Probabilistic Engineering Mechanics最新文献

{"title":"Reliability-based global sensitivity updating method considering new input observation information","authors":"Xinyao Li,&nbsp;Xinfa Chen,&nbsp;Liangli He","doi":"10.1016/j.probengmech.2026.103983","DOIUrl":"10.1016/j.probengmech.2026.103983","url":null,"abstract":"<div><div>Reliability-based global sensitivity analysis (GSA) aims to quantify the influence of each model input on structural reliability, thereby laying the foundation for simplifying reliability-based design and optimization models. Existing research on reliability-based GSA often assumes that the stochastic characterization model of the model inputs is deterministic. Consequently, it has not yet considered how sensitivity is affected when new input observation information becomes available. To address this, this paper proposes a Bayesian updating method for reliability-based GSA applicable to scenarios with new input observation information. First, based on Bayesian updating theory, the posterior stochastic characterization model of the model inputs under the condition of new input observation information is constructed, and the posterior failure probability of the structure is further derived. Next, by measuring the average difference between the posterior failure probability and the conditional posterior failure probability across the entire model inputs space, a posterior sensitivity index is defined. Finally, combining a single-loop numerical simulation technique with an active-learning Kriging model, an efficient algorithm for solving this index is investigated. The Bayesian updating framework established in this paper can dynamically update structural sensitivity as new input observation information becomes available. This provides real-time decision-making support for dimensionality reduction in reliability-based design and optimization models.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 103983"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148568399","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":"Risk analysis of high-speed maglev train-track collisions on bridges under crosswinds","authors":"Weixu Wang,&nbsp;Bin Wang,&nbsp;Mengze Lyu,&nbsp;Yan Jiang,&nbsp;Huoyue Xiang","doi":"10.1016/j.probengmech.2026.104003","DOIUrl":"10.1016/j.probengmech.2026.104003","url":null,"abstract":"<div><div>The narrow magnetic gaps inherent to electromagnetic suspension (EMS) high-speed maglev systems critically constrain operational safety, rendering maglev train-track collision a primary failure mode under intense crosswinds. Accurately assessing this low-probability, high-consequence hazard is challenging because high-dimensional coupled modelling must be combined with tail-region probability estimation. This study establishes a unified cross-platform modelling framework for the wind-maglev train-track-bridge (WMTTB) system. The framework integrates the dimension-reduced probability density evolution equation (DR-PDEE) with an absorbing boundary process (ABP) to express physical clearance limits as a first-passage probability (FPP) metric. Quantitative analyses reveal that crosswinds induce both mean drift and broadening in magnetic gap fluctuations. Within the examined wind velocity range of 0-30 m/s, the guide gap provides the dominant contribution to the computed collision risk. Electromagnets at the windward-side ends are most vulnerable. Neither reducing running speed nor increasing girder depth independently mitigates collision risk substantially; deeper girders yield only marginal FPP reductions in suspension gap fluctuations. By coupling WMTTB co-simulation with DR-PDEE-ABP-based first-passage analysis, the framework provides an efficient tool for quantifying maglev train-track collision risk under stochastic crosswinds.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 104003"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148737196","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":"Parametric inference of generalized Shiha distribution under type-I progressively hybrid censoring scheme","authors":"F.A. Shiha,&nbsp;Ehab M. Almetwally,&nbsp;Rabab S. Gomaa,&nbsp;Ahlam H. Tolba","doi":"10.1016/j.probengmech.2026.103997","DOIUrl":"10.1016/j.probengmech.2026.103997","url":null,"abstract":"<div><div>In reliability analysis, it remains a difficult task to model lifetime data with complicated hazard rate patterns under censoring. In this study, we present a three-parameter generalized Shiha (GSh) distribution that is defined as a mixture of three gamma distributions. The suggested model extends the traditional Shiha distribution and provides more flexibility in illustrating a range of hazard rate forms, including rising, unimodal, and non-monotonic behavior often seen in practice. Under the type-I progressive hybrid censoring system, statistical inference is developed for the model parameters. The maximum likelihood approach is applied for parameter estimation, then, based on the observed Fisher information and the Delta method, approximate confidence intervals are derived. In addition, Bayesian inference is performed based on independent gamma priors, where posterior estimates are obtained via the Metropolis–Hastings algorithm under the squared error loss function and the general entropy loss function. Simulations using the Monte Carlo technique are conducted at different sample sizes and censoring rates to evaluate the performance of the proposed methods. Bayesian estimators tend to be more robust and have higher precision in estimating the parameters of the model, especially with mild to moderate censoring. The applicability of the proposed model is illustrated through several data applications. The goodness-of-fit measures and information criteria indicate that the GSh distribution can provide better fitting results than the existing models in some instances. Overall, the proposed method offers a practical framework for studying censored lifetime data, especially for data exhibiting heterogeneous failure modes.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 103997"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148737199","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":"Probability analysis of landslide occurrence under the coupling condition of rainfall intensity and soil parameter uncertainty","authors":"Min Pan,&nbsp;Min-Hao Wan,&nbsp;Xiang-Wei Zeng,&nbsp;Zhi-Ping Deng,&nbsp;Min Zhong,&nbsp;Shui-Hua Jiang,&nbsp;Annan Zhou","doi":"10.1016/j.probengmech.2026.104020","DOIUrl":"10.1016/j.probengmech.2026.104020","url":null,"abstract":"<div><div>Accurate probabilistic analysis of slope stability under rainfall requires comprehensive consideration of both rainfall randomness and the spatial variability of soil parameters. However, the coupled effects of rainfall uncertainty and soil-parameter spatial variability have received limited attention in year-long, daily-resolution probabilistic analyses that aim to capture the temporal evolution of slope failure probability. To bridge this gap, a probabilistic analysis framework that explicitly couples random rainfall with spatially variable soil parameters is proposed for assessing the slope reliability. The Karhunen-Loève expansion method is employed to simulate the spatial variability of soil parameters, while the Bounded Random Cascade (BRC) model is used to simulate the randomness of rainfall. The generated rainfall time series and the spatially variable soil parameters are coupled sequentially for seepage and stability analysis. The Latin hypercube sampling (LHS) method is then applied to estimate the slope failure probability (<em>P</em>_<em>f</em>). A landslide in Suichuan County, Ji'an City, Jiangxi Province, is taken as a case study. The calculated results show distinct temporal evolution patterns of the slope failure probability under the considered rainfall and soil-parameter uncertainty conditions. Under different modes, the slope <em>P</em>_<em>f</em> shows an overall increasing trend with rainfall duration, and its rate of increase is positively correlated with the monthly average rainfall intensity. Under the random rainfall mode, <em>P</em>_<em>f</em> fluctuates obviously due to the variation of daily rainfall intensity. Furthermore, the redistribution effect of uniform rainfall has an impact on <em>P</em>_<em>f</em>, and the coupled analysis of random rainfall and soil parameter uncertainty yields a more gradual change in <em>P</em>_<em>f</em> compared with the uncoupled case.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 104020"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148951228","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":"Non-stationary stochastic vessel roll dynamics with hereditary fractional-order hydrodynamic damping and added-inertia nonlinearity","authors":"Ioannis P. Mitseas","doi":"10.1016/j.probengmech.2026.104000","DOIUrl":"10.1016/j.probengmech.2026.104000","url":null,"abstract":"<div><div>In this paper, an efficient semi-analytical methodology for the non-stationary stochastic analysis of nonlinear ship rolling in irregular seas is developed. To account for the underlying maritime complexity, the roll dynamics are described by a physically consistent fractional-order system that incorporates added inertia nonlinearity, cubic-quintic restoring characteristics, and nonlinear quadratic viscous damping. A defining feature of the model is the representation of hereditary hydrodynamic damping via a fractional derivative operator, which naturally captures the memory effects inherent in fluid-hull interactions. The non-stationary sea-wave excitation is modeled through a shaping-filter approach, specifically by means of a calibrated fourth-order filter combined with deterministic amplitude modulation, yielding a compact finite-dimensional Markovian representation. The proposed method leverages a refined blend of statistical linearization (SL), harmonic balancing (HB), and a time-varying covariance Lyapunov equation. Its effectiveness rests on a parsimonious yet physically consistent Markovian augmentation of the ship-roll dynamics. Local-in-time nonlinearities are treated via SL, while the fractional-memory contribution is embedded into an evolving equivalent-linear closure through time-dependent HB components. A key methodological refinement involves updating the representative carrier frequency used in the HB step solely from the statistically linearized backbone to avoid implicit coupling. The framework efficiently delivers estimations of time-dependent response variances, evolutionary power spectra, and roll-amplitude probability-density function surfaces. Validation against benchmark Monte Carlo simulations demonstrates a high level of agreement across various sea states and fractional orders. Ultimately, the proposed methodology offers a reliable, physically interpretable, and computationally efficient tool for stochastic ship-roll response and stability assessment in uncertain and dynamically evolving open sea environments.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 104000"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148737202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fragility assessment of transmission line supports under non-synoptic wind loads using multi-fidelity stochastic emulators","authors":"Felipe C. Macedo,&nbsp;André T. Beck,&nbsp;Katerina Giannoukou,&nbsp;Luis G.L. Costa,&nbsp;Henrique M. Kroetz,&nbsp;Leandro F. Fadel Miguel,&nbsp;Stefano Marelli,&nbsp;Bruno Sudret","doi":"10.1016/j.probengmech.2026.103971","DOIUrl":"10.1016/j.probengmech.2026.103971","url":null,"abstract":"<div><div>Fragility functions are central to the Performance-Based Wind Engineering (PBWE) framework for assessing the reliability of transmission lines (TLs) under tornado and downburst wind loads. Traditionally, these curves are constructed using Monte Carlo simulations; however, the extensive number of replications required by nonlinear dynamic time-history analyses renders such simulations computationally prohibitive for practical fragility estimation. In this study, a multi-fidelity stochastic surrogate modeling approach is applied to efficiently construct fragility functions for TL structures subjected to tornado-induced wind loads. The framework employs the recently developed multi-fidelity generalized lambda model (MF-GLaM) emulator combining low- and high-fidelity simulations to reproduce the full probabilistic relationship between intensity measures (IMs) and engineering demand parameters (EDPs). This approach avoids reliance on replication-based methods or restrictive assumptions regarding the probability distributions of the fragility functions. A case study is presented on a simplified linear-elastic transmission tower, where the MF-GLaM accurately predicts non-monotonic and heteroscedastic bi-dimensional fragility surfaces under stochastic tornadic wind fields. The results demonstrate that the MF-GLaM significantly outperforms single-fidelity emulators, achieving lower prediction errors, faster convergence, and enhanced accuracy while reducing computational costs compared to the single-fidelity approach. Overall, the proposed framework offers a general and scalable methodology for probabilistic fragility assessment of structures under complex, transient wind phenomena, facilitating efficient risk-based design within the PBWE paradigm.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 103971"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148568031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Correlation redefinition and analysis for monitoring data-based operational bridge evaluation","authors":"Shenao Zhang,&nbsp;Wensheng Jia,&nbsp;Qiwen Jin,&nbsp;Xin Cui,&nbsp;Mohammad Noori,&nbsp;Wael A.A.,&nbsp;Ahmed Silik","doi":"10.1016/j.probengmech.2026.103986","DOIUrl":"10.1016/j.probengmech.2026.103986","url":null,"abstract":"<div><div>This study is dedicated to propose a new correlation coefficient to cope with the limitations of the traditional Pearson correlation coefficient, Spearman correlation coefficient and Kendall correlation coefficient in specific scenarios such as in-service bridge monitoring. Firstly, the scope, essential meaning and differences of these three traditional correlation coefficients are systematically analyzed and compared. The characteristics of the bridge monitoring data were then further analyzed and a new correlation coefficient was designed, taking into account the local slope and distance, to capture the dynamic characteristics between data points. Finally, the independence tests of the newly proposed correlation coefficients and three traditional correlation coefficients are carried out considering three working conditions, namely, bridge measured data, very strong correlation data, and very weak correlation data, in order to validate and explore the actual performance of the new correlation coefficients. Study shows that, First, when the sample size of the very strong correlation data is large enough, the value of the newly proposed correlation coefficient reaches 0.8376, which is close to 1. This indicates that it is effective in capturing strong correlations between variables in very strong linear relationships. Second, The value of the new correlation coefficient is 0.002 when the sample size of very weakly correlated data is sufficient, which proves the excellence of the new correlation coefficient in accurately measuring the true correlation even when the correlation between the variables is not obvious. Third, When the number of samples of the measured bridge monitoring data is large enough, the value of the new correlation coefficient reaches 0.7378, which is obviously larger than the three traditional correlation coefficients, reflecting the potential advantage of the new correlation coefficient in dealing with the abnormal data in the real environment. However, it is worth noting that, upon further verification, the new correlation coefficient still has limitations when reflecting non-monotonic relationships between variables (as evidenced in this study by quadratic dependencies in distributions symmetric about zero). The correlation coefficient formula proposed in this study can provide a new expectation for the analysis of long-term monitoring data of bridges, and the applicability of the coefficient can also be verified through the analysis in other fields, so that the study of the correlation coefficient can be more perfect.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 103986"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148635366","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":"Stationary response of a MDOF frictional system with a single vibration mode excited by random excitation","authors":"Xiaole Luan,&nbsp;Qinhan Chen,&nbsp;Zhiqiang Wang,&nbsp;Zefei Zhu,&nbsp;Zhilong Huang","doi":"10.1016/j.probengmech.2026.103980","DOIUrl":"10.1016/j.probengmech.2026.103980","url":null,"abstract":"<div><div>In this paper, the stationary response of a multi-degree-of-freedom frictional stochastic system is studied. The corresponding conservative system is approximately linear, while the damping effect induced by friction is obtained using the generalized harmonic transformation. Based on the principle of stochastic averaging, the properties of the corresponding conservative system are utilized, and the system is decoupled by modal analysis techniques, with the modal amplitudes treated as slow variables. The structure is excited by colored noises, and only one vibration mode is activated. By leveraging the slow-varying effect of the modal amplitudes and modal transformation, the damping effect of friction can be expressed as a function of the modal amplitude. The original system is equivalently reduced to a quasi-linear single-degree-of-freedom system excited by white Gaussian noise. An analytical solution exists for this equivalent system. The response of each degree of freedom in the original system is obtained through modal transformation. Three-degree-of-freedom stochastic systems with Dahl friction are studied as examples, and the effectiveness of proposed method is validated through comparison with Monte Carlo simulations.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 103980"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148568040","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 knowledge-integrated Bayesian framework for shear capacity prediction of steel reinforced concrete beams with uncertainty quantification","authors":"Jiayi Chen,&nbsp;Jinjun Xu,&nbsp;Giuseppe Carlo Marano,&nbsp;Tianyu Xie,&nbsp;Chenhao Wu","doi":"10.1016/j.probengmech.2026.103998","DOIUrl":"10.1016/j.probengmech.2026.103998","url":null,"abstract":"<div><div>Accurate prediction of steel reinforced concrete (SRC) beam shear capacity is critical for structural safety, yet traditional deterministic formulas cannot quantify uncertainties from materials, geometry and simplified mechanical assumptions. This study develops a knowledge-enhanced Bayesian model under the framework of “canonical knowledge prior + data correction + uncertainty quantification”, which embeds code-specified mechanical laws into Bayesian updating with experimental data. A dataset of 93 SRC beam specimens with diverse material and geometric parameters is adopted for MCMC probabilistic calibration. Validated via residual diagnosis, posterior inspection, cross-validation and 13 external test groups, the proposed model yields a mean prediction-to-experiment ratio of 0.93, reducing systematic bias by 76% compared with YB 9082-2006 and outperforming JGJ 138-2016 and ACI 318-19. Three types of correction terms are compared, and linear superposition balances prediction accuracy and physical interpretability best. The knowledge-data integrated framework supports reliability-oriented SRC structural design, and insufficient data for deep beams and high-strength concrete points out subsequent research directions.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 103998"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148735731","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":"On stochastic free vibrations of Eringen's two-phase elastic nanobeams","authors":"Marcin Kamiński,&nbsp;Roozbeh Ashrafian,&nbsp;Marzia Sara Vaccaro,&nbsp;Raffaele Barretta","doi":"10.1016/j.probengmech.2026.103969","DOIUrl":"10.1016/j.probengmech.2026.103969","url":null,"abstract":"<div><div>This study develops a probabilistic framework for analyzing free vibration of nanobeams using the generalized differential quadrature method (GDQM) as the numerical solver. The approach's configuration (asymmetrical and bi-orthogonal) requires a procedure distinct from existing works to couple with the second-order stochastic perturbation method (SOSPM). Specifically, a particular form of undamped vibration based on a primary displacement field (Bernoulli-Euler) and harmonic assumption is investigated in this work. Furthermore, integrating small-scale effects of Eringen's two-phase (local/nonlocal) elasticity theory, a consistent mathematical size-dependent theory, with probabilistic uncertainties provide an opportunity to predict the nonlocal factor, which is an essential parameter in the approach. Ultimately, the reliability of the second-order stochastic perturbation method is evaluated.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 103969"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148568036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}