Probabilistic Engineering Mechanics最新文献_第2页

Time-variant reliability analysis based on an improved Kriging method for industrial robot joint rotational accuracy subject to temperature 基于改进Kriging方法的温度下工业机器人关节旋转精度时变可靠性分析

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-12-24 DOI: 10.1016/j.probengmech.2025.103883

Jia Li , Liang Wang , Jialong He , Yan Liu , Guofa Li , Liyao Yu

Industrial robot joints experience time-varying temperature changes during operation, which directly affect rotational accuracy. However, systematic investigations into how dynamic and cumulative temperature effects lead to accuracy failure within a single work cycle remain limited. Moreover, the difficulty of precisely controlling temperature in practical environments complicates the acquisition of sufficient joint accuracy data under varying thermal conditions. To address these issues, this paper develops a joint rotation simulation model that explicitly incorporates temperature effects, allowing precise temperature control and accurate identification of the maximum rotational accuracy error under different operating conditions. Based on the simulated responses, a time-variant reliability analysis framework is employed to evaluate the probability of accuracy failure over the work cycle. Nevertheless, conventional active Kriging methods often suffer from inefficient sampling strategies. To overcome this limitation, a Rapid Uncertainty Assessment-guided Active Kriging (RUA-AK) method is proposed, in which a rapid uncertainty assessment function is constructed for time trajectories and sampling is adaptively refined according to uncertainty indicators, thereby improving computational efficiency. Numerical examples demonstrate that RUA-AK can substantially reduce the number of model evaluations required to achieve a prescribed accuracy level. Finally, the proposed method is applied to the time-variant reliability analysis of industrial robot joint rotational accuracy, elucidating the influence of temperature variations on reliability evolution throughout the work cycle.

工业机器人关节在工作过程中会经历时变的温度变化，直接影响旋转精度。然而，对动态和累积温度效应如何导致单个工作周期内精度失效的系统调查仍然有限。此外，在实际环境中精确控制温度的难度使得在不同热条件下获得足够的关节精度数据变得复杂。为了解决这些问题，本文开发了一个明确纳入温度影响的关节旋转仿真模型，可以精确控制温度并准确识别不同操作条件下的最大旋转精度误差。基于仿真响应，采用时变可靠性分析框架，对整个工作周期精度失效概率进行评估。然而，传统的主动克里格方法往往存在采样策略效率低下的问题。针对这一局限性，提出了一种基于快速不确定性评估的主动克里格（RUA-AK）方法，该方法对时间轨迹构建快速不确定性评估函数，并根据不确定性指标自适应细化采样，从而提高了计算效率。数值算例表明，RUA-AK可以大大减少达到规定精度水平所需的模型评估次数。最后，将该方法应用于工业机器人关节旋转精度的时变可靠性分析，阐明了温度变化对整个工作周期可靠性演化的影响。

{"title":"Time-variant reliability analysis based on an improved Kriging method for industrial robot joint rotational accuracy subject to temperature","authors":"Jia Li , Liang Wang , Jialong He , Yan Liu , Guofa Li , Liyao Yu","doi":"10.1016/j.probengmech.2025.103883","DOIUrl":"10.1016/j.probengmech.2025.103883","url":null,"abstract":"<div><div>Industrial robot joints experience time-varying temperature changes during operation, which directly affect rotational accuracy. However, systematic investigations into how dynamic and cumulative temperature effects lead to accuracy failure within a single work cycle remain limited. Moreover, the difficulty of precisely controlling temperature in practical environments complicates the acquisition of sufficient joint accuracy data under varying thermal conditions. To address these issues, this paper develops a joint rotation simulation model that explicitly incorporates temperature effects, allowing precise temperature control and accurate identification of the maximum rotational accuracy error under different operating conditions. Based on the simulated responses, a time-variant reliability analysis framework is employed to evaluate the probability of accuracy failure over the work cycle. Nevertheless, conventional active Kriging methods often suffer from inefficient sampling strategies. To overcome this limitation, a Rapid Uncertainty Assessment-guided Active Kriging (RUA-AK) method is proposed, in which a rapid uncertainty assessment function is constructed for time trajectories and sampling is adaptively refined according to uncertainty indicators, thereby improving computational efficiency. Numerical examples demonstrate that RUA-AK can substantially reduce the number of model evaluations required to achieve a prescribed accuracy level. Finally, the proposed method is applied to the time-variant reliability analysis of industrial robot joint rotational accuracy, elucidating the influence of temperature variations on reliability evolution throughout the work cycle.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"83 ","pages":"Article 103883"},"PeriodicalIF":3.5,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145840781","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}

引用次数: 0

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 : 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

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 : 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

Data-driven identification of time-delayed hybrid energy harvesting system under non-Gaussian noise 非高斯噪声下时滞混合能量采集系统的数据驱动辨识

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-12-04 DOI: 10.1016/j.probengmech.2025.103872

Yanxia Zhang , Pengfei Xu , Yanfei Jin

In engineering applications, the strongly nonlinear multistable hybrid vibration energy harvester (HVEH) with time delay poses significant challenges for stochastic dynamic modeling due to its non-Markovian characteristics and non-Gaussian noise. This difficulty is particularly pronounced in time-delayed systems driven by non-Gaussian noise, where conventional modeling approaches often fail to yield accurate results. From a machine learning perspective, we devise a data-driven identification method to identify the time-delayed non-Gaussian governing equation of HVEH. Leveraging the nonlocal Kramers-Moyal formulas and sparse identification, we first obtain a delay-free approximation from trajectory data. The complete time-delayed equation is then identified by applying Laplace transform algebra. To validate the proposed method, we compare the probability density functions of the identified systems with the original system. Results demonstrate that the identified time-delayed system achieves about 14 % higher precision than the identified delay-free system. Furthermore, we develop a dynamic analysis framework for energy harvesting performance based on the identified time-delayed system. This work advances data-driven modeling and dynamic analysis of HVEH in practical engineering.

在工程应用中，具有时滞的强非线性多稳态混合振动能量采集器（HVEH）由于其非马尔可夫特性和非高斯噪声，给随机动力学建模带来了很大的挑战。这种困难在由非高斯噪声驱动的时滞系统中尤为明显，在这种情况下，传统的建模方法往往无法产生准确的结果。从机器学习的角度出发，我们设计了一种数据驱动的识别方法来识别HVEH的时滞非高斯控制方程。利用非局部Kramers-Moyal公式和稀疏识别，我们首先从轨迹数据中获得无延迟近似。然后应用拉普拉斯变换代数辨识完整的时滞方程。为了验证所提出的方法，我们将识别系统的概率密度函数与原始系统进行了比较。结果表明，识别出的时滞系统比识别出的无时滞系统精度提高了14%左右。此外，我们开发了一个基于识别的时滞系统的能量收集性能动态分析框架。该工作为实际工程中数据驱动的HVEH建模和动态分析提供了新的方法。

{"title":"Data-driven identification of time-delayed hybrid energy harvesting system under non-Gaussian noise","authors":"Yanxia Zhang , Pengfei Xu , Yanfei Jin","doi":"10.1016/j.probengmech.2025.103872","DOIUrl":"10.1016/j.probengmech.2025.103872","url":null,"abstract":"<div><div>In engineering applications, the strongly nonlinear multistable hybrid vibration energy harvester (HVEH) with time delay poses significant challenges for stochastic dynamic modeling due to its non-Markovian characteristics and non-Gaussian noise. This difficulty is particularly pronounced in time-delayed systems driven by non-Gaussian noise, where conventional modeling approaches often fail to yield accurate results. From a machine learning perspective, we devise a data-driven identification method to identify the time-delayed non-Gaussian governing equation of HVEH. Leveraging the nonlocal Kramers-Moyal formulas and sparse identification, we first obtain a delay-free approximation from trajectory data. The complete time-delayed equation is then identified by applying Laplace transform algebra. To validate the proposed method, we compare the probability density functions of the identified systems with the original system. Results demonstrate that the identified time-delayed system achieves about 14 % higher precision than the identified delay-free system. Furthermore, we develop a dynamic analysis framework for energy harvesting performance based on the identified time-delayed system. This work advances data-driven modeling and dynamic analysis of HVEH in practical engineering.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"83 ","pages":"Article 103872"},"PeriodicalIF":3.5,"publicationDate":"2025-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145738182","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}

引用次数: 0

Practical enhancement of failure-probability estimation using probability density-driven active learning 利用概率密度驱动主动学习实际增强故障概率估计

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-12-02 DOI: 10.1016/j.probengmech.2025.103871

Tomoka Nakamura , Ikumasa Yoshida , Masahiro Takenobu , Daijiro Mizutani , Yu Otake

This study proposes a novel learning function, referred to as the T-learning function (TLF), that incorporates prior probability density into active learning for failure probability estimation. The method is developed within the framework of Adaptive Kriging-based Monte Carlo Simulation (AK-MCS), with the goal of improving estimation efficiency and robustness. The TLF prioritizes sampling in high-probability regions near the limit state by combining three components: prior density weighting, prediction uncertainty, and a redundancy suppression term. Comparative evaluations were conducted with two established learning functions, the U-function (ULF) and the Expected Feasibility function (EFF), using three benchmark problems and a practical application to port structure design. Numerical results show that the TLF achieves more accurate and stable failure probability estimates under limited computational resources and outperforms ULF in robustness to random initial conditions. Additionally, the EFF exhibited high compatibility with the stopping criterion and strong reliability in estimation. The proposed TLF enables an efficient and stable single reliability analysis, which is commonly required in engineering practice. This approach significantly reduces computational cost while maintaining estimation accuracy, and it offers practical applicability to real-world structural design problems.

本研究提出了一种新的学习函数，称为t学习函数（TLF），该函数将先验概率密度纳入主动学习中，用于故障概率估计。该方法是在自适应Kriging-based Monte Carlo Simulation （AK-MCS）框架下开发的，目的是提高估计效率和鲁棒性。TLF通过结合三个组成部分：先验密度加权、预测不确定性和冗余抑制项，在接近极限状态的高概率区域优先抽样。利用三个基准问题和港口结构设计的实际应用，对两个已建立的学习函数，即u函数（ULF）和预期可行性函数（EFF）进行了比较评价。数值结果表明，在有限的计算资源下，TLF获得了更准确和稳定的失效概率估计，并且在对随机初始条件的鲁棒性方面优于ULF。此外，EFF与停止准则的兼容性高，估计可靠性强。所提出的TLF能够实现高效、稳定的单次可靠性分析，这是工程实践中普遍需要的。该方法在保持估计精度的同时显著降低了计算成本，并为现实世界的结构设计问题提供了实际的适用性。

{"title":"Practical enhancement of failure-probability estimation using probability density-driven active learning","authors":"Tomoka Nakamura , Ikumasa Yoshida , Masahiro Takenobu , Daijiro Mizutani , Yu Otake","doi":"10.1016/j.probengmech.2025.103871","DOIUrl":"10.1016/j.probengmech.2025.103871","url":null,"abstract":"<div><div>This study proposes a novel learning function, referred to as the T-learning function (TLF), that incorporates prior probability density into active learning for failure probability estimation. The method is developed within the framework of Adaptive Kriging-based Monte Carlo Simulation (AK-MCS), with the goal of improving estimation efficiency and robustness. The TLF prioritizes sampling in high-probability regions near the limit state by combining three components: prior density weighting, prediction uncertainty, and a redundancy suppression term. Comparative evaluations were conducted with two established learning functions, the U-function (ULF) and the Expected Feasibility function (EFF), using three benchmark problems and a practical application to port structure design. Numerical results show that the TLF achieves more accurate and stable failure probability estimates under limited computational resources and outperforms ULF in robustness to random initial conditions. Additionally, the EFF exhibited high compatibility with the stopping criterion and strong reliability in estimation. The proposed TLF enables an efficient and stable single reliability analysis, which is commonly required in engineering practice. This approach significantly reduces computational cost while maintaining estimation accuracy, and it offers practical applicability to real-world structural design problems.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"83 ","pages":"Article 103871"},"PeriodicalIF":3.5,"publicationDate":"2025-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145652127","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}

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 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。

{"title":"Bayesian updating method considering the uncertainty of distribution parameters of random model inputs","authors":"Kaixuan Feng , Zhenzhou Lu","doi":"10.1016/j.probengmech.2025.103867","DOIUrl":"10.1016/j.probengmech.2025.103867","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103867"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145617948","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}

引用次数: 0

Asymmetric probabilistic solutions for stochastic oscillators with strong even-powered nonlinearities via a novel trial-shape function PINN framework 基于新型试形函数PINN框架的强偶幂非线性随机振子的非对称概率解

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-10-01 DOI: 10.1016/j.probengmech.2025.103864

Huanping Li , Guo-Peng Bai , Guilin Wen , Jie Liu , Guo-Kang Er

This paper proposes a novel TS-PINN framework, a physics-informed neural network incorporating trial and shape functions, for the probabilistic analysis of complex systems with strong even-powered nonlinearities. The presence of such nonlinearities in stochastic systems consistently induces asymmetry in probabilistic solutions. Unlike Gaussian closure which collapses under strong even-powered nonlinearities, TS-PINN delivers precise probabilistic solutions for these challenging stochastic systems. Within TS-PINN, the probabilistic solution takes the form of an exponential trial function applied to the sum of a Gaussian shape function and a neural network output. This solution formulation offers two key advantages: the exponential trial function guarantees solution positivity, preserving the physical interpretation of probability; and the Gaussian shape function provides an informed initial estimate, accelerating neural network convergence. The effectiveness of TS-PINN is validated through four numerical examples, demonstrating its capability to characterize asymmetric probabilistic solutions for stochastic oscillators with strong even-powered nonlinearities under correlated multiplicative and additive excitations. Verification is performed through comparative analysis with both Gaussian closure method and Monte Carlo simulation, confirming the framework’s accuracy and reliability.

本文提出了一种新的TS-PINN框架，一种包含试验函数和形状函数的物理信息神经网络，用于具有强偶幂非线性的复杂系统的概率分析。随机系统中这种非线性的存在总是导致概率解的不对称性。不像高斯闭包在强偶数幂非线性下崩溃，TS-PINN为这些具有挑战性的随机系统提供精确的概率解决方案。在TS-PINN中，概率解采用指数试验函数的形式，应用于高斯形状函数和神经网络输出的和。这种解的表述有两个关键的优点：指数试函数保证解的正性，保留了概率的物理解释；高斯形状函数提供了一个知情的初始估计，加速了神经网络的收敛。通过4个数值算例验证了TS-PINN的有效性，证明了其在相关的乘性和加性激励下表征强偶幂非线性随机振子的非对称概率解的能力。通过高斯闭包法和蒙特卡罗仿真的对比分析，验证了该框架的准确性和可靠性。

{"title":"Asymmetric probabilistic solutions for stochastic oscillators with strong even-powered nonlinearities via a novel trial-shape function PINN framework","authors":"Huanping Li , Guo-Peng Bai , Guilin Wen , Jie Liu , Guo-Kang Er","doi":"10.1016/j.probengmech.2025.103864","DOIUrl":"10.1016/j.probengmech.2025.103864","url":null,"abstract":"<div><div>This paper proposes a novel TS-PINN framework, a physics-informed neural network incorporating trial and shape functions, for the probabilistic analysis of complex systems with strong even-powered nonlinearities. The presence of such nonlinearities in stochastic systems consistently induces asymmetry in probabilistic solutions. Unlike Gaussian closure which collapses under strong even-powered nonlinearities, TS-PINN delivers precise probabilistic solutions for these challenging stochastic systems. Within TS-PINN, the probabilistic solution takes the form of an exponential trial function applied to the sum of a Gaussian shape function and a neural network output. This solution formulation offers two key advantages: the exponential trial function guarantees solution positivity, preserving the physical interpretation of probability; and the Gaussian shape function provides an informed initial estimate, accelerating neural network convergence. The effectiveness of TS-PINN is validated through four numerical examples, demonstrating its capability to characterize asymmetric probabilistic solutions for stochastic oscillators with strong even-powered nonlinearities under correlated multiplicative and additive excitations. Verification is performed through comparative analysis with both Gaussian closure method and Monte Carlo simulation, confirming the framework’s accuracy and reliability.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103864"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145571735","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}

引用次数: 0

Research on Adaptive Probabilistic Regularization (APR) method for damage parameter identification of laminated structures 基于自适应概率正则化（APR）的层合结构损伤参数识别方法研究

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-10-01 DOI: 10.1016/j.probengmech.2025.103852

Qinghe Shi , Chen Xu , Lei Wang , Juxi Hu , Weimin Chen

This paper proposes an adaptive probabilistic regularization method for damage parameter identification in composite laminated plates. Element-level damage parameters are introduced to describe the damage extent of composite laminated plates. A regularization methodology incorporating adaptive weighting coefficients is developed, enabling the dynamic adjustment of the weights assigned to each unknown parameter within the regularization term based on damage identification results throughout the solution process. To address the uncertainties encountered in the damage identification process, a damage identification strategy based on probabilistic regularization is proposed. Building on the Generalized Cross-Validation (GCV) method, the influence of uncertain parameters on the selection of regularization parameters is considered, yielding more robust regularization parameter selection results. Meanwhile, probabilistic methods are employed to quantify the uncertainties in the identification results, obtaining the uncertainty distribution of damage parameters in composite materials, with a focus on the distribution of in-plane and out-of-plane damage parameters for each element. By incorporating the principles of system reliability theory, the damage probability of each element can be derived. The computational precision and robustness of the proposed methodology are validated through a series of numerical examples and experimental validation case.

提出了一种复合材料层合板损伤参数识别的自适应概率正则化方法。引入单元级损伤参数来描述复合材料层合板的损伤程度。提出了一种包含自适应加权系数的正则化方法，在整个求解过程中，可以根据损伤识别结果对正则化项内每个未知参数的权重进行动态调整。针对损伤识别过程中遇到的不确定性，提出了一种基于概率正则化的损伤识别策略。在广义交叉验证（GCV）方法的基础上，考虑了不确定参数对正则化参数选择的影响，得到了更鲁棒的正则化参数选择结果。同时，采用概率方法对识别结果中的不确定性进行量化，得到复合材料损伤参数的不确定性分布，重点研究了各单元的面内和面外损伤参数的分布。结合系统可靠性理论的原理，推导出各部件的损坏概率。通过一系列数值算例和实验验证，验证了该方法的计算精度和鲁棒性。

{"title":"Research on Adaptive Probabilistic Regularization (APR) method for damage parameter identification of laminated structures","authors":"Qinghe Shi , Chen Xu , Lei Wang , Juxi Hu , Weimin Chen","doi":"10.1016/j.probengmech.2025.103852","DOIUrl":"10.1016/j.probengmech.2025.103852","url":null,"abstract":"<div><div>This paper proposes an adaptive probabilistic regularization method for damage parameter identification in composite laminated plates. Element-level damage parameters are introduced to describe the damage extent of composite laminated plates. A regularization methodology incorporating adaptive weighting coefficients is developed, enabling the dynamic adjustment of the weights assigned to each unknown parameter within the regularization term based on damage identification results throughout the solution process. To address the uncertainties encountered in the damage identification process, a damage identification strategy based on probabilistic regularization is proposed. Building on the Generalized Cross-Validation (GCV) method, the influence of uncertain parameters on the selection of regularization parameters is considered, yielding more robust regularization parameter selection results. Meanwhile, probabilistic methods are employed to quantify the uncertainties in the identification results, obtaining the uncertainty distribution of damage parameters in composite materials, with a focus on the distribution of in-plane and out-of-plane damage parameters for each element. By incorporating the principles of system reliability theory, the damage probability of each element can be derived. The computational precision and robustness of the proposed methodology are validated through a series of numerical examples and experimental validation case.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103852"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145267043","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}

引用次数: 0

A probabilistic evaluation of fatigue crack growth in plain concrete using inverse reliability approach 基于逆可靠度方法的素混凝土疲劳裂纹扩展概率评估

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-10-01 DOI: 10.1016/j.probengmech.2025.103853

Sumit Singh Thakur , K.M. Pervaiz Fathima

This study presents a probabilistic approach for predicting fatigue crack growth (FCG) parameters in plain concrete beams under constant amplitude cyclic loading. The method incorporates a size-adjusted Paris’ law, treating the initial crack length (

a_{0}

) and Paris’ coefficients (

C

and

m

) as random variables. The inverse first-order reliability method (FORM) is used to determine the Paris’ law coefficients corresponding to a target reliability level of 0.95. A limit state function (LSF) is formulated based on the theoretical and experimental number of load cycles to failure. The theoretical value is derived from the crack growth rate law, while the experimental value is obtained from stress versus the number of cycles to failure (S-N curve) data. The effectiveness of the proposed method is evaluated by comparing its results with those from inverse Monte Carlo simulation (MCS). The model is validated using experimental data from various concrete compositions and specimen sizes, including alkali-activated concrete. Larger specimens yielded lower prediction errors for the parameter

m

, while smaller specimens showed lower errors for

C

. Additionally, a sensitivity analysis is conducted to investigate how variations in input parameters influence the predicted crack growth parameters. Among the input random variables,

m

exhibited the highest sensitivity, followed by

a_{0}

and

C

. The proposed method improves fatigue life assessment and provides a predictive framework for structures where experimental data may be limited.

提出了一种预测素混凝土梁在等幅循环荷载作用下疲劳裂纹扩展参数的概率方法。该方法结合了一个调整尺寸的Paris定律，将初始裂纹长度（a0）和Paris系数（C和m）作为随机变量。采用反一阶可靠度法（FORM）确定了目标可靠度水平为0.95时所对应的帕里斯定律系数。基于理论和实验的载荷循环数，建立了极限状态函数（LSF）。理论值由裂纹扩展速率规律得出，实验值由应力与破坏循环次数（S-N曲线）数据得出。通过与反蒙特卡罗模拟（MCS）结果的比较，对该方法的有效性进行了评价。该模型使用各种混凝土成分和试样尺寸的实验数据进行验证，包括碱活化混凝土。较大的试件对参数m的预测误差较小，而较小的试件对参数c的预测误差较小。此外，还进行了敏感性分析，以研究输入参数的变化如何影响预测的裂纹扩展参数。在输入的随机变量中，m的灵敏度最高，其次是a0和c。该方法改进了疲劳寿命评估，并为实验数据有限的结构提供了预测框架。

{"title":"A probabilistic evaluation of fatigue crack growth in plain concrete using inverse reliability approach","authors":"Sumit Singh Thakur , K.M. Pervaiz Fathima","doi":"10.1016/j.probengmech.2025.103853","DOIUrl":"10.1016/j.probengmech.2025.103853","url":null,"abstract":"<div><div>This study presents a probabilistic approach for predicting fatigue crack growth (FCG) parameters in plain concrete beams under constant amplitude cyclic loading. The method incorporates a size-adjusted Paris’ law, treating the initial crack length (<span><math><msub><mrow><mi>a</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>) and Paris’ coefficients (<span><math><mi>C</mi></math></span> and <span><math><mi>m</mi></math></span>) as random variables. The inverse first-order reliability method (FORM) is used to determine the Paris’ law coefficients corresponding to a target reliability level of 0.95. A limit state function (LSF) is formulated based on the theoretical and experimental number of load cycles to failure. The theoretical value is derived from the crack growth rate law, while the experimental value is obtained from stress versus the number of cycles to failure (S-N curve) data. The effectiveness of the proposed method is evaluated by comparing its results with those from inverse Monte Carlo simulation (MCS). The model is validated using experimental data from various concrete compositions and specimen sizes, including alkali-activated concrete. Larger specimens yielded lower prediction errors for the parameter <span><math><mi>m</mi></math></span>, while smaller specimens showed lower errors for <span><math><mi>C</mi></math></span>. Additionally, a sensitivity analysis is conducted to investigate how variations in input parameters influence the predicted crack growth parameters. Among the input random variables, <span><math><mi>m</mi></math></span> exhibited the highest sensitivity, followed by <span><math><msub><mrow><mi>a</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and <span><math><mi>C</mi></math></span>. The proposed method improves fatigue life assessment and provides a predictive framework for structures where experimental data may be limited.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103853"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145267029","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}

引用次数: 0

Momentum gradient based first order reliability method for efficient identification of the most probable failure point 基于动量梯度的一阶可靠度方法有效识别最可能失效点

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-10-01 DOI: 10.1016/j.probengmech.2025.103862

Hong Xiang, Jiajian Zhu, Yi Zhang, Yuting Zhang, Huadeng Wu, Zhonghang Lv

In structural reliability analysis, the first order reliability method (FORM) is an effective tool for identifying the most probable failure point (MPP), which represents the region where structural failure is most likely to occur. However, the traditional Hasofer-Lind and Rackwitz-Flessler (HL-RF) algorithm in FORM often encounters numerical instabilities in highly nonlinear scenarios, hindering the determination of the MPP. This paper proposes a novel momentum gradient based algorithm capable of accurately locating the MPP. It searches for the MPP along a novel direction determined by a weighted moving average of historical gradients, such that the highly oscillatory behavior caused by reliance on the current gradient alone is smoothed. Criteria based on the cosine of the angle between the position vector and gradient vector are introduced to guide the selection of the momentum factor to further enhance the computational efficiency, in light of different characteristics of iterative points. The effectiveness of the proposed algorithm is demonstrated through four nonlinear examples, including two benchmark numerical cases and two practical structural applications. The results indicate that the proposed algorithm significantly improves efficiency compared to some commonly used FORMs, establishing it as a reliable and practical solution for accurate MPP determination.

在结构可靠度分析中，一阶可靠度法（FORM）是确定最可能失效点（MPP）的有效工具，MPP代表了结构最可能发生失效的区域。然而，传统的FORM中的hasfer - lind和Rackwitz-Flessler （HL-RF）算法在高度非线性情况下经常遇到数值不稳定性，阻碍了MPP的确定。本文提出了一种基于动量梯度的新算法，该算法能够精确定位MPP。它沿着一个由历史梯度加权移动平均确定的新方向搜索MPP，这样，仅依赖当前梯度引起的高度振荡行为就被平滑了。针对迭代点的不同特点，引入基于位置矢量与梯度矢量夹角余弦值的准则来指导动量因子的选择，进一步提高计算效率。通过四个非线性算例，包括两个基准数值算例和两个实际结构应用，验证了该算法的有效性。结果表明，与一些常用的表单相比，该算法显著提高了效率，为精确确定MPP提供了可靠和实用的解决方案。

{"title":"Momentum gradient based first order reliability method for efficient identification of the most probable failure point","authors":"Hong Xiang, Jiajian Zhu, Yi Zhang, Yuting Zhang, Huadeng Wu, Zhonghang Lv","doi":"10.1016/j.probengmech.2025.103862","DOIUrl":"10.1016/j.probengmech.2025.103862","url":null,"abstract":"<div><div>In structural reliability analysis, the first order reliability method (FORM) is an effective tool for identifying the most probable failure point (MPP), which represents the region where structural failure is most likely to occur. However, the traditional Hasofer-Lind and Rackwitz-Flessler (HL-RF) algorithm in FORM often encounters numerical instabilities in highly nonlinear scenarios, hindering the determination of the MPP. This paper proposes a novel momentum gradient based algorithm capable of accurately locating the MPP. It searches for the MPP along a novel direction determined by a weighted moving average of historical gradients, such that the highly oscillatory behavior caused by reliance on the current gradient alone is smoothed. Criteria based on the cosine of the angle between the position vector and gradient vector are introduced to guide the selection of the momentum factor to further enhance the computational efficiency, in light of different characteristics of iterative points. The effectiveness of the proposed algorithm is demonstrated through four nonlinear examples, including two benchmark numerical cases and two practical structural applications. The results indicate that the proposed algorithm significantly improves efficiency compared to some commonly used FORMs, establishing it as a reliable and practical solution for accurate MPP determination.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103862"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145571736","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}

引用次数: 0