{"title":"Multi-point active learning probability density evolution method","authors":"Tong Zhou , Tong Guo , Xujia Zhu , Alexandros A. Taflanidis , Jize Zhang","doi":"10.1016/j.strusafe.2025.102633","DOIUrl":"10.1016/j.strusafe.2025.102633","url":null,"abstract":"<div><div>Probability density evolution method has been efficiently adapted for structural reliability analysis, owing to it rooting in the principle of preservation of probability. Despite achieving significant progress in the past decades, there remains a critical need to enhance its theoretical foundations and improve computational efficiency. In this paper, we develop a multi-point active learning probability density evolution method distinguished by the following four key features: (i) <em>Quantification</em>. An explicit formulation of failure probability is proposed for probability density evolution method by combining the finite difference scheme and the Dirac sequence scheme. Then, an epistemic uncertainty measure of Kriging-based failure probability estimation is quantified. (ii) <em>Reduction</em>. A multi-point learning function is deduced in closed form, aiming to select a batch of new samples to optimally reduce such epistemic uncertainty measure. (iii) <em>Maximization</em>. The multi-point enrichment process is directly conducted based on stepwise maximization of learning function, eliminating the traditional practice of combining a single-point learning function with some additional batch selection procedures. (iv) <em>Termination</em>. The termination of multi-point enrichment process is checked from the actual reduction of epistemic uncertainty of failure probability. The proposed method is tested on four examples and compared against several existing ones in the literature. The results indicate that the proposed method comes with high accuracy of failure probability estimate, whilst gaining favorable savings of the number of iterations and the total computational time, particularly when tackling with complex dynamic reliability problems.</div></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"117 ","pages":"Article 102633"},"PeriodicalIF":5.7,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144597543","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}
Structural SafetyPub Date : 2025-07-04DOI: 10.1016/j.strusafe.2025.102634
Simone Celati , Agnese Natali , Walter Salvatore , Ivar Björnsson , Sebastian Thöns
{"title":"Spatial and time-dependent reliability analysis for post-tensioned concrete decks subjected to multiple failure modes","authors":"Simone Celati , Agnese Natali , Walter Salvatore , Ivar Björnsson , Sebastian Thöns","doi":"10.1016/j.strusafe.2025.102634","DOIUrl":"10.1016/j.strusafe.2025.102634","url":null,"abstract":"<div><div>The durability of existing infrastructures is a worldwide challenge in structural engineering. Societal demands for reducing greenhouse gas emissions, coupled with the financial constraints faced by many countries, push infrastructure management companies and owners to extend the lifespan of existing structures. However, extending the lifespan comes with a set of problems related to safety and time-dependent degradation. The latter problem is particularly acute for prestressed bridge decks with post-tensioned tendons, which are especially prone to degradation due to defects observed for bridges built using older construction techniques.</div><div>To address this problem, we propose an approach for evaluating the global time-dependent reliability of prestressed concrete bridge decks with post-tensioned tendons, which are subject to corrosion-related degradation. A model for the time-dependent corrosion process is proposed that combines physics-based formulations with empirical evidence from existing structures, accounting for the necessary thermodynamic conditions and the quality of both the concrete and the grout. Furthermore, the sections of each deck element are assessed for two failure modes, namely, bending and shear failure. The time-dependent reliability is then computed for the bridge deck as a system accounting for the spatial and failure mode dependencies. The approach is applied to evaluate the reliability and technical service life of a prestressed structure representing a typical deck configuration for Italian prestressed bridges, and the main input variables for the case study are identified through a sensitivity analysis. Finally, it is demonstrated that the comparison with consequence-related target reliabilities facilitates the determination of a structure's remaining lifespan and provides the basis for economically efficient and sustainable integrity management.</div></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"117 ","pages":"Article 102634"},"PeriodicalIF":5.7,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144571176","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}
Structural SafetyPub Date : 2025-06-18DOI: 10.1016/j.strusafe.2025.102607
Morgane Menz , Miguel Munoz Zuniga , Delphine Sinoquet
{"title":"Estimation of simulation failure set with active learning based on Gaussian Process classifiers and random set theory","authors":"Morgane Menz , Miguel Munoz Zuniga , Delphine Sinoquet","doi":"10.1016/j.strusafe.2025.102607","DOIUrl":"10.1016/j.strusafe.2025.102607","url":null,"abstract":"<div><div>A wide range of industrial applications require numerous time-consuming simulations across various input sets, such as for optimization, calibration, or reliability assessments. In that context, some simulation failures or instabilities can be observed, due for instance, to convergence issues of the numerical scheme of complex partial derivative equations. Most of the time, the set of inputs corresponding to failures is not known a priori and thus may be associated to a hidden constraint. Since the observation of a simulation failure regarding this unknown constraint may be as costly as a feasible expensive simulation, we seek to learn the feasible set of inputs and thus target areas without simulation failure before further analysis. In this classification context, we propose to learn the feasible domain with a new adaptive Gaussian Process Classifier. The proposed methodology is a batch-mode active learning classification strategy that reduces uncertainty step by step, using a random set paradigm and a Gaussian Process Classifiers. The performance of this strategy is demonstrated on several hidden-constrained problems, particularly in the context of a wind turbine simulator-based reliability analysis.</div></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"117 ","pages":"Article 102607"},"PeriodicalIF":5.7,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144502235","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}
Structural SafetyPub Date : 2025-06-18DOI: 10.1016/j.strusafe.2025.102631
Sergio Belluco, Flora Faleschini
{"title":"Probabilistic calibration of design resistance models for the anchorage length of prestressing strands considering model uncertainty","authors":"Sergio Belluco, Flora Faleschini","doi":"10.1016/j.strusafe.2025.102631","DOIUrl":"10.1016/j.strusafe.2025.102631","url":null,"abstract":"<div><div>This study investigates the reliability and the model uncertainty of the anchorage length resistance models proposed in the 2nd generation Eurocode 2 and <em>fib</em> Model Code 2020. First, the two resistance models and their safety format are presented and discussed. Then, the probability distribution of the model uncertainty is estimated comparing the model predictions with a large set of flexural tests collected from the scientific literature. According to the results, the prestress release method and the strand surface conditions are the two variables affecting most the model uncertainty. Furthermore, it is demonstrated that anchorage lengths predicted with <em>fib</em> Model Code 2020 exceed the expected target level of reliability and they could be reduced, particularly for gradual prestress release. Conversely, anchorage lengths calculated according to the 2nd generation Eurocode 2 in case of sudden prestress release need to be increased to guarantee the expected level of reliability. For the same code, no significant changes are necessary in case of gradual prestress release.</div></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"117 ","pages":"Article 102631"},"PeriodicalIF":5.7,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144472418","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}
Structural SafetyPub Date : 2025-06-18DOI: 10.1016/j.strusafe.2025.102632
Thanh-Binh Tran , Emilio Bastidas-Arteaga
{"title":"Spatial variability identification of carbonation depth in concrete using Bayesian networks","authors":"Thanh-Binh Tran , Emilio Bastidas-Arteaga","doi":"10.1016/j.strusafe.2025.102632","DOIUrl":"10.1016/j.strusafe.2025.102632","url":null,"abstract":"<div><div>Accurate prediction of carbonation depth is crucial for evaluating the durability and service life of reinforced concrete structures.<!--> <!-->Traditional methods for assessing carbonation depth often involve destructive testing,<!--> <!-->which is both costly and time-consuming, and yields results with limited accuracy,<!--> <!-->thus restricting their practical applicability.<!--> <!-->To address these shortcomings,<!--> <!-->this research introduces a novel two-step procedure that leverages inspection data on concrete porosity and saturation degree to estimate carbonation depth.<!--> <!-->By integrating Bayesian networks and considering the influence of spatial variability,<!--> <!-->the proposed methodology aims to enhance prediction accuracy compared to existing techniques.<!--> <!-->The study comprehensively investigates the impact of various factors,<!--> <!-->including the use of individual or combined inspection data,<!--> <!-->spatial dependence,<!--> <!-->and inspection distance,<!--> <!-->on prediction performance.<!--> <!-->The findings demonstrate the effectiveness of the proposed approach in capturing complex interactions between concrete properties, carbonation depth, and spatial variability.<!--> <!-->This research contributes to the advancement of non-destructive evaluation methods for concrete structures and provides valuable insights for optimizing inspection strategies.</div></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"117 ","pages":"Article 102632"},"PeriodicalIF":5.7,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144366112","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}
Structural SafetyPub Date : 2025-06-11DOI: 10.1016/j.strusafe.2025.102621
Anderson V. Pires, Maliki Moustapha, Stefano Marelli, Bruno Sudret
{"title":"Reliability analysis for non-deterministic limit-states using stochastic emulators","authors":"Anderson V. Pires, Maliki Moustapha, Stefano Marelli, Bruno Sudret","doi":"10.1016/j.strusafe.2025.102621","DOIUrl":"10.1016/j.strusafe.2025.102621","url":null,"abstract":"<div><div>Reliability analysis is a sub-field of uncertainty quantification that assesses the probability of a system performing as intended under various uncertainties. Traditionally, this analysis relies on deterministic models, where experiments are repeatable, <em>i.e.</em> they produce consistent outputs for a given set of inputs. However, real-world systems often exhibit stochastic behavior, leading to non-repeatable outcomes. These so-called stochastic simulators produce different outputs each time the model is run, even with fixed inputs.</div><div>This paper formally introduces reliability analysis for stochastic models and addresses it by using suitable surrogate models to lower its typically high computational cost. Specifically, we focus on the recently introduced generalized lambda models and stochastic polynomial chaos expansions. These emulators are designed to learn the inherent randomness of the simulator’s response and enable efficient uncertainty quantification at a much lower cost than traditional Monte Carlo simulation.</div><div>We validate our methodology through three case studies. First, using an analytical function with a closed-form solution, we demonstrate that the emulators converge to the correct solution. Second, we present results obtained from the surrogates using a toy example of a simply supported beam. Finally, we apply the emulators to perform reliability analysis on a realistic wind turbine case study, where only a dataset of simulation results is available.</div></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"117 ","pages":"Article 102621"},"PeriodicalIF":5.7,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144279732","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":"Corrigendum to “Evaluating the importance of spatial variability of corrosion initiation parameters for the risk-based maintenance of reinforced concrete marine structures” [Struct. Saf. 114 (2025) 102568]","authors":"Romain Clerc , Charbel-Pierre El-Soueidy , Franck Schoefs","doi":"10.1016/j.strusafe.2025.102618","DOIUrl":"10.1016/j.strusafe.2025.102618","url":null,"abstract":"","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"116 ","pages":"Article 102618"},"PeriodicalIF":5.7,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144242447","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}
Structural SafetyPub Date : 2025-06-04DOI: 10.1016/j.strusafe.2025.102623
Santiago López , Brais Barros , Manuel Buitrago , Jose M. Adam , Belen Riveiro
{"title":"Reliability-based vulnerability assessment of steel truss bridge components","authors":"Santiago López , Brais Barros , Manuel Buitrago , Jose M. Adam , Belen Riveiro","doi":"10.1016/j.strusafe.2025.102623","DOIUrl":"10.1016/j.strusafe.2025.102623","url":null,"abstract":"<div><div>Bridges are among the most vulnerable and expensive assets of transportation networks. The failure of a bridge component can lead to catastrophic consequences for the entire structure. Therefore, vulnerability assessments have gained prominence to ensure their structural safety. However, as bridges age, performing a reliable assessment becomes increasingly challenging. This paper proposed a framework for the component-based vulnerability assessment of steel truss bridges. An index (SoD) that quantifies the State of Demand of each structural element is proposed. The level of vulnerability of all bridge elements is evaluated through a FEM-based approach that considers the uncertainty of the variables affecting the structural behaviour. The proposed framework has been tested in a real steel truss bridge located in Galicia, Spain. The framework finally integrates finite element modelling, uncertainty quantification and propagation, and probabilistic tools into a systematic approach for evaluating the component-level vulnerability of steel truss bridges. The outputs can be used to optimise inspection routines, reduce costs, and support the decision of authorities regarding bridge safety, monitoring, and maintenance. This work breaks new ground in the practical application of new knowledge, as the methodology could be further automated, simplifying engineering efforts and supporting bridge management entities to improve the bridge’s structural safety.</div></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"117 ","pages":"Article 102623"},"PeriodicalIF":5.7,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144222169","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}
Structural SafetyPub Date : 2025-06-02DOI: 10.1016/j.strusafe.2025.102619
Yongfeng Zhou , Jie Li
{"title":"Analytical solution of the generalized density evolution equation for stochastic systems: Euler-Bernoulli beam under noisy excitations and nonlinear vibration of Kirchhoff plate","authors":"Yongfeng Zhou , Jie Li","doi":"10.1016/j.strusafe.2025.102619","DOIUrl":"10.1016/j.strusafe.2025.102619","url":null,"abstract":"<div><div>The Generalized Density Evolution Equation (GDEE) describes the evolution of probability densities driven by physical processes. The numerical solution of the GDEE, implemented through a fully developed computational framework, is referred to as the Probability Density Evolution Method (PDEM). However, the absence of analytical solutions presents challenges for error calibration in numerical methods. In this study, analytical solutions of the GDEE are derived, focusing primarily on stochastic dynamic systems. The forced vibration of an Euler-Bernoulli beam subjected to random excitations is first analyzed, yielding analytical solutions for mid-span displacement response. For lower dimensional scenarios, two cases are examined: random harmonic loading and random step loading, both involving uncertainties in structural parameters. Results reveal that the corresponding displacement responses are non-Gaussian and non-stationary random processes. For higher dimensional scenarios, additional noise excitation is considered. By employing the Stochastic Harmonic Function (SHF) representation, noise excitation is effectively approximated as a superposition of finite random harmonic loads. Analytical derivations demonstrate that the SHF representation gradually converges toward the actual noise as the expansion terms increase. Furthermore, to illustrate the versatility of the developed analytical method, a nonlinear free vibration analysis of a Kirchhoff plate without external excitations is presented, showcasing its applicability to broader structural dynamic problems. These analytical solutions provide valuable benchmarks for further in-depth research into the PDEM, especially for the calibration of numerical methods.</div></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"117 ","pages":"Article 102619"},"PeriodicalIF":5.7,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144262721","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}
Structural SafetyPub Date : 2025-06-01DOI: 10.1016/j.strusafe.2025.102622
Siyi Jia , Mitsuyoshi Akiyama , Dan M. Frangopol , Zhejun Xu
{"title":"Failure probability estimate of corroded reinforced concrete structures based on sparse representation of steel weight loss distributions","authors":"Siyi Jia , Mitsuyoshi Akiyama , Dan M. Frangopol , Zhejun Xu","doi":"10.1016/j.strusafe.2025.102622","DOIUrl":"10.1016/j.strusafe.2025.102622","url":null,"abstract":"<div><div>Uncertainties associated with the non-uniform spatial distribution of steel weight loss (SWL) should be considered appropriately when estimating the load-bearing capacity loss of corroded reinforced concrete (RC) structures. Addressing these uncertainties necessitates a probabilistic analysis using high-dimensional SWL data, which can lead to inaccurate condition assessments for corroded RC structures. This paper presents a dimension-reduction approach for SWL distribution based on the K-means singular vector decomposition (K-SVD) algorithm, which enforces a sparse representation of SWL distributions using a combination of non-standard distribution features learned from experimental SWL data. The K-SVD algorithm involves an iterative two-stage supervised learning process. In the dictionary learning stage, K-SVD identifies non-standard distribution features tailored to the localized characteristics of SWL data, based on which the orthogonal matching pursuit (OMP) algorithm is employed in the coding learning stage to derive a sparse representation of SWL distributions. The efficacy of K-SVD is evaluated using 83 experimental samples of SWL distributions. The results reveal that the K-SVD algorithm can derive a sparse representation of SWL distribution while preserving the distribution details of SWL. With just 15 learned non-standard distribution features, K-SVD achieves the same accuracy in reconstructing 168-dimensional SWL distribution data as the baseline Karhunen-Loève OMP (KL-OMP) method, which uses 75 standard features. Subsequently, the sparse representation is used to compute the flexural failure probability of corroded RC beams, for which a Kriging surrogate model is constructed. The results show that the sparse representation significantly enhances the accuracy of the Kriging surrogate model and improves the computational stability of the flexural failure probabilities, which is crucial for accurately assessing the condition of corroded RC structures.</div></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"117 ","pages":"Article 102622"},"PeriodicalIF":5.7,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144241153","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}