Uncertainty-Aware Degradation Prediction of PEM Fuel Cells Using PatchTST and Weighted Quantile Random Forests

Uncertainty-Aware Degradation Prediction of PEM Fuel Cells Using PatchTST and Weighted Quantile Random Forests | 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 Uncertainty-Aware Degradation Prediction of PEM Fuel Cells Using PatchTST and Weighted Quantile Random Forests Zainab Imad al-Tamimi, Abdullahi Ibrahim This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8660939/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 10 You are reading this latest preprint version Abstract Accurate and reliable degradation prediction is essential for ensuring the long-term performance and safety of proton exchange membrane fuel cells (PEMFCs) operating under dynamic conditions. Existing data-driven approaches often struggle to capture long-range degradation dependencies, neglect non-stationary aging behavior, or provide only deterministic predictions without uncertainty information. To address these limitations, this paper proposes an uncertainty-aware degradation prediction framework that integrates a Patch-Based Transformer (PatchTST) with a degradation-aware weighted quantile random forest. PatchTST is employed to learn robust temporal degradation representations from multivariate operational data, while the proposed degradation-aware weighting strategy emphasizes late-life aging behavior and quantile regression enables probabilistic prediction with calibrated uncertainty intervals. Experimental evaluation on a publicly available PEMFC dataset demonstrates that the proposed method achieves superior performance, with an RMSE of 0.0018 , an MAE of 0.0022 , and a MAPE of 0.028 , outperforming representative deep learning and tree-based baselines. In addition, the proposed framework attains a prediction interval coverage probability of 0.91 with a narrow mean prediction interval width of 0.063 , confirming its reliability for uncertainty-aware prognostics. The results indicate that the proposed approach provides an effective and robust solution for PEM fuel cell degradation prediction and health monitoring. Proton exchange membrane fuel cell Degradation prediction Patch-based Transformer Uncer-tainty quantification Random forest Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 24 Mar, 2026 Reviewers agreed at journal 11 Mar, 2026 Reviews received at journal 11 Mar, 2026 Reviewers agreed at journal 09 Mar, 2026 Reviews received at journal 27 Feb, 2026 Reviewers agreed at journal 23 Feb, 2026 Reviewers invited by journal 10 Feb, 2026 Editor assigned by journal 29 Jan, 2026 Submission checks completed at journal 29 Jan, 2026 First submitted to journal 21 Jan, 2026 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-8660939","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":588789196,"identity":"eed9a59d-5db5-43ee-86b9-44dbe06ea8e7","order_by":0,"name":"Zainab Imad al-Tamimi","email":"data:image/png;base64,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","orcid":"","institution":"Altinbas University","correspondingAuthor":true,"prefix":"","firstName":"Zainab","middleName":"Imad","lastName":"al-Tamimi","suffix":""},{"id":588789197,"identity":"30d3f52c-172b-42fe-a64a-310f91f2d8e7","order_by":1,"name":"Abdullahi Ibrahim","email":"","orcid":"","institution":"Altinbas University","correspondingAuthor":false,"prefix":"","firstName":"Abdullahi","middleName":"","lastName":"Ibrahim","suffix":""}],"badges":[],"createdAt":"2026-01-21 14:24:03","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8660939/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8660939/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102599512,"identity":"8b73dcdb-4054-4153-bba7-959869d6285e","added_by":"auto","created_at":"2026-02-13 12:41:39","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":843250,"visible":true,"origin":"","legend":"","description":"","filename":"zainab.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8660939/v1_covered_fc755d1e-a8c5-4e7c-acd8-99ee53077ab1.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Uncertainty-Aware Degradation Prediction of PEM Fuel Cells Using PatchTST and Weighted Quantile Random Forests","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"discover-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Computing](https://link.springer.com/journal/10791)","snPcode":"10791","submissionUrl":"https://submission.springernature.com/new-submission/10791/3","title":"Discover Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Proton exchange membrane fuel cell, Degradation prediction, Patch-based Transformer, Uncer-tainty quantification, Random forest","lastPublishedDoi":"10.21203/rs.3.rs-8660939/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8660939/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAccurate and reliable degradation prediction is essential for ensuring the long-term performance and safety of proton exchange membrane fuel cells (PEMFCs) operating under dynamic conditions. Existing data-driven approaches often struggle to capture long-range degradation dependencies, neglect non-stationary aging behavior, or provide only deterministic predictions without uncertainty information. To address these limitations, this paper proposes an uncertainty-aware degradation prediction framework that integrates a Patch-Based Transformer (PatchTST) with a degradation-aware weighted quantile random forest. PatchTST is employed to learn robust temporal degradation representations from multivariate operational data, while the proposed degradation-aware weighting strategy emphasizes late-life aging behavior and quantile regression enables probabilistic prediction with calibrated uncertainty intervals. Experimental evaluation on a publicly available PEMFC dataset demonstrates that the proposed method achieves superior performance, with an RMSE of \u003cb\u003e0.0018\u003c/b\u003e, an MAE of \u003cb\u003e0.0022\u003c/b\u003e, and a MAPE of \u003cb\u003e0.028\u003c/b\u003e, outperforming representative deep learning and tree-based baselines. In addition, the proposed framework attains a prediction interval coverage probability of \u003cb\u003e0.91\u003c/b\u003e with a narrow mean prediction interval width of \u003cb\u003e0.063\u003c/b\u003e, confirming its reliability for uncertainty-aware prognostics. The results indicate that the proposed approach provides an effective and robust solution for PEM fuel cell degradation prediction and health monitoring.\u003c/p\u003e","manuscriptTitle":"Uncertainty-Aware Degradation Prediction of PEM Fuel Cells Using PatchTST and Weighted Quantile Random Forests","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-13 12:40:46","doi":"10.21203/rs.3.rs-8660939/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-03-24T09:20:45+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"20103062706017174360856673166684053284","date":"2026-03-11T06:12:05+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-03-11T04:00:17+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"134096881176064286733578486023823566941","date":"2026-03-09T06:15:00+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-27T05:05:25+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"250024769914875358898961764964121149379","date":"2026-02-24T00:17:23+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-02-10T07:48:33+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-01-29T13:37:09+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-01-29T13:32:53+00:00","index":"","fulltext":""},{"type":"submitted","content":"Discover Computing","date":"2026-01-21T14:03:43+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"discover-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Computing](https://link.springer.com/journal/10791)","snPcode":"10791","submissionUrl":"https://submission.springernature.com/new-submission/10791/3","title":"Discover Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"89f9a7a8-6790-4c50-929f-34a26e0cca76","owner":[],"postedDate":"February 13th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-28T09:24:43+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-13 12:40:46","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8660939","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8660939","identity":"rs-8660939","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}