Probabilistic Engineering Mechanics最新文献

{"title":"Reliable uncertainty quantification for fiber orientation in composite molding processes using multilevel polynomial surrogates","authors":"Stjepan Salatovic ,&nbsp;Sebastian Krumscheid ,&nbsp;Florian Wittemann ,&nbsp;Luise Kärger","doi":"10.1016/j.probengmech.2025.103806","DOIUrl":"10.1016/j.probengmech.2025.103806","url":null,"abstract":"<div><div>Fiber orientation is decisive for the mechanical performance of composite materials. During manufacturing, variations in material and process parameters can influence fiber orientation. We employ multilevel polynomial surrogates to model the propagation of uncertain material properties in the injection molding process. To ensure reliable uncertainty quantification, a key focus is deriving novel error bounds for statistical measures of a quantity of interest. Numerical experiments employ the Cross-WLF viscosity model and Hagen–Poiseuille flow to investigate the impact of uncertainties in fiber length and matrix temperature on the fractional anisotropy of fiber orientation. The Folgar–Tucker equation and the improved anisotropic rotary diffusion model, incorporating analytical solutions, are used for verification. Results show that the method improves significantly upon standard Monte Carlo estimation, while also providing error guarantees. These findings offer the first step towards a reliable and practical tool for optimizing fiber-reinforced polymer manufacturing processes in the future.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103806"},"PeriodicalIF":3.0,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144656614","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}

{"title":"Joint stationary response prediction of high-dimension strongly nonlinear systems with both uncertain parameters and stochastic excitation by solving FPK equation","authors":"Yangyang Xiao ,&nbsp;Lincong Chen ,&nbsp;Zhongdong Duan ,&nbsp;Jianqiao Sun","doi":"10.1016/j.probengmech.2025.103795","DOIUrl":"10.1016/j.probengmech.2025.103795","url":null,"abstract":"<div><div>Uncertainties in system parameters and dynamic loading are pervasive in engineering and significantly influence the dynamic response of systems. While random response analysis has been studied since the 1960s, predicting responses for high-dimension strongly nonlinear systems under both types of uncertainties remains a significant challenge. This study extends a decoupled Fokker–Planck–Kolmogorov (FPK) equation approach to predict the joint stationary response of high-dimension strongly nonlinear systems with uncertain parameters under additive and/or multiplicative white noise excitations. Leveraging the law of total probability and the subspace method, the decoupled FPK equation governing the unconditional joint probability density function (PDF) of the state variables of interest are derived. These decoupled equations can effectively handle both uncertainties while avoiding the complications of high dimensionality and large numbers of uncertain parameters. Subsequently, the neural network-based methods combined with an efficient hypersphere sampling strategy are used to deal with the decoupled FPK equation, yielding non-Gaussian joint PDFs. Three examples, including the Rayleigh system, the inclined nonlinear cable system, and a high-dimension nonlinear base-isolation frame system with the maximum number of uncertain parameters up to 25, are studied for illustration. Extensive Monte Carlo simulation data validate the accuracy and efficiency of the proposed scheme. The results demonstrate that the proposed approach successfully captures the complex-shaped joint PDF of the strongly nonlinear system, even for the challenging five dimension case. Notably, parameter uncertainties can lead to a reduction of up to 20% in the peak PDF of the responses and an increase in the tail PDF by several orders of magnitude compared to deterministic systems.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103795"},"PeriodicalIF":3.0,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144564091","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}

{"title":"A comparative analysis of intrusive and non-intrusive PCE methods for random mode computation","authors":"Eric Jacquelin ,&nbsp;Sondipon Adhikari ,&nbsp;Denis Brizard","doi":"10.1016/j.probengmech.2025.103792","DOIUrl":"10.1016/j.probengmech.2025.103792","url":null,"abstract":"<div><div>Random eigenmodes present a significant challenge in the analysis of uncertain dynamical systems, particularly when traditional Monte Carlo methods become computationally prohibitive for high-dimensional problems. While Polynomial Chaos Expansion (PCE) offers a promising alternative, the choice between intrusive (physics-based) and non-intrusive (data-driven) implementations remains a critical yet understudied decision. This paper presents the first comprehensive comparison of these PCE approaches for random eigenmode computation, examining their theoretical foundations, implementation complexities, and computational efficiency. Through systematic analysis of a three-degree-of-freedom system with varying uncertainty parameters, we demonstrate that intrusive PCE achieves superior accuracy for low-dimensional problems, while non-intrusive PCE shows better scalability for higher-dimensional systems. Our findings reveal a previously undocumented trade-off between implementation complexity and computational efficiency, establishing clear criteria for approach selection based on problem dimensionality and accuracy requirements. These insights extend beyond modal analysis to the broader field of uncertainty quantification in computational mechanics, providing practical guidelines for selecting optimal PCE strategies in various engineering applications. The methodological framework presented here opens new possibilities for efficient uncertainty analysis in large-scale dynamical systems.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103792"},"PeriodicalIF":3.0,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144523065","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}

{"title":"Variations in the reliability performance of free-form single-layer grid structures during deterministic optimization, and optimization method improvement","authors":"Dong Li,&nbsp;Baoshi Jiang,&nbsp;Bowen Hou","doi":"10.1016/j.probengmech.2025.103813","DOIUrl":"10.1016/j.probengmech.2025.103813","url":null,"abstract":"<div><div>Structural optimization can be categorized into deterministic optimization (DO) and reliability‐based design optimization (RBDO). Although RBDO yields designs with better reliability than DO, it incurs substantially greater computational costs. Existing studies typically compare the final outcomes of RBDO and DO, without examining how structural reliability evolves during DO. In this study, we track how the reliability of a free‐form single‐layer grid structure evolves during DO. The strain energy is adopted as the objective, and the <em>probability density evolution method</em> is used to compute the structural-response probability density function. Based on the observed trends, we propose an enhanced optimization strategy that balances the simultaneous improvements in the vertical and horizontal mechanical performance and reliability performance. The improved method is then applied to a cantilever‐type free‐form surface structure to assess its generality. The results indicate that the mechanical and reliability performances vary in the same manner along the load direction. Moreover, by improving the objective function, the proposed method effectively enhances both the mechanical and reliability performances under horizontal seismic and vertical loads. It achieves concurrent improvements in both directions and performs well across different structural types.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103813"},"PeriodicalIF":3.0,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144680401","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}

{"title":"Data-driven modeling of high-speed maglev track irregularity","authors":"Junqi Xu ,&nbsp;Zhanghang Chen ,&nbsp;Qinghua Zheng ,&nbsp;Fei Ni","doi":"10.1016/j.probengmech.2025.103798","DOIUrl":"10.1016/j.probengmech.2025.103798","url":null,"abstract":"<div><div>Ensuring the stability of high-speed maglev trains hinges on track smoothness, which is influenced by track irregularities that act as key excitations for train vibrations. These irregularities, stemming from various factors including track design and environmental conditions, are unpredictable and dynamic. Current models often fail to accurately represent these irregularities, leading to unreliable dynamic analyses. This paper introduces a non-stationary, non-Gaussian stochastic process model, enhanced with Iterative Amplitude Adjusted Fourier Transform (IAAFT) and Time-series Generative Adversarial Network (TimeGAN) algorithms, to more accurately simulate track irregularities. The model’s ability to generate independent, high-fidelity data supports improved design, operation, and maintenance of maglev systems.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103798"},"PeriodicalIF":3.0,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144518695","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}

{"title":"Mechanical and data-driven probabilistic model for axial strength of circular concrete-filled aluminum alloy tube short columns","authors":"Junlei Tang ,&nbsp;Hao Cheng ,&nbsp;Bo Yu","doi":"10.1016/j.probengmech.2025.103808","DOIUrl":"10.1016/j.probengmech.2025.103808","url":null,"abstract":"<div><div>A mechanical and data-driven probabilistic model was proposed to overcome the limitation that traditional deterministic models are unable to rationally consider the influences of aleatory and epistemic uncertainties on the axial strength of circular concrete-filled aluminum alloy tube (CCFAT) short columns. Firstly, a deterministic model for the axial strength of CCFAT short columns was established based on the Lame's solution, the theory of elasticity, and the unified theory. Subsequently, a probabilistic model for axial strength of CCFAT short columns was developed by considering both probabilistic model parameters and systematic errors. Meanwhile, the posterior distributions of probabilistic model parameters were updated based on the Bayesian theory and the Markov Chain Monte Carlo method. Furthermore, the predictive performance of the proposed probabilistic model was validated by comparing it with experimental datasets and traditional deterministic models. Finally, the proposed probabilistic model's probability density function, cumulative distribution function, and confidence intervals were employed to calibrate traditional deterministic models. Analysis shows that the proposed probabilistic model not only has a satisfactory predictive performance in that it rationally describes the probabilistic characteristics of the axial strength of CCFAT short columns, but also provides a dependable method for calibrating the prediction accuracy of traditional deterministic models for the axial strength of CCFAT short columns.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103808"},"PeriodicalIF":3.0,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144680402","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}

{"title":"Successive Pareto simulation method for efficient structural reliability analysis","authors":"Rodrigo S. de Oliveira,&nbsp;Mariella F. de L.O. Santos,&nbsp;Silvana M.B. Afonso,&nbsp;Renato de S. Motta","doi":"10.1016/j.probengmech.2025.103819","DOIUrl":"10.1016/j.probengmech.2025.103819","url":null,"abstract":"<div><div>The Monte Carlo (MC) method is a traditional approach for structural reliability analysis, known for its robustness in terms of accuracy. However, it can be inefficient when the sample size needs to be very large to obtain an adequate estimate. A novel approach, named successive Pareto simulation (SPS), is proposed to reduce the number of failure function evaluations in structural engineering problems, in which variables can be grouped into capacity and demand, by employing an efficient selection procedure on the MC sample. The proposed approach uses the Pareto optimality concept to obtain a small subset of the sample, formed mainly by points within the failure domain, thus considerably reducing the number of function evaluations while maintaining accuracy. Five benchmark problems and three structural problems are solved to validate the proposed method. Compared to MC, the reduction in the number of function evaluations varied from 95.61 % to 99.93 %. SPS also showed good results compared to variance reduction methods presented in the literature, requiring up to 77.31 %, 98.38 %, and 85.18 % fewer function evaluations than importance sampling, subset simulation, and the improved cross-entropy-based importance sampling, respectively. Moreover, although the selection procedure of SPS is applied to traditional MC in this work, it can also be applied to other simulation-based methods to enhance their efficiency.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103819"},"PeriodicalIF":3.5,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144766899","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}

{"title":"Efficient survival probability determination of nonlinear multi-degree-of-freedom oscillators with fractional derivatives and subject to non-stationary excitation","authors":"João G.C.S. Duarte,&nbsp;Ketson R.M. dos Santos","doi":"10.1016/j.probengmech.2025.103801","DOIUrl":"10.1016/j.probengmech.2025.103801","url":null,"abstract":"<div><div>Determining the survival probability of nonlinear dynamical systems subject to random excitation is a persistent challenge in engineering dynamics, and addressing this challenge requires efficient and accurate mathematical and numerical methodologies. To this end, we propose a semi-analytical technique for estimating the survival probability of a nonlinear/hysteretic multi-degree-of-freedom (MDOF) oscillator endowed with fractional derivatives, subject to non-stationary excitation. In this technique, <span><math><mi>n</mi></math></span> single-degree-of-freedom (SDOF) oscillators with time-dependent effective damping and stiffness terms are determined based on the variances of the system response displacement and velocity, approximated using statistical linearization. These oscillators govern the dynamics of the response of each degree of freedom (DOF) of an <span><math><mi>n</mi></math></span>-DOF nonlinear/hysteretic oscillator. Novel expressions for the effective properties of the SDOF oscillators are proposed, incorporating an appropriate approximation for Caputo’s fractional derivative using hypergeometric functions. Additionally, approximated closed-form expressions are derived for the transition probability density function of the response amplitude process, enabling the estimation of conditional probabilities along the time domain at minimal computational cost, which is necessary for approximating the survival probability. To assess the accuracy and computational performance of the proposed methodology, we consider numerical examples involving a hardening Duffing, a softening stiffness, and a Bouc–Wen MDOF oscillator with fractional derivatives and subject to a non-stationary excitation with a non-separable evolutionary power spectrum. Comparisons with Monte Carlo simulation data are included to evaluate the accuracy and computational performance of the proposed approach.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103801"},"PeriodicalIF":3.0,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144513897","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}

{"title":"Stochastic analysis model for metro vehicle-floating slab track coupled system considering shear hinges","authors":"Weihua Fu ,&nbsp;Yu Guo ,&nbsp;Baomin Wang","doi":"10.1016/j.probengmech.2025.103811","DOIUrl":"10.1016/j.probengmech.2025.103811","url":null,"abstract":"<div><div>To analyze the stochastic vibration characteristics of the metro vehicle-track coupled system, this paper proposed a time-varying stochastic vibration model of the metro vehicle-floating slab track system. Based on the theory of vehicle-track coupled dynamics, a vertical coupled dynamic model is developed, incorporating the shear hinge devices at the ends of the floating slab track. Simulation results shows that the shear hinge constraints effectively reduce the vertical wheel-rail dynamic interaction. Thus, car body mass, fastener stiffness, and steel spring stiffness are selected as random parameters, while the random track irregularities serve as the external excitation source for the system. Both impacts of the internal and external randomness on the vibration characteristics of the coupled system are simulated. Critical random parameter values are determined by the combination of random simulation and number theory method. The effects of different random parameters with varying variation coefficients on the vertical car body acceleration and the wheel-rail interaction force are simulated and compared. Through the probability density evolution method (PDEM), the vibration characteristics of the car body acceleration caused by random track irregularities are analyzed. The results demonstrate that the established stochastic vibration model can be used for the randomness analysis of the metro vehicle-floating slab track coupled system. The vehicle-dynamic responses indicate that running safety and riding comfort are subject to greater impact. In addition, among these random parameters, the car body mass has the most significant impact on the vehicle-track dynamic interaction.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103811"},"PeriodicalIF":3.0,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144670196","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}

{"title":"Gaussian processes-based Bayesian updating framework for time-dependent reliability assessment of aging bridges with limited inspection data","authors":"Yi Chen ,&nbsp;Hui Yang ,&nbsp;Wenwei Fu ,&nbsp;Yaozhi Luo ,&nbsp;Zhi Ma ,&nbsp;Biran Zheng","doi":"10.1016/j.probengmech.2025.103820","DOIUrl":"10.1016/j.probengmech.2025.103820","url":null,"abstract":"<div><div>Accurate time-varying reliability assessment of aging infrastructure is essential for informed maintenance and operational decisions but is often limited by uncertainties in available data, complicating decision-making under budget constraints. This highlights the need for advanced uncertainty quantification methods in reliability analysis. This study presents a Gaussian processes-based Bayesian updating for evaluating the time-varying reliability of aging bridges under the uncertainty of limited field inspections and sparse traffic survey data. The approach integrates Monte Carlo simulation, vehicle-bridge interaction (VBI) analysis, and progressive deterioration modeling to iteratively update key parameters and improve the reliability assessment of aging infrastructure. Stochastic vehicle flows (SVF) are simulated using Monte Carlo methods, with Bayesian inference employed to progressively update parameters such as vehicle speed distributions, axle weights, and spacing based on newly available traffic data. This iterative updating process ensures the simulations reflect the dynamic characteristics of real-world traffic, providing a robust foundation for the subsequent reliability analysis. VBI analysis is used to model the maximum load induced by traffic, resulting in a probability-based load model that characterizes load distribution for further reliability assessment. The temporal evolution of random variables related to resistance deterioration, such as material degradation, is monitored using an integrated approach combining conditional random fields with Bayesian inference, enabling the development of a progressive deterioration model. An active learning reliability assessment framework is developed to prioritize evaluating high-risk failure modes, enabling a dynamic assessment of the bridge's failure probability and reliability indices over time. This framework reduces prior epistemic uncertainties and provides a more accurate and comprehensive reliability analysis for aging infrastructure under limited inspection data.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103820"},"PeriodicalIF":3.5,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144766901","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}