Probabilistic Engineering Mechanics最新文献

{"title":"Graph-theory-driven configuration synthesis and evidence-based reliability optimization for lightweight morphing wings","authors":"Jianghong Yu ,&nbsp;Renrui Liu ,&nbsp;Jiachang Tang ,&nbsp;Penglin Dong ,&nbsp;Qishui Yao","doi":"10.1016/j.probengmech.2026.103939","DOIUrl":"10.1016/j.probengmech.2026.103939","url":null,"abstract":"<div><div>To address the challenges of high complexity in configuration synthesis of multi-bar mechanisms for morphing wings, the oversight of parameter correlation in reliability optimization, and the difficulty in balancing lightweight design with structural reliability, this paper proposes a graph theory-driven configuration synthesis method for 8-bar morphing wing mechanisms and a reliability optimization approach integrating Copula functions with evidence theory. Based on graph theory, isomorphism discrimination between kinematic chains and topological graphs is implemented, overcoming the challenge of nonlinear polynomial equations encountered in traditional analytical methods for 8-bar mechanisms. A novel morphing wing mechanism configuration is designed to satisfy requirements for large deformation and high stiffness. Local sensitivity analysis is employed to quantify the quantitative relationships between structural dimensions and stiffness, total deformation, and mass, enabling the selection of optimal optimization parameters. The Copula function is introduced into evidence theory to construct a joint basic probability assignment (JBPA) that accounts for structural parameter correlations. Addressing the issue that the independence assumption in evidence theory may lead to significant errors in reliability analysis. Compared with traditional graph theory-based configuration synthesis methods, the proposed method enables systematic screening and innovative design of 8-bar mechanism topologies, eliminating configuration redundancy and motion interference. Unlike conventional structural topology optimization, this method achieves lightweight design under reliability constraints, better aligning with the uncertain operating conditions of practical engineering. Finally, optimization results show that at a 95% target reliability, the structural mass is reduced by 16.43% compared with the original mechanism, with the maximum deformation and equivalent stress both meeting safety limits.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"84 ","pages":"Article 103939"},"PeriodicalIF":3.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147858245","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 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}

{"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 single-loop active learning framework for rare-event time-dependent reliability analysis under hybrid uncertainties","authors":"Jia Li ,&nbsp;Chi Ma ,&nbsp;Jialong He ,&nbsp;Yan Liu ,&nbsp;Liyao Yu","doi":"10.1016/j.probengmech.2026.103941","DOIUrl":"10.1016/j.probengmech.2026.103941","url":null,"abstract":"<div><div>Time-dependent rare-event reliability analysis under hybrid uncertainties is challenging because the effective failure region becomes highly localized and may shift with interval and time conditions, which makes efficient sampling and reliable boundary characterization difficult to achieve simultaneously. This study proposes a unified single-loop global-local cooperative active learning framework for estimating the lower and upper bounds of time-dependent rare-event failure probabilities under hybrid uncertainties that include random variables, interval variables, and stochastic processes. In the global stage, cross-entropy importance sampling (CE-IS) progressively focuses the proposal density toward potential failure regions in the random-variable space, while an expected risk function (ERF) constructed from Kriging prediction statistics guides the identification of high-risk interval-time conditions. After the high-risk region becomes sufficiently concentrated, boundary-oriented local refinement is activated to improve failure-boundary resolution within the same iterative structure. To further enhance efficiency, a failure-severity-based weighting factor is introduced into the cross-entropy updating step to accelerate proposal focusing and reduce unnecessary model evaluations during global exploration. Three numerical examples and one engineering case demonstrate that the proposed framework provides stable and accurate estimates of time-dependent failure probability bounds with improved computational efficiency.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"84 ","pages":"Article 103941"},"PeriodicalIF":3.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147858247","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":"Reliability analysis of slurry modified stiffened deep cement mixing (SDCM) pile considering spatial variability of multi-layer soil","authors":"Yu-Liang Yan ,&nbsp;Bang-Long Xie ,&nbsp;Peng-Yuan Zhao ,&nbsp;Yong-Chao Liu","doi":"10.1016/j.probengmech.2026.103932","DOIUrl":"10.1016/j.probengmech.2026.103932","url":null,"abstract":"<div><div>With the increasing demand for foundation bearing capacity in transportation engineering projects such as embankments and bridges, composite piles have been widely used in engineering practices due to their superior bearing characteristics. In this study, a slurry modified technology was proposed to improve stiffened deep cement mixing (SDCM) piles, aiming to prevent slurry pollution and protect the environment. Many studies rely on deterministic analysis, overlooking the spatial variability of multi-layer soil, which may lead to inaccurate predictions of bearing capacity and stability for SDCM piles. Therefore, a random finite difference method (RFDM) model based on the random field was established in this study to conduct parameter sensitivity analysis on the scale of fluctuation (SOF) and coefficient of variation (COV) for different soil parameters. The results indicate that increases in SOF and COV of soil parameters both lead to significant enhancement of uncertainty in the bearing characteristics of SDCM piles and decrease in the mean values of ultimate bearing capacity and ultimate displacement. Finally, reliability analysis was conducted on the relationship between the factor of safety (<em>FS</em>) and the probability of failure (<em>P</em>). These findings not only emphasize the critical effect of spatial variability of soil on the design of SDCM piles but also highlight the importance of incorporating appropriate safety margins into the design.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"84 ","pages":"Article 103932"},"PeriodicalIF":3.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147713830","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":"Seismic fragility of pile groups with batter piles in slope: A three-dimensional finite element investigation","authors":"Shankar Kumar ,&nbsp;Rajib Sarkar ,&nbsp;Lohitkumar Nainegali","doi":"10.1016/j.probengmech.2026.103937","DOIUrl":"10.1016/j.probengmech.2026.103937","url":null,"abstract":"<div><div>The performance of pile groups in slope has still not been adequately investigated, especially for seismic loading conditions. In this study, the seismic fragility of a 2 × 2 pile group, considering both vertical and batter piles with angles of 5° and 10°, is investigated for a sandy soil slope with a height of 15.9 m and a slope angle of 30°. Three-dimensional (3D) finite element (FE) models are developed using an advanced hardening soil constitutive model for sand with different relative densities of 50% and 70%. Nonlinear dynamic analyses are then conducted using five real earthquake time histories with a diverse range of frequencies. The results indicate that the pile cap displacement reduces by 12-26% and the bending moment reduces by 5-20% for battered pile groups on slope compared to the vertical pile group. Furthermore, using the scaled spectrum-compatible time histories with PGA values ranging from 0.05 g to 1.0 g, seismic fragility curves are developed for three damage states. The probability of damage for batter pile groups reduces by 1-11% compared to a vertical pile group on slope for pile cap displacement demand, and the range of reduction for bending moment demand is 3-15%. Overall, the probability of damage for pile head displacement and bending moment demands decreased by 20-40% for the relative densities of 70% compared to 50% considered in the study. Finally, the probability of damage to pile groups with batter piles in the slope for different levels of seismicity in India, represented by six cities across varying seismotectonic settings, is presented.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"84 ","pages":"Article 103937"},"PeriodicalIF":3.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147802316","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":"Experimental investigation of non-Gaussian extreme value distribution for wind loads on photovoltaic arrays","authors":"Shaopeng Li ,&nbsp;Wenjun Guo ,&nbsp;Xin Li ,&nbsp;Tian Li ,&nbsp;Qingshan Yang ,&nbsp;Wenshan Shan","doi":"10.1016/j.probengmech.2026.103938","DOIUrl":"10.1016/j.probengmech.2026.103938","url":null,"abstract":"<div><div>This study investigates the extreme wind pressures acting on a five-row, three-span photovoltaic (PV) array based on wind tunnel experiments and generalized extreme value (GEV) modeling. The wind tunnel experimental results show that wind-induced pressures on the PV array exhibit pronounced non-Gaussian behavior, with spatially varying skewness and kurtosis governed by flow separation and wake interactions. Severe non-Gaussian characteristics are concentrated at windward stagnation regions under the 0° wind direction and at leeward separation zones under the 180° wind direction. To model the extremes, GEV distributions were fitted to block maxima of pressure-coefficient time histories, and non-Gaussian peak factors were derived from the 0.57-quantile of the fitted cumulative distribution function. The resulting GEV-based peak factors consistently exceed the value prescribed in the Chinese load code (g = 2.5), indicating that Gaussian peak-factor assumptions significantly underestimate extreme wind pressures in PV arrays. Furthermore, a normalized shielding coefficient was defined by referencing peak factors and force coefficients to the spanwise leading-edge row. The results demonstrate that, under head-on inflow, downstream rows experience varying degrees of attenuation, whereas oblique and reverse inflows weaken classical shielding and may induce wake-driven amplification of non-Gaussian extremes in interior rows. These findings provide crucial insights for wind-resistant design, extreme load prediction, and future code refinements for large-scale PV support systems.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"84 ","pages":"Article 103938"},"PeriodicalIF":3.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147802317","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}