Probabilistic Engineering Mechanics最新文献

{"title":"An integrated reliability framework for phased mission systems with backup missions under cascading failures and epistemic uncertainty","authors":"Rongxing Duan,&nbsp;Xiwei Liu,&nbsp;Zikang Zou","doi":"10.1016/j.probengmech.2026.103992","DOIUrl":"10.1016/j.probengmech.2026.103992","url":null,"abstract":"<div><div>This paper develops an integrated reliability assessment framework for phased mission systems (PMS) with backup missions under cascading common-cause failures (CCF) and epistemic uncertainty. The framework uses generalized stochastic Petri nets (GSPN) to describe phase execution, serial/parallel backup missions, and probabilistic cascading CCF, while dynamic fault trees provide engineering fault-logic templates. To quantify interval-valued lifetime parameters, a PMS-BDD modularization strategy identifies monotonic and non-monotonic modules, reducing the dimension of the subsequent optimization. The remaining boundary-parameter search is solved by a GA-MCS procedure, in which confidence-interval-based adaptive sampling determines the required number of simulations. A spacecraft propulsion case shows that backup missions increase task success probability by more than 4 percentage points, whereas cascading CCF substantially reduces reliability; compared with DLMCS, the proposed algorithm reduces computation time by 57.7% and yields a subsystem <em>S</em> reliability interval of [0.9926, 0.9977].</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 103992"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148635277","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":"Optimising classical and non-traditional tuned mass dampers topology in deterministic and random vibration environments","authors":"Yubin Gu,&nbsp;Navneet Kumar,&nbsp;Uraz Tarker,&nbsp;Timothy Waters,&nbsp;Daniil Yurchenko","doi":"10.1016/j.probengmech.2026.103989","DOIUrl":"10.1016/j.probengmech.2026.103989","url":null,"abstract":"<div><div>We investigate the optimal design of both conventional and non-traditional tuned mass dampers (TMDs) subjected to narrowband random excitation, with the objective of minimising the kinetic energy of the primary structure. A key contribution of this work is the development of a novel analytical formulation for the narrowband excitation case, yielding exact steady-state second-order moment equations for the conventional TMD. Although these expressions can, in principle, be written in closed form, they are prohibitively lengthy and do not lead to practical tuning rules. Instead, the exact moment equations are solved numerically to evaluate the mean-square velocities of the primary and secondary masses, providing a direct and accurate measure of their kinetic energy. The analysis demonstrates that, under narrowband stochastic excitation, the optimal tuning deviates fundamentally from classical deterministic results and does not coincide with existing optimal solutions. To identify optimal parameters, three optimisation strategies, reinforcement learning (RL), particle swarm optimisation (PSO), and surrogate-based Kriging optimisation (SO+KRG), were systematically benchmarked and validated under both deterministic and stochastic conditions. Among these, reinforcement learning consistently delivers superior performance in terms of accuracy and computational efficiency, particularly as the dimensionality of the design space increases. Moving beyond classical configurations, this study presents a comprehensive exploration of non-traditional TMD topologies, which have not previously been examined in a unified framework. An automated incidence-matrix approach was implemented to generate all admissible spring–damper network configurations connecting the primary and secondary masses. From a set of 29 candidate topologies with up to two springs and two dampers, several non-conventional layouts were identified that outperform the classical TMD across both deterministic and stochastic regimes. The optimisation of topologies reveals a common structural characteristic shared by the most effective absorbers, providing a simple yet robust design principle for next-generation TMD systems operating in deterministic and stochastic environments.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 103989"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148737193","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":"Fokker-Planck-driven structured Bayesian inference framework for nonlinear stochastic dynamical systems","authors":"Tong Ren,&nbsp;Di Liu,&nbsp;Meng-Ze Lyu","doi":"10.1016/j.probengmech.2026.103996","DOIUrl":"10.1016/j.probengmech.2026.103996","url":null,"abstract":"<div><div>This paper presents a structured Bayesian inference framework for parameter estimation in nonlinear stochastic dynamical systems. The proposed framework aims to improve parameter uncertainty quantification and provide a probabilistic basis for predicting the stationary response. First, we adopt the stochastic averaging method to derive an approximate analytical expression for the stationary probability density function (PDF). Subsequently, this expression is used as the likelihood function within the structured Bayesian framework, enabling accurate characterisation of the stationary statistical properties and facilitating parameter estimation. Second, an empirical Bayesian approach is employed to construct an informative prior distribution from historical data. Specifically, marginal likelihood maximisation is used to determine the hyperparameters of the prior distribution, thereby improving the informativeness of the prior model. These two steps collectively enhance the consistency between prior information and stationary response statistics. To improve posterior sampling quality and convergence, a hybrid Metropolis-within-Gibbs (MWG) algorithm integrated with particle swarm optimisation (PSO), named PSO-MWG, is developed. Finally, the proposed method is validated through four representative nonlinear systems to demonstrate its applicability and reliability. Meanwhile, multiple metrics are employed to evaluate the sensitivity to historical data and the sampling performance of the proposed algorithm. The comparative analysis with the MWG algorithm demonstrates that the proposed PSO-MWG algorithm achieves clear improvements in estimation accuracy, effective sample size of the posterior samples, and the reconstruction capability of the system response PDF. Overall, the results confirm the effectiveness and robustness of the proposed structured Bayesian inference framework for parameter estimation and associated uncertainty quantification in nonlinear stochastic dynamical systems.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 103996"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148635276","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 novel multiscale composite optimization fluctuation dispersion entropy for fault diagnosis of rolling bearings","authors":"Haiming Wang,&nbsp;Shaopu Yang,&nbsp;Yongqiang Liu,&nbsp;Wenpeng Liu,&nbsp;Yanli Wang","doi":"10.1016/j.probengmech.2026.103999","DOIUrl":"10.1016/j.probengmech.2026.103999","url":null,"abstract":"<div><div>Due to the complex work conditions of rolling bearings, the vibration signals generated exhibit nonlinear characteristics, which means that single-scale feature extraction techniques are hard to extract fault features accurately. Despite its application in mechanical engineering, multiscale fluctuation dispersion entropy (MFDE) is hindered by an inadequate coarse-graining process, which leads to poor stability and large errors. Consequently, a novel multiscale composite optimization fluctuation dispersion entropy (MCOFDE) is proposed for feature extraction. This MCOFDE designs a novel slippage-averaging multiscale approach for signal coarsening, accounting for the connection between data before and after breakpoints, thereby reducing loss of key message in the entropy value. The proposed MCOFDE has been validated through simulation experiments. Comprehensive experiments under varying training ratios, scales, and classifiers demonstrate that MCOFDE outperforms classical methods in diagnostic accuracy and reliability.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 103999"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148735730","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":"Probabilistic model updating via approximate Bayesian computation and synthetic likelihood function","authors":"Pinghe Ni,&nbsp;Zifan Tian,&nbsp;Qiang Li,&nbsp;Yulei Bai,&nbsp;Jinlong Fu","doi":"10.1016/j.probengmech.2026.104005","DOIUrl":"10.1016/j.probengmech.2026.104005","url":null,"abstract":"<div><div>Approximate Bayesian Computation (ABC) provides an effective way to solve the problem of model likelihood function that is difficult to express or computationally expensive to evaluate. However, traditional ABC methods face critical limitations in selecting appropriate distance functions and tolerance thresholds. This paper proposes a probabilistic model updating method based on the combination of ABC and Synthetic Likelihood (SL), referred to as SL-ABC. This method assumes that the statistics follow a multivariate normal distribution and uses simulated data to estimate the mean and covariance matrix of the statistics, thereby constructing an approximate likelihood function. This likelihood is then embedded into the Transitional Markov Chain Monte Carlo framework to efficiently approximate the true posterior distribution of the structural parameters. Compared to traditional ABC method, SL-ABC eliminates the need for complex selection of distance metrics and tolerance thresholds while demonstrating superior computational efficiency and accuracy. Two numerical simulations verify the method's effectiveness in structural probabilistic model updating when appropriate summary statistics are selected. Application to a Benchmark structural damage identification problem further demonstrates SL-ABC's capability to accurately detect both damage locations and severity, highlighting its potential for engineering structural assessments.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 104005"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148776259","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 CDF evolution approach for efficient time-dependent reliability analysis of aging RC structures","authors":"Filippo Landi,&nbsp;Massimiliano Lucchesi","doi":"10.1016/j.probengmech.2026.104011","DOIUrl":"10.1016/j.probengmech.2026.104011","url":null,"abstract":"<div><div>Evolution problems involving uncertain initial conditions naturally lead to stochastic formulations in which the state variable evolves as a random process. Classical Monte Carlo simulation (MCS) is commonly employed to track the time evolution of associated probability distributions. Still its accuracy requires a very large number of deterministic realizations, resulting in prohibitive computational costs for high-dimensional problems. In the present paper, an efficient method is presented to calculate the evolution of the cumulative distribution function (CDF), even in the presence of many random variables. This approach relies on a one-to-one mapping between the integration domain and a subset of the unit cube, enabling the use of good lattice point sets to evaluate the required integrals with substantially fewer deterministic analyses than MCS. The method is particularly suitable for structural reliability applications, where failure probabilities depend on multiple uncertain parameters. These probabilities may be very small and vary over time due to material degradation, evolving environmental conditions, and non-stationary loads that are sometimes modeled as stochastic processes. Its effectiveness is demonstrated in the context of durability assessment of aging reinforced concrete structures, with a specific focus on the evaluation of the time-dependent probability of corrosion damage under changing climate scenarios.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 104011"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148776942","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":"Bridge temperature-induced strain prediction and uncertainty quantification in nonstationary environments via stochastic variational heteroscedastic Gaussian process","authors":"Bachao Zhang,&nbsp;Yafei Ma,&nbsp;Lei Wang","doi":"10.1016/j.probengmech.2026.104017","DOIUrl":"10.1016/j.probengmech.2026.104017","url":null,"abstract":"<div><div>Temperature-induced strain prediction provides a benchmark for structural condition assessment, but existing methods are still limited in quantifying the uncertainty of bridge performance evolution under nonstationary environments. This study develops a framework for bridge temperature-induced strain prediction and uncertainty quantification based on a stochastic variational heteroscedastic Gaussian process (SVHGP). The heteroscedastic relationship between non-uniform temperature field and bridge strain is analyzed. A two-layer probabilistic framework is established that integrates mean-response learning with noise-variance estimation to explicitly characterize input-dependent noise. Following this, the sparse inducing points are introduced for the latent mean and noise functions, respectively. The factorized evidence lower bound (ELBO) is derived to enable mini-batch stochastic variational inference. The variations in epistemic and aleatoric uncertainty are investigated on long-term and short-term time scales. The proposed method was validated using field monitoring data from an in-service concrete cable-stayed bridge under multiple operating scenarios. The results show that the proposed model provides probabilistic predictions of bridge temperature-induced strain and adaptively characterizes input-dependent uncertainty. It also distinguishes epistemic and aleatoric uncertainty across different time scales, while the high-frequency intraday experiment indicates its computational feasibility for nearly million-scale monitoring samples. The proposed model provides an uncertainty-calibrated probabilistic baseline for temperature-induced strain prediction under normal operating conditions.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 104017"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148951223","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 density evolution equation for solving finite-dimensional distributions of a stochastic process","authors":"Changhou Wu,&nbsp;Jie Li","doi":"10.1016/j.probengmech.2026.103970","DOIUrl":"10.1016/j.probengmech.2026.103970","url":null,"abstract":"<div><div>In the fields of stochastic dynamics and engineering reliability analysis, the finite-dimensional probability density function of a stochastic process provides a fundamental tool for characterizing the probabilistic structure and temporal evolution. Based on the conditional independence property of stochastic states across different time instants, this paper establishes a set of partial differential equations to determine the finite-dimensional probability density function of a stochastic process. An efficient numerical implementation strategy is developed, in which the evaluation of high-dimensional joint probability density functions is recast into solving generalized density evolution equation (GDEE). Compared with conventional high-dimensional finite difference frameworks, this method significantly reduces computational burden while maintaining accuracy. Numerical examples illustrate that the proposed equation and corresponding computational method accurately captures the evolution of two-dimensional and higher-order probability densities of stochastic processes.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 103970"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148568033","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":"An NGauss-translation model for spatially variable material properties","authors":"Pei-Pei Fang,&nbsp;Zou-Nan Wang,&nbsp;Qiang Wang,&nbsp;Guo-Jun Cai,&nbsp;Yong Liu","doi":"10.1016/j.probengmech.2026.103984","DOIUrl":"10.1016/j.probengmech.2026.103984","url":null,"abstract":"<div><div>Most material properties are nonnegative and simulated by non-Gaussian random processes, which are generally generated via the conventional Gauss-translation methodology from a Gaussian process. However, translating a Gaussian random process directly to a non-Gaussian random process distorts the correlation structure. To mitigate this kind of distortion, this study proposed an NGauss-translation model for generating non-Gaussian random processes, where the underlying random process is replaced by the Gamma random process. In contrast to the Gaussian distribution, the Gamma distribution has a higher flexibility in its distribution function. As such, the underlying Gamma distribution function can be determined by adjusting its statistical parameters so that its shape is close to that of the target non-Gaussian distribution function. In this manner, the distortion in correlation from Gamma to the target non-Gaussian process can be reduced to a negligible level. On the other hand, many non-Gaussian distributions are special cases of the Gamma distribution, such as Chi-square distribution and Exponential distribution. For those cases, no distortion occurs in correlation structure. The capabilities of the methodology are also demonstrated by numerical examples. The NGauss-translation model was employed to simulate the soil parameters of the sludge disposal site and was combined with numerical simulation for calculating the foundation bearing capacity. The results demonstrate that the proposed method exhibits practical engineering application value.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 103984"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148568403","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":"Probabilistic modeling of the spatio-temporal characteristics of a high-resolution extreme rainfall event","authors":"Antonios Lyras,&nbsp;George Deodatis,&nbsp;Upmanu Lall","doi":"10.1016/j.probengmech.2026.103994","DOIUrl":"10.1016/j.probengmech.2026.103994","url":null,"abstract":"<div><div>A methodology is proposed for establishing the spatio-temporal probabilistic characteristics of an extreme rainfall event, including its major propagation characteristics, through the computation of its empirical frequency–wavenumber (F–K) spectrum. The approach is entirely data-driven and does not rely on assuming a physical model for the precipitation-generating process. The spatio-temporal characteristics of the rainfall field are features discovered directly from the data, without a priori assumptions about the form of the correlation function, the number of relevant scales, or the nature of the anisotropy. The rainfall event is modeled as a non-Gaussian, stationary and homogeneous stochastic wave in two spatial dimensions and time. After the F–K spectrum is computed by applying the appropriate 3D Fourier transform on the observed rainfall field data, it is translated into the corresponding “slowness” function, utilizing a methodology first developed to analyze propagating earthquake waves. Specifically, this framework translates each point of the 3D F–K spectrum, representing a monochromatic wave component of the rainfall field, into a point in the two-dimensional slowness plane, where the angle between that point and the positive <span><math><mi>y</mi></math></span> axis indicates the azimuth of propagation of that monochromatic wave, while the inverse of the distance between the point and the origin is equal to its velocity. In that way, it is possible to determine the propagation characteristics of the rainfall field’s dominant components. This methodology is put to the test using data from a recorded extreme rainfall event from a frontal-convective system that occurred in the Gard region of southern France in 2002. The ensuing analysis identified the F–K spectrum of this event and its major propagation characteristics. The stationarity and homogeneity assumptions were justified by the contents of the spatio-temporal window considered. However, these assumptions can be relaxed in the future. Based on the established F–K spectrum and empirical probability distribution function, sample functions of the rainfall field were generated using a Monte Carlo simulation framework. These generated sample rain fields are critically important for probabilistic flood risk analysis and mitigation. The F–K spectrum methodology in this work is specifically developed for future flood risk analyses of dense urban environments.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 103994"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148635367","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}