Hybrid EKF - Machine Learning Framework for SOC -SOH Estimation in Sodium ION Batteries

Hybrid EKF - Machine Learning Framework for SOC -SOH Estimation in Sodium ION Batteries | 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 Hybrid EKF - Machine Learning Framework for SOC -SOH Estimation in Sodium ION Batteries KANDREGULA PRIYASWI, K RAMA SUDHA, A SUPRAJA This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9596965/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 12 You are reading this latest preprint version Abstract Reliable battery management in emerging sodium-ion systems depends heavily on how well internal states can be estimated, especially parameters such as state of charge (SOC) and state of health(SOH). While sodium -ion chemistry offers clear advantage’s in terms of material abundance and cost, its electrochemical behaviour introduces Unique’s challenges for conventional estimation techniques, including reduced voltage sensitivity over extended SOC regions and pronounced temperature-dependent resistance variations. In this work, a unified estimation strategy is developed by incorporating a physics -driven Extended Kalman Filter(EKF) for improved performance with a lightweight neural network designed to compensate for model inaccuracies .In this work, the EKF is applied using a three-RC equivalent circuit representation to follow the dynamic response of Hard Carbon Na-ion battery packs, and a neural network is included to further improve the estimation and utilizes internal filter signals -particularly the voltage innovation to learn residual error patterns arising from parameter drift, temperature mismatch and non linear electrochemical effects .In addition SOH evolution is modelled using an Arrhenius -based degradation formulation, supported by an innovation -driven correction mechanism that links long -term estimation trends with aging behaviour .The system is studied under different temperature levels and changing current condition, and its behaviour is also observed over a longer aging duration. Results indicate significant improvements in estimation accuracy compared to standalone EKF and purely data -driven methods ,while maintaining low computational complexity suitable for embedded battery management systems . Sodium -ion batteries Hybrid EKF ANN Three RC equivalent circuit State of charge (SOC) Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 17 May, 2026 Reviewers agreed at journal 14 May, 2026 Reviews received at journal 14 May, 2026 Reviewers agreed at journal 13 May, 2026 Reviews received at journal 13 May, 2026 Reviewers agreed at journal 13 May, 2026 Reviewers agreed at journal 12 May, 2026 Reviewers agreed at journal 12 May, 2026 Reviewers invited by journal 12 May, 2026 Editor assigned by journal 10 May, 2026 Submission checks completed at journal 10 May, 2026 First submitted to journal 02 May, 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-9596965","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":633493974,"identity":"5f195e24-d8ec-43aa-a37f-fde8996e9f26","order_by":0,"name":"KANDREGULA PRIYASWI","email":"data:image/png;base64,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","orcid":"","institution":"Andhra University","correspondingAuthor":true,"prefix":"","firstName":"KANDREGULA","middleName":"","lastName":"PRIYASWI","suffix":""},{"id":633493975,"identity":"63c3fd47-4ea3-44be-a9da-0918cf685ee9","order_by":1,"name":"K RAMA SUDHA","email":"","orcid":"","institution":"Andhra University","correspondingAuthor":false,"prefix":"","firstName":"K","middleName":"RAMA","lastName":"SUDHA","suffix":""},{"id":633493979,"identity":"055c901c-d498-4a23-bf7a-a7185901597b","order_by":2,"name":"A SUPRAJA","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"A","middleName":"","lastName":"SUPRAJA","suffix":""}],"badges":[],"createdAt":"2026-05-03 02:38:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9596965/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9596965/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108508508,"identity":"82638b46-f844-482c-981c-9828d3975e9c","added_by":"auto","created_at":"2026-05-05 12:12:31","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1216106,"visible":true,"origin":"","legend":"","description":"","filename":"MESMTA243PAPERSIMILARITY8PERCENT.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9596965/v1_covered_6147e594-0011-456c-b966-61f94075efc0.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eHybrid EKF - Machine Learning Framework for SOC -SOH Estimation in Sodium ION Batteries\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"ionics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":" Learn more about [Ionics](https://www.springer.com/journal/11581) ","snPcode":"11581","submissionUrl":"https://mc.manuscriptcentral.com/ionics","title":"Ionics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Sodium -ion batteries, Hybrid EKF, ANN, Three RC equivalent circuit, State of charge (SOC)","lastPublishedDoi":"10.21203/rs.3.rs-9596965/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9596965/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e \u003cem\u003eReliable battery management in emerging sodium-ion systems depends heavily on how well internal states can be estimated, especially parameters such as state of charge (SOC) and state of health(SOH). While sodium -ion chemistry offers clear advantage\u0026rsquo;s in terms of material abundance and cost, its electrochemical behaviour introduces Unique\u0026rsquo;s challenges for conventional estimation techniques, including reduced voltage sensitivity over extended SOC regions and pronounced temperature-dependent resistance variations. In this work, a unified estimation strategy is developed by incorporating a physics -driven Extended Kalman Filter(EKF) for improved performance with a lightweight neural network designed to compensate for model inaccuracies .In this work, the EKF is applied using a three-RC equivalent circuit representation to follow the dynamic response of Hard Carbon Na-ion battery packs, and a neural network is included to further improve the estimation and utilizes internal filter signals -particularly the voltage innovation to learn residual error patterns arising from parameter drift, temperature mismatch and non linear electrochemical effects .In addition SOH evolution is modelled using an Arrhenius -based degradation formulation, supported by an innovation -driven correction mechanism that links long -term estimation trends with aging behaviour .The system is studied under different temperature levels and changing current condition, and its behaviour is also observed over a longer aging duration. Results indicate significant improvements in estimation accuracy compared to standalone EKF and purely data -driven methods ,while maintaining low computational complexity suitable for embedded battery management systems\u003c/em\u003e .\u003c/p\u003e","manuscriptTitle":"Hybrid EKF - Machine Learning Framework for SOC -SOH Estimation in Sodium ION Batteries","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-05-05 12:11:41","doi":"10.21203/rs.3.rs-9596965/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorInvitedReview","content":"","date":"2026-05-18T00:39:33+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"43529747860905155791744135530123166912","date":"2026-05-14T21:57:14+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-14T14:48:42+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"235203981374482764093335737608817330068","date":"2026-05-13T09:06:56+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-13T06:22:32+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"270602139628552800826342140018391065248","date":"2026-05-13T06:08:50+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"226147132158131288889149951233685781225","date":"2026-05-13T00:37:17+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"182938089821285136817894269548574068869","date":"2026-05-13T00:28:33+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-05-12T21:27:50+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-05-11T01:15:45+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-05-11T01:15:38+00:00","index":"","fulltext":""},{"type":"submitted","content":"Ionics","date":"2026-05-03T02:24:50+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"ionics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":" Learn more about [Ionics](https://www.springer.com/journal/11581) ","snPcode":"11581","submissionUrl":"https://mc.manuscriptcentral.com/ionics","title":"Ionics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"4adc77d7-1337-437e-8ffd-232b1612f794","owner":[],"postedDate":"May 5th, 2026","published":true,"recentEditorialEvents":[{"type":"editorInvitedReview","content":"","date":"2026-05-18T00:39:33+00:00","index":41,"fulltext":""},{"type":"reviewerAgreed","content":"43529747860905155791744135530123166912","date":"2026-05-14T21:57:14+00:00","index":40,"fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-14T14:48:42+00:00","index":39,"fulltext":""},{"type":"reviewerAgreed","content":"235203981374482764093335737608817330068","date":"2026-05-13T09:06:56+00:00","index":37,"fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-13T06:22:32+00:00","index":36,"fulltext":""},{"type":"reviewerAgreed","content":"270602139628552800826342140018391065248","date":"2026-05-13T06:08:50+00:00","index":35,"fulltext":""},{"type":"reviewerAgreed","content":"226147132158131288889149951233685781225","date":"2026-05-13T00:37:17+00:00","index":34,"fulltext":""},{"type":"reviewerAgreed","content":"182938089821285136817894269548574068869","date":"2026-05-13T00:28:33+00:00","index":33,"fulltext":""},{"type":"reviewersInvited","content":"25","date":"2026-05-12T21:27:50+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-05-11T01:15:45+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-05-11T01:15:38+00:00","index":"","fulltext":""},{"type":"submitted","content":"Ionics","date":"2026-05-03T02:24:50+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-12T21:38:50+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-05 12:11:41","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9596965","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9596965","identity":"rs-9596965","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}