Time-Invariant Learning and History-Based Inference for Time-Varying Survival Models in Predictive Maintenance

Time-Invariant Learning and History-Based Inference for Time-Varying Survival Models in Predictive Maintenance | 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 Research Article Time-Invariant Learning and History-Based Inference for Time-Varying Survival Models in Predictive Maintenance Iulii Vasilev, Mark Goverdovskiy, Mikhail Petrovskiy, Igor Mashechkin This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8763202/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Technical failure prediction is commonly carried out using time-invariant models, which analyze a single object state, and time-varying models, which consider state sequences over time. In practice, monitoring data is collected as temporal chains reflecting system degradation. Considering system failure as a terminal event, survival analysis methods provide an estimation of the event risk at future times. However, most existing approaches exploit the time-varying data only during model training, while at the inference stage, they rely on the last observation. The gap between training and inference can lead to the loss of operational history, limiting model effectiveness in reliability analysis, where failure risk depends on accumulated degradation rather than the current state. This work proposes a methodology to address this gap. The proposed algorithm for sampling time-invariant observations from complete temporal monitoring chains enables training time-invariant models on time-varying data. A class of time-conditioned models uses a prediction horizon as a covariate, allowing flexible construction of individual forecasts on a continuous time scale. To utilize operational history during the inference, we propose a method for aggregating sequential model predictions collected at various time points. The weighting schemes control the contribution of past observations and define a trade-off between survival function accuracy and risk-based ranking quality. An experimental study on the Backblaze hard drive failure dataset compares the classical time-varying Cox model, alternative statistical formulations, and the proposed time-conditioned neural network. The results demonstrate that the proposed algorithm for sampling time-invariant observations improves the performance of time-invariant models, while prediction aggregation significantly enhances survival function approximation measured by the Integrated Brier Score compared to single-point prediction. The proposed time-conditioned neural network shows the best overall performance. The results confirm that the proposed methodology enhances historical data utilization and improves failure prediction accuracy in intelligent industrial monitoring systems. Artificial Intelligence and Machine Learning Time-to-Event Analysis Survival Analysis Predictive Maintenance Time-Varying Aggregation Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted 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. We do this by developing innovative software and high quality services for the global research community. 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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-8763202","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":584230183,"identity":"70098ca3-7e53-4d70-9ed3-179e9e99b4bb","order_by":0,"name":"Iulii Vasilev","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA40lEQVRIiWNgGAWjYBACNgbmhgMJIAY7kPgAY+DXwgjVwszAwDgDyiAAGBsgNFAlMw+UgRfwSSQ2HnjYZmfPx8x8TNrm1zZ5PmYGxg8fc/A4TCKx4UBiW3JiGzNbmnRu323DNmYGZsmZ2whoSTjDnMDGzGNsnNtzmxGohY2Zl7CWens2Zv7PxpY9t+2J1FJxGGg4D+Njhh+3Ewlr4XkI0nIc5BfDh70Nt5PbmBmb8fpFvj358McfBtX28u3NDw78+HPbdn5788EPH/FoQQWMbWCygVj1IPCHFMWjYBSMglEwUgAA6j1KlM4J2JQAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0001-9210-5544","institution":"Shenzhen MSU-BIT University","correspondingAuthor":true,"prefix":"","firstName":"Iulii","middleName":"","lastName":"Vasilev","suffix":""},{"id":584230189,"identity":"2ec0af84-e1c8-46f2-a14b-f84465dd34a0","order_by":1,"name":"Mark Goverdovskiy","email":"","orcid":"https://orcid.org/0009-0008-6026-8208","institution":"Lomonosov Moscow State University","correspondingAuthor":false,"prefix":"","firstName":"Mark","middleName":"","lastName":"Goverdovskiy","suffix":""},{"id":584230191,"identity":"1891f433-8479-447f-b742-d58fb233daa4","order_by":2,"name":"Mikhail Petrovskiy","email":"","orcid":"https://orcid.org/0000-0002-1236-398X","institution":"Lomonosov Moscow State University","correspondingAuthor":false,"prefix":"","firstName":"Mikhail","middleName":"","lastName":"Petrovskiy","suffix":""},{"id":584230199,"identity":"b035a8e6-1d93-41a8-b095-78422d885d82","order_by":3,"name":"Igor Mashechkin","email":"","orcid":"https://orcid.org/0000-0002-9837-585X","institution":"Lomonosov Moscow State University","correspondingAuthor":false,"prefix":"","firstName":"Igor","middleName":"","lastName":"Mashechkin","suffix":""}],"badges":[],"createdAt":"2026-02-02 09:42:45","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-8763202/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8763202/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":101942733,"identity":"0a39c8d7-516b-461a-9154-684cafead320","added_by":"auto","created_at":"2026-02-05 09:36:07","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2185400,"visible":true,"origin":"","legend":"","description":"","filename":"ENTimeVaryingmethodsinSurvivalAnalysis.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8763202/v1_covered_51efbf3f-fcfb-4013-a727-8775844a7615.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eTime-Invariant Learning and History-Based Inference for Time-Varying Survival Models in Predictive Maintenance\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Shenzhen MSU-BIT University","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Time-to-Event Analysis, Survival Analysis, Predictive Maintenance, Time-Varying, Aggregation","lastPublishedDoi":"10.21203/rs.3.rs-8763202/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8763202/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTechnical failure prediction is commonly carried out using time-invariant models, which analyze a single object state, and time-varying models, which consider state sequences over time. In practice, monitoring data is collected as temporal chains reflecting system degradation.\u003c/p\u003e\n\u003cp\u003eConsidering system failure as a terminal event, survival analysis methods provide an estimation of the event risk at future times. However, most existing approaches exploit the time-varying data only during model training, while at the inference stage, they rely on the last observation. The gap between training and inference can lead to the loss of operational history, limiting model effectiveness in reliability analysis, where failure risk depends on accumulated degradation rather than the current state.\u003c/p\u003e\n\u003cp\u003eThis work proposes a methodology to address this gap. The proposed algorithm for sampling time-invariant observations from complete temporal monitoring chains enables training time-invariant models on time-varying data. A class of time-conditioned models uses a prediction horizon as a covariate, allowing flexible construction of individual forecasts on a continuous time scale.\u003c/p\u003e\n\u003cp\u003eTo utilize operational history during the inference, we propose a method for aggregating sequential model predictions collected at various time points. The weighting schemes control the contribution of past observations and define a trade-off between survival function accuracy and risk-based ranking quality.\u003c/p\u003e\n\u003cp\u003eAn experimental study on the Backblaze hard drive failure dataset compares the classical time-varying Cox model, alternative statistical formulations, and the proposed time-conditioned neural network. The results demonstrate that the proposed algorithm for sampling time-invariant observations improves the performance of time-invariant models, while prediction aggregation significantly enhances survival function approximation measured by the Integrated Brier Score compared to single-point prediction. The proposed time-conditioned neural network shows the best overall performance.\u003c/p\u003e\n\u003cp\u003eThe results confirm that the proposed methodology enhances historical data utilization and improves failure prediction accuracy in intelligent industrial monitoring systems.\u003c/p\u003e","manuscriptTitle":"Time-Invariant Learning and History-Based Inference for Time-Varying Survival Models in Predictive Maintenance","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-03 14:47:07","doi":"10.21203/rs.3.rs-8763202/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"80a8b86e-fdf2-47c8-b092-354b072408d3","owner":[],"postedDate":"February 3rd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":62150217,"name":"Artificial Intelligence and Machine Learning"}],"tags":[],"updatedAt":"2026-02-03T14:47:07+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-03 14:47:07","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8763202","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8763202","identity":"rs-8763202","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}