Application of Machine Learning to Evaluate the Influence of PI Control Parameters on the Stability of Neutral Equilibrium Mechanism as a Virtual Pier in Bridge Systems

Application of Machine Learning to Evaluate the Influence of PI Control Parameters on the Stability of Neutral Equilibrium Mechanism as a Virtual Pier in Bridge Systems | 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 Article Application of Machine Learning to Evaluate the Influence of PI Control Parameters on the Stability of Neutral Equilibrium Mechanism as a Virtual Pier in Bridge Systems Wen-Pei Sung, Ming-Hsiang Shih This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6624091/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 21 Oct, 2025 Read the published version in Scientific Reports → Version 1 posted 11 You are reading this latest preprint version Abstract This study investigates the application of Neutral Equilibrium Mechanism (NEM) in active control systems for bridge structures, with a focus on analyzing the effects of proportional gain (GP) and integral gain (GI) parameters on vertical displacement stability. A scaled bridge model equipped with dual NEMs, displacement sensors, and servo motors was used to simulate dynamic loading responses in a closed-loop control system. Machine learning techniques, including Random Forest Regression and Neural Networks, were employed to develop nonlinear predictive models. These were supplemented by K-means clustering and feature sensitivity analysis to evaluate control strategies and identify optimal parameter settings. The experiment collected over 21.3 million high-resolution time-series data points across four PI control parameter combinations. Results demonstrated that the optimal parameter configuration (GP = 1.0, GI = 0.010) significantly reduced maximum vertical displacement from 5.02 mm and 5.23 mm (at points A and B) to 0.39 mm and 0.38 mm, respectively, while cutting stabilization time to 9.8 seconds. The Neural Network model achieved excellent predictive performance with an R² of 0.934 and RMSE of 0.038. Clustering and sensitivity analyses revealed that medium-gain settings (GP = 1.0, GI = 0.010) optimally balanced system stability and structural symmetry. This research confirms the feasibility of machine learning-based analytical models for bridge displacement control and provides data-driven guidance for parameter optimization, offering valuable insights for future intelligent bridge control system design. Physical sciences/Engineering Physical sciences/Mathematics and computing Neutral Equilibrium Mechanism Virtual Pier Machine Learning PID Control Neural Network Random Forest K-means Clustering Control Performance Analysis Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 21 Oct, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 17 Aug, 2025 Reviews received at journal 16 Aug, 2025 Reviewers agreed at journal 27 Jul, 2025 Reviewers agreed at journal 23 Jun, 2025 Reviews received at journal 23 Jun, 2025 Reviewers agreed at journal 03 Jun, 2025 Reviewers invited by journal 03 Jun, 2025 Editor assigned by journal 29 May, 2025 Editor invited by journal 22 May, 2025 Submission checks completed at journal 22 May, 2025 First submitted to journal 08 May, 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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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-6624091","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":465816987,"identity":"c2d2633a-704e-48cc-85fe-3a39e651770e","order_by":0,"name":"Wen-Pei Sung","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAArElEQVRIiWNgGAWjYHACxgdQhgHRWphBSiUgWhKI08ImQZoWg9vtz6oLag7XMbA3b5Ng/HGYCC13zpjdnnHssAQDz7EyCYYEIrSY3chhu83bANQikWMG1HKbGC3pz4rBWuTfEK0lwYwZYgsPkVrs75wxluY5li7ZxpNWbJGQ9p+wFsnZ7Q8/89RY8/OzH95444NNGmEt4AgBATYQkUCEBoSWUTAKRsEoGAU4AQCF2zM8jbPC/wAAAABJRU5ErkJggg==","orcid":"","institution":"National Chin-Yi University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Wen-Pei","middleName":"","lastName":"Sung","suffix":""},{"id":465816988,"identity":"c4431b48-619d-49db-be70-d6b9a955f10b","order_by":1,"name":"Ming-Hsiang Shih","email":"","orcid":"","institution":"National Chi Nan University","correspondingAuthor":false,"prefix":"","firstName":"Ming-Hsiang","middleName":"","lastName":"Shih","suffix":""}],"badges":[],"createdAt":"2025-05-09 01:38:02","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6624091/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6624091/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-20482-z","type":"published","date":"2025-10-21T16:16:12+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":94490325,"identity":"36c74e7a-a626-474e-ad6e-e8eb971e25b1","added_by":"auto","created_at":"2025-10-27 17:09:11","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":815494,"visible":true,"origin":"","legend":"","description":"","filename":"PaperMLSUBNew.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6624091/v1_covered_cb96e2f1-9ab3-499d-9b92-35e58f7e1156.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Application of Machine Learning to Evaluate the Influence of PI Control Parameters on the Stability of Neutral Equilibrium Mechanism as a Virtual Pier in Bridge Systems","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":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Neutral Equilibrium Mechanism, Virtual Pier, Machine Learning, PID Control, Neural Network, Random Forest, K-means Clustering, Control Performance Analysis","lastPublishedDoi":"10.21203/rs.3.rs-6624091/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6624091/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study investigates the application of Neutral Equilibrium Mechanism (NEM) in active control systems for bridge structures, with a focus on analyzing the effects of proportional gain (GP) and integral gain (GI) parameters on vertical displacement stability. A scaled bridge model equipped with dual NEMs, displacement sensors, and servo motors was used to simulate dynamic loading responses in a closed-loop control system. Machine learning techniques, including Random Forest Regression and Neural Networks, were employed to develop nonlinear predictive models. These were supplemented by K-means clustering and feature sensitivity analysis to evaluate control strategies and identify optimal parameter settings. The experiment collected over 21.3\u0026nbsp;million high-resolution time-series data points across four PI control parameter combinations. Results demonstrated that the optimal parameter configuration (GP\u0026thinsp;=\u0026thinsp;1.0, GI\u0026thinsp;=\u0026thinsp;0.010) significantly reduced maximum vertical displacement from 5.02 mm and 5.23 mm (at points A and B) to 0.39 mm and 0.38 mm, respectively, while cutting stabilization time to 9.8 seconds. The Neural Network model achieved excellent predictive performance with an R\u0026sup2; of 0.934 and RMSE of 0.038. Clustering and sensitivity analyses revealed that medium-gain settings (GP\u0026thinsp;=\u0026thinsp;1.0, GI\u0026thinsp;=\u0026thinsp;0.010) optimally balanced system stability and structural symmetry. This research confirms the feasibility of machine learning-based analytical models for bridge displacement control and provides data-driven guidance for parameter optimization, offering valuable insights for future intelligent bridge control system design.\u003c/p\u003e","manuscriptTitle":"Application of Machine Learning to Evaluate the Influence of PI Control Parameters on the Stability of Neutral Equilibrium Mechanism as a Virtual Pier in Bridge Systems","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-05 08:42:34","doi":"10.21203/rs.3.rs-6624091/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-08-18T03:32:40+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-08-16T07:02:07+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"313817350422940859001213182897357785081","date":"2025-07-27T22:11:28+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"221044428390735134203179506916328074579","date":"2025-06-23T14:47:42+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-06-23T14:44:46+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"222494779618520171406117830439855724575","date":"2025-06-03T11:05:13+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-06-03T07:16:48+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-05-29T05:55:08+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-05-22T08:15:36+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-05-22T06:46:21+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-05-09T01:22:02+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"d7630584-1b45-4bfe-a3d3-9dee0de2aece","owner":[],"postedDate":"June 5th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":49451562,"name":"Physical sciences/Engineering"},{"id":49451563,"name":"Physical sciences/Mathematics and computing"}],"tags":[],"updatedAt":"2025-10-27T16:31:29+00:00","versionOfRecord":{"articleIdentity":"rs-6624091","link":"https://doi.org/10.1038/s41598-025-20482-z","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2025-10-21 16:16:12","publishedOnDateReadable":"October 21st, 2025"},"versionCreatedAt":"2025-06-05 08:42:34","video":"","vorDoi":"10.1038/s41598-025-20482-z","vorDoiUrl":"https://doi.org/10.1038/s41598-025-20482-z","workflowStages":[]},"version":"v1","identity":"rs-6624091","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6624091","identity":"rs-6624091","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}