Probabilistic Engineering Mechanics最新文献_第8页

Stochastic response of fractional oscillators subjected to non-stationary random excitations via hybrid pseudo-force approach 非平稳随机激励下分数阶振子的混合伪力法随机响应

IF 3 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-07-01 Epub Date: 2025-06-06 DOI: 10.1016/j.probengmech.2025.103799

Giuseppe Muscolino , Federica Genovese

In this paper, a novel “hybrid pseudo-force approach” is proposed for evaluating the stochastic response of fractional oscillators subjected to non-stationary input processes. The fractional oscillator analysed here is a second-order linear system that includes a term with a fractional derivative, capable of capturing the dissipative properties of viscoelastic materials. The convolution integral method is adopted to evaluate the response. The fractional term in the equation of motion is then treated as a pseudo-force, allowing for a decomposition of the convolution integral into two distinct parts. The first part, related to the modulating function, is solved analytically in closed form using “classical” stochastic dynamics techniques. The second part, which involves the pseudo-force contribution of the fractional term, requires the discretization of the fractional derivative using the Grünwald-Letnikov approximation and a piecewise linear interpolation. Finally, the stochastic response statistics are obtained via numerical integration in the frequency domain. Numerical examples validate the stability, accuracy and applicability of the proposed method through comparisons with Monte Carlo simulation.

本文提出了一种新的“混合伪力法”来评估分数阶振子在非平稳输入过程下的随机响应。这里分析的分数振子是一个二阶线性系统，它包含一个具有分数阶导数的项，能够捕捉粘弹性材料的耗散特性。采用卷积积分法计算响应。然后将运动方程中的分数项视为伪力，允许将卷积积分分解为两个不同的部分。第一部分与调制函数有关，使用“经典”随机动力学技术以封闭形式解析求解。第二部分涉及分数项的伪力贡献，需要使用gr nwald- letnikov近似和分段线性插值对分数阶导数进行离散化。最后，在频域上通过数值积分得到随机响应统计量。数值算例通过与蒙特卡罗模拟的比较，验证了所提方法的稳定性、准确性和适用性。

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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 : 2025-07-01 Epub 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

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 : 2025-07-01 Epub 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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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 : 2025-07-01 Epub 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

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 : 2025-07-01 Epub 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

Data-driven modeling of high-speed maglev track irregularity 高速磁浮轨道不平顺度数据驱动建模

IF 3 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-07-01 Epub Date: 2025-06-28 DOI: 10.1016/j.probengmech.2025.103798

Junqi Xu , Zhanghang Chen , Qinghua Zheng , Fei Ni

Ensuring the stability of high-speed maglev trains hinges on track smoothness, which is influenced by track irregularities that act as key excitations for train vibrations. These irregularities, stemming from various factors including track design and environmental conditions, are unpredictable and dynamic. Current models often fail to accurately represent these irregularities, leading to unreliable dynamic analyses. This paper introduces a non-stationary, non-Gaussian stochastic process model, enhanced with Iterative Amplitude Adjusted Fourier Transform (IAAFT) and Time-series Generative Adversarial Network (TimeGAN) algorithms, to more accurately simulate track irregularities. The model’s ability to generate independent, high-fidelity data supports improved design, operation, and maintenance of maglev systems.

确保高速磁悬浮列车的稳定性取决于轨道的平整度，而轨道平整度是列车振动的关键激励因素。这些不规则现象是由各种因素造成的，包括轨道设计和环境条件，是不可预测的和动态的。目前的模型往往不能准确地表示这些不规则性，导致不可靠的动态分析。本文介绍了一种非平稳、非高斯随机过程模型，该模型采用迭代调幅傅立叶变换（IAAFT）和时间序列生成对抗网络（TimeGAN）算法进行增强，以更准确地模拟航迹不规则性。该模型生成独立、高保真数据的能力支持磁悬浮系统的改进设计、运行和维护。

引用次数: 0

Finite element limit analysis of undrained vertical bearing capacity of skirted foundations in anisotropic random cohesive soils 各向异性随机粘性土中裙边基础不排水竖向承载力的有限元极限分析

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-07-01 Epub Date: 2025-08-29 DOI: 10.1016/j.probengmech.2025.103829

Nibir Rahman , Lipon Paul

Skirted foundations consist of a raft with vertical skirts that trap soil beneath, enhancing load transfer, stability, and reducing settlement for floating structures like barges and buoys. While most studies have focused on skirted foundations in homogeneous cohesive soils, the effects of spatial variability have often been overlooked. This study addresses this gap by using Karhunen-Loeve expansion (KL) and Monte Carlo Simulation (MCS) to investigate the probabilistic impact of undrained shear strength variability on skirted foundations, employing finite-element meshes for upper and lower-bound analyses. Various coefficients of variation and correlation length-to-footing width ratios are explored, with comparisons to previous studies using local average subdivision (LAS) and Cholesky decomposition (CD) techniques. The results provide probabilistic safety factors to ensure acceptable failure probabilities for skirted foundations under varying soil conditions. The study also finds that anisotropic soil behavior requires higher safety factors than isotropic conditions.

裙边基础由一个带有垂直裙边的木筏组成，它可以将土壤困在下面，增强荷载传递、稳定性，并减少驳船和浮标等浮动结构的沉降。虽然大多数研究都集中在均匀粘性土壤中的裙边基础上，但空间变异性的影响往往被忽视。本研究通过使用Karhunen-Loeve展开（KL）和蒙特卡罗模拟（MCS）来研究不排水剪切强度变化对裙边基础的概率影响，采用有限元网格进行上限和下限分析，从而解决了这一差距。研究了不同的变异系数和相关的长度-基础宽度比，并与先前使用局部平均细分（LAS）和Cholesky分解（CD）技术的研究进行了比较。计算结果提供了概率安全系数，以保证在不同土壤条件下裙边基础可接受的破坏概率。研究还发现，各向异性土壤特性比各向同性条件需要更高的安全系数。

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引用次数: 0

Successive Pareto simulation method for efficient structural reliability analysis 结构可靠度分析的连续Pareto模拟方法

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-07-01 Epub Date: 2025-07-29 DOI: 10.1016/j.probengmech.2025.103819

Rodrigo S. de Oliveira, Mariella F. de L.O. Santos, Silvana M.B. Afonso, Renato de S. Motta

The Monte Carlo (MC) method is a traditional approach for structural reliability analysis, known for its robustness in terms of accuracy. However, it can be inefficient when the sample size needs to be very large to obtain an adequate estimate. A novel approach, named successive Pareto simulation (SPS), is proposed to reduce the number of failure function evaluations in structural engineering problems, in which variables can be grouped into capacity and demand, by employing an efficient selection procedure on the MC sample. The proposed approach uses the Pareto optimality concept to obtain a small subset of the sample, formed mainly by points within the failure domain, thus considerably reducing the number of function evaluations while maintaining accuracy. Five benchmark problems and three structural problems are solved to validate the proposed method. Compared to MC, the reduction in the number of function evaluations varied from 95.61 % to 99.93 %. SPS also showed good results compared to variance reduction methods presented in the literature, requiring up to 77.31 %, 98.38 %, and 85.18 % fewer function evaluations than importance sampling, subset simulation, and the improved cross-entropy-based importance sampling, respectively. Moreover, although the selection procedure of SPS is applied to traditional MC in this work, it can also be applied to other simulation-based methods to enhance their efficiency.

蒙特卡罗（MC）方法是一种传统的结构可靠性分析方法，以其精度方面的鲁棒性而闻名。然而，当样本量需要非常大才能获得足够的估计时，它可能是低效的。提出了一种新的方法，即连续帕累托模拟（SPS），通过对MC样本进行有效的选择，减少了结构工程问题中可将变量分为容量和需求的失效函数评估的数量。该方法利用Pareto最优性概念获得样本的一个小子集，主要由故障域内的点组成，从而在保持准确性的同时大大减少了函数评估的次数。通过对5个基准问题和3个结构问题的求解，验证了该方法的有效性。与MC相比，功能评估次数减少了95.61%至99.93%。与文献中提出的方差缩减方法相比，SPS也显示出良好的结果，与重要性抽样、子集模拟和改进的基于交叉熵的重要性抽样相比，SPS所需的函数评估分别减少了77.31%、98.38%和85.18%。此外，虽然本工作将SPS的选择过程应用到传统的MC中，但也可以将其应用到其他基于仿真的方法中，以提高其效率。

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引用次数: 0

Influence of noise on First Passage Time maps and their use in damage detection 噪声对首次通过时间图的影响及其在损伤检测中的应用

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-07-01 Epub Date: 2025-07-27 DOI: 10.1016/j.probengmech.2025.103804

Kevin Theunissen , Vincent Denoël

Due to the aging of existing infrastructures and the growing of urbanisation among other things, Structural Health Monitoring has become a key element in various engineering fields. Numerous methods already exist to detect and localise damage to structures. However, the performances of such methods are reduced when subjected to unknown disturbances. In this paper, the influence of noise on a recent method based on the First Passage Time is studied. First, the description of the methodology is summarised and illustrated. Then, the efficacy of the method is assessed through four different scenarios. The first scenario considers the repeatability in identifying damage in ideal conditions, without any added noise. The other scenarios focus on the influence of additive loading (wind load) and measurement noise in detecting damage. It has been shown that the method excels in damage detection in each scenario. Indeed, even when the frequency change is approximately 1%, the method is still capable of identifying a small damage. However, in particular cases where the added measurement noise becomes too large, the method fails to distinguish the reference and damaged cases. Finally, due to the effectiveness of the bandpass filter in the processing of the method, the influence of wind load is limited, making the method efficient in detecting damage.

由于现有基础设施的老化和城市化进程的不断发展，结构健康监测已成为各个工程领域的关键因素。已经存在许多方法来检测和定位结构的损伤。然而，当受到未知干扰时，这种方法的性能会降低。本文研究了噪声对一种基于首次通过时间的新方法的影响。首先，对方法的描述进行了总结和说明。然后，通过四种不同的场景来评估该方法的有效性。第一种方案考虑了在理想条件下识别损伤的可重复性，没有任何额外的噪音。其他场景主要关注附加载荷（风荷载）和测量噪声对损伤检测的影响。实验结果表明，该方法在各种情况下都具有较好的损伤检测效果。事实上，即使频率变化约为1%，该方法仍然能够识别小损伤。但是，在附加测量噪声过大的特殊情况下，该方法无法区分参考和损坏情况。最后，由于该方法在处理过程中采用了有效的带通滤波器，使得风荷载的影响受到限制，使得该方法能够有效地检测出损伤。

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引用次数: 0

Mechanical and data-driven probabilistic model for axial strength of circular concrete-filled aluminum alloy tube short columns 圆形铝合金管状混凝土短柱轴向强度的力学和数据驱动概率模型

IF 3 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-07-01 Epub Date: 2025-07-17 DOI: 10.1016/j.probengmech.2025.103808

Junlei Tang , Hao Cheng , Bo Yu

A mechanical and data-driven probabilistic model was proposed to overcome the limitation that traditional deterministic models are unable to rationally consider the influences of aleatory and epistemic uncertainties on the axial strength of circular concrete-filled aluminum alloy tube (CCFAT) short columns. Firstly, a deterministic model for the axial strength of CCFAT short columns was established based on the Lame's solution, the theory of elasticity, and the unified theory. Subsequently, a probabilistic model for axial strength of CCFAT short columns was developed by considering both probabilistic model parameters and systematic errors. Meanwhile, the posterior distributions of probabilistic model parameters were updated based on the Bayesian theory and the Markov Chain Monte Carlo method. Furthermore, the predictive performance of the proposed probabilistic model was validated by comparing it with experimental datasets and traditional deterministic models. Finally, the proposed probabilistic model's probability density function, cumulative distribution function, and confidence intervals were employed to calibrate traditional deterministic models. Analysis shows that the proposed probabilistic model not only has a satisfactory predictive performance in that it rationally describes the probabilistic characteristics of the axial strength of CCFAT short columns, but also provides a dependable method for calibrating the prediction accuracy of traditional deterministic models for the axial strength of CCFAT short columns.

针对传统确定性模型不能合理考虑随机不确定性和认知不确定性对圆形铝合金管混凝土短柱轴向强度影响的局限性，提出了一种力学和数据驱动的概率模型。首先，基于拉梅解、弹性理论和统一理论，建立了CCFAT短柱轴向强度的确定性模型；在此基础上，建立了考虑概率模型参数和系统误差的CCFAT短柱轴向强度概率模型。同时，基于贝叶斯理论和马尔可夫链蒙特卡罗方法更新了概率模型参数的后验分布。通过与实验数据集和传统确定性模型的比较，验证了该概率模型的预测性能。最后，利用该概率模型的概率密度函数、累积分布函数和置信区间对传统的确定性模型进行校正。分析表明，所提出的概率模型不仅合理地描述了CCFAT短柱轴向强度的概率特征，具有令人满意的预测性能，而且为传统的CCFAT短柱轴向强度确定性模型的预测精度提供了一种可靠的校正方法。

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引用次数: 0