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":"2026-01-01","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}
Pub Date : 2026-01-01Epub Date: 2026-02-20DOI: 10.1016/j.probengmech.2026.103900
Youbao Jiang, Yi Xiao, Xuyang Zhang
The direct probability integral method uses generalized F-discrepancy point selection approach and Dirac function smoothing technique to compute the probability density function of structural responses with only a small number of representative points. However, the representative points generated based on generalized F-discrepancy typically concentrate around the probabilistic center of the sample space, lacking attention to the failure boundary. To address this issue, this paper proposes a global search representative point generation algorithm. The algorithm uses an adaptive Kriging to explore the failure boundary and applies directional sampling to generate representative points. This algorithm reduces computational errors in reliability analysis based on the direct probability integral method that are caused by insufficient boundary coverage and by intersections between representative regions and the failure boundary. Meanwhile, by incorporating the generalized F-discrepancy representative points, the method ensures uniformity in both assigned probabilities and spatial distribution. Finally, three examples are investigated and compared with other reliability methods, demonstrating that the proposed approach offers significant advantages in estimating failure probabilities and solving probability density function.
{"title":"An efficient algorithm for global searching of representative points in reliability evaluation with adaptive Kriging model and direct probability integral method","authors":"Youbao Jiang, Yi Xiao, Xuyang Zhang","doi":"10.1016/j.probengmech.2026.103900","DOIUrl":"10.1016/j.probengmech.2026.103900","url":null,"abstract":"<div><div>The direct probability integral method uses generalized F-discrepancy point selection approach and Dirac function smoothing technique to compute the probability density function of structural responses with only a small number of representative points. However, the representative points generated based on generalized F-discrepancy typically concentrate around the probabilistic center of the sample space, lacking attention to the failure boundary. To address this issue, this paper proposes a global search representative point generation algorithm. The algorithm uses an adaptive Kriging to explore the failure boundary and applies directional sampling to generate representative points. This algorithm reduces computational errors in reliability analysis based on the direct probability integral method that are caused by insufficient boundary coverage and by intersections between representative regions and the failure boundary. Meanwhile, by incorporating the generalized F-discrepancy representative points, the method ensures uniformity in both assigned probabilities and spatial distribution. Finally, three examples are investigated and compared with other reliability methods, demonstrating that the proposed approach offers significant advantages in estimating failure probabilities and solving probability density function.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"83 ","pages":"Article 103900"},"PeriodicalIF":3.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147395572","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 : 2026-01-01Epub Date: 2026-02-13DOI: 10.1016/j.probengmech.2026.103899
Sina Fallahzadeh Rastehkenari, Javad Dargahi, Muthukumaran Packirisamy
This paper presents a unified integral two-phase local/nonlocal model with a Gaussian attenuation kernel for deterministic and random vibration analysis of shear-deformable piezoelectric nanobeams on a viscoelastic foundation under concentrated wide-band white-noise excitation. The piezoelectric constitutive laws are kept in their original integral local/nonlocal form and coupled with a unified higher-order shear deformation beam theory that recovers Euler–Bernoulli, Timoshenko, Reddy, sinusoidal, hyperbolic, and exponential shear models. By avoiding the differential transformation and its additional constitutive boundary conditions, the proposed formulation eliminates the well-known inconsistencies of classical differential nonlocal models and remains paradox free. Deterministic results show that nonlocality systematically softens PZT-4 nanobeams and reduces natural frequencies, with the Gaussian kernel inducing stronger softening than the conventional exponential kernel, while higher local phase fraction, greater slenderness, and stiffer foundations restore more classical behavior. In the stochastic regime, a frequency-response-based spectral approach reveals that stronger nonlocal effects and higher temperatures amplify the mean-square transverse response, whereas increased piezoelectric actuation, foundation stiffness, and damping significantly reduce it. Shear deformation is relevant for moderately thick nanobeams but becomes negligible in slender configurations. The proposed framework provides a transparent and robust basis for analyzing and designing piezoelectric MEMS/NEMS components operating in stochastic environments.
{"title":"Random vibrations of two phase shear deformable pieozoelectric nanobeams based on Gaussian local/nonlocal integral model","authors":"Sina Fallahzadeh Rastehkenari, Javad Dargahi, Muthukumaran Packirisamy","doi":"10.1016/j.probengmech.2026.103899","DOIUrl":"10.1016/j.probengmech.2026.103899","url":null,"abstract":"<div><div>This paper presents a unified integral two-phase local/nonlocal model with a Gaussian attenuation kernel for deterministic and random vibration analysis of shear-deformable piezoelectric nanobeams on a viscoelastic foundation under concentrated wide-band white-noise excitation. The piezoelectric constitutive laws are kept in their original integral local/nonlocal form and coupled with a unified higher-order shear deformation beam theory that recovers Euler–Bernoulli, Timoshenko, Reddy, sinusoidal, hyperbolic, and exponential shear models. By avoiding the differential transformation and its additional constitutive boundary conditions, the proposed formulation eliminates the well-known inconsistencies of classical differential nonlocal models and remains paradox free. Deterministic results show that nonlocality systematically softens PZT-4 nanobeams and reduces natural frequencies, with the Gaussian kernel inducing stronger softening than the conventional exponential kernel, while higher local phase fraction, greater slenderness, and stiffer foundations restore more classical behavior. In the stochastic regime, a frequency-response-based spectral approach reveals that stronger nonlocal effects and higher temperatures amplify the mean-square transverse response, whereas increased piezoelectric actuation, foundation stiffness, and damping significantly reduce it. Shear deformation is relevant for moderately thick nanobeams but becomes negligible in slender configurations. The proposed framework provides a transparent and robust basis for analyzing and designing piezoelectric MEMS/NEMS components operating in stochastic environments.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"83 ","pages":"Article 103899"},"PeriodicalIF":3.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147395579","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 : 2026-01-01Epub Date: 2026-01-30DOI: 10.1016/j.probengmech.2026.103897
Mingjin Zhang , Haochao Wang , Shenghan Zhuang , Tingyuan Yan , Jinxiang Zhang
The valley wind field has a highly complex characteristic and lacks long-term measurements on bridge sites. Directly estimating long-term extreme wind speeds from short-term measured data has strong uncertainty. This study develops a temporal correlation model linking bridge-site wind parameters to those from nearby national meteorological stations, extending limited measurement data. A mixture copula-based joint probability model is then proposed to derive multi-directional extreme wind speeds. Using a long-span bridge in a deep-cut gorge as a case study, two years of measurements are extended to a ten-year period. Results show that integrating the four-day block maxima method with a BP neural network better captures parameter interactions and achieves higher accuracy. The improved mixture copula more accurately represents joint distributions than traditional models. For a 100-year return period, extreme winds in certain sectors are over 30 % lower than values ignoring direction. The model thus offers practical guidance for determining bridge design wind parameters in mountainous regions.
{"title":"A multi-directional extreme wind speeds model based on multi-site temporal correlations","authors":"Mingjin Zhang , Haochao Wang , Shenghan Zhuang , Tingyuan Yan , Jinxiang Zhang","doi":"10.1016/j.probengmech.2026.103897","DOIUrl":"10.1016/j.probengmech.2026.103897","url":null,"abstract":"<div><div>The valley wind field has a highly complex characteristic and lacks long-term measurements on bridge sites. Directly estimating long-term extreme wind speeds from short-term measured data has strong uncertainty. This study develops a temporal correlation model linking bridge-site wind parameters to those from nearby national meteorological stations, extending limited measurement data. A mixture copula-based joint probability model is then proposed to derive multi-directional extreme wind speeds. Using a long-span bridge in a deep-cut gorge as a case study, two years of measurements are extended to a ten-year period. Results show that integrating the four-day block maxima method with a BP neural network better captures parameter interactions and achieves higher accuracy. The improved mixture copula more accurately represents joint distributions than traditional models. For a 100-year return period, extreme winds in certain sectors are over 30 % lower than values ignoring direction. The model thus offers practical guidance for determining bridge design wind parameters in mountainous regions.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"83 ","pages":"Article 103897"},"PeriodicalIF":3.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147395582","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 : 2026-01-01Epub Date: 2026-01-07DOI: 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 : 2026-01-01Epub Date: 2026-01-08DOI: 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 : 2026-01-01Epub Date: 2025-12-04DOI: 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.
{"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":"2026-01-01","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}
Pub Date : 2026-01-01Epub Date: 2025-12-29DOI: 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 : 2026-01-01Epub Date: 2025-12-26DOI: 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 : 2026-01-01Epub Date: 2026-01-08DOI: 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}
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