 : 2025-06-06DOI: 10.1016/j.probengmech.2025.103802
Qiang Li , Gang Li , Gang Zhao , Qiang Li
2D woven C/SiC ceramic matrix composites inherently exhibit dispersion in mechanical properties, posing great challenges to their structural design and engineering applications. This dispersion primarily stems from the random distribution of voids and defects within the composite material, as well as the uneven thermochemical damage incurred during manufacturing. To address this issue, this paper proposes a probabilistic volume element model to characterize the dispersion in the mechanical properties of C/SiC composites and investigate the propagation of uncertainties and correlations across scales. To capture the typical nonlinear behavior of C/SiC composites under uniaxial tension, a progressive damage constitutive law was developed within the mesoscale finite element model based on the Linde criterion. Uncertainties in material properties were modeled by implementing Weibull and normal distributions for strength and modulus, respectively. Bivariate copula functions combined with the Bootstrap method were employed to quantify the correlation between strength and modulus, as observed in limited experimental data. Convolutional neural networks were introduced to model the propagation of uncertainty in these correlated parameters. The networks were iteratively updated through transfer learning and optimization algorithms to address the correlation inverse problem, enabling the identification of dependence between mesoscale parameters based on macroscale experimental data, with subsequent quantification using copula functions. Statistical analysis emphasizes the significance of incorporating parameter correlations in multiscale simulations for achieving accurate uncertainty quantification of mechanical properties.
{"title":"Probabilistic volume element model of 2D woven C/SiC composites considering copula dependence between strength and modulus","authors":"Qiang Li , Gang Li , Gang Zhao , Qiang Li","doi":"10.1016/j.probengmech.2025.103802","DOIUrl":"10.1016/j.probengmech.2025.103802","url":null,"abstract":"<div><div>2D woven C/SiC ceramic matrix composites inherently exhibit dispersion in mechanical properties, posing great challenges to their structural design and engineering applications. This dispersion primarily stems from the random distribution of voids and defects within the composite material, as well as the uneven thermochemical damage incurred during manufacturing. To address this issue, this paper proposes a probabilistic volume element model to characterize the dispersion in the mechanical properties of C/SiC composites and investigate the propagation of uncertainties and correlations across scales. To capture the typical nonlinear behavior of C/SiC composites under uniaxial tension, a progressive damage constitutive law was developed within the mesoscale finite element model based on the Linde criterion. Uncertainties in material properties were modeled by implementing Weibull and normal distributions for strength and modulus, respectively. Bivariate copula functions combined with the Bootstrap method were employed to quantify the correlation between strength and modulus, as observed in limited experimental data. Convolutional neural networks were introduced to model the propagation of uncertainty in these correlated parameters. The networks were iteratively updated through transfer learning and optimization algorithms to address the correlation inverse problem, enabling the identification of dependence between mesoscale parameters based on macroscale experimental data, with subsequent quantification using copula functions. Statistical analysis emphasizes the significance of incorporating parameter correlations in multiscale simulations for achieving accurate uncertainty quantification of mechanical properties.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103802"},"PeriodicalIF":3.0,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144254319","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}
The gantry machining center is a critical piece of equipment in modern manufacturing, with its structural design playing a crucial role in determining machining precision, production efficiency, and product quality. To achieve both high performance and a lightweight design, this paper presents an optimization method for the key components of the gantry machining center based on reliability. The goal is to minimize the system's mass while ensuring that the static deformation does not increase, first-order modal frequency does not decrease, and the reliability meets the predetermined confidence level. Sensitivity analysis is performed to identify the parameters with significant impacts on the gantry machining center's performance. To overcome the time-consuming nature of the finite element method (FEM), an adaptive Kriging surrogate model is employed. An efficient metaheuristic algorithm is then used to solve for the optimal design. The effectiveness of the proposed optimization method is verified through comparative analysis. The results show that the reliability optimization method can effectively balance the mass and reliability of the gantry machining center, significantly improving the system's performance stability under random uncertainties, thus providing a theoretical foundation for the structural optimization of gantry machining centers.
{"title":"Reliability-based design optimization of key components in a gantry machining center","authors":"Yumo Chen, Xianzhen Huang, Mingfei Ma, Jiaxin Luo, Boyang Ding","doi":"10.1016/j.probengmech.2025.103786","DOIUrl":"10.1016/j.probengmech.2025.103786","url":null,"abstract":"<div><div>The gantry machining center is a critical piece of equipment in modern manufacturing, with its structural design playing a crucial role in determining machining precision, production efficiency, and product quality. To achieve both high performance and a lightweight design, this paper presents an optimization method for the key components of the gantry machining center based on reliability. The goal is to minimize the system's mass while ensuring that the static deformation does not increase, first-order modal frequency does not decrease, and the reliability meets the predetermined confidence level. Sensitivity analysis is performed to identify the parameters with significant impacts on the gantry machining center's performance. To overcome the time-consuming nature of the finite element method (FEM), an adaptive Kriging surrogate model is employed. An efficient metaheuristic algorithm is then used to solve for the optimal design. The effectiveness of the proposed optimization method is verified through comparative analysis. The results show that the reliability optimization method can effectively balance the mass and reliability of the gantry machining center, significantly improving the system's performance stability under random uncertainties, thus providing a theoretical foundation for the structural optimization of gantry machining centers.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103786"},"PeriodicalIF":3.0,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144270815","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 : 2025-06-06DOI: 10.1016/j.probengmech.2025.103799
Giuseppe Muscolino , Federica Genovese
In this paper, a novel “hybrid pseudo-force approach” is proposed for evaluating the stochastic response of fractional oscillators subjected to non-stationary input processes. The fractional oscillator analysed here is a second-order linear system that includes a term with a fractional derivative, capable of capturing the dissipative properties of viscoelastic materials. The convolution integral method is adopted to evaluate the response. The fractional term in the equation of motion is then treated as a pseudo-force, allowing for a decomposition of the convolution integral into two distinct parts. The first part, related to the modulating function, is solved analytically in closed form using “classical” stochastic dynamics techniques. The second part, which involves the pseudo-force contribution of the fractional term, requires the discretization of the fractional derivative using the Grünwald-Letnikov approximation and a piecewise linear interpolation. Finally, the stochastic response statistics are obtained via numerical integration in the frequency domain. Numerical examples validate the stability, accuracy and applicability of the proposed method through comparisons with Monte Carlo simulation.
{"title":"Stochastic response of fractional oscillators subjected to non-stationary random excitations via hybrid pseudo-force approach","authors":"Giuseppe Muscolino , Federica Genovese","doi":"10.1016/j.probengmech.2025.103799","DOIUrl":"10.1016/j.probengmech.2025.103799","url":null,"abstract":"<div><div>In this paper, a novel “<em>hybrid pseudo-force approach</em>” is proposed for evaluating the stochastic response of fractional oscillators subjected to non-stationary input processes. The fractional oscillator analysed here is a second-order linear system that includes a term with a fractional derivative, capable of capturing the dissipative properties of viscoelastic materials. The <em>convolution integral method</em> is adopted to evaluate the response. The fractional term in the equation of motion is then treated as a pseudo-force, allowing for a decomposition of the <em>convolution integral</em> into two distinct parts. The first part, related to the modulating function, is solved analytically in closed form using “classical” stochastic dynamics techniques. The second part, which involves the pseudo-force contribution of the fractional term, requires the discretization of the fractional derivative using the <em>Grünwald-Letnikov</em> approximation and a piecewise linear interpolation. Finally, the stochastic response statistics are obtained via numerical integration in the frequency domain. Numerical examples validate the stability, accuracy and applicability of the proposed method through comparisons with Monte Carlo simulation.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103799"},"PeriodicalIF":3.0,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144470353","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 : 2025-06-06DOI: 10.1016/j.probengmech.2025.103791
Zhiping Qiu, Bowen Zhang
Differential equations are widely used to model engineering problems, while the uncertainty caused by material dispersity, load dispersity and measurement error cannot be ignored. The Monte Carlo simulation (MCS) is mostly used. However, it has low efficiency in many complex scenarios. This paper proposes a novel method for calculating the uncertainty based on the Kronecker product and straightening operation of matrices. An equivalent formation is established for variance solving based on the Kronecker product. Numerical examples, including a heat equation example and the dynamic response of an airplane wing, are conducted using the proposed method, MCS, and polynomial expansion. The obtained results show that the proposed method and MCS have almost the same accuracy. However, the former exhibits a higher efficiency.
{"title":"Solution of ordinary differential equation with random parameters using Kronecker product","authors":"Zhiping Qiu, Bowen Zhang","doi":"10.1016/j.probengmech.2025.103791","DOIUrl":"10.1016/j.probengmech.2025.103791","url":null,"abstract":"<div><div>Differential equations are widely used to model engineering problems, while the uncertainty caused by material dispersity, load dispersity and measurement error cannot be ignored. The Monte Carlo simulation (MCS) is mostly used. However, it has low efficiency in many complex scenarios. This paper proposes a novel method for calculating the uncertainty based on the Kronecker product and straightening operation of matrices. An equivalent formation is established for variance solving based on the Kronecker product. Numerical examples, including a heat equation example and the dynamic response of an airplane wing, are conducted using the proposed method, MCS, and polynomial expansion. The obtained results show that the proposed method and MCS have almost the same accuracy. However, the former exhibits a higher efficiency.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103791"},"PeriodicalIF":3.0,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144270917","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 : 2025-06-06DOI: 10.1016/j.probengmech.2025.103777
T. Chatterjee , S. El-Borgi , M. Trabelssi , M.I. Friswell
This study examines the stochastic response of a metamaterial (MM) nanobeam, focusing on bandgap formation and analyzed using machine learning. The nanobeam is modeled as an infinitely long Euler–Bernoulli beam with two length scale parameters: the nonlocal and strain gradient parameter. Periodically distributed linear resonators along its length introduce periodicity. The deterministic analysis is conducted by estimating bandgap edge frequencies using the dispersion of elastic waves in a representative unit cell. The impact of uncertainties on wave propagation behavior indicate that geometric properties predominantly influence variability in frequency response, followed by material properties, affecting the location and width of the bandgap. Scale dependent parameters, however, have a negligible effect. A Gaussian process (GP) surrogate model is employed to efficiently capture the stochastic behavior of the nanobeam. To highlight the utility of machine learning in computationally intensive tasks, a multi-objective optimization problem is formulated to tailor the bandgap features of the nanobeam. The offline-trained GP model yields a Pareto front of design configurations closely aligned with actual simulations, eliminating the need for repeated analyses during optimization. This surrogate based optimizer efficiently facilitates reverse engineering of MM designs for user defined wave dispersion characteristics, showcasing its potential for large scale optimization. Importantly, the stochastic dispersion framework grounded in nonlocal strain gradient theory can be directly applied to other periodic MM nanostructures. By varying unit cell configurations and materials within the same computational pipeline, new insights into bandgap emergence across applications ranging from phononic waveguides, nanoscale acoustic devices to structure–property relationships in next-generation MMs can be rapidly obtained.
{"title":"Stochastic dispersion behavior and optimal design of locally resonant metamaterial nanobeams using nonlocal strain gradient theory","authors":"T. Chatterjee , S. El-Borgi , M. Trabelssi , M.I. Friswell","doi":"10.1016/j.probengmech.2025.103777","DOIUrl":"10.1016/j.probengmech.2025.103777","url":null,"abstract":"<div><div>This study examines the stochastic response of a metamaterial (MM) nanobeam, focusing on bandgap formation and analyzed using machine learning. The nanobeam is modeled as an infinitely long Euler–Bernoulli beam with two length scale parameters: the nonlocal and strain gradient parameter. Periodically distributed linear resonators along its length introduce periodicity. The deterministic analysis is conducted by estimating bandgap edge frequencies using the dispersion of elastic waves in a representative unit cell. The impact of uncertainties on wave propagation behavior indicate that geometric properties predominantly influence variability in frequency response, followed by material properties, affecting the location and width of the bandgap. Scale dependent parameters, however, have a negligible effect. A Gaussian process (GP) surrogate model is employed to efficiently capture the stochastic behavior of the nanobeam. To highlight the utility of machine learning in computationally intensive tasks, a multi-objective optimization problem is formulated to tailor the bandgap features of the nanobeam. The offline-trained GP model yields a Pareto front of design configurations closely aligned with actual simulations, eliminating the need for repeated analyses during optimization. This surrogate based optimizer efficiently facilitates reverse engineering of MM designs for user defined wave dispersion characteristics, showcasing its potential for large scale optimization. Importantly, the stochastic dispersion framework grounded in nonlocal strain gradient theory can be directly applied to other periodic MM nanostructures. By varying unit cell configurations and materials within the same computational pipeline, new insights into bandgap emergence across applications ranging from phononic waveguides, nanoscale acoustic devices to structure–property relationships in next-generation MMs can be rapidly obtained.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103777"},"PeriodicalIF":3.0,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144240763","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 : 2025-06-06DOI: 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":"2025-06-06","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 : 2025-06-06DOI: 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.
{"title":"Closed-form solutions for non-stationary responses of Euler beams with general boundary conditions under fully coherent stochastic wheel-rail forces","authors":"Bin Wang , Helu Yu , Zewen Wang , Huiding Wang , Yongle Li","doi":"10.1016/j.probengmech.2025.103796","DOIUrl":"10.1016/j.probengmech.2025.103796","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103796"},"PeriodicalIF":3.0,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144254567","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 : 2025-06-06DOI: 10.1016/j.probengmech.2025.103800
Quan Song , Baofeng Zhou , Ruizhi Wen , Yefei Ren , Maosheng Gong
This paper presents a two-step identification framework to estimate gradually varying physical parameters and unknown seismic excitations in shear structures using only acceleration measurements. In the first step, a Fading-Factor Extended Kalman Filter with Unknown Input (FEKF-UI) is employed to locate time-varying stiffness parameters and estimate unmeasured excitations. In the second step, a Discrete Cosine Transform (DCT) is incorporated into a Kalman Filter to refine the parameter identification. The proposed approach addresses the challenges of sparse sensor deployment and unknown inputs by reformulating the observation model into a single-regression form, improving computational efficiency and estimation robustness. The effectiveness of the proposed method is demonstrated through both numerical simulations and shaking table experiments on multi-story reinforced concrete (RC) frame structures.
{"title":"Identification of gradually varying physical parameters for shear buildings under unknown earthquake excitation","authors":"Quan Song , Baofeng Zhou , Ruizhi Wen , Yefei Ren , Maosheng Gong","doi":"10.1016/j.probengmech.2025.103800","DOIUrl":"10.1016/j.probengmech.2025.103800","url":null,"abstract":"<div><div>This paper presents a two-step identification framework to estimate gradually varying physical parameters and unknown seismic excitations in shear structures using only acceleration measurements. In the first step, a Fading-Factor Extended Kalman Filter with Unknown Input (FEKF-UI) is employed to locate time-varying stiffness parameters and estimate unmeasured excitations. In the second step, a Discrete Cosine Transform (DCT) is incorporated into a Kalman Filter to refine the parameter identification. The proposed approach addresses the challenges of sparse sensor deployment and unknown inputs by reformulating the observation model into a single-regression form, improving computational efficiency and estimation robustness. The effectiveness of the proposed method is demonstrated through both numerical simulations and shaking table experiments on multi-story reinforced concrete (RC) frame structures.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103800"},"PeriodicalIF":3.0,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144331100","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 : 2025-05-31DOI: 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":"2025-05-31","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}
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