Probabilistic Engineering Mechanics最新文献

英文中文

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

On a stochastic model of nonlocal elastic beams using the generalized perturbation method 用广义摄动法研究非局部弹性梁随机模型

IF 3 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-06-10 DOI: 10.1016/j.probengmech.2025.103803

Marcin Kamiński , Marzia Sara Vaccaro , Raffaele Barretta

This work presents an initial investigation into uncertainty quantification and propagation in Bernoulli–Euler nonlocal elastic beams. The beams are analyzed using both classical (local) and nonlocal approaches, where the basic uncertainty sources are attributed to their geometrical parameters—i.e. the length and the nonlocal parameter. The generalized iterative stochastic perturbation technique enables theoretical development and computational determination of the basic probabilistic moments and coefficients of uncertain beam displacements. We find that the uncertainty propagation in nonlocal models of engineering beams exhibits unexpected behaviour, which is markedly different from that observed in traditional engineering mechanics. This work offers insight into what can be expected in the vibration analysis of beams using nonlocal models, as well as in broader extensions of well-established engineering theories involving frames, plates, and shells.

本文对伯努利-欧拉非局部弹性梁的不确定性量化和传播进行了初步研究。采用经典（局部）和非局部方法对光束进行分析，其中基本不确定性源归因于它们的几何参数-即。长度和非局部参数。广义迭代随机摄动技术使不确定梁位移的基本概率矩和系数的理论发展和计算得以实现。我们发现工程梁非局部模型中的不确定性传播表现出与传统工程力学中观察到的明显不同的非预期行为。这项工作提供了对使用非局部模型的梁的振动分析的预期，以及对涉及框架，板和壳的成熟工程理论的更广泛扩展的见解。

引用次数: 0

Research on the non-probabilistic convex modeling method based on the potential connection between probabilistic and convex models 基于概率模型与凸模型潜在联系的非概率凸建模方法研究

IF 3 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-06-07 DOI: 10.1016/j.probengmech.2025.103794

Gang Zhao, Mingdong Wang, Yangyang Liu, Xiaoyu Wang, Wanyue Song

In existing research, probabilistic models and non-probabilistic convex models are typically treated as separate entities, with little attention given to their potential connections. This gap hinders a deeper understanding and rational application of non-probabilistic convex models. To address this issue, this paper proposes a novel non-probabilistic convex modeling method that leverages the potential relationship between probabilistic and convex models to achieve precise uncertainty quantification under limited data conditions. First, the mathematical formulations of the probabilistic and non-probabilistic convex models are presented. Then, a dimension-reduction technique is introduced to provide a feasible way to elucidate the potential connection between these two distinct modeling frameworks, establishing an effective bridge between them. On this basis, a new non-probabilistic convex modeling method is proposed for quantifying uncertainty under limited data. The performance of the proposed convex modeling method is evaluated through numerical examples, and its accuracy and effectiveness are further validated using engineering applications.

在现有的研究中，概率模型和非概率凸模型通常被视为独立的实体，很少关注它们之间的潜在联系。这种差距阻碍了对非概率凸模型的更深入的理解和合理的应用。为了解决这一问题，本文提出了一种新的非概率凸建模方法，利用概率模型和凸模型之间的潜在关系，在有限的数据条件下实现精确的不确定性量化。首先，给出了概率凸模型和非概率凸模型的数学表达式。然后，引入了一种降维技术，提供了一种可行的方法来阐明这两个不同的建模框架之间的潜在联系，在它们之间建立了有效的桥梁。在此基础上，提出了一种新的非概率凸建模方法来量化有限数据下的不确定性。通过数值算例对所提凸建模方法的性能进行了评价，并通过工程应用进一步验证了所提凸建模方法的准确性和有效性。

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引用次数: 0

Stochastic extended finite element analysis based on sparse polynomial chaos expansion 基于稀疏多项式混沌展开的随机扩展有限元分析

IF 3 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-06-07 DOI: 10.1016/j.probengmech.2025.103787

Zi Han , Zhentian Huang

In structural manufacturing, uncertainty is a fundamental factor. For models with inclusions or heterogeneous materials, the extended finite element method (XFEM) enables numerical simulations while avoiding the complexities of intricate meshing. However, when XFEM is integrated with polynomial chaos expansion (PCE) for intrusive stochastic analysis, a significant challenge arises: as the number of random variables and the order of the polynomial increase, the cost of constructing computational equations increases exponentially. To address this issue, a non-embedded PCE approach combined with XFEM is proposed for uncertainty analysis. To enhance the identification of effective basis functions in PCE, this paper introduces a novel forward-backward adaptive sparse polynomial selection algorithm. This algorithm effectively distinguishes significant basis functions from irrelevant ones and employs cross validation to identify the optimal set. A comparison with the least angle regression (LARs) sparse optimization algorithm reveals that the proposed method, through three case studies, demonstrates the efficacy of sparse PCE combined with XFEM in addressing challenges associated with inclusions or heterogeneous materials. The results indicate that the proposed algorithm achieves more concentrated results than those obtained with LARs.

在结构制造中，不确定性是一个基本因素。对于含有夹杂物或非均质材料的模型，扩展有限元法（XFEM）可以进行数值模拟，同时避免了复杂网格划分的复杂性。然而，当将XFEM与多项式混沌展开（PCE）相结合用于侵入式随机分析时，出现了一个重大挑战：随着随机变量数量和多项式阶数的增加，构建计算方程的成本呈指数增长。为了解决这一问题，提出了一种结合XFEM的非嵌入式PCE方法进行不确定性分析。为了提高PCE中有效基函数的识别能力，提出了一种新的自适应稀疏多项式选择算法。该算法有效地区分了重要基函数和不相关基函数，并采用交叉验证识别出最优集。与最小角度回归（LARs）稀疏优化算法的对比表明，通过三个案例研究，该方法证明了稀疏PCE与XFEM相结合在解决内含物或非均质材料相关挑战方面的有效性。结果表明，该算法得到的结果比用LARs得到的结果更集中。

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