Pub Date : 2026-01-01DOI: 10.1016/j.probengmech.2025.103886
Samrul Hoda, Biswarup Bhattacharyya
Surrogate models serve as a pivotal tool in addressing the computational hurdles in analyzing the dynamical systems, especially in the presence of parametric uncertainty. In the context of uncertainty quantification (UQ) for dynamical systems, computing surrogate model parameters at each time step is often challenging, as it necessitates the computation of model parameters at each time step. This paper introduces an online reduced-order surrogate model for UQ in dynamical systems. An online Proper Orthogonal Decomposition (POD) approach is employed to represent stochastic response quantities using a minimal number of POD bases at each time instance. This approach allows for the fast updating of POD bases and coefficients at each time step in an online manner without needing to use all the data for the calculation. Further, the uncertainty propagation is facilitated through the utilization of the Kriging model. The efficacy of the proposed online POD–Kriging model is demonstrated for UQ in both linear and nonlinear dynamical systems, with results compared against a state-of-the-art method and full-scale Monte Carlo simulations. The consistently low predictive epistemic uncertainty observed across all cases confirms that the model achieves high accuracy, thereby establishing its efficiency and reliability for UQ in dynamical systems.
{"title":"Online POD–Kriging surrogate for efficient uncertainty quantification of dynamical systems","authors":"Samrul Hoda, Biswarup Bhattacharyya","doi":"10.1016/j.probengmech.2025.103886","DOIUrl":"10.1016/j.probengmech.2025.103886","url":null,"abstract":"<div><div>Surrogate models serve as a pivotal tool in addressing the computational hurdles in analyzing the dynamical systems, especially in the presence of parametric uncertainty. In the context of uncertainty quantification (UQ) for dynamical systems, computing surrogate model parameters at each time step is often challenging, as it necessitates the computation of model parameters at each time step. This paper introduces an online reduced-order surrogate model for UQ in dynamical systems. An online Proper Orthogonal Decomposition (POD) approach is employed to represent stochastic response quantities using a minimal number of POD bases at each time instance. This approach allows for the fast updating of POD bases and coefficients at each time step in an online manner without needing to use all the data for the calculation. Further, the uncertainty propagation is facilitated through the utilization of the Kriging model. The efficacy of the proposed online POD–Kriging model is demonstrated for UQ in both linear and nonlinear dynamical systems, with results compared against a state-of-the-art method and full-scale Monte Carlo simulations. The consistently low predictive epistemic uncertainty observed across all cases confirms that the model achieves high accuracy, thereby establishing its efficiency and reliability for UQ in dynamical systems.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"83 ","pages":"Article 103886"},"PeriodicalIF":3.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884332","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}
Pub Date : 2026-01-01DOI: 10.1016/j.probengmech.2025.103889
Ying Ma , Zebin Wu , Dongsheng Wang , Chengqing Liu , Zhiguo Sun
This study develops a comprehensive probabilistic framework for predicting the hysteresis loops of reinforced concrete (RC) columns with different failure modes and cross-section types. A database of cyclic loading tests on 373 rectangular and spiral RC columns is compiled from the PEER-Structural Performance Database. The Bouc-Wen-Baber-Noori (BWBN) model is employed to describe the hysteretic behavior. The twelve BWBN model parameters are probabilistically identified for each specimen using a Bayesian parameter identification approach, yielding their full posterior distributions. Analysis of the identified posterior distributions reveals a systematic dependence of the BWBN parameters on the RC column's failure mode (flexure, flexural-shear, or shear failure) and cross-section type (rectangular or spiral), alongside a weak linear correlation with the RC column parameters. To address this complex nonlinear mapping, separate Bayesian Neural Network (BNN) models are trained for rectangular and spiral RC columns. The proposed probabilistic framework establishes an end-to-end predictive process: given RC column parameters, the BNN predicts the statistical distributions of the BWBN model parameters, which are then used to generate the hysteresis loop and its associated uncertainty bounds. The framework's accuracy is validated against experimental data, demonstrating high fidelity across different failure modes and cross-section types. The framework provides a robust tool for incorporating multifaceted uncertainties into the inelastic seismic analysis of RC columns.
{"title":"A probabilistic framework for predicting hysteresis loops of reinforced concrete columns with different failure modes and cross-section types","authors":"Ying Ma , Zebin Wu , Dongsheng Wang , Chengqing Liu , Zhiguo Sun","doi":"10.1016/j.probengmech.2025.103889","DOIUrl":"10.1016/j.probengmech.2025.103889","url":null,"abstract":"<div><div>This study develops a comprehensive probabilistic framework for predicting the hysteresis loops of reinforced concrete (RC) columns with different failure modes and cross-section types. A database of cyclic loading tests on 373 rectangular and spiral RC columns is compiled from the PEER-Structural Performance Database. The Bouc-Wen-Baber-Noori (BWBN) model is employed to describe the hysteretic behavior. The twelve BWBN model parameters are probabilistically identified for each specimen using a Bayesian parameter identification approach, yielding their full posterior distributions. Analysis of the identified posterior distributions reveals a systematic dependence of the BWBN parameters on the RC column's failure mode (flexure, flexural-shear, or shear failure) and cross-section type (rectangular or spiral), alongside a weak linear correlation with the RC column parameters. To address this complex nonlinear mapping, separate Bayesian Neural Network (BNN) models are trained for rectangular and spiral RC columns. The proposed probabilistic framework establishes an end-to-end predictive process: given RC column parameters, the BNN predicts the statistical distributions of the BWBN model parameters, which are then used to generate the hysteresis loop and its associated uncertainty bounds. The framework's accuracy is validated against experimental data, demonstrating high fidelity across different failure modes and cross-section types. The framework provides a robust tool for incorporating multifaceted uncertainties into the inelastic seismic analysis of RC columns.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"83 ","pages":"Article 103889"},"PeriodicalIF":3.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884333","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}
Pub Date : 2026-01-01DOI: 10.1016/j.probengmech.2026.103892
Tianci Gong , Jingjing He , Xuefei Guan
This study presents a continuously nested moment quadrature method for uncertainty quantification of stochastic systems with arbitrary random input distributions. The method allows for continuous nesting and convergence testing simultaneously; therefore, existing model evaluation results can fully be reused to obtain a converged result at a minimum incremental computational demand. By incorporating a dynamic precision adjustment strategy and adopting criteria on the allowable number of negative weights, the proposed method overcomes the potential limitations of nesting only once under uniform distributions in the conventional Gauss-Kronrod formula, while achieving the highest possible algebraic precision in terms of polynomial degrees. The proposed method is applied to multiple classical and complex engineering and mathematical cases, including a computationally intensive 3D crack propagation problem. Results show that the proposed method requires less computational effort to achieve the same algebraic precision compared to the regular moment quadrature method and the Monte Carlo method. Notably, for problems with uniform random inputs, the computational demand can be reduced to one-fifth of that required by the regular moment quadrature method.
{"title":"Continuously nested moment quadrature for uncertainty quantification of black-box models","authors":"Tianci Gong , Jingjing He , Xuefei Guan","doi":"10.1016/j.probengmech.2026.103892","DOIUrl":"10.1016/j.probengmech.2026.103892","url":null,"abstract":"<div><div>This study presents a continuously nested moment quadrature method for uncertainty quantification of stochastic systems with arbitrary random input distributions. The method allows for continuous nesting and convergence testing simultaneously; therefore, existing model evaluation results can fully be reused to obtain a converged result at a minimum incremental computational demand. By incorporating a dynamic precision adjustment strategy and adopting criteria on the allowable number of negative weights, the proposed method overcomes the potential limitations of nesting only once under uniform distributions in the conventional Gauss-Kronrod formula, while achieving the highest possible algebraic precision in terms of polynomial degrees. The proposed method is applied to multiple classical and complex engineering and mathematical cases, including a computationally intensive 3D crack propagation problem. Results show that the proposed method requires less computational effort to achieve the same algebraic precision compared to the regular moment quadrature method and the Monte Carlo method. Notably, for problems with uniform random inputs, the computational demand can be reduced to one-fifth of that required by the regular moment quadrature method.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"83 ","pages":"Article 103892"},"PeriodicalIF":3.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976643","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}
Pub Date : 2026-01-01DOI: 10.1016/j.probengmech.2026.103891
Fujia Li , Tianzhe Wang , Guofa Li , Yatao Huo , Xiaodian Meng
In the field of structural reliability analysis, the high computational cost of function calls has long been a significant challenge. The Adaptive Kriging combined with Monte Carlo Simulation (AK-MCS) method effectively improves the efficiency of structural reliability analysis by substituting the actual performance function with a surrogate. However, this method still suffers from poor fitting performance for complex failure boundaries. Therefore, this paper proposes a novel dynamic failure-aware adaptive learning method, referred to as QH-DFA, based on the Quantile–Huber (QH) loss function. The method constructs a risk-aware metric centered on the QH loss function, thereby enhancing the metamodel's robustness. Subsequently, a failure-aware sampling weight function is designed to direct sampling toward critical boundary regions, improving the metamodel's ability to capture failure boundaries. To clearly demonstrate the effectiveness of the proposed method, three numerical examples and one engineering example are used for comparative verification. The results indicate that, compared with the U/EFF/ERF, QH-DFA shows significant advantages in both efficiency and accuracy.
{"title":"An adaptive Kriging framework with Quantile-Huber loss and dynamic failure-aware sampling for efficient structural reliability analysis","authors":"Fujia Li , Tianzhe Wang , Guofa Li , Yatao Huo , Xiaodian Meng","doi":"10.1016/j.probengmech.2026.103891","DOIUrl":"10.1016/j.probengmech.2026.103891","url":null,"abstract":"<div><div>In the field of structural reliability analysis, the high computational cost of function calls has long been a significant challenge. The Adaptive Kriging combined with Monte Carlo Simulation (AK-MCS) method effectively improves the efficiency of structural reliability analysis by substituting the actual performance function with a surrogate. However, this method still suffers from poor fitting performance for complex failure boundaries. Therefore, this paper proposes a novel dynamic failure-aware adaptive learning method, referred to as QH-DFA, based on the Quantile–Huber (QH) loss function. The method constructs a risk-aware metric centered on the QH loss function, thereby enhancing the metamodel's robustness. Subsequently, a failure-aware sampling weight function is designed to direct sampling toward critical boundary regions, improving the metamodel's ability to capture failure boundaries. To clearly demonstrate the effectiveness of the proposed method, three numerical examples and one engineering example are used for comparative verification. The results indicate that, compared with the U/EFF/ERF, QH-DFA shows significant advantages in both efficiency and accuracy.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"83 ","pages":"Article 103891"},"PeriodicalIF":3.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976642","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}
Pub Date : 2026-01-01DOI: 10.1016/j.probengmech.2026.103890
Hojun Choi, Eunho Heo, Dongjin Lee
Dimensionally decomposed generalized polynomial chaos expansion (DD-GPCE) efficiently performs forward uncertainty quantification (UQ) in complex engineering systems with high-dimensional random inputs of arbitrary distributions. However, constructing the measure-consistent orthonormal polynomial bases in DD-GPCE requires prior knowledge of input distributions, which is often unavailable in practice. This work introduces a data-driven DD-GPCE method that eliminates the need for such prior knowledge, extending its applicability to UQ with high-dimensional inputs. Input distributions are inferred directly from sample data using smoothed-bootstrap kernel density estimation (KDE), while the DD-GPCE framework enables KDE to handle high-dimensional inputs through low-dimensional marginal estimation. We then use the estimated input distributions to perform a whitening transformation via Monte Carlo Simulation, which enables generation of measure-consistent orthonormal basis functions. We demonstrate the accuracy of the proposed method in both mathematical examples and stochastic dynamic analysis for a practical three-dimensional mobility design involving twenty random inputs. The results indicate that the proposed method produces more accurate estimates of the output mean and variance compared to the conventional data-driven approach that assumes Gaussian input distributions.
维分解广义多项式混沌展开（DD-GPCE）有效地解决了具有任意分布的高维随机输入的复杂工程系统的前向不确定性量化问题。然而，在DD-GPCE中构造测度一致的标准正交多项式基需要事先知道输入分布，这在实践中往往是不可用的。这项工作引入了一种数据驱动的DD-GPCE方法，该方法消除了对此类先验知识的需求，将其扩展到具有高维输入的UQ。输入分布是使用平滑引导核密度估计（smooth -bootstrap kernel density estimation， KDE）直接从样本数据推断出来的，而DD-GPCE框架使KDE能够通过低维边际估计处理高维输入。然后，我们使用估计的输入分布通过蒙特卡罗模拟执行白化变换，从而生成测量一致的标准正交基函数。我们在数学实例和随机动力学分析中证明了所提出方法的准确性，该方法涉及20个随机输入的实际三维机动性设计。结果表明，与假设高斯输入分布的传统数据驱动方法相比，该方法可以更准确地估计输出均值和方差。
{"title":"Data-driven dimensionally decomposed generalized polynomial chaos expansion for forward uncertainty quantification","authors":"Hojun Choi, Eunho Heo, Dongjin Lee","doi":"10.1016/j.probengmech.2026.103890","DOIUrl":"10.1016/j.probengmech.2026.103890","url":null,"abstract":"<div><div>Dimensionally decomposed generalized polynomial chaos expansion (DD-GPCE) efficiently performs forward uncertainty quantification (UQ) in complex engineering systems with high-dimensional random inputs of arbitrary distributions. However, constructing the measure-consistent orthonormal polynomial bases in DD-GPCE requires prior knowledge of input distributions, which is often unavailable in practice. This work introduces a data-driven DD-GPCE method that eliminates the need for such prior knowledge, extending its applicability to UQ with high-dimensional inputs. Input distributions are inferred directly from sample data using smoothed-bootstrap kernel density estimation (KDE), while the DD-GPCE framework enables KDE to handle high-dimensional inputs through low-dimensional marginal estimation. We then use the estimated input distributions to perform a whitening transformation via Monte Carlo Simulation, which enables generation of measure-consistent orthonormal basis functions. We demonstrate the accuracy of the proposed method in both mathematical examples and stochastic dynamic analysis for a practical three-dimensional mobility design involving twenty random inputs. The results indicate that the proposed method produces more accurate estimates of the output mean and variance compared to the conventional data-driven approach that assumes Gaussian input distributions.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"83 ","pages":"Article 103890"},"PeriodicalIF":3.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976645","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}
Pub Date : 2026-01-01DOI: 10.1016/j.probengmech.2025.103888
Haoyu Wang , Ning Guo , Hao Wang , Shilong Li , Zexing Yu , Chao Xu
Bistable composite thin-walled column–shells combine high specific stiffness and compact stowage, making them critical elements in aerospace deployable structures. Their curling and deployment involve strong geometric nonlinearities and stress concentrations near edges and transition zones, while material and manufacturing uncertainties complicate reliable design. This paper presents a hybrid surrogate model that couples enhanced Kriging, polynomial chaos expansion, and a radial basis function neural network to accurately predict curling strength under uncertainty. Leveraging the HSM (hybrid surrogate model), a derivative-based global sensitivity measure is employed to identify the dominant design variables, and a reliability-based design optimization is utilized to minimize the probability of matrix tensile failure. Numerical validation demonstrates that the proposed framework achieves a favorable balance between predictive accuracy and computational efficiency, substantially improving the reliability and engineering applicability of bistable composite structures.
{"title":"Hybrid-surrogate-based prediction and reliability-based optimization of curling strength for bistable cylindrical shells","authors":"Haoyu Wang , Ning Guo , Hao Wang , Shilong Li , Zexing Yu , Chao Xu","doi":"10.1016/j.probengmech.2025.103888","DOIUrl":"10.1016/j.probengmech.2025.103888","url":null,"abstract":"<div><div>Bistable composite thin-walled column–shells combine high specific stiffness and compact stowage, making them critical elements in aerospace deployable structures. Their curling and deployment involve strong geometric nonlinearities and stress concentrations near edges and transition zones, while material and manufacturing uncertainties complicate reliable design. This paper presents a hybrid surrogate model that couples enhanced Kriging, polynomial chaos expansion, and a radial basis function neural network to accurately predict curling strength under uncertainty. Leveraging the HSM (hybrid surrogate model), a derivative-based global sensitivity measure is employed to identify the dominant design variables, and a reliability-based design optimization is utilized to minimize the probability of matrix tensile failure. Numerical validation demonstrates that the proposed framework achieves a favorable balance between predictive accuracy and computational efficiency, substantially improving the reliability and engineering applicability of bistable composite structures.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"83 ","pages":"Article 103888"},"PeriodicalIF":3.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884334","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}
Pub Date : 2026-01-01DOI: 10.1016/j.probengmech.2025.103887
Guangquan Yu , Ning Li , Xiaohang Zhang , Yuchen Hu , Cheng Chen
Accurate reliability estimation under tight computational budgets requires sampling strategies that both concentrate evaluations near the limit state and maintain sufficient global coverage. This study introduces Voronoi partitioning of key regions with cross-validation (CV) of failure probabilities (VK-CVF), a plug-in, learning-function-agnostic adaptive sampling framework that (i) identifies a critical region via surrogate model, (ii) partitions only that region into Voronoi subdomains, and (iii) ranks subdomains with a leave-one-out (LOO) failure-probability CV metric. New samples are placed preferentially in the most influential subdomains and, importantly, also near the centers of sub-sensitive units to provide directional, exploration-oriented guidance that balances exploitation and global learning. This targeted partitioning avoids global tessellation, yields quasi-uniform refinement near the limit state, and remains fully compatible with common learning functions (e.g., U-function, H-function). Across four benchmarks and a multi-hazard offshore jacket case, VK-CVF achieves accuracy comparable to that of AK-MCS while requiring about 50% fewer performance-function calls (range 35%–65%) and yields more uniform near-limit-state sampling. As a plug-in wrapper, it integrates with standard acquisition rules without altering their definitions.
{"title":"Plug-in adaptive sampling for structural reliability: Key region Voronoi partitioning with cross-validated failure probability","authors":"Guangquan Yu , Ning Li , Xiaohang Zhang , Yuchen Hu , Cheng Chen","doi":"10.1016/j.probengmech.2025.103887","DOIUrl":"10.1016/j.probengmech.2025.103887","url":null,"abstract":"<div><div>Accurate reliability estimation under tight computational budgets requires sampling strategies that both concentrate evaluations near the limit state and maintain sufficient global coverage. This study introduces Voronoi partitioning of key regions with cross-validation (CV) of failure probabilities (<span>VK-CVF</span>), a plug-in, learning-function-agnostic adaptive sampling framework that (i) identifies a critical region via surrogate model, (ii) partitions only that region into Voronoi subdomains, and (iii) ranks subdomains with a leave-one-out (LOO) failure-probability CV metric. New samples are placed preferentially in the most influential subdomains and, importantly, also near the centers of sub-sensitive units to provide directional, exploration-oriented guidance that balances exploitation and global learning. This targeted partitioning avoids global tessellation, yields quasi-uniform refinement near the limit state, and remains fully compatible with common learning functions (e.g., U-function, H-function). Across four benchmarks and a multi-hazard offshore jacket case, <span>VK-CVF</span> achieves accuracy comparable to that of AK-MCS while requiring about 50% fewer performance-function calls (range 35%–65%) and yields more uniform near-limit-state sampling. As a plug-in wrapper, it integrates with standard acquisition rules without altering their definitions.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"83 ","pages":"Article 103887"},"PeriodicalIF":3.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884512","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}
Pub Date : 2026-01-01DOI: 10.1016/j.probengmech.2025.103882
Lili Weng , Jianbing Chen , Hector A. Jensen
Reliability-based design optimization (RBDO) offers a powerful framework for structural design by effectively incorporating uncertainties into the optimization process. However, the computational challenges involved in RBDO hinder its application in real-world engineering, especially earthquake engineering, where the analyses of detailed finite element models accounting for nonlinear behaviors could be necessary. Within the framework of the “three-level, two-stage” seismic design methodology currently adopted in China, this contribution proposes a two-stage design optimization framework for seismic reinforced concrete (RC) structures under uncertainties. Specifically, in the first stage, RBDO is applied to elastic RC structures subjected to frequently-occurring seismic actions, while incorporating two levels of reliability constraints, i.e., the performance or deformation requirements and the requirements of guaranteeing linearity of materials, to ensure structural performance. In the second stage, the dynamic reliability of the structure corresponding to the optimized design obtained from the first stage is checked under rare seismic loading conditions, considering the nonlinear behaviors of the structures. The probability density evolution method (PDEM) is employed for evaluating the dynamic reliability, and the quantum evolutionary algorithm (QEA) is adopted to solve the optimization problems involving discrete design variables. The core idea of the proposed framework is to enhance the “three-level, two-stage” seismic design methodology from a “semi-deterministic” procedure to a “fully probabilistic” optimization design approach, ensuring the global reliability of the structures is effectively quantified and accounted for. By decomposing the design procedure of RC structures considering uncertainties into two distinct sub-procedures, the proposed framework can ensure structural safety under extreme seismic actions with significantly reduced computational burden typically associated with structural nonlinear dynamic analyses. Three examples are studied to demonstrate the feasibility and effectiveness of the proposed framework.
{"title":"A pragmatic two-stage design optimization framework for seismic RC structures under uncertainties incorporating two-level reliability constraints","authors":"Lili Weng , Jianbing Chen , Hector A. Jensen","doi":"10.1016/j.probengmech.2025.103882","DOIUrl":"10.1016/j.probengmech.2025.103882","url":null,"abstract":"<div><div>Reliability-based design optimization (RBDO) offers a powerful framework for structural design by effectively incorporating uncertainties into the optimization process. However, the computational challenges involved in RBDO hinder its application in real-world engineering, especially earthquake engineering, where the analyses of detailed finite element models accounting for nonlinear behaviors could be necessary. Within the framework of the “three-level, two-stage” seismic design methodology currently adopted in China, this contribution proposes a two-stage design optimization framework for seismic reinforced concrete (RC) structures under uncertainties. Specifically, in the first stage, RBDO is applied to elastic RC structures subjected to frequently-occurring seismic actions, while incorporating two levels of reliability constraints, i.e., the performance or deformation requirements and the requirements of guaranteeing linearity of materials, to ensure structural performance. In the second stage, the dynamic reliability of the structure corresponding to the optimized design obtained from the first stage is checked under rare seismic loading conditions, considering the nonlinear behaviors of the structures. The probability density evolution method (PDEM) is employed for evaluating the dynamic reliability, and the quantum evolutionary algorithm (QEA) is adopted to solve the optimization problems involving discrete design variables. The core idea of the proposed framework is to enhance the “three-level, two-stage” seismic design methodology from a “semi-deterministic” procedure to a “fully probabilistic” optimization design approach, ensuring the global reliability of the structures is effectively quantified and accounted for. By decomposing the design procedure of RC structures considering uncertainties into two distinct sub-procedures, the proposed framework can ensure structural safety under extreme seismic actions with significantly reduced computational burden typically associated with structural nonlinear dynamic analyses. Three examples are studied to demonstrate the feasibility and effectiveness of the proposed framework.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"83 ","pages":"Article 103882"},"PeriodicalIF":3.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976644","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}
Pub Date : 2026-01-01DOI: 10.1016/j.probengmech.2025.103884
Zonghui Wu , Jian He , Chenyang Wang , Xiaodan Sun , Di Yao
The fundamental purpose of structural reliability analysis is defined as the quantitative measurement of structural failure possibilities. The surrogate model method is currently regarded as the most widely used reliability evaluation method, but it has problems such as low fitting accuracy, high computational cost, low convergence efficiency and high parameter sensitivity when dealing with small probability events. Although there are some methods to accelerate the analysis, such as Adaptive Kriging combined with Monte Carlo Simulation (AK-MCS), the construction of the model still requires a large number of samples, resulting in a very large amount of calculation of the surrogate model. Therefore, this study combines the adaptive Kriging model with advanced subset simulation (AK-ASS) to solve these problems. In this paper, through the verification of mathematical examples and engineering examples, it is proved that this method reduces the analysis time required to deal with the problem of small probability failure, and overcomes some limitations of subset simulation. Furthermore, it has the potential to be used in combination with new efficient learning functions in the future.
结构可靠度分析的根本目的是对结构破坏可能性进行定量测量。代理模型法是目前应用最广泛的可靠性评估方法，但在处理小概率事件时存在拟合精度低、计算成本高、收敛效率低和参数灵敏度高等问题。虽然有一些加速分析的方法，如Adaptive Kriging结合Monte Carlo Simulation (AK-MCS)，但模型的构建仍然需要大量的样本，导致代理模型的计算量非常大。因此，本研究将自适应Kriging模型与先进子集仿真（AK-ASS）相结合来解决这些问题。本文通过数学实例和工程实例的验证，证明了该方法减少了处理小概率故障问题所需的分析时间，克服了子集仿真的一些局限性。此外，它在未来有可能与新的高效学习函数结合使用。
{"title":"AK-ASS: An improvement of the Kriging model for dealing with small failure probability problems","authors":"Zonghui Wu , Jian He , Chenyang Wang , Xiaodan Sun , Di Yao","doi":"10.1016/j.probengmech.2025.103884","DOIUrl":"10.1016/j.probengmech.2025.103884","url":null,"abstract":"<div><div>The fundamental purpose of structural reliability analysis is defined as the quantitative measurement of structural failure possibilities. The surrogate model method is currently regarded as the most widely used reliability evaluation method, but it has problems such as low fitting accuracy, high computational cost, low convergence efficiency and high parameter sensitivity when dealing with small probability events. Although there are some methods to accelerate the analysis, such as Adaptive Kriging combined with Monte Carlo Simulation (AK-MCS), the construction of the model still requires a large number of samples, resulting in a very large amount of calculation of the surrogate model. Therefore, this study combines the adaptive Kriging model with advanced subset simulation (AK-ASS) to solve these problems. In this paper, through the verification of mathematical examples and engineering examples, it is proved that this method reduces the analysis time required to deal with the problem of small probability failure, and overcomes some limitations of subset simulation. Furthermore, it has the potential to be used in combination with new efficient learning functions in the future.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"83 ","pages":"Article 103884"},"PeriodicalIF":3.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884335","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}
Pub Date : 2025-12-24DOI: 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.
{"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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号