Probabilistic Engineering Mechanics最新文献_第10页

Harnessing physics-informed operators for high-dimensional reliability analysis problems 利用物理知识的操作员进行高维可靠性分析问题

IF 3 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-07-01 DOI: 10.1016/j.probengmech.2025.103807

Navaneeth N. , Tushar , Souvik Chakraborty

Quantifying the reliability of complex engineering systems under uncertainty is a computationally demanding task, particularly when the system response depends on a large number of stochastic parameters. Traditional reliability analysis techniques, anchored in repeated high-fidelity simulations or experimental evaluations, become prohibitively expensive in high-dimensional settings, especially for systems governed by partial differential equations (PDEs) that require discretization-based solvers such as the finite element or finite volume methods. Surrogate modeling offers a viable alternative by approximating the input–output mapping of such systems with reduced computational overhead. Among these, neural operators have recently gained attention for their ability to learn solution operators of PDEs from limited data. In this work, we investigate the utility of the physics-informed wavelet neural operator (PI-WNO) for high-dimensional reliability analysis. We demonstrate that PI-WNO can accurately learn the stochastic input-to-solution map without resorting to repeated numerical simulations, thereby enabling efficient and scalable reliability estimation. Through benchmark problems, we illustrate the effectiveness of the proposed framework in handling high-dimensional uncertainty while preserving accuracy. Furthermore, we extend this approach to systems governed by coupled PDEs, highlighting the broad applicability and potential of physics-informed neural operators for reliability analysis in complex physical systems.

对不确定条件下复杂工程系统的可靠性进行量化是一项计算要求很高的任务，特别是当系统响应依赖于大量随机参数时。传统的可靠性分析技术依赖于重复的高保真度模拟或实验评估，在高维环境中变得非常昂贵，特别是对于需要基于离散化的求解器（如有限元或有限体积方法）的偏微分方程（pde）控制的系统。代理建模提供了一种可行的替代方案，通过减少计算开销来近似此类系统的输入-输出映射。其中，神经算子因其从有限数据中学习偏微分方程解算子的能力而受到关注。在这项工作中，我们研究了物理信息小波神经算子（PI-WNO）在高维可靠性分析中的应用。我们证明PI-WNO可以准确地学习随机输入-解映射，而无需诉诸重复的数值模拟，从而实现高效和可扩展的可靠性估计。通过基准问题，我们证明了该框架在处理高维不确定性的同时保持精度的有效性。此外，我们将这种方法扩展到由耦合偏微分方程控制的系统，强调了物理信息神经算子在复杂物理系统可靠性分析中的广泛适用性和潜力。

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引用次数: 0

AGP-SYS: An adaptive learning and Gaussian process modeling-based system reliability method AGP-SYS：基于自适应学习和高斯过程建模的系统可靠性方法

IF 3 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-07-01 DOI: 10.1016/j.probengmech.2025.103805

K. Wen , W. Zeng , S.Y. Zeng

Various system reliability analysis methods based on surrogate models have recently been developed for problems reliant on costly performance function (PF) evaluation. Existing surrogate-based methods approximate the system performance function (SPF) using the max/min of component performance functions (CPFs), which may introduce errors in failure probability estimation. Through SPF analysis across diverse scenarios, we demonstrate that substituting a certain CPF for SPF may introduce significant errors. Furthermore, SPF distributions exhibit non-Gaussian characteristics in specific contexts. According to these cases, we propose the AGP-SYS method. This approach employs Gaussian process modeling to predict CPFs, then rigorously derives the mean and variance of SPF using all CPF predictions—thereby avoiding errors induced by maximum/minimum approximations. Given that the SPF distribution is non-Gaussian, the probability of misclassification (PMC) is used as the learning function instead of the conventional U-function, whose physical significance is strictly confined to Gaussian-distributed SPF. Furthermore, an adaptive shrinking distance criterion preventing training-point clustering is introduced for enhancing model-updating efficiency. The effectiveness of AGP-SYS is demonstrated through three case studies: a series system, a parallel system, and a column-based independent foundation in civil engineering.

基于代理模型的各种系统可靠性分析方法最近被开发出来用于依赖于昂贵性能函数（PF）评估的问题。现有的基于代理的方法使用部件性能函数（cpf）的最大/最小值来近似系统性能函数（SPF），这可能会在故障概率估计中引入错误。通过不同场景下的SPF分析，我们证明用特定的CPF代替SPF可能会引入显著的误差。此外，SPF分布在特定环境中表现出非高斯特征。针对这些情况，我们提出了AGP-SYS方法。该方法采用高斯过程建模来预测CPF，然后使用所有CPF预测严格推导SPF的均值和方差，从而避免了由最大/最小近似引起的误差。考虑到SPF的非高斯分布，采用误分类概率（probability of misclassification， PMC）代替传统的u函数作为学习函数，其物理意义严格局限于高斯分布的SPF。此外，为了提高模型更新效率，引入了防止训练点聚类的自适应距离缩小准则。通过串联系统、并联系统和柱式独立基础在土木工程中的应用，验证了AGP-SYS的有效性。

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引用次数: 0

A novel double-layer kriging model-based reliability analysis framework for time-dependent structural system with stochastic process 基于双层kriging模型的随机过程时变结构系统可靠度分析框架

IF 3 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-07-01 DOI: 10.1016/j.probengmech.2025.103812

Nan Ye , Zhenzhou Lu

In the surrogate model-based time-dependent reliability analysis, the discretization of stochastic process may lead to a great increase of input dimensionality, which poses challenges to the construction and training of surrogate model. To address this issue, a novel Double-Layer Kriging model-based Reliability Analysis Framework (nDLK-RAF) is proposed for time-dependent structural system with stochastic process in this paper. The random vector and stochastic process are treated separately in nDLK-RAF. Specifically, the Kriging model of time-dependent performance function under given random vector realization is established in the inner layer of nDLK-RAF, thus the conditional time-dependent failure probability (TDFP) corresponding to given random vector realization can be estimated by the inner convergent Kriging model. On this basis, the relationship between conditional TDFP and random vector is further surrogated by the Kriging model of outer-layer, and the final TDFP can be estimated by the outer convergent Kriging model. Further, aiming at the rare failure problem in engineering, this paper designs the variance reduction strategies of embedding directional sampling and importance sampling in the inner and outer layers, respectively, which improves the training efficiency of double-layer Kriging models in nDLK-RAF. Compared with the existing methods that simultaneously consider random vector and stochastic process, the nDLK-RAF reasonably balances the input dimensionalities of inner and outer Kriging models, which avoids the construction of high-dimensional surrogate models. Meanwhile, the two combined variance reduction sampling methods reduce the required candidate sample pool size for updating Kriging model, ultimately achieving efficient time-dependent reliability analysis. The superiority of nDLK-RAF over existing Kriging model-based methods is demonstrated by the example analysis.

在基于代理模型的时变可靠性分析中，随机过程的离散化可能导致输入维数的大幅增加，这给代理模型的构建和训练带来了挑战。针对这一问题，本文提出了一种基于双层Kriging模型的时变随机结构系统可靠性分析框架（nDLK-RAF）。在nDLK-RAF中，随机向量和随机过程是分开处理的。具体而言，在nDLK-RAF的内层建立了给定随机向量实现下的时变性能函数的Kriging模型，从而可以通过内部收敛的Kriging模型估计给定随机向量实现对应的条件时变失效概率（TDFP）。在此基础上，进一步用外层的Kriging模型代替条件TDFP与随机向量之间的关系，并通过外层收敛Kriging模型估计最终的TDFP。进一步，针对工程中罕见的失效问题，设计了分别在内层和外层嵌入定向采样和重要采样的方差缩减策略，提高了nDLK-RAF中双层Kriging模型的训练效率。与现有同时考虑随机向量和随机过程的方法相比，nDLK-RAF合理平衡了内外克里格模型的输入维数，避免了高维代理模型的构建。同时，两种联合方差缩减抽样方法减少了更新Kriging模型所需的候选样本池大小，最终实现了高效的时变信度分析。通过算例分析，证明了nDLK-RAF相对于现有基于Kriging模型的方法的优越性。

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引用次数: 0

A sensitivity-based separation approach for the experimental calibration of probabilistic computational models 基于灵敏度分离的概率计算模型实验标定方法

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-07-01 DOI: 10.1016/j.probengmech.2025.103810

Darwish Alzeort , Anas Batou , Rubens Sampaio , Thiago G. Ritto

This paper is concerned with the identification of the hyperparameters of probabilistic computational models using experimental data collected on a family of structures nominally identical but exhibiting some variability in its parameters (mechanical properties, geometry, …) resulting in random fluctuations in the observed responses. Such a problem generally yields a challenging multivariate probabilistic inverse problems to be solved in high dimensions. High dimensionality requires the use of a global optimisation algorithm to efficiently explore the input parameter space. In this paper, we propose an alternative algorithm that allows each random variable of the stochastic model to be identified separately and sequentially by solving a set of low-dimension probabilistic inverse problems. For each parameter, a devoted stochastic inverse problem is introduced by identifying a random output, which is sensitive to this parameter only, the sensitivity being quantified using Sobol indices. The proposed method is illustrated through two numerical examples: the first one concerns the frequency analysis of a clamped beam, and the second one is related to the vibration of a bridge.

本文关注的是利用在一组结构上收集的实验数据来识别概率计算模型的超参数，这些结构在名义上是相同的，但在其参数（力学性能、几何形状等）上表现出一些可变性，从而导致观察到的响应的随机波动。这样的问题通常会产生一个具有挑战性的多维概率反问题，需要在高维上解决。高维要求使用全局优化算法来有效地探索输入参数空间。在本文中，我们提出了一种替代算法，该算法允许随机模型的每个随机变量通过求解一组低维概率逆问题来单独和顺序地识别。对于每个参数，通过识别随机输出引入一个专门的随机逆问题，该随机输出仅对该参数敏感，灵敏度使用Sobol指标进行量化。通过两个数值算例说明了所提出的方法：第一个是关于固定梁的频率分析，第二个是关于桥梁的振动。

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引用次数: 0

A full-domain moment method for reliability analysis based on the NIG distribution, monotonic transformation and new PEM 基于NIG分布、单调变换和新PEM的全域矩法可靠性分析

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-07-01 DOI: 10.1016/j.probengmech.2025.103823

Wenliang Fan , Shujun Yu , XinYue Jiang

The moments method is an attractive non-intrusive method, where estimating statistical moments and reconstructing the probability density function (PDF) are crucial to this approach. However, existing methods for estimating statistical moments face challenges in balancing efficiency and accuracy. Furthermore, the flexible distributions used to construct the PDF may have limited applicability for certain performance functions. In this paper, a full-domain moment method, which is based on a new point estimate method (PEM), monotonic transformation, and the normal inverse Gaussian (NIG) distribution, is proposed. First, an equivalent performance function is constructed through a properly designed monotonic transformation, which maintains the same failure probability as the original performance function but shifts the statistical moments into the applicable domain of the NIG distribution. Then, a new PEM, which combines the bivariate adaptive hybrid dimension reduction method (B-AH-DRM) and the Kriging surrogate model, is employed to estimate the first four central moments of the equivalent performance function. Based on the estimated first four central moments and the NIG distribution, the PDF of the equivalent performance function is constructed, and the failure probability is then calculated. Finally, several examples are used to validate the effectiveness of the proposed method in structural reliability analysis.

矩量法是一种有吸引力的非侵入式方法，其中估计统计矩量和重构概率密度函数是该方法的关键。然而，现有的统计矩估计方法在平衡效率和准确性方面面临挑战。此外，用于构造PDF的灵活发行版对于某些性能函数的适用性可能有限。本文提出了一种基于新的点估计方法（PEM）、单调变换和正态反高斯分布（NIG）的全域矩方法。首先，通过适当设计的单调变换构造等效性能函数，使其保持与原性能函数相同的失效概率，但将统计矩移至NIG分布的适用域；然后，结合双变量自适应混合降维方法（B-AH-DRM）和Kriging代理模型，采用新的PEM估计等效性能函数的前四个中心矩。根据估计的前4个中心矩和NIG分布，构造等效性能函数的PDF，并计算失效概率。最后，通过算例验证了该方法在结构可靠度分析中的有效性。

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引用次数: 0

Probabilistic analysis of the steady-state response to nonlinear oscillators with polynomial cross-nonlinearity using stochastic equivalent linearization 多项式交叉非线性非线性振子稳态响应的随机等效线性化概率分析

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-07-01 DOI: 10.1016/j.probengmech.2025.103830

J.-C. Cortés, J.-V. Romero, M.-D. Roselló, J.F. Valencia Sullca

The stochastic equivalent linearization technique is employed to analyze the steady-state probabilistic response of a class of weakly nonlinear oscillators featuring cross-nonlinearities in position and velocity, represented by an arbitrary bivariate polynomial. The input or external source is driven by a zero-mean stationary Gaussian stochastic process. The theoretical results are numerically checked in two relevant scenarios where the input is defined by white noise and Ornstein–Uhlenbeck processes. We also compare the results against alternative approaches showing consistency and superiority of the proposed approach. Furthermore, we take advantage of the Principle of Maximum Entropy to approximate the probability density function of the steady-state response via the stochastic equivalent linearization technique. These results are compared with the ones obtained by the combination of Monte Carlo simulations and kernel-based density estimations.

采用随机等效线性化技术分析了一类位置和速度具有交叉非线性的弱非线性振子的稳态概率响应，其形式为任意二元多项式。输入或外部源由零均值平稳高斯随机过程驱动。在输入由白噪声和Ornstein-Uhlenbeck过程定义的两种相关情况下，对理论结果进行了数值检验。我们还将结果与其他方法进行比较，显示所提出方法的一致性和优越性。此外，我们利用最大熵原理，通过随机等效线性化技术来近似稳态响应的概率密度函数。这些结果与蒙特卡罗模拟和基于核的密度估计相结合的结果进行了比较。

引用次数: 0

An efficient hybrid uncertainty analysis method dealing with random and interval uncertainties 一种处理随机和区间不确定性的高效混合不确定性分析方法

IF 3 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-06-24 DOI: 10.1016/j.probengmech.2025.103785

Ruping Wang , Lihua Meng , Chongshuai Wang , Jia Wang

In performing reliability analysis of complex structural systems, the simultaneous presence of random and interval parameters significantly increases the complexity of structural reliability assessment. In this paper, an efficient probability-interval hybrid uncertainty analysis method based on chaos control and multiplicative dimensional reduction techniques is proposed. In the proposed method, the modified chaos control method is introduced to solve the iterative non-convergence problem in Hasofer-Lind-Rackwitz–Fiessler (HL-RF) algorithm, and the multiplicative dimensional reduction method is used to transform the interval analysis as the function extremum problem, which effectively improves the solving efficiency. The effectiveness of the proposed method is validated through benchmark numerical examples, and its practical applicability is exemplified by fatigue fracture analysis of the flexspline in harmonic drives and stiffness failure analysis of a 10-bar aluminum truss. The results demonstrate that the presented method can significantly reduce the time required for hybrid uncertainty analysis while maintaining the accuracy.

在对复杂结构系统进行可靠性分析时，随机参数和区间参数的同时存在大大增加了结构可靠性评估的复杂性。本文提出了一种基于混沌控制和乘法降维技术的概率-区间混合不确定性分析方法。在该方法中，引入改进混沌控制方法来解决hasfer - lnd - rackwitz - fiessler （HL-RF）算法中的迭代不收敛问题，并采用乘法降维方法将区间分析转化为函数极值问题，有效提高了求解效率。通过基准数值算例验证了该方法的有效性，并通过谐波传动柔轮疲劳断裂分析和10杆铝桁架刚度失效分析验证了该方法的实用性。结果表明，该方法在保持混合不确定度分析精度的前提下，显著减少了混合不确定度分析所需的时间。

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引用次数: 0

Performance analysis of an energy harvester with a nonlinear energy sink and time delay under narrow-band noise excitation 窄带噪声激励下具有非线性能量汇和时延的能量采集器性能分析

IF 3 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-06-24 DOI: 10.1016/j.probengmech.2025.103789

De-Xin Dai , Yong-Ge Yang , Yang Liu

Piezoelectric energy harvesters can convert undesirable vibrations in the environment into useful electrical energy. Time delay is inevitable in the operation of mechanical systems. Very few works have explored the effects of time delay factor on an integrated system that includes nonlinear energy sinks and piezoelectric energy harvesters (NES-PEH) subjected to stochastic excitation. Unlike previous research, this paper investigates the dynamics of an NES-PEH system with time delay under narrow-band noise excitation to realize vibration suppression and energy harvesting simultaneously. The steady-state response moments of the system are obtained by using the multi-scale method, and the effectiveness of the method is verified by comparing the numerical solutions and analytical solutions. Then, the influences of different parameters on the amplitude–frequency response of the first-order moments are analyzed. Finally, the effects of time delay factor on the vibration suppression and energy harvesting performance are studied via the second-order amplitude response moments and mean output power.

压电能量收集器可以将环境中不受欢迎的振动转化为有用的电能。在机械系统的运行中，时间延迟是不可避免的。很少有研究探讨时滞因子对随机激励下包含非线性能量汇和压电能量采集器（NES-PEH）的集成系统的影响。与以往的研究不同，本文研究了窄带噪声激励下具有时滞的NES-PEH系统的动力学特性，以同时实现振动抑制和能量收集。采用多尺度方法得到了系统的稳态响应矩，并通过数值解与解析解的比较验证了该方法的有效性。然后分析了不同参数对一阶矩幅频响应的影响。最后，通过二阶幅值响应矩和平均输出功率研究了时滞因子对振动抑制和能量收集性能的影响。

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引用次数: 0

An adaptive double-loop reliability-based design optimization method for solving structural nonlinear problems 基于自适应双环可靠性的结构非线性优化设计方法

IF 3 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-06-18 DOI: 10.1016/j.probengmech.2025.103793

Junfeng Wang, Jiqing Chen, Fengchong Lan, Yunjiao Zhou

Reliability-based design optimization (RBDO) aims to generate optimal structural designs that satisfy probabilistic requirements. However, the implicit nonlinear complexity of the response often limits the efficiency and accuracy of RBDO. To address this challenge, this paper proposes an adaptive double-loop framework for RBDO. In the inner loop, an active learning Kriging (AK) metamodel is used to replace the computationally expensive implicit nonlinear response model. Taking advantage of the superior ergodic capability of the directional sampling (DS) method, a new learning function is developed to reduce the number of training samples through local updating, enhancing the efficiency and accuracy of AK modeling in critical domains. Additionally, the DS method is used to evaluate the reliability of the AK metamodel. In the outer loop, an adaptive genetic algorithm is proposed. This algorithm constructs an adaptive penalty function based on the proportion of feasible solutions and the degree of violation of probability constraints during the population evolution process, transforming the probability constraint problem in the inner loop into an unconstrained optimization problem. The algorithm can adaptively improve the global convergence rate and local optimization accuracy. By synergizing both loops, this paper offers an efficient solution for nonlinear RBDO problems. The accuracy and efficiency of the proposed method are validated by three numerical examples and one engineering application.

基于可靠性的设计优化（RBDO）旨在生成满足概率要求的最优结构设计。然而，响应的隐式非线性复杂性往往限制了RBDO的效率和准确性。为了解决这一挑战，本文提出了一种自适应的RBDO双环框架。在内环中，采用主动学习Kriging （AK）元模型代替计算量大的隐式非线性响应模型。利用方向采样（DS）方法优越的遍历能力，提出了一种新的学习函数，通过局部更新来减少训练样本的数量，提高了关键域AK建模的效率和准确性。此外，采用DS方法对AK元模型的可靠性进行了评价。在外环中，提出了一种自适应遗传算法。该算法根据种群进化过程中可行解的比例和概率约束的违反程度构造自适应惩罚函数，将内环中的概率约束问题转化为无约束优化问题。该算法能够自适应地提高全局收敛速度和局部寻优精度。通过将这两个循环协同，本文提供了一种求解非线性RBDO问题的有效方法。通过3个算例和1个工程实例验证了该方法的准确性和有效性。

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引用次数: 0

Simultaneous identification of the parameters in the plasticity function for power hardening materials: A Bayesian approach 动力硬化材料塑性函数参数的同时识别：贝叶斯方法

IF 3 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-06-17 DOI: 10.1016/j.probengmech.2025.103797

Salih Tatar , Mohamed BenSalah

In this paper, we address the simultaneous identification of the strain hardening exponent, the shear modulus, and the yield stress through an inverse problem formulation. We begin by analyzing both the direct and inverse problems, and subsequently reformulate the inverse problem within a Bayesian framework. The direct problem is solved using an iterative approach, followed by the development of a numerical method based on Bayesian inference to address the inverse problem. Numerical examples with noisy data are presented to demonstrate the applicability and the accuracy of the proposed method.

在本文中，我们通过反问题公式解决了应变硬化指数、剪切模量和屈服应力的同时识别问题。我们首先分析正问题和反问题，然后在贝叶斯框架内重新表述反问题。直接问题是用迭代方法解决的，其次是基于贝叶斯推理的数值方法的发展，以解决逆问题。给出了含噪声数据的数值算例，验证了该方法的适用性和准确性。

引用次数: 0