{"title":"Surrogate modeling with functional nonlinear autoregressive models (F-NARX)","authors":"Styfen Schär, Stefano Marelli, Bruno Sudret","doi":"10.1016/j.ress.2025.111276","DOIUrl":"10.1016/j.ress.2025.111276","url":null,"abstract":"<div><div>We propose a novel functional approach to surrogate modeling of dynamical systems with exogenous inputs. This approach, named Functional Nonlinear AutoRegressive with eXogenous inputs (<span><math><mi>F</mi></math></span>-NARX), approximates the system response based on temporal features of the exogenous inputs and the system response. This marks a major step away from the discrete-time-centric approach of classical NARX models, which determines the relationship between selected time steps of the input/output time series. By modeling the system in a time-feature space, <span><math><mi>F</mi></math></span>-NARX takes advantage of the temporal smoothness of the process being modeled, providing more stable predictions and reducing the dependence of model performance on the discretization of the time axis.</div><div>In this work, we introduce an <span><math><mi>F</mi></math></span>-NARX implementation based on principal component analysis and polynomial regression. To further improve prediction accuracy, we also introduce a modified hybrid least angle regression approach to identify a sparse model structure and minimize the expected forecast error, rather than the one-step-ahead prediction error.</div><div>We investigate the behavior and capabilities of our <span><math><mi>F</mi></math></span>-NARX implementation on two case studies: an eight-story building under wind loading and a three-story steel frame under seismic loading. Our results demonstrate that <span><math><mi>F</mi></math></span>-NARX has several favorable properties that make it well-suited to surrogate modeling applications.</div></div>","PeriodicalId":54500,"journal":{"name":"Reliability Engineering & System Safety","volume":"264 ","pages":"Article 111276"},"PeriodicalIF":9.4,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144260910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Stress-strength reliability estimation based on probability weighted moments in small sample scenario with three-parameter Weibull distribution","authors":"Qingrong Zou , Jici Wen","doi":"10.1016/j.ress.2025.111340","DOIUrl":"10.1016/j.ress.2025.111340","url":null,"abstract":"<div><div>Stress-strength reliability is a fundamental concept in engineering and reliability analysis, crucial for assessing whether a system or component will perform adequately under given stress and strength conditions. The three-parameter Weibull distribution, a mainstay in reliability engineering and life testing, is renowned for its effectiveness in modeling failure data across a spectrum of engineering and scientific disciplines. Despite its utility, traditional parameter estimation methods, such as maximum likelihood estimation (MLE), are constrained by the absence of estimators for shape parameters below one and by inefficiency for those between one and two. Additionally, these methods often necessitate extensive sample sizes for achieving reliable outcomes. Bridging this gap, we introduce a reliability analysis framework anchored in the probability weighted moments (PWM) method, which are efficient in handling heavy-tailed or skewed distributions, ensuring the existence of estimators for arbitrary parameter scenarios. Our comprehensive evaluation using diverse datasets, including Monte Carlo simulations and real-world experimental data, demonstrates that the PWM method excels in robust parameter estimation, performs exceptionally well with small and moderate sample sizes. These advantages make the proposed analysis framework particularly effective for evaluating the stress-strength reliability of engineering structures under the three-parameter Weibull distribution.</div></div>","PeriodicalId":54500,"journal":{"name":"Reliability Engineering & System Safety","volume":"264 ","pages":"Article 111340"},"PeriodicalIF":9.4,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144272522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Strengthening and protecting hubs against sequential unintentional and intentional disruptions considering decision-dependent uncertainty","authors":"Qing Li, Guodong Yu, Peixin Zhao, Qingchun Meng","doi":"10.1016/j.ress.2025.111277","DOIUrl":"10.1016/j.ress.2025.111277","url":null,"abstract":"<div><div>This paper studies the strengthening and protection of multiple allocation hub networks subject to sequential unintentional and intentional disruptions, with the unintentional impacts occurring first, followed by the intentional impacts. We develop a two-stage stochastic bi-level programming model that incorporates decision-dependent uncertainty, where the first stage focuses on strengthening against unintentional impacts, and the second stage addresses protection against intentional impacts. The first stage determines the optimal strengthening strategy, incorporating various types to address multiple unintentional impacts, each with varying levels of intensity. The imperfect effect of strengthening and unintentional impacts makes decision-dependent uncertainty in the hub’s post-disruption operation state, which probabilistically depends on the strengthening decision and the intensity level of unintentional disruptions, and is interpreted using the contest success function. The second stage corresponds to a scenario-based bi-level hub interdiction median problem with fortification, formulated as a Stackelberg game between the defender and the attacker. To solve the proposed model, we develop a novel hybrid algorithm based on its structure, which utilizes the benefits of genetic algorithms, simulated annealing, and a greedy heuristic separation approach. We also develop a maximum-likelihood sampling method as a core component of the proposed hybrid algorithm to enhance its performance. Experimental results demonstrate the effectiveness of our proposed model and hybrid algorithm. The results also analyze the impact of the discount factor and strengthening budget on the expected network cost. Additionally, the results highlight the advantage of our model in incorporating multi-level disruption intensity, decision-dependent uncertainty, and sequential disruptions.</div></div>","PeriodicalId":54500,"journal":{"name":"Reliability Engineering & System Safety","volume":"264 ","pages":"Article 111277"},"PeriodicalIF":9.4,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144239471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Combined dimensionality reduction based adaptive polynomial chaos expansion for high-dimensional reliability analysis","authors":"Donghui Hao , Jian Zhang , Xinxin Yue , Lei Chen","doi":"10.1016/j.ress.2025.111324","DOIUrl":"10.1016/j.ress.2025.111324","url":null,"abstract":"<div><div>Polynomial chaos expansion (PCE) is increasingly used for structural reliability analysis in various engineering fields. However, due to the curse of dimensionality, full PCE computation is often unaffordable for high-dimensional problems. In this paper, a combined dimensionality reduction based adaptive polynomial chaos expansion (CDR-PCE) is proposed for high-dimensional reliability analysis. Taking advantage of different kernel functions and low-fidelity model gradients to construct transformation matrix, a combined dimensionality reduction (CDR) method is first introduced to map high-dimensional input data to a low-dimensional space for effective dimension reduction. Then, an adaptive PCE model is constructed by employing the sparrow search algorithm to optimize the polynomial order and regularization parameter in the solving process of recently developed Bregman-iterative greedy coordinate descent. A novel CDR-PCE framework is finally conceived by incorporating the CDR method into the adaptive PCE model for enhancing both efficiency and accuracy. The performance of the proposed CDR-PCE is evaluated on five numerical examples of varying dimensionality and complexity through comparison with several state-of-the-art methods. Results show that the proposed method is superior to the benchmark algorithms in terms of accuracy, efficiency and robustness for high-dimensional reliability analysis, and its superiority becomes more significant for complex engineering structures with high nonlinearities.</div></div>","PeriodicalId":54500,"journal":{"name":"Reliability Engineering & System Safety","volume":"264 ","pages":"Article 111324"},"PeriodicalIF":9.4,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144261515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Explainable neural-networked variational inference: A new and fast paradigm with automatic differentiation for high-dimensional Bayesian inverse problems","authors":"Jiang Mo, Wang-Ji Yan","doi":"10.1016/j.ress.2025.111337","DOIUrl":"10.1016/j.ress.2025.111337","url":null,"abstract":"<div><div>Bayesian inference offers a rigorous framework for parameter inversion and uncertainty quantification in engineering disciplines. Despite advancements introduced by Variational Bayesian Inference (VBI), Bayesian Inverse Problems (BIPs) with implicit and non-differentiable forward solvers still face significant limitations associated with mean-field approximation, computational difficulties, poor scalability, and high-dimensional data complexities. In response to these challenges, a novel Variational Inference (VI) framework featuring equivalent neural network representation with automatic differentiation is proposed. The network architecture “VBI-Net”, comprising a variational distribution sampler, a likelihood function approximator, and a variational free energy loss function, is designed to mirror the VI framework with multivariate Gaussian variational distributions. The sampler yields posterior samples of the system model parameters and prediction errors, while incorporating the variational parameters as differentiable and explainable network parameters by reparameterization trick. The likelihood function approximator employs a neural network as a viable replacement for time-intensive and non-differentiable forward solvers, enabling efficient likelihood function evaluations. The loss function measures the goodness of the variational distribution. The seamless integration of the sampler and approximator guarantees the overall differentiability of the architecture, facilitating the utilization of automatic differentiation, gradient-based optimization methods, and enabling scalability to high-dimensional scenarios. Furthermore, the explainable neural-networked implementation scheme leverages CUDA support embedded in deep learning frameworks to inherently enable parallel computation, GPU acceleration, and optimized tensor operations. To demonstrate its efficacy, the method is applied in Bayesian model updating scenarios involving a numerical shear building and a practical structure.</div></div>","PeriodicalId":54500,"journal":{"name":"Reliability Engineering & System Safety","volume":"264 ","pages":"Article 111337"},"PeriodicalIF":9.4,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144329533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Zhen Hu , Jingcong Zhu , Haiming Jiao , Wen Zeng , Zhijiang Yang
{"title":"Risk assessment of water distribution networks through an integrated model based on machine learning and statistical methods","authors":"Zhen Hu , Jingcong Zhu , Haiming Jiao , Wen Zeng , Zhijiang Yang","doi":"10.1016/j.ress.2025.111338","DOIUrl":"10.1016/j.ress.2025.111338","url":null,"abstract":"<div><div>Water distribution networks (WDNs) are critical for urban infrastructure, but as they expand and age, the risk of pipeline ruptures and leaks grows. Predicting these risks is essential for preventing accidents, improving management, and protecting public safety. The Support Vector Machine (SVM) model, renowned for handling small samples, nonlinearity, and high-dimensional data, is well-suited for assessing WDN risks with limited failure data. However, it faces challenges such as difficulties with large datasets, selecting optimal kernel functions, and offering clear interpretability. To address these challenges and accurately assess pipeline risks, this study introduces an integrated CF-SVM model, combining the Certainty Factor (CF) model with SVM. The CF model, grounded in statistical theory, effectively manages uncertainties arising from multiple factors in pipeline failures. Results show the CF-SVM model outperforms standalone SVM and CF models, with an AUC of 0.92—improving accuracy by 17.95 % and 12.20 %, respectively. The model effectively allocates 71.31 % of faulty pipes to a smaller high-risk zone (22.96 %), enhancing both accuracy and regional applicability. Its application in real WDNs in China demonstrates its effectiveness in risk assessment and network safety management.</div></div>","PeriodicalId":54500,"journal":{"name":"Reliability Engineering & System Safety","volume":"264 ","pages":"Article 111338"},"PeriodicalIF":9.4,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144239791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A developed Fick's law and HSV-based fatigue reliability modeling method for CFRP/Epoxy adhesive structures considering environmental stresses and size effects","authors":"Zhenjiang Shao, Zheng Liu, Jinlong Liang, Haodong Liu, Yuhao Zhang","doi":"10.1016/j.ress.2025.111336","DOIUrl":"10.1016/j.ress.2025.111336","url":null,"abstract":"<div><div>This manuscript, set against the backdrop of offshore wind turbine blades, focuses on the adhesive structure of carbon fiber and epoxy resin. By incorporating Fick's law and the High Stress Volume (HSV) method, a fatigue analysis and fatigue reliability modeling approach for adhesive structures under multi-environmental stresses, considering size effects, is proposed. This study applies Fick's law to analyze material moisture diffusion and assesses adhesive layer failure in aged samples. It develops a probabilistic fatigue life prediction model using the HSV method, delving into the fatigue degradation of adhesive structures. Through environmental aging and fatigue testing on CFRP/Epoxy adhesive structures revealed that extreme conditions of temperature, humidity, and salt fog expedite epoxy corrosion, diminishing load-bearing capacity and shortening the fatigue life. The study highlights that the aging environment, along with adhesive length and thickness, profoundly influence the performance of these structures. The model's predicted results have an average error of less than 5 % compared to experimental values, validating the feasibility of the proposed method. Furthermore, this research provides a theoretical basis for the life prediction and maintenance of offshore wind turbine blades.</div></div>","PeriodicalId":54500,"journal":{"name":"Reliability Engineering & System Safety","volume":"264 ","pages":"Article 111336"},"PeriodicalIF":9.4,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144280534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yongfu Tian, Shan Ding, Lida Huang, Guofeng Su, Jianguo Chen
{"title":"A new approach for deep prediction of urban complex system risk process during natural disasters","authors":"Yongfu Tian, Shan Ding, Lida Huang, Guofeng Su, Jianguo Chen","doi":"10.1016/j.ress.2025.111339","DOIUrl":"10.1016/j.ress.2025.111339","url":null,"abstract":"<div><div>In recent years, advancements in weather forecasting systems have led to increased accuracy. Despite more accurate disaster input conditions, predicting the risk evolution process of the urban complex system remains an unresolved issue which represents a vulnerable link. Currently, there are numerous methods for risk prediction. However, a universally applicable approach and fundamental model that can dynamically predict the urban risk process under varying disaster input conditions have not been established yet. To address these challenges, we propose an event graph model within the framework of the extended risk concept. Furthermore we introduce the theory of Directed Markov Random Field to construct an Urban Spatio-temporal Risk Process model (USTRP), which enables the dynamic forecasting of risk process. The USTRP model can address basic problems in application such as identifying the most or more probable event chains, calculating the node marginal distribution, and determining the first hitting time under different disaster conditions. Moreover, to improve computational efficiency, we leverage the characteristics of the USTRP and present a sparse low-entropy approximate direct inference algorithm (SLEADIA) while proving its convergence. Finally, we apply this model to a hypothetical case. We analyze the medical service acquisition capabilities of nursing homes and the leakage risks of chemical storage tanks under varying flood conditions, demonstrating the computational efficiency advantage of the proposed SLEADIA.</div></div>","PeriodicalId":54500,"journal":{"name":"Reliability Engineering & System Safety","volume":"264 ","pages":"Article 111339"},"PeriodicalIF":9.4,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144260911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Constrained optimal maintenance strategies for k-out-of-n systems with dependent components and mission duration","authors":"Azam Kheyri, Sharareh Taghipour","doi":"10.1016/j.ress.2025.111265","DOIUrl":"10.1016/j.ress.2025.111265","url":null,"abstract":"<div><div>Many existing maintenance strategies for <span><math><mi>k</mi></math></span>-out-of-<span><math><mi>n</mi></math></span> systems lack practical applicability, often neglecting essential operational constraints in real-world scenarios. Performing maintenance during active operations is generally impractical, emphasizing the need to account for mission duration in maintenance planning. Additionally, the assumption of independent component failures is unrealistic, particularly in challenging environments where failures are often correlated. In critical missions, strategies must go beyond cost-efficiency to maintain system availability at acceptable levels throughout the mission. To address these issues we propose three maintenance policies simple replacement, replacement first, and replacement last to various dependency structures using copula models, including Clayton, Gumbel, and FGM. Our framework integrates mission duration into decision making, optimizing both the number of components and replacement timing to achieve a balance between cost and system availability. By explicitly accounting for component dependencies and the availability constraint, this study provides a comprehensive and realistic strategy for optimizing maintenance in <span><math><mi>k</mi></math></span>-out-of-<span><math><mi>n</mi></math></span> systems under operational conditions.</div></div>","PeriodicalId":54500,"journal":{"name":"Reliability Engineering & System Safety","volume":"264 ","pages":"Article 111265"},"PeriodicalIF":9.4,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144220477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Two-stage stochastic optimization for emergency management of metro systems under uncertain storm floods","authors":"Renfei He , Limao Zhang , Robert L.K. Tiong","doi":"10.1016/j.ress.2025.111325","DOIUrl":"10.1016/j.ress.2025.111325","url":null,"abstract":"<div><div>Climate change and urbanization have increasingly exacerbated the threat of storm floods to urban metro systems. To enhance the flood emergency management of metro systems, this study proposes a two-stage stochastic optimization model. In this model, the closure decisions for risky stations and the allocation of flood control resources are implemented before and during the rainstorm, respectively, to maximize the average utility of passengers in the metro network. A case study on the Shanghai metro system is conducted to demonstrate the applicability and effectiveness of the proposed model. The results indicate that the two-stage stochastic optimization model can generate refined closure schemes and dynamically adaptive protection schemes for risky metro stations. Compared to one-stage strategies that do not consider the uncertainty of rainstorms, the two-stage model achieves higher passenger utility. Furthermore, the mechanisms behind the closure decisions made by the two-stage model are interpreted using an explainable artificial intelligence (XAI) technique, SHAP (SHapley Additive explanation). It is revealed that a metro station with low passenger volume in a high-rainfall sub-catchment has a greater probability of being closed before floods. Future works can be conducted to further explore feedback mechanisms between the two optimization stages or optimize the location and inventory of resource warehouses for metro systems.</div></div>","PeriodicalId":54500,"journal":{"name":"Reliability Engineering & System Safety","volume":"264 ","pages":"Article 111325"},"PeriodicalIF":9.4,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144272520","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}