Online Identification of Time-Variant Structural Parameters Under Unknown Inputs Basing On Extended Kalman Filter

Online Identification of Time-Variant Structural Parameters Under Unknown Inputs Basing On Extended Kalman Filter | 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 Online Identification of Time-Variant Structural Parameters Under Unknown Inputs Basing On Extended Kalman Filter Xiaoxiong Zhang, Jia He, Xugang Hua, Zhengqing Chen, Ou Yang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1106079/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract To date, a number of parameter identification methods have been developed for the purpose of structural health monitoring and vibration control. Among them, the extended Kalman filter (EKF) series methods are attractive in view of the efficient unbiased estimation in recursive manner. However, most of these methods are performed on the premise that the parameters are time-invariant and/or the loadings are known. To circumvent the aforementioned limitations, an online EKF with unknown input (OEKF-UI) approach is proposed in this paper for the identification of time-varying parameters and the unknown excitation. A revised observation equation is obtained with the aid of projection matrix. To capture the changes of structural parameters in real-time, an online tracking matrix (OTM) associated with the time-varying parameters is introduced and determined via an optimization procedure. Then, based on the principle of EKF, the recursive solution of structural states including the time-variant parameters can be analytically derived. Finally, using the estimated structural states, the unknown inputs are identified by means of least-squares estimation (LSE) at the same time-step. The effectiveness of the proposed approach is validated via linear and nonlinear numerical examples with the consideration of parameters being varied abruptly. Electrical Engineering Mechanical Engineering extended Kalman filter time-varying parameters identification unknown loads revised observation equation online tracking matrix Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Full Text Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 07 Dec, 2021 Reviewers invited by journal 07 Dec, 2021 Editor assigned by journal 25 Nov, 2021 First submitted to journal 22 Nov, 2021 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. 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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-1106079","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":68520862,"identity":"46fe1e64-05f7-4d73-836d-d2f62d7f88ed","order_by":0,"name":"Xiaoxiong Zhang","email":"","orcid":"","institution":"Hunan University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Xiaoxiong","middleName":"","lastName":"Zhang","suffix":""},{"id":68520863,"identity":"79453051-34f4-4355-a099-85b0e6ecf7fe","order_by":1,"name":"Jia He","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAtElEQVRIiWNgGAWjYBACxmYGNgaGigNgjgQJWs6QogUI2BgY20jRwtzO/OzBx3l38gwOMB+8zcNgl0eEw9jMDWdue1ZscIAt2ZqHIbmYCC0MZtK82w4nbjjAYybNw3AgsYGwFvZv0n/ngLTwfyNWC9BwxgawLWxEaymT7Dl2OHHmYTZjyzkGyYS1GPYf3ybxo+ZwYt/x5oc33lTYEaEFroIZRBgQUg8E8kSoGQWjYBSMgpEOAO21PARsAvTMAAAAAElFTkSuQmCC","orcid":"","institution":"Hunan University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Jia","middleName":"","lastName":"He","suffix":""},{"id":68520864,"identity":"0a8d2731-55e0-4fe2-8af2-b361738b71ae","order_by":2,"name":"Xugang Hua","email":"","orcid":"","institution":"Hunan University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Xugang","middleName":"","lastName":"Hua","suffix":""},{"id":68520865,"identity":"051cee22-3b29-429b-bbc3-c764e16ec1b3","order_by":3,"name":"Zhengqing Chen","email":"","orcid":"","institution":"Hunan University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Zhengqing","middleName":"","lastName":"Chen","suffix":""},{"id":68520866,"identity":"bd385041-66be-4f8c-9a4f-222f82e33e0c","order_by":4,"name":"Ou Yang","email":"","orcid":"","institution":"Hunan University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Ou","middleName":"","lastName":"Yang","suffix":""}],"badges":[],"createdAt":"2021-11-23 07:15:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-1106079/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-1106079/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":16297717,"identity":"91c0aa7b-ffda-4543-9202-6bf3e7cd2d06","added_by":"auto","created_at":"2021-12-08 23:22:37","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":63290,"visible":true,"origin":"","legend":"Flowchart of the proposed approach","description":"","filename":"Figure1.png","url":"https://assets-eu.researchsquare.com/files/rs-1106079/v1/f8ed0fbe8647c97a5c94d480.png"},{"id":16297722,"identity":"0242cca7-0b64-42a5-b4d2-e22a4e42f8c3","added_by":"auto","created_at":"2021-12-08 23:22:37","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":40870,"visible":true,"origin":"","legend":"The Identified structural parameters (linear model). (a) k1; (b) k2; (c) k3; (d) k4","description":"","filename":"Figure2.png","url":"https://assets-eu.researchsquare.com/files/rs-1106079/v1/c53283ef195ed08f88205287.png"},{"id":16297763,"identity":"d9ac1e6e-acb3-4c16-a672-31b10fd5b73d","added_by":"auto","created_at":"2021-12-08 23:25:37","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":30240,"visible":true,"origin":"","legend":"The identified unknown input (linear model)","description":"","filename":"Figure3.png","url":"https://assets-eu.researchsquare.com/files/rs-1106079/v1/6b7bb331f7a3d5cb789f4e75.png"},{"id":16297723,"identity":"eb016ca6-b68d-4958-a4c3-46c32793204f","added_by":"auto","created_at":"2021-12-08 23:22:37","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":48004,"visible":true,"origin":"","legend":"The identified coefficients (nonlinear Duffing system). (a) k1; (b) k3; (c) kd1; (d) kd2; (e) α; (f) β","description":"","filename":"Figure4.png","url":"https://assets-eu.researchsquare.com/files/rs-1106079/v1/76993fc92da2a06030f1c4c4.png"},{"id":16297802,"identity":"ccbf8271-9cff-4132-92fa-1b3e8d4f36f7","added_by":"auto","created_at":"2021-12-08 23:28:37","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":35597,"visible":true,"origin":"","legend":"The identified unknown seismic input (Duffing system). (a) The entire time history; (b) The segment from 4 to 8s","description":"","filename":"Figure5.png","url":"https://assets-eu.researchsquare.com/files/rs-1106079/v1/af891f8e508c72474e9f77d1.png"},{"id":16297765,"identity":"c27819d5-1cbe-4762-be9b-7131cd5c688f","added_by":"auto","created_at":"2021-12-08 23:25:37","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":85052,"visible":true,"origin":"","legend":"The identified coefficients (Bouc-Wen model). (a) k1; (b) k2; (c) c1; (d) c2 ; (e) β1; (f) β2 ; (g) γ1; (h) γ2","description":"","filename":"Figure6.png","url":"https://assets-eu.researchsquare.com/files/rs-1106079/v1/e8919988744f26832e34b297.png"},{"id":16297719,"identity":"8212d084-7d74-4bb6-bdab-3827ba22d340","added_by":"auto","created_at":"2021-12-08 23:22:37","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":45223,"visible":true,"origin":"","legend":"The identified unknown input (Bouc-Wen model). (a) The entire time history; (b) The segment from 7 to 7.1s","description":"","filename":"Figure7.png","url":"https://assets-eu.researchsquare.com/files/rs-1106079/v1/1939476d6ee5cbd77ed6309f.png"},{"id":16297803,"identity":"c26b32dc-cffd-4f9a-94f1-c350604abec7","added_by":"auto","created_at":"2021-12-08 23:28:43","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":381641,"visible":true,"origin":"","legend":"","description":"","filename":"manuscriptnonlineardynamicsv2maintext.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1106079/v1_covered.pdf"}],"financialInterests":"","formattedTitle":"\u003cp\u003eOnline Identification of Time-Variant Structural Parameters Under Unknown Inputs Basing On Extended Kalman Filter\u003c/p\u003e","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-1106079/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e."}],"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":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nonlinear-dynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"nody","sideBox":"Learn more about [Nonlinear Dynamics](https://www.springer.com/journal/11071)","snPcode":"11071","submissionUrl":"https://submission.nature.com/new-submission/11071/3","title":"Nonlinear Dynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"extended Kalman filter, time-varying parameters identification, unknown loads, revised observation equation, online tracking matrix","lastPublishedDoi":"10.21203/rs.3.rs-1106079/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1106079/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTo date, a number of parameter identification methods have been developed for the purpose of structural health monitoring and vibration control. Among them, the extended Kalman filter (EKF) series methods are attractive in view of the efficient unbiased estimation in recursive manner. However, most of these methods are performed on the premise that the parameters are time-invariant and/or the loadings are known. To circumvent the aforementioned limitations, an online EKF with unknown input (OEKF-UI) approach is proposed in this paper for the identification of time-varying parameters and the unknown excitation. A revised observation equation is obtained with the aid of projection matrix. To capture the changes of structural parameters in real-time, an online tracking matrix (OTM) associated with the time-varying parameters is introduced and determined via an optimization procedure. Then, based on the principle of EKF, the recursive solution of structural states including the time-variant parameters can be analytically derived. Finally, using the estimated structural states, the unknown inputs are identified by means of least-squares estimation (LSE) at the same time-step. The effectiveness of the proposed approach is validated via linear and nonlinear numerical examples with the consideration of parameters being varied abruptly.\u0026nbsp;\u0026nbsp;\u003c/p\u003e","manuscriptTitle":"Online Identification of Time-Variant Structural Parameters Under Unknown Inputs Basing On Extended Kalman Filter","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2021-12-08 23:22:35","doi":"10.21203/rs.3.rs-1106079/v1","editorialEvents":[{"type":"communityComments","content":1},{"type":"editorInvitedReview","content":"","date":"2021-12-07T11:59:59+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2021-12-07T11:58:33+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2021-11-25T11:46:52+00:00","index":"","fulltext":""},{"type":"submitted","content":"Nonlinear Dynamics","date":"2021-11-23T02:15:02+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nonlinear-dynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"nody","sideBox":"Learn more about [Nonlinear Dynamics](https://www.springer.com/journal/11071)","snPcode":"11071","submissionUrl":"https://submission.nature.com/new-submission/11071/3","title":"Nonlinear Dynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"62573c5b-bbe4-4c7c-9e9e-0c6026101647","owner":[],"postedDate":"December 8th, 2021","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":9023902,"name":"Electrical Engineering"},{"id":9023903,"name":"Mechanical Engineering"}],"tags":[],"updatedAt":"2022-04-27T07:37:48+00:00","versionOfRecord":[],"versionCreatedAt":"2021-12-08 23:22:35","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-1106079","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-1106079","identity":"rs-1106079","version":["v1"]},"buildId":"WrCJVZZCHTDjtuVLN7oU0","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}