Hierarchical Bayesian Fusion of Inspection and Monitoring Data for Probabilistic Bridge Deterioration Assessment

Hierarchical Bayesian Fusion of Inspection and Monitoring Data for Probabilistic Bridge Deterioration Assessment | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Hierarchical Bayesian Fusion of Inspection and Monitoring Data for Probabilistic Bridge Deterioration Assessment Benyu Wang, Ke Chen, Bingjian Wang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8023672/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 21 Jan, 2026 Read the published version in Scientific Reports → Version 1 posted 10 You are reading this latest preprint version Abstract Bridges are susceptible to long-term deterioration due to environmental exposure and cyclic loading, making the accurate evaluation of crack evolution crucial for predictive maintenance and structural safety management. Traditional deterioration models that rely solely on periodic inspection data often fail to capture the dynamic and stochastic nature of crack propagation. To address this limitation, this study proposes a hierarchical Bayesian inference framework that integrates discrete inspection data with continuous crack monitoring data to achieve a unified probabilistic characterization of bridge deterioration. First, a Bayesian Accelerated Failure Time (AFT) model based on the Weibull distribution is developed to model the failure risk of bridge deck slabs. The model robustly handles right-censored data through sampling and incorporates multiple covariates, including crack number, type, damage category, bridge span, and geometric parameters. Posterior distributions of the shape and scale parameters, together with hazard ratio analysis, quantitatively reveal the influence of each factor on structural failure risk. Second, by combining field monitoring data of crack width and ambient temperature, a Metropolis–Hastings-based regression model is constructed to estimate incremental crack growth, which is then aggregated monthly to form a continuous degradation trend series. This method effectively captures the response of crack development to environmental fluctuations and supports predictive analysis for on-site maintenance planning. Finally, the failure risk model and the crack evolution model are coupled within a hierarchical Bayesian framework to enable joint risk estimation. The proposed model integrates multi-source information with varying temporal resolutions and uncertainty levels and employs a Bayesian posterior updating mechanism to adaptively refine parameters as new monitoring data become available. Validation using real bridge monitoring datasets demonstrates that the posterior-updated model significantly outperforms traditional inspection-based approaches in capturing crack failure behavior and long-term deterioration trends. Physical sciences/Engineering Physical sciences/Mathematics and computing Hierarchical Bayesian inference Bridge health monitoring Data fusion Bridge deterioration model Predictive maintenance Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 21 Jan, 2026 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 04 Dec, 2025 Reviews received at journal 02 Dec, 2025 Reviews received at journal 26 Nov, 2025 Reviewers agreed at journal 11 Nov, 2025 Reviewers agreed at journal 06 Nov, 2025 Reviewers invited by journal 06 Nov, 2025 Editor invited by journal 06 Nov, 2025 Editor assigned by journal 04 Nov, 2025 Submission checks completed at journal 04 Nov, 2025 First submitted to journal 03 Nov, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8023672","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":545802193,"identity":"400e1878-76cd-47b9-8cfc-e87913848033","order_by":0,"name":"Benyu Wang","email":"","orcid":"","institution":"Research Institute of Highway","correspondingAuthor":false,"prefix":"","firstName":"Benyu","middleName":"","lastName":"Wang","suffix":""},{"id":545802194,"identity":"d48314ef-c322-464b-bba9-c0b7341c8bd8","order_by":1,"name":"Ke Chen","email":"","orcid":"","institution":"Research Institute of 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Traditional deterioration models that rely solely on periodic inspection data often fail to capture the dynamic and stochastic nature of crack propagation. To address this limitation, this study proposes a hierarchical Bayesian inference framework that integrates discrete inspection data with continuous crack monitoring data to achieve a unified probabilistic characterization of bridge deterioration.\nFirst, a Bayesian Accelerated Failure Time (AFT) model based on the Weibull distribution is developed to model the failure risk of bridge deck slabs. The model robustly handles right-censored data through sampling and incorporates multiple covariates, including crack number, type, damage category, bridge span, and geometric parameters. Posterior distributions of the shape and scale parameters, together with hazard ratio analysis, quantitatively reveal the influence of each factor on structural failure risk.\nSecond, by combining field monitoring data of crack width and ambient temperature, a Metropolis–Hastings-based regression model is constructed to estimate incremental crack growth, which is then aggregated monthly to form a continuous degradation trend series. This method effectively captures the response of crack development to environmental fluctuations and supports predictive analysis for on-site maintenance planning.\nFinally, the failure risk model and the crack evolution model are coupled within a hierarchical Bayesian framework to enable joint risk estimation. The proposed model integrates multi-source information with varying temporal resolutions and uncertainty levels and employs a Bayesian posterior updating mechanism to adaptively refine parameters as new monitoring data become available. Validation using real bridge monitoring datasets demonstrates that the posterior-updated model significantly outperforms traditional inspection-based approaches in capturing crack failure behavior and long-term deterioration trends.","manuscriptTitle":"Hierarchical Bayesian Fusion of Inspection and Monitoring Data for Probabilistic Bridge Deterioration Assessment","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-17 03:28:39","doi":"10.21203/rs.3.rs-8023672/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-12-04T05:31:13+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-03T03:18:28+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-26T15:34:56+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"105848479613229476589342584353383415177","date":"2025-11-11T09:43:01+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"335139123505797013296905345279967971714","date":"2025-11-06T14:38:53+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-11-06T14:34:52+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-11-06T10:19:17+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-11-04T12:04:22+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-11-04T12:03:11+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-11-04T02:44:07+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"22607aa5-e8fc-46c5-8cb5-4cd52a9f7302","owner":[],"postedDate":"November 17th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":58065889,"name":"Physical sciences/Engineering"},{"id":58065890,"name":"Physical sciences/Mathematics and computing"}],"tags":[],"updatedAt":"2026-01-26T16:05:35+00:00","versionOfRecord":{"articleIdentity":"rs-8023672","link":"https://doi.org/10.1038/s41598-026-36808-4","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2026-01-21 15:58:51","publishedOnDateReadable":"January 21st, 2026"},"versionCreatedAt":"2025-11-17 03:28:39","video":"","vorDoi":"10.1038/s41598-026-36808-4","vorDoiUrl":"https://doi.org/10.1038/s41598-026-36808-4","workflowStages":[]},"version":"v1","identity":"rs-8023672","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8023672","identity":"rs-8023672","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}