Probabilistic Engineering Mechanics最新文献

{"title":"An efficient multi-dimensional P-box propagation method via overlapping domain recognition and sample reusing","authors":"Yang Liu,&nbsp;Chunlin Gong,&nbsp;Chunna Li,&nbsp;Hua Su","doi":"10.1016/j.probengmech.2026.103974","DOIUrl":"10.1016/j.probengmech.2026.103974","url":null,"abstract":"<div><div>Probability-box (P-box) is increasingly employed to quantify both aleatory and epistemic uncertainties in aerospace engineering problems. However, P-box propagation, typically implemented with an inherent double-loop structure, often incurs an unaffordable computational burden, exacerbated by the expensive simulations in the aerospace system. Considering there are overlapping domains of input samples between inner loops during P-box propagation, we propose an innovative method for recognizing the overlapping domains to reuse the historical samples. For each inner loop, the multi-dimensional sampling space is first identified via the integral of probability, and then decomposed into a set of subspaces by using a rooted directed tree based on a hybrid strategy with three decomposition criteria. A sequential selection strategy, based on the maximum average distance, selects the reusable samples within each complete subspace. The applications of the proposed method are validated through three analytical case studies, as well as two engineering case studies involving a solid rocket and a space truss. The results indicate that compared with the existing double-loop Monte-Carlo and local surrogate model, the proposed method can reduce the function calls by 88∼94%. Compared with the sparse-decomposition-based polynomial chaos expansion, the proposed method can further reduce the computational cost by 56%, highlighting good potential in aerospace engineering applications.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 103974"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148568032","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 efficient focal element classification strategy for evidence theory-based reliability analysis using Kriging model","authors":"Zhenzhong Chen,&nbsp;Chuqi Wang,&nbsp;Shengli Zhang,&nbsp;Peiyu Wang,&nbsp;Qianghua Pan,&nbsp;Guangming Guo,&nbsp;Xiaoke Li,&nbsp;Xuehui Gan,&nbsp;Ge Chen","doi":"10.1016/j.probengmech.2026.103972","DOIUrl":"10.1016/j.probengmech.2026.103972","url":null,"abstract":"<div><div>To address the high computational cost of joint focal element (JFE) classification in evidence theory under the surrogate model framework, this paper proposes an efficient classification method that improves the efficiency of JFE classification through a three-level collaborative strategy: a sparse grid strategy is adopted to construct discrete points; drastically reducing the computation for JFE category judgment; a focal element freezing mechanism is introduced to lock stably classified JFEs, thus eliminating redundant computations; and a dual-point active learning method is employed to accelerate iterative convergence. Verification results from three numerical examples with different dimensions show that this method can effectively reduce the computational burden at the surrogate-model level, and maintain high classification accuracy without increasing the number of true performance function evaluations.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 103972"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148568034","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 reliability of single-degree-of-freedom nonlinear systems excited by combined Gaussian and Poisson white noise based on extreme value process","authors":"Wantao Jia,&nbsp;Xianzheng Li,&nbsp;Qinyu Guo,&nbsp;Mengze Lyu,&nbsp;Wanrong Zan","doi":"10.1016/j.probengmech.2026.103976","DOIUrl":"10.1016/j.probengmech.2026.103976","url":null,"abstract":"<div><div>Complex engineering dynamic systems are often subject to combined stochastic excitations, making reliability a core design and optimization concern. Existing reliability analysis methods incur high computational costs with varying safety thresholds, as they must reset the absorbing boundaries and recalculate the reliability. To overcome this limitation, this paper develops a method based on the system response’s extreme value process (EVP) for reliability analysis of single-degree-of-freedom (SDOF) nonlinear systems under combined Gaussian and Poisson white noise. First, for systems under combined noise, the time-varying EVP combined with its underlying response process (forming the Augmented Markov Vector, AMV) is proven to be a Markov vector. Subsequently, the probability evolution equation for the AMV is derived and iterative formulas based on the path integral (PI) method are developed to solve it for both continuous and discrete Poisson jump amplitude distributions. This extends the AMV framework for solving the transient probability density function (PDF) of the time-varying EVP, allowing the analysis of the reliability of the system. Three typical SDOF nonlinear systems are analyzed to demonstrate the method’s application and effectiveness in reliability analysis. Comparisons with the PI method based on absorbing boundary condition are reported under the tested systems and discretization settings. The main practical advantage of the proposed method is that one computed extreme-value distribution can be reused when the safety threshold changes, thereby avoiding repeated absorbing-boundary calculations. The results demonstrate that the proposed approach effectively captures the dynamic behavior of the systems, offering novel methodological support for reliability analysis of engineering systems under combined noise excitations.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 103976"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148568039","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 interpretable deep generative framework for direct prediction of structural response probability distribution","authors":"Xuhui He,&nbsp;Haiquan Jing,&nbsp;Zhengliang Xiang","doi":"10.1016/j.probengmech.2026.103988","DOIUrl":"10.1016/j.probengmech.2026.103988","url":null,"abstract":"<div><div>Predicting the probability distribution of structural responses is critical for uncertainty quantification and reliability analysis. However, conventional methods still face challenges in predicting the probability distribution of complex structural responses. To address this issue, this study proposes an interpretable deep generative framework for efficient probability distribution prediction of structural responses. The proposed framework integrates a generative model with a smooth monotonic network, reformulating the learning process as a multi-objective task that combines the probability distribution fitting of random variables and the interpretability learning of structural response of the generative network output samples. This design effectively establishes an explicit monotonic mapping relationship from Gaussian variable to structural response, enabling direct prediction of the cumulative probability distribution of structural response. Furthermore, a flow-based generative network is constructed to directly predict the probability distribution function of structural responses by reusing the learned mapping, thereby eliminating the need for additional expensive simulations. The proposed method is validated through six numerical examples, where the Hellinger distances between predicted and reference probability distribution functions are consistently below 0.05. The results demonstrate that the proposed approach provides an accurate, efficient, and interpretable alternative for probabilistic analysis of engineering structures.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 103988"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148568052","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":"Modeling the stochastic dynamics of moving turbulent spots over a slender cone during laminar–turbulent transition","authors":"B.A. Robbins,&nbsp;R.V. Field Jr,&nbsp;K.M. Casper,&nbsp;P. Coffin,&nbsp;L.J. DeChant,&nbsp;M. Mesh","doi":"10.1016/j.probengmech.2026.103995","DOIUrl":"10.1016/j.probengmech.2026.103995","url":null,"abstract":"<div><div>The transition from laminar to turbulent flow is thought to be characterized by laminar flow interrupted by the intermittent formation of localized turbulent patches or spots. These interruptions are assumed to occur randomly but with increasing frequency until the spots grow and coalesce into a fully turbulent boundary layer. Herein we develop a probabilistic model to describe the birth, time evolution, and pressure loading of multiple turbulent spots within a transitional boundary layer. The model is calibrated to experimental wind tunnel data, showing good agreement with data and theory for quantities of interest to high speed transitional flow problems, such as the intermittency fraction and burst rate. The approach produces realizations of a time- and spatially-varying random pressure field, which are then applied as input to a finite element model for a flexible cone structure to quantify the resulting vibration response.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 103995"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148635275","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":"Effect of Karhunen-Loève Eigensolution accuracy on the reliability of foundation engineering","authors":"Mingjie Dai,&nbsp;Xiaohui Tan,&nbsp;Shanwei Liu,&nbsp;Zhihao Jiang,&nbsp;Zhitang Lu","doi":"10.1016/j.probengmech.2026.104007","DOIUrl":"10.1016/j.probengmech.2026.104007","url":null,"abstract":"<div><div>In the Karhunen–Loève (KL) series expansion framework for random field discretization, computational errors in common KL methods (e.g., the orthogonal series expansion (OSE) and Jacobi–Legendre–Galerkin (JLG) methods) arise not only from the truncation error due to the number of retained terms (<em>M</em>), but also from eigensolution accuracy related to the number of Gauss integration points (<em>N</em>1D GP) and basis function terms (<em>N</em>^1D). The OSE method with a full tensor-product construction and the JLG method with total-order truncation were employed for separable and nonseparable autocorrelation functions, respectively, thereby revealing the decoupled effects of the number of <em>N</em>1D GP and the number of <em>N</em>^1D on the eigenvalues and eigenfunctions. The results indicate that the global covariance error may not fully capture local reconstruction errors within the physical domain. For <em>N</em>^1D ≥ <em>M</em> + 2, <em>N</em>1D GP primarily influences eigenvalues (<em>λ</em>), while <em>N</em>^1D dictates fluctuations in eigenfunctions (<em>f</em>(<em>x</em>)). Accordingly, parameter selection criteria are established for one-dimensional and multi-dimensional random fields, respectively. Engineering case studies indicate that eigensolution accuracy affects the range of variation in load-settlement curves for shallow foundations and that the tilting failure mode of a pile group is particularly sensitive to it. Insufficient accuracy of the eigensolution causes drifts at the most unfavorable failure points and shifts in parameter sensitivity rankings within pile group systems. Furthermore, the convergence pattern of eigensolution errors directly maps onto the convergence behavior of the reliability assessment for pile group systems. This research provides a vital theoretical basis and accuracy parameter selection benchmarks for geotechnical reliability analysis within the KL framework.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 104007"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148737201","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 time-dependent reliability-based design optimization method for rolling bearings with thermal failure probability constraints","authors":"Yifan Li,&nbsp;Yongyong Xiang,&nbsp;Baisong Pan","doi":"10.1016/j.probengmech.2026.104013","DOIUrl":"10.1016/j.probengmech.2026.104013","url":null,"abstract":"<div><div>Thermal failure is a critical failure mode in rolling bearings, particularly under high-speed or heavy-load conditions, resulting in severe consequences such as lubrication failure or bearing seizure. However, existing optimization approaches that consider thermal characteristics frequently neglect time-dependent uncertainties, including dynamic loads and ambient temperature variations, which influence thermal failure risk. This study proposes a reliability-based design optimization framework to derive structural parameter designs for rolling bearings that satisfy thermal failure probability constraints. First, a thermal network model is established to capture the bearing's dynamic thermal response using a quasi-static mechanical model combined with a thermal resistance approach. Subsequently, a two-stage time-series sampling method is developed for time-dependent reliability analysis, enabling efficient evaluation of thermal failure probability under dynamic operating conditions. To maximize the bearing's dynamic load capacity, an optimization formulation is introduced that decouples the optimization loop from failure probability estimation. Finally, the effectiveness of the proposed method is demonstrated in a case study involving a deep-groove ball bearing for an electric motor.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 104013"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148776941","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":"Multi-objective optimization of a viscoelastic-filled honeycomb composite for vibration isolation and load bearing","authors":"Shu Yang,&nbsp;Guanlong Wu,&nbsp;Rui Li,&nbsp;Chang Qi,&nbsp;Jiaheng Deng,&nbsp;Yanxiao Hong,&nbsp;Zipeng Wang","doi":"10.1016/j.probengmech.2026.104014","DOIUrl":"10.1016/j.probengmech.2026.104014","url":null,"abstract":"<div><div>The demand for effective vibration suppression in mechanical and engineering structures continues to grow, motivating the development of vibration-isolation composite metamaterials filled with viscoelastic damping materials. When properly designed, such viscoelastic-filled composite metamaterials can simultaneously deliver enhanced vibration isolation and high load-bearing capacity. However, existing studies remain limited, and the coupled optimization of vibration isolation performance and load capacity has not been fully addressed. In this work, a positive Poisson's ratio honeycomb composite structure (PHCS) filled with a viscoelastic material is proposed and evaluated using finite element analysis (FEA). A surrogate-assisted multi-objective optimization design (MOD) framework, combined with a genetic algorithm, is developed to efficiently achieve global optimization. The geometric parameters of the PHCS are selected as design variables, and a design of experiments (DOE) strategy is used to generate datasets for surrogate-model training and testing. Before surrogate-model construction, geometric and material uncertainty propagation analyses are conducted for the baseline PHCS to quantify the effects of prescribed manufacturing and material-property variations on <em>T</em>_max, <em>f</em>_n, and <em>F</em>_max, indicating limited response dispersion within the considered uncertainty ranges. The Pareto-optimal solution set is then obtained using the Non-dominated sorting genetic algorithm-II (NSGA-II), and a linear multi-criterion decision making (MCDM) method is subsequently applied to select a representative trade-off design that outperforms the baseline configuration, demonstrating the effectiveness and robustness of the proposed MOD procedure. Finally, quasi-static compression and swept-sine experiments are conducted to validate the numerical predictions and confirm the accuracy of the FEA model. Overall, this study provides an efficient and reliable methodology for improving both vibration isolation performance and load-bearing capacity of viscoelastic-filled PHCS metamaterials with high computational efficiency.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 104014"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148843045","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 efficient time-variant reliability analysis method based on sparse grid and improved saddlepoint approximation","authors":"Haibo Liu,&nbsp;Wenqiang Pan,&nbsp;Shufeng Zhang,&nbsp;Hongwei Liu,&nbsp;Tongrong Zhang,&nbsp;Huichao Xie","doi":"10.1016/j.probengmech.2026.103981","DOIUrl":"10.1016/j.probengmech.2026.103981","url":null,"abstract":"<div><div>To address the issues of low computational efficiency and high computational cost in time-variant reliability analysis for practical engineering applications, a time-variant reliability analysis method based on sparse grid integration and an improved saddlepoint approximation is proposed. First, the input stochastic process is discretized into a linear combination of multiple random variables using the Expansion Optimal Linear Estimation (EOLE) method. On this basis, the Efficient Global Optimization (EGO) algorithm is employed to transform the system's time-variant reliability problem into a time-invariant problem in which only the extreme value response needs to be considered. Subsequently, sparse grid numerical integration is applied to compute the first four statistical moments of the extreme value distribution of the time-variant performance function. Finally, an improved saddlepoint approximation method is used to estimate the extreme value distribution of the response, from which the time-variant structural reliability is determined. The effectiveness of the proposed method is validated through one numerical example and three practical engineering case studies. The results demonstrate that the proposed method simplifies the entire time-variant reliability analysis process and significantly improves computational efficiency while maintaining high accuracy, by converting the complex time-variant problem into a conventional time-invariant problem.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 103981"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148568037","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":"Evolutionary spectral estimation from a single non-stationary sample using multiple generalized Morse wavelets","authors":"Tianyou Tao,&nbsp;Hao Wang,&nbsp;Sheng Wang,&nbsp;Liang Hu","doi":"10.1016/j.probengmech.2026.103973","DOIUrl":"10.1016/j.probengmech.2026.103973","url":null,"abstract":"<div><div>Estimating the EPSD (evolutionary power spectral density) of a univariate non-stationary process from a single-sample time series is critical, given the often non-repeatable nature of in situ measurements in engineering applications. Existing methods usually exhibit substantial bias and random errors in EPSD estimation. To resolve this issue, an approach based on the multiple generalized Morse wavelet (GMW) is proposed in this study. The core of this method lies in multi-taper estimation based on the orthogonality of GMW functions to reduce errors, which is accompanied by a direct mapping between the wavelet transform and the EPSD, thereby avoiding matrix operations and reducing computational demands. In the numerical examples, the method is validated by comparing its performance with existing approaches under two scenarios: a limited number of sample time histories and a single sample time history. The results indicate that the ensemble average of the estimated EPSDs obtained from the proposed approach enhances the time–frequency representation by reducing both bias and random errors. Since the time–frequency resolution of the GMW function decreases as its order increases, using the first three to five orders generally yields a satisfactory EPSD estimation for the single non-stationary sample. Consequently, the proposed approach improves EPSD estimation by using fewer, more robust preset parameters than those commonly used.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"85 ","pages":"Article 103973"},"PeriodicalIF":4.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148568041","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}