Probabilistic Engineering Mechanics最新文献

{"title":"Research on the stochastic dynamic response and reliability of asphalt concrete core dams considering the spatial nonstationary characteristics of material parameters","authors":"Zongkai Wang,&nbsp;Zhiqiang Song,&nbsp;Chuang Li,&nbsp;Xueyang Qu,&nbsp;Yunhe Liu","doi":"10.1016/j.probengmech.2026.103945","DOIUrl":"10.1016/j.probengmech.2026.103945","url":null,"abstract":"<div><div>Rockfill materials of asphalt concrete core dams (ACCDs) exhibit significant spatial variability, and their statistical parameters demonstrate notable nonstationary distribution characteristics in three-dimensional space. The traditional stationary random field assumption can hardly effectively capture the actual evolution trend in material properties with spatial position. To address this issue, a three-dimensional nonstationary random field generation method based on the number theoretic method and the Karhunen–Loève (K-L) expansion is developed, which can simultaneously capture the spatial nonstationarity of the mean, coefficient of variation, and correlation distance of parameters. Furthermore, by combining the nonstationary random field model with the generalized probability density evolution method via the number theoretic method, a reliability analysis method for nonstationary random fields based on the equivalent extreme value principle is established. Adopting a practical ACCD as an engineering case example, a specific ground motion is selected to analyze the stochastic dynamic response and reliability under nonstationary random fields, and the calculated results are compared with those obtained under the stationary random field assumption. The results reveal that under the same strong ground motion input, although the dynamic response modes of the two types of random fields are essentially consistent, the nonstationary random field significantly amplifies the discrete degree of the response, leading to an obvious broadening of the peak acceleration distribution interval. The reliability analysis results confirm that after the nonstationary characteristics are considered, the probability of the dam suffering moderate damage increases from 16% to 24%, indicating that neglecting the spatial nonstationarity of parameters may lead to underestimation of the structural failure risk.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"84 ","pages":"Article 103945"},"PeriodicalIF":3.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148177931","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":"First passage probability of overturning problem for the rocking motion of rigid block excited by the Poisson white noise","authors":"Muyan Bai ,&nbsp;Shichao Ma ,&nbsp;Ping Han ,&nbsp;Wantao Jia ,&nbsp;Xin Ning","doi":"10.1016/j.probengmech.2026.103929","DOIUrl":"10.1016/j.probengmech.2026.103929","url":null,"abstract":"<div><div>Precision instruments in spacecrafts may overturn under stochastic impulse excitation, leading to irreparable consequences. This phenomenon can be regarded as a reliability problem involving the rocking motion of rigid blocks. So, in this paper, the first passage time statistics and exit location distributions are discussed to characterize the overturning problem of the rigid block rocking motion subjected to the Poisson white noise. The proposed generalized cell mapping method is introduced to obtain key reliability indicators, including the mean first passage time, probability density function of the first passage time, reliability function, and exit location distributions. Monte Carlo simulations are used to validate the accuracy of the proposed method. Detailed numerical results indicate that increasing the impulse excitation intensity, restitution coefficient and slenderness ratio decreases the reliability of the rocking motion. For cases where overturning is inevitable, analysis of the exit velocity distribution, shows that the restitution coefficient does not influence the exit velocity at the onset of overturning. In contract, a larger slenderness ratio leads to higher a larger exit velocity, while stronger noise excitation broadens the distribution range of exit velocity.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"84 ","pages":"Article 103929"},"PeriodicalIF":3.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147713831","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":"Higher-order analysis for random vibration of stochastic structures under multi-point stationary Gaussian excitations","authors":"Wenliang Fan ,&nbsp;Ran Zhang ,&nbsp;Xiaoyang Yang ,&nbsp;Wei Hu","doi":"10.1016/j.probengmech.2026.103930","DOIUrl":"10.1016/j.probengmech.2026.103930","url":null,"abstract":"<div><div>In hybrid random vibration analysis under multi-point excitations, the structural response generally exhibits non-Gaussian characteristics, and higher-order statistical information of the excitations is necessary for higher-order analysis of the response. However, no theoretical model currently exists for multi-point correlated excitations, and naturally the higher-order analysis of the response is also unavailable. To address these challenges, a new method integrating vector decomposition, conditional expectation, the pseudo excitation method (PEM), and the mixed-degree cubature formula (MDCF) is proposed. First, the vector of multi-point correlated excitations is decomposed into multiple independent excitation vectors. Second, based on the power spectral density (PSD) of Gaussian excitation and the superposition principle, formulas for the PSD and higher-order spectra of the response of the deterministic structure are derived. Third, the PEM is employed to establish a more efficient and practical formula for the higher-order spectra. Fourth, by introducing the concept of conditional expectation, the hybrid random vibration analysis is transformed into a series of conventional random vibration analyses for deterministic structures. The MDCF is then introduced to evaluate the integral of the conditional expectation, yielding the PSD and higher-order spectra of the response. Finally, two examples are provided to verify the accuracy and efficiency of the proposed method and to demonstrate the necessity of hybrid random vibration analysis.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"84 ","pages":"Article 103930"},"PeriodicalIF":3.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147713859","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 Bayesian parameter inversion method based on saddlepoint approximation prior","authors":"Jikang Su ,&nbsp;Yuping Wang ,&nbsp;Jiaxin Luo ,&nbsp;Zhiyuan Lu ,&nbsp;Xianzhen Huang","doi":"10.1016/j.probengmech.2026.103944","DOIUrl":"10.1016/j.probengmech.2026.103944","url":null,"abstract":"<div><div>Parameter inversion is a fundamental challenge in uncertainty quantification and reliability analysis, and the prior distribution construction often relies on empirical assumptions, which makes it difficult to accurately characterize the statistical properties of the parameters in the case of small samples. As a consequence, inversion accuracy and reliability analysis results are both compromised. To address these challenges, this paper proposes a Bayesian structural parameter inversion framework integrating saddlepoint approximation (SPA). By using the statistical moments of finite samples, SPA is used to reconstruct the cumulant generating function (CGF) and probability density function (PDF) of parameters, leading to a flexible prior representation of parameters. Building upon this, posterior inference is carried out using the improved transitional Markov chain Monte Carlo (iTMCMC) algorithm. In case that the forward model is implicit or expensive, a Kriging surrogate model is incorporated to enhance computational efficiency. Numerical examples demonstrate the advantages of the proposed approach in distribution fitting and failure probability estimation for complex structural uncertainty quantification problems. The results indicate that SPA-based prior distributions effectively capture parameter skewness and tail behavior, thereby improving the reliability of extreme response prediction and structural failure probability estimation.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"84 ","pages":"Article 103944"},"PeriodicalIF":3.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147858243","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 and scalable sparse PCE for uncertainty quantification via randomized greedy basis selection","authors":"Yiren Li,&nbsp;Ranzhe Wang,&nbsp;Yinghao Ye","doi":"10.1016/j.probengmech.2026.103948","DOIUrl":"10.1016/j.probengmech.2026.103948","url":null,"abstract":"<div><div>Polynomial Chaos Expansion (PCE) is a widely used technique for uncertainty quantification due to its high modeling accuracy. However, its applicability in practical scenarios is often limited by the need for prior statistical information about input variables and its inefficiency in handling high-dimensional problems. This paper proposes an efficient and accurate data-driven sparse PCE approach that builds upon existing data-driven frameworks while significantly improving computational efficiency. The method employs a randomized greedy algorithm combined with a data-driven strategy to iteratively identify the most significant polynomial using a limited number of input samples. Compared to state-of-the-art data-driven methods, the proposed approach achieves similar accuracy while offering over a 50-fold improvement in computational efficiency. Its scalability makes it particularly well-suited for complex engineering uncertainty quantification problems where samples are scarce. The effectiveness and advantages of the method are demonstrated through four numerical examples.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"84 ","pages":"Article 103948"},"PeriodicalIF":3.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148001187","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":"Uncertainty quantification of a short-term thermal aging model of a peroxide-cured EPDM rubber: Standard Bayesian inference versus multilevel Bayesian inference","authors":"A. Kadhambariyil ,&nbsp;S.P.A. Bordas ,&nbsp;L.A.A. Beex","doi":"10.1016/j.probengmech.2026.103936","DOIUrl":"10.1016/j.probengmech.2026.103936","url":null,"abstract":"<div><div>Deterministic least-squares calibration only identifies one set of model parameters. However, if the number of measurements is limited and the experimental scatter is substantial, it may be worth to identify all possible sets of model parameters, because the parameter values of each set may vary substantially. Bayesian inference (BI) can achieve this task. The aim of this study is to help pave the way for the use of BI in the field of rubber and elastomer research. It tries to accomplish this by providing a systematic comparison between conventional and multilevel BI, based on a thermal aging model for relatively short aging durations of a peroxide-cured ethylene propylene diene monomer (EPDM) rubber. Although conventional BI indeed treats the model parameters as random variables, it still assumes that only a single set of model parameters is responsible for the experimental observations. This entails that if an abundance of experimental observations were available, conventional BI would only yield a single set of model parameters, just like a deterministic calibration. This does not reflect the situation in which rubber is intrinsically uncertain, which can originate from imperfect spatial distributions of fillers, and small differences in raw materials and manufacturing conditions. To incorporate specimen-to-specimen variations, this study also develops multilevel BI. The different assumptions of the conventional and multilevel BI have a clear qualitative and quantitative impact on the results.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"84 ","pages":"Article 103936"},"PeriodicalIF":3.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147945392","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":"Mission reliability modeling for multi-level systems considering competing shock-degradation failures under heterogeneous mission cycles","authors":"Shiqun Li,&nbsp;Yonghua Li,&nbsp;Qing Xia,&nbsp;Zhiyang Zhang,&nbsp;Zhen Xu","doi":"10.1016/j.probengmech.2026.103940","DOIUrl":"10.1016/j.probengmech.2026.103940","url":null,"abstract":"<div><div>With the advancement of high-end equipment towards intelligent and precise development, multi-level mechanical systems require integrated subsystems to accomplish complex mission profiles, resulting in temporal asynchrony between system-level macro-cycle and component-level micro-cycle tasks—termed heterogeneous mission cycles (HMC). Traditional phased mission system (PMS) models, based on synchronization assumptions, struggle to characterize such systems accurately. This paper proposes a multi-level coupled reliability modeling and assessment framework for heterogeneous mission systems (HMS). At the system level, a multi-phase fault tree analysis - binary decision diagram (FTA-BDD) coupled model is constructed, incorporating inter-phase dependencies and disjoint path aggregation operations to characterize the structural evolution and time-dependent success criteria across mission phases. At the component level, addressing the simplified characteristics of component micro-cycles under cumulative shock-two-phase degradation competing failure mechanisms, a modeling method based on the spectrally decomposed backward Kolmogorov equation is proposed. This establishes a unified Partial Integro-Differential Equation dynamics solving framework. The spectral method is employed for dimension reduction, transforming the path-dependent problem into a finite-dimensional dynamical system. The component's full-cycle reliability is output via finite-dimensional Legendre coefficients and integrated into subsystem and system-level mission reliability. A combine harvester case study validates the method's effectiveness, providing systematic modeling theory and method for complex mechanical systems with HMC characteristics.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"84 ","pages":"Article 103940"},"PeriodicalIF":3.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147858246","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 framework for probabilistic prediction of remaining useful life in structural materials","authors":"Victor Maudonet ,&nbsp;Carlos Frederico Trotta Matt ,&nbsp;Americo Cunha Jr.","doi":"10.1016/j.probengmech.2026.103943","DOIUrl":"10.1016/j.probengmech.2026.103943","url":null,"abstract":"<div><div>Accurate prediction of remaining useful life under creep conditions is essential for the structural reliability of high-temperature components in critical engineering systems. Traditional approaches based on deterministic parametric models often overlook the substantial variability inherent in experimental data, compromising the accuracy and robustness of long-term predictions. This study introduces a probabilistic framework to quantify uncertainties in creep rupture time prediction. Robust regression techniques are first applied to mitigate the influence of outliers and enhance the stability of model estimates. Global sensitivity analysis using Sobol indices is then employed to identify the dominant contributors to model uncertainty, followed by Monte Carlo simulations to propagate these uncertainties and estimate the distribution of the remaining useful life. Finally, model selection is guided by statistical criteria, including the Akaike and Bayesian information criteria, to identify the most reliable predictive model. The proposed framework not only enables the definition of safe operational limits with quantifiable confidence levels but is also general and extensible to other time-dependent degradation phenomena, such as fatigue and creep-fatigue interaction.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"84 ","pages":"Article 103943"},"PeriodicalIF":3.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147945391","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 algorithm for generalized RBDO under probabilistic input and fuzzy state","authors":"Xiaomin Wu,&nbsp;Zhenzhou Lu","doi":"10.1016/j.probengmech.2026.103934","DOIUrl":"10.1016/j.probengmech.2026.103934","url":null,"abstract":"<div><div>For the commonly encountered scenarios of probabilistic input and fuzzy state in engineering applications, generalized RBDO (GRBDO) aims at an optimal scheme by balancing generalized failure probability (GFP) constraint and performance objective. However, solving GRBDO is time-consuming due to the nested framework of searching optimal design parameters and analyzing GFP constraints, particularly for extremely small target GFP. To address this issue, a <strong>s</strong>equential <strong>o</strong>ffset estimation and <strong>d</strong>eterministic <strong>o</strong>ptimization is proposed by combining stratified <strong>i</strong>mportance <strong>s</strong>ampling (SODO-IS). In the SODO-IS, the GFP constraint is sequentially replaced as the deterministic one by the performance function offset corresponding to the target GFP, on which the nested framework in GRBDO is decoupled as the sequence of the inverse GFP analysis for estimating offset and the deterministic optimization for searching design parameters. To efficiently estimate the offset corresponding to the extremely small target GFP with rare important region, a stratified IS method, where an explicit and easy-to-sample IS density is adaptively constructed to cover the rare important region by clustering analysis, is developed to reduce the variance of estimating the offset. Due to the sequential decoupling in solving GRBDO assisted by IS variance reduction in estimating offset, the proposed SODO-IS shows higher efficiency than existing methods under acceptable accuracy, which is verified by several examples.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"84 ","pages":"Article 103934"},"PeriodicalIF":3.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147748146","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 new MFk-discrepancy for improving point selection in high-dimensional stochastic system analysis involving uncertain parameters","authors":"Xin Huang,&nbsp;Jian-Bing Chen,&nbsp;Jie Li","doi":"10.1016/j.probengmech.2026.103925","DOIUrl":"10.1016/j.probengmech.2026.103925","url":null,"abstract":"<div><div>Randomness is greatly pervasive and non-negligible across many engineering systems in different disciplines. For stochastic analysis of structural systems involving random parameters, such as stochastic response analysis and stochastic system identification, some computational methods in stochastic mechanics have been developed based on high-efficacy point sets. The accuracy and efficiency of such methods highly rely on the efficacy of representative point sets, based on which deterministic evaluations of the function are conducted. The point-set discrepancy is a crucial tool for measuring the efficacy of global point sets and improving point selection. The existing discrepancy metrics, including both classical types such as the discrepancy, F-discrepancy and EF-discrepancy, along with computationally efficient variants like GF-discrepancy and MF-discrepancy, all face fundamental limitations in simultaneously achieving computational efficiency and effective global uniformity characterization, particularly in high-dimensional cases. In this paper, a maximal k-dimensional marginal EF-discrepancy (MF_k-discrepancy) is proposed as a generalization of both the EF-discrepancy and the MF-discrepancy, successfully trading off the computational cost and measurement efficacy measure by adjusting the parameter k. The analytical and quantitative properties of MF_k-discrepancy are investigated, including deriving the analytical expression and revealing its relationship with EF-discrepancy, thereby establishing a worst-case error estimation incorporated with MF_k-discrepancy for numerical integration. A new perspective for partitioning the probability space is established by defining the k-dimensional mean-assigned probability, and a novel MF_k-discrepancy-optimized point-selection strategy, which involves hierarchical screening of point sets with globally minimized MF-discrepancy using MF_k-discrepancy, is proposed to further enhance the overall structural uniformity of the point sets. The efficiency and robustness of the proposed point-selection method are validated through two numerical examples.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"84 ","pages":"Article 103925"},"PeriodicalIF":3.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147657378","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}