A novel GMFO-based identification method for MIMO Hammerstein model with heavy-tailed noise

A novel GMFO-based identification method for MIMO Hammerstein model with heavy-tailed noise | 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 A novel GMFO-based identification method for MIMO Hammerstein model with heavy-tailed noise JIAQI WANG, FUYU LING This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6259360/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 29 May, 2025 Read the published version in Neural Processing Letters → Version 1 posted 16 You are reading this latest preprint version Abstract This paper deals with the identification of multi-input multi-output (MIMO) Hammerstein system with combined nonlinearities under the heavy-tailed noise. Considering the outliers in the noises may lead to the unsatisfactory identification results using analytical method, this paper proposes a novel identification scheme combining the advantages of Radial Basis Function Neural Network (RBFNN) and a recently proposed nature-inspired algorithm called Moth-Flame Optimization (MFO). We use RBFNN to construct the static nonlinear block. The identification problem could be converted to an optimization problem, and the parameters of the linear part and nonlinear part are updated simultaneously. To improve its performance for identification, a novel version of MFO based on Gaussian-mixture distribution, which is named Gaussian-mixture Moth-Flame Optimization (GMFO), is proposed. The main innovation is the discrete population initialization and the individual position adjustment using Gaussian-mixture distribution, which is conducive to jumping out of local optima caused by outliers. The simulation results illustrate the proposed method is effective and outperforms other common evolutionary algorithms. Heavy-tailed noise MIMO Hammerstein model Moth-Flame Optimization Radial Basis Function Neural Network system identification Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 29 May, 2025 Read the published version in Neural Processing Letters → Version 1 posted Editorial decision: Revision requested 19 Apr, 2025 Reviews received at journal 14 Apr, 2025 Reviewers agreed at journal 01 Apr, 2025 Reviews received at journal 24 Mar, 2025 Reviewers agreed at journal 24 Mar, 2025 Reviews received at journal 24 Mar, 2025 Reviewers agreed at journal 24 Mar, 2025 Reviewers agreed at journal 23 Mar, 2025 Reviewers agreed at journal 23 Mar, 2025 Reviewers agreed at journal 22 Mar, 2025 Reviewers agreed at journal 22 Mar, 2025 Reviewers agreed at journal 22 Mar, 2025 Reviewers invited by journal 22 Mar, 2025 Editor assigned by journal 19 Mar, 2025 Submission checks completed at journal 19 Mar, 2025 First submitted to journal 19 Mar, 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. 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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-6259360","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":433466239,"identity":"b68b70db-a238-476f-9985-477cd8dd159a","order_by":0,"name":"JIAQI WANG","email":"","orcid":"","institution":"Yingkou Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"JIAQI","middleName":"","lastName":"WANG","suffix":""},{"id":433466240,"identity":"f77c31be-412d-47b5-9688-951b7baa7992","order_by":1,"name":"FUYU LING","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2UlEQVRIie3PsQrCMBCA4ZPAuRy6RpD6CgGhkw+TIHSq4NhBsKDYQcQ30FdwdIwWMkVnB4eK4O6mi4izYurmkG++n7sD8Lw/hNWR1urRCbA6PxUyGbiTGhmlC4zaNbJMFNa4k4DH7U2BW7XgMTZOY1biMDJSS9KVCfRMolKEejaV7l8kPzKEfXRQ6yZwu1uV2CIuiJU0PCiLIHjPkfBYaClzQgZhX01Y2UTnHJFCKJe8DlNpJJCwy6U15PyllY3y6z3tDJfL8+Z6SwZBPZt9T97Qb+Oe53neR0/Ce06DyUa9ogAAAABJRU5ErkJggg==","orcid":"","institution":"Yingkou Institute of Technology","correspondingAuthor":true,"prefix":"","firstName":"FUYU","middleName":"","lastName":"LING","suffix":""}],"badges":[],"createdAt":"2025-03-19 08:23:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6259360/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6259360/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11063-025-11768-4","type":"published","date":"2025-05-29T15:57:06+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":83783628,"identity":"6491ea5f-e738-4f1d-8538-f7fe98942fd0","added_by":"auto","created_at":"2025-06-02 16:12:11","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":900447,"visible":true,"origin":"","legend":"","description":"","filename":"AnovelGMFObasedidentificationmethodforMIMOHammersteinmodelwithheavytailednoise.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6259360/v1_covered_05e166d6-33b4-41be-953c-6c57b970dea5.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A novel GMFO-based identification method for MIMO Hammerstein model with heavy-tailed noise","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":"neural-processing-letters","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"nepl","sideBox":"Learn more about [Neural Processing Letters](http://link.springer.com/journal/11063)","snPcode":"11063","submissionUrl":"https://submission.nature.com/new-submission/11063/3","title":"Neural Processing Letters","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Heavy-tailed noise, MIMO Hammerstein model, Moth-Flame Optimization, Radial Basis Function Neural Network, system identification","lastPublishedDoi":"10.21203/rs.3.rs-6259360/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6259360/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper deals with the identification of multi-input multi-output (MIMO) Hammerstein system with combined nonlinearities under the heavy-tailed noise. 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