Probabilistic Engineering Mechanics最新文献

英文中文

A novel multidimensional parallelepiped model for structural uncertainty quantification and propagation analysis 一种新的多维平行六面体模型，用于结构不确定性量化和传播分析

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2026-01-01 Epub Date: 2025-12-23 DOI: 10.1016/j.probengmech.2025.103881

Xinzhou Qiao , Yan Li , Isaac Elishakoff , Naigang Hu

The currently available multidimensional parallelepiped models in non-probabilistic convex treatment of uncertainty are applicable for the multi-source uncertainty problem with the coexistence of dependent and independent uncertain parameters. However, these may encounter obstacles either in possessing the minimum volume or in enclosing all experimental data, or in both. In this paper, a novel multidimensional parallelepiped model, which is defined as the intersection of a finite number of halfspaces, is proposed to bound the uncertainty domain to address the above issue. Based on the proposed model, two uncertainty propagation analysis methods, namely the Monte Carlo simulation method and the sub-multidimensional parallelepiped analysis method, are developed to predict the structural response interval. Three numerical examples are provided to demonstrate the superiority of the proposed model over the existing ones and to illustrate the effectiveness and validity of the proposed methods.

现有的非概率凸处理多维平行六面体模型适用于独立不确定参数和相关不确定参数并存的多源不确定问题。然而，这些方法可能会遇到障碍，要么是拥有最小的体积，要么是包含所有的实验数据，或者两者兼而有之。为了解决上述问题，本文提出了一种新的多维平行六面体模型，该模型被定义为有限个半空间的交集，以约束不确定性域。在此基础上，提出了两种不确定性传播分析方法，即蒙特卡罗模拟法和亚多维平行六面体分析法来预测结构响应区间。给出了三个数值算例，证明了所提模型相对于现有模型的优越性，也说明了所提方法的有效性和有效性。

引用次数: 0

AK-ASS: An improvement of the Kriging model for dealing with small failure probability problems AK-ASS：对Kriging模型的改进，用于处理小失效概率问题

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2026-01-01 Epub Date: 2025-12-23 DOI: 10.1016/j.probengmech.2025.103884

Zonghui Wu , Jian He , Chenyang Wang , Xiaodan Sun , Di Yao

The fundamental purpose of structural reliability analysis is defined as the quantitative measurement of structural failure possibilities. The surrogate model method is currently regarded as the most widely used reliability evaluation method, but it has problems such as low fitting accuracy, high computational cost, low convergence efficiency and high parameter sensitivity when dealing with small probability events. Although there are some methods to accelerate the analysis, such as Adaptive Kriging combined with Monte Carlo Simulation (AK-MCS), the construction of the model still requires a large number of samples, resulting in a very large amount of calculation of the surrogate model. Therefore, this study combines the adaptive Kriging model with advanced subset simulation (AK-ASS) to solve these problems. In this paper, through the verification of mathematical examples and engineering examples, it is proved that this method reduces the analysis time required to deal with the problem of small probability failure, and overcomes some limitations of subset simulation. Furthermore, it has the potential to be used in combination with new efficient learning functions in the future.

结构可靠度分析的根本目的是对结构破坏可能性进行定量测量。代理模型法是目前应用最广泛的可靠性评估方法，但在处理小概率事件时存在拟合精度低、计算成本高、收敛效率低和参数灵敏度高等问题。虽然有一些加速分析的方法，如Adaptive Kriging结合Monte Carlo Simulation (AK-MCS)，但模型的构建仍然需要大量的样本，导致代理模型的计算量非常大。因此，本研究将自适应Kriging模型与先进子集仿真（AK-ASS）相结合来解决这些问题。本文通过数学实例和工程实例的验证，证明了该方法减少了处理小概率故障问题所需的分析时间，克服了子集仿真的一些局限性。此外，它在未来有可能与新的高效学习函数结合使用。

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引用次数: 0

An efficient method for continuously estimating posterior failure probabilities based on a single reliability analysis 基于单次可靠性分析的后验失效概率连续估计方法

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2026-01-01 Epub Date: 2026-01-30 DOI: 10.1016/j.probengmech.2026.103895

Hengchao Li , Zhenzhou Lu , Yuhua Yan , Yixin Lu

When distribution parameters are uncertain, it is necessary to employ a continuous estimation method for posterior failure probabilities (PFPs) to efficiently track changes in structural reliability as new observations become available. This study proposes an efficient method for continuously estimating PFPs, thereby addressing the lack of efficient and robust methods. In the proposed method, the integrand of PFP can be equivalently expressed as an explicit updating factor operation related to the observations and the estimations of the conditional failure probabilities based on a single reliability analysis in an augmented space. Thus, repeated reliability analyses are prevented when new observations are gradually incorporated. An interpolation-based method is designed to estimate all necessary conditional failure probabilities. This method first leverages the sifting property of the Dirac delta function to derive the transformed expression of the conditional probability density for the random input vector. A normal density approximating the Dirac delta function is then adopted as the interpolation weight function to solve the integral. This enables sifting the same set of sample information in the augmented space to calculate all conditional failure probabilities. An adaptive Kriging model of the performance function is introduced to further enhance the efficiency of the reliability analysis. Examples demonstrate that compared with existing advanced methods, the proposed method notably improves the efficiency of continuous PFP estimation while maintaining high accuracy.

当分布参数不确定时，有必要采用后验失效概率（pfp）的连续估计方法，以有效地跟踪结构可靠性随新观测值的变化。本研究提出了一种有效的连续估计pfp的方法，从而解决了缺乏有效和稳健的方法。在本文提出的方法中，PFP的被积可以等效地表示为与增广空间中基于单个可靠性分析的条件失效概率的观测值和估计相关的显式更新因子运算。因此，当逐渐纳入新的观测时，重复的可靠性分析被阻止。设计了一种基于插值的方法来估计所有必要的条件失效概率。该方法首先利用狄拉克函数的筛选特性，推导出随机输入向量的条件概率密度的变换表达式。然后采用近似狄拉克函数的正态密度作为插值权函数求解积分。这允许在增强空间中筛选相同的样本信息集，以计算所有条件故障概率。引入了性能函数的自适应Kriging模型，进一步提高了可靠性分析的效率。实例表明，与现有的先进方法相比，该方法在保持较高精度的同时，显著提高了连续PFP估计的效率。

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引用次数: 0

Refining the masonry shear modulus in masonry towers via Bayesian model updating 基于贝叶斯模型修正的砌体塔楼砌体剪切模量优化

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2026-01-01 Epub Date: 2026-02-13 DOI: 10.1016/j.probengmech.2026.103903

Silvia Monchetti , Gianni Bartoli , Michele Betti , Siro Casolo , Francesco Clementi

The assessment of the structural behavior of masonry towers often involves developing and identifying computational models to be used to perform static and/or time-history nonlinear analyses. Such models are frequently developed assuming isotropic masonry behavior, with model identification carried out - based on available experimental data - through deterministic tuning of a limited set of representative parameters. However, masonry exhibits complex structural textures that often deviate significantly from the commonly made assumption of isotropic behaviour. This paper investigates the effects of this assumption by focusing on the masonry shear modulus. A two-dimensional rigid body–spring model is adopted as computational approach, as its fully discrete formulation allows overcoming the limitations of the Cauchy continuum while maintaining a reduced computational cost. A Bayesian updating framework based on dynamic experimental data is employed to account for multiple sources of uncertainty, including parameter uncertainty, model inadequacy, and observation errors. Three masonry towers with different slenderness ratios are considered as representative case studies. The adopted Bayesian model updating approach allows for the estimation of their shear modulus while accounting for uncertainties, and the results show that the common assumption of isotropic behaviour in masonry numerical modelling does not hold. Using a fully discrete computational approach in combination with experimental frequency data, this behaviour has been observed for squat masonry towers.

砌体塔结构性能的评估通常涉及开发和识别用于执行静态和/或时程非线性分析的计算模型。这些模型通常是在假定砌体各向同性的情况下建立的，模型识别是基于现有的实验数据，通过对一组有限的代表性参数进行确定性调整。然而，砌体表现出复杂的结构纹理，经常明显偏离通常假设的各向同性行为。本文以砌体剪切模量为研究对象，探讨了这一假设的影响。采用二维刚体-弹簧模型作为计算方法，因为其完全离散的公式可以克服柯西连续体的局限性，同时保持较低的计算成本。采用基于动态实验数据的贝叶斯更新框架来考虑多种不确定性来源，包括参数不确定性、模型不完备性和观测误差。以三个不同长细比的砌体塔为代表性案例进行了研究。所采用的贝叶斯模型更新方法允许在考虑不确定性的同时估计其剪切模量，结果表明砌体数值模拟中各向同性行为的常见假设不成立。使用完全离散的计算方法结合实验频率数据，这种行为已经观察到深蹲砌体塔。

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引用次数: 0

Nonstationary translation processes 非平稳平移过程

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2026-01-01 Epub Date: 2025-11-19 DOI: 10.1016/j.probengmech.2025.103865

M. Grigoriu

Translation models of stationary non-Gaussian processes, referred to as stationary translation models, are extended to models for nonstationary non-Gaussian processes, referred to as nonstationary translation models. The stationary/nonstationary translation models are time-invariant/time-variant memoryless transformations of stationary/nonstationary Gaussian processes. We give and prove properties of nonstationary translation models and specialize them to stationary translation models. Numerous examples are presented to illustrate the construction of nonstationary translation models and highlight some of their properties.

平稳非高斯过程的平移模型称为平稳平移模型，它被推广到非平稳非高斯过程的模型，称为非平稳平移模型。平稳/非平稳平移模型是平稳/非平稳高斯过程的时不变/时变无记忆变换。我们给出并证明了非平稳翻译模型的性质，并将它们专门归于平稳翻译模型。给出了许多例子来说明非平稳平移模型的构造，并强调了它们的一些性质。

引用次数: 0

Stochastic toughening mechanism of two-dimensional random soft network metamaterials 二维随机软网络超材料的随机增韧机理

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2026-01-01 Epub Date: 2026-02-12 DOI: 10.1016/j.probengmech.2026.103898

Tengfei Xing , Xiaodan Ren , Jie Li

Biological tissue materials exhibit high tensile properties and a typical “J-shaped” stress-strain response under external loading due to their unique microstructural architecture. Inspired by this, soft network metamaterials have been widely applied due to their outstanding tensile performance and nonlinear mechanical response. However, achieving both high fracture toughness and defect insensitivity in two-dimensional random soft network metamaterials (2D-RSMs) remains a significant challenge in biomimetic design. In this study, we propose a 2D-RSM with tunable fracture toughness and defect insensitivity. To comprehensively investigate the probabilistic mechanical response of the material post-failure, we employ the Probability Density Evolution Method (PDEM) to analyze the stochastic toughening mechanism of 2D-RSMs under various characteristic conditions, including random control parameters, microstructural geometric configurations, and scale control vectors. We found that, compared to two-dimensional regular soft network metamaterials (2D-SMs), 2D-RSMs leverage randomness to enhance robustness, resulting in remarkable defect insensitivity. This characteristic significantly mitigates the impact of defects on the mechanical response of the material, providing critical reliability for material fabrication and practical applications under complex conditions.

生物组织材料由于其独特的微观结构结构，在外部载荷作用下具有较高的拉伸性能和典型的“j”型应力应变响应。受此启发，软网络超材料以其优异的拉伸性能和非线性力学响应得到了广泛的应用。然而，在二维随机软网络超材料（2d - rsm）中实现高断裂韧性和缺陷不敏感性仍然是仿生设计中的一个重大挑战。在这项研究中，我们提出了一个具有可调断裂韧性和缺陷不敏感性的2D-RSM。为了全面研究材料失效后的概率力学响应，采用概率密度演化方法（PDEM）分析了二维rsm在随机控制参数、微观结构几何构型和尺度控制向量等不同特征条件下的随机增韧机理。我们发现，与二维规则软网络超材料（2D-SMs）相比，2D-RSMs利用随机性增强鲁棒性，从而产生显著的缺陷不敏感性。这一特性显著减轻了缺陷对材料机械响应的影响，为复杂条件下的材料制造和实际应用提供了关键的可靠性。

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引用次数: 0

A novel ESN-DeepONet and kriging double layer model for time-dependent reliability analysis with random process 随机过程时变可靠性分析的一种新的ESN-DeepONet和kriging双层模型

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2026-01-01 Epub Date: 2026-02-12 DOI: 10.1016/j.probengmech.2026.103894

Haolin Zhang , Linfang Qian , Longmiao Chen , Taisu Liu , Weiwei Chen , Liu Yang

Time-dependent reliability analysis of mechanisms involving stochastic processes and random variables has always been a challenge. Enhancing the efficiency of reliability analysis for complex nonlinear systems while ensuring accuracy is a critical focus recently. In this study, a double-layer surrogate model-based reliability analysis method is proposed: the first layer constructs a novel deep learning operator net surrogate model to implement uncertainty propagation; the second layer estimates failure probability based on an active learning kriging model. The extended optimal linear estimation discretization method is employed to transform stochastic processes into time-independent random variables. To improve the training efficiency, a sample selection iterative training method is applied to the first-layer model training. Two numerical examples and an engineering application demonstrate the efficiency and accuracy of the proposed method. The methodology proposed in this paper can also be further extended to other reliability analysis problems with high nonlinearity and without an explicit performance function.

涉及随机过程和随机变量的机制的时变可靠性分析一直是一个挑战。提高复杂非线性系统可靠性分析的效率，同时保证可靠性分析的准确性是当前研究的热点。本文提出了一种基于双层代理模型的可靠性分析方法：第一层构建新的深度学习算子网络代理模型，实现不确定性传播；第二层基于主动学习克里格模型估计故障概率。采用扩展最优线性估计离散化方法将随机过程转化为与时间无关的随机变量。为了提高训练效率，将样本选择迭代训练方法应用于第一层模型训练。算例和工程应用验证了该方法的有效性和准确性。本文所提出的方法也可以进一步推广到其他具有高非线性且没有明确性能函数的可靠性分析问题。

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引用次数: 0

An adaptive subinterval univariate dimension reduction method for uncertain problems with large interval parameters 大区间参数不确定问题的自适应子区间单变量降维方法

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2026-01-01 Epub Date: 2025-12-23 DOI: 10.1016/j.probengmech.2025.103885

Wenchao Ding, Feng Li, Zhaojie Yu, Fei Cheng

An adaptive subinterval univariate dimension reduction method is proposed to address uncertain problems involving large interval parameters, where the traditional subinterval method often suffers from prohibitive computing costs. The key innovation lies in the development of an adaptive iterative partitioning strategy guided by sensitivity analysis, which dynamically decomposes the original large interval into smaller subintervals. Within each subinterval, the univariate dimension reduction method is used to estimate the response bounds, leveraging the high-order terms in the Taylor expansion series to improve both precision and convergence speed. Three numerical examples demonstrate that the proposed method significantly reduces computational cost while achieving higher accuracy.

针对传统子区间方法计算成本过高的不确定性问题，提出了一种自适应子区间单变量降维方法。该方法的关键创新在于开发了一种以灵敏度分析为指导的自适应迭代划分策略，将原有的大区间动态分解为小区间。在每个子区间内，采用单变量降维方法估计响应边界，利用泰勒展开级数中的高阶项提高精度和收敛速度。三个算例表明，该方法在获得较高精度的同时显著降低了计算量。

引用次数: 0

Local reliability sensitivity analysis with directional sampling framework in complex failure domain 复杂失效域定向采样框架局部可靠性灵敏度分析

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2026-01-01 Epub Date: 2026-01-13 DOI: 10.1016/j.probengmech.2026.103893

Xiaobo Zhang

Local reliability sensitivity (LRS), defined as the partial derivatives of structural failure probability with respect to limit state parameters and distribution parameter, provides critical gradient information for reliability-based design optimization and safety-informed decision-making. LRS analysis typically relies on a post-processing step of existing reliability analysis results. In this study, LRS analysis in complex failure domains is investigated using the Directional Sampling (DS) framework. DS achieves computational efficiency through unit-hypersphere sampling and conditional one-dimensional reliability analysis. However, complex failure domains, characterized by disconnected regions, high nonlinearity, or multiple failure modes, may have multiple intersections between a sampled direction and the limit-state surface, posing significant challenges to both reliability and LRS analysis. Existing DS-based sensitivity approaches lack consideration of complex failure domains. Therefore, for LRS with respect to limit-state parameters, an improved domain integral method within the DS framework is developed, transforming the surface integral over complex boundaries into a tractable domain integral coupled with sequential conditional sensitivity analysis. For LRS with respect to distribution parameters, an extended score function method within the DS framework is derived by introducing a directional score function, enabling sensitivity estimation without requiring additional limit-state function calls. The accuracy and efficiency of the proposed methods are validated through challenging examples with complex failure domains, including the modified Rastrigin function and a nonlinear oscillator under white noise base excitation.

局部可靠性灵敏度（LRS）定义为结构失效概率对极限状态参数和分布参数的偏导数，为基于可靠性的设计优化和安全决策提供了关键的梯度信息。LRS分析通常依赖于现有可靠性分析结果的后处理步骤。本文采用定向采样（DS）框架对复杂失效域的LRS分析进行了研究。DS通过单位超球采样和条件一维可靠性分析来提高计算效率。然而，复杂的失效域以不连通区域、高非线性或多种失效模式为特征，在采样方向和极限状态面之间可能存在多个交叉点，这对可靠性和LRS分析都提出了重大挑战。现有的基于离散度的灵敏度方法缺乏对复杂失效域的考虑。因此，对于极限状态参数下的LRS，本文提出了一种改进的DS框架下的域积分方法，将复杂边界上的曲面积分转化为可处理的域积分，并结合顺序条件敏感性分析。对于分布参数的LRS，通过引入方向性评分函数，导出了DS框架内的扩展评分函数方法，无需额外调用极限状态函数即可进行灵敏度估计。通过具有复杂失效域的挑战性实例，包括改进的Rastrigin函数和白噪声基激励下的非线性振荡器，验证了所提方法的准确性和效率。

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引用次数: 0

Bayesian updating method considering the uncertainty of distribution parameters of random model inputs 考虑随机模型输入分布参数不确定性的贝叶斯更新方法

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-10-01 Epub Date: 2025-11-21 DOI: 10.1016/j.probengmech.2025.103867

Kaixuan Feng , Zhenzhou Lu

The Bayesian updating method is an effective approach for calibrating model characteristics when new observational data become available. In most existing Bayesian updating methods, the distribution parameters of random model inputs are considered constants. However, these parameters may themselves be uncertain due to limited knowledge of the model inputs. Therefore, a new Bayesian updating method is developed herein considering the uncertainty in the distribution parameters of random model inputs. In the proposed method, new observations may include input data, output data, or a combination of both. The principal contribution of this work lies in the adaptive construction of the likelihood function for the distribution parameters based on different sources of observations. Using the likelihood function and the prior probability density function (PDF) of the distribution parameters, the posterior PDF of these parameters is first obtained. Subsequently, the posterior PDF of the model output can be derived via either a direct or an indirect approach. The theoretical equivalence of these two perspectives is demonstrated. Finally, an example is provided to illustrate the feasibility and validity of the proposed method.

当有新的观测数据时，贝叶斯更新方法是校正模型特征的有效方法。在现有的大多数贝叶斯更新方法中，随机模型输入的分布参数被认为是常数。然而，由于模型输入的知识有限，这些参数本身可能是不确定的。因此，本文提出了一种考虑随机模型输入分布参数不确定性的贝叶斯更新方法。在提出的方法中，新的观测值可以包括输入数据、输出数据或两者的组合。这项工作的主要贡献在于基于不同观测源的分布参数的似然函数的自适应构造。利用分布参数的似然函数和先验概率密度函数（PDF），首先得到分布参数的后验概率密度函数。随后，模型输出的后验PDF可以通过直接或间接的方法得到。论证了这两种观点的理论等价性。最后，通过一个算例说明了所提方法的可行性和有效性。

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