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}