A Grey Wolf Optimized Deep Learning Framework for Robust Prediction of Subgrade Resilient Modulus

A Grey Wolf Optimized Deep Learning Framework for Robust Prediction of Subgrade Resilient Modulus | 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 Grey Wolf Optimized Deep Learning Framework for Robust Prediction of Subgrade Resilient Modulus Aman Mishra, Laxmikant Yadu, Shrabony Adhikary This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8826415/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 17 Mar, 2026 Read the published version in Transportation Infrastructure Geotechnology → Version 1 posted You are reading this latest preprint version Abstract The precise calculation of the resilient modulus (M R ) of compacted subgrade soil is a crucial step in designing safe and sustainable flexible pavement systems. The M R is a key parameter governing the structural performance of pavements under repeated traffic loading. The proposed research investigates the applicability of nature-inspired, population-based metaheuristic swarm intelligence algorithms for estimating the M R of pavement subgrade soil. A dataset comprising 2,813 samples was systematically divided into training and testing subsets, considering important soil, stress, moisture, and environmental variables. Three widely used machine learning (ML) models - Multivariate Adaptive Regression Splines (MARS), Extreme Learning Machine (ELM), and Deep Neural Network (DNN) - were developed to predict M R values. To further improve prediction accuracy, a swarm intelligence-based approach, namely the Grey Wolf Optimizer (GWO), was employed to optimize and combine the outputs of the independent ML models. The reliability and robustness of the developed models were evaluated using 10-fold cross-validation, Shapley Additive Explanation (SHAP) analysis, partial dependence plots (PDP), and error box plots. The generalization capability of the proposed models was additionally assessed using an independent experimental dataset consisting of 40 M R specimens. The results demonstrate that the GWO-DNN model outperformed the other algorithms, achieving the highest prediction accuracy with an R² value of 0.971 and an RMSE of 4.05 MPa. To enhance practical applicability, a graphical user interface (GUI) was developed, enabling engineers and researchers to input basic parameters and directly estimate M R . This study contributes to data-driven advancements in geo-transportation engineering, improving the efficiency and sustainability of M R estimation. Resilient Modulus Grey Wolf Optimizer Deep Neural Network Multivariate Adaptive Regression Splines Extreme Learning Machine Graphical User Interface Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 17 Mar, 2026 Read the published version in Transportation Infrastructure Geotechnology → Version 1 posted 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-8826415","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":591165440,"identity":"3e19c594-e94d-41ed-ac79-1d506b0963cc","order_by":0,"name":"Aman Mishra","email":"data:image/png;base64,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","orcid":"","institution":"National Institute of Technology Raipur","correspondingAuthor":true,"prefix":"","firstName":"Aman","middleName":"","lastName":"Mishra","suffix":""},{"id":591165444,"identity":"fd694426-c44d-4a0c-ae0d-b2b96e3b139a","order_by":1,"name":"Laxmikant Yadu","email":"","orcid":"","institution":"National Institute of Technology Raipur","correspondingAuthor":false,"prefix":"","firstName":"Laxmikant","middleName":"","lastName":"Yadu","suffix":""},{"id":591165454,"identity":"e658bad0-6b6c-40f2-893f-4580f7c12162","order_by":2,"name":"Shrabony Adhikary","email":"","orcid":"","institution":"Visvesvaraya National Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Shrabony","middleName":"","lastName":"Adhikary","suffix":""}],"badges":[],"createdAt":"2026-02-09 06:10:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8826415/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8826415/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s40515-026-00842-6","type":"published","date":"2026-03-17T15:57:35+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":105223256,"identity":"39715ec0-fd4c-4d82-aefd-c59a23c91f43","added_by":"auto","created_at":"2026-03-23 16:00:46","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1458816,"visible":true,"origin":"","legend":"","description":"","filename":"MishraAMANAGreyWolfOptimizedDeepLearningFrameworkforRobustPredictionofSubgradeResilientModulus.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8826415/v1_covered_c15f3ce0-e463-48ca-8591-2fa8da33f609.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Grey Wolf Optimized Deep Learning Framework for Robust Prediction of Subgrade Resilient Modulus","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Resilient Modulus, Grey Wolf Optimizer, Deep Neural Network, Multivariate Adaptive Regression Splines, Extreme Learning Machine, Graphical User Interface","lastPublishedDoi":"10.21203/rs.3.rs-8826415/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8826415/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe precise calculation of the resilient modulus (M\u003csub\u003eR\u003c/sub\u003e) of compacted subgrade soil is a crucial step in designing safe and sustainable flexible pavement systems. The M\u003csub\u003eR\u003c/sub\u003e is a key parameter governing the structural performance of pavements under repeated traffic loading. The proposed research investigates the applicability of nature-inspired, population-based metaheuristic swarm intelligence algorithms for estimating the M\u003csub\u003eR\u003c/sub\u003e of pavement subgrade soil. A dataset comprising 2,813 samples was systematically divided into training and testing subsets, considering important soil, stress, moisture, and environmental variables. Three widely used machine learning (ML) models - Multivariate Adaptive Regression Splines (MARS), Extreme Learning Machine (ELM), and Deep Neural Network (DNN) - were developed to predict M\u003csub\u003eR\u003c/sub\u003e values. To further improve prediction accuracy, a swarm intelligence-based approach, namely the Grey Wolf Optimizer (GWO), was employed to optimize and combine the outputs of the independent ML models. The reliability and robustness of the developed models were evaluated using 10-fold cross-validation, Shapley Additive Explanation (SHAP) analysis, partial dependence plots (PDP), and error box plots. The generalization capability of the proposed models was additionally assessed using an independent experimental dataset consisting of 40 M\u003csub\u003eR\u003c/sub\u003e specimens. The results demonstrate that the GWO-DNN model outperformed the other algorithms, achieving the highest prediction accuracy with an R\u0026sup2; value of 0.971 and an RMSE of 4.05 MPa. To enhance practical applicability, a graphical user interface (GUI) was developed, enabling engineers and researchers to input basic parameters and directly estimate M\u003csub\u003eR\u003c/sub\u003e. This study contributes to data-driven advancements in geo-transportation engineering, improving the efficiency and sustainability of M\u003csub\u003eR\u003c/sub\u003e estimation.\u003c/p\u003e","manuscriptTitle":"A Grey Wolf Optimized Deep Learning Framework for Robust Prediction of Subgrade Resilient Modulus","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-17 18:21:22","doi":"10.21203/rs.3.rs-8826415/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"c9e6df73-c373-4bca-9b5f-d05fafb8c1d6","owner":[],"postedDate":"February 17th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-03-23T16:00:06+00:00","versionOfRecord":{"articleIdentity":"rs-8826415","link":"https://doi.org/10.1007/s40515-026-00842-6","journal":{"identity":"transportation-infrastructure-geotechnology","isVorOnly":false,"title":"Transportation Infrastructure Geotechnology"},"publishedOn":"2026-03-17 15:57:35","publishedOnDateReadable":"March 17th, 2026"},"versionCreatedAt":"2026-02-17 18:21:22","video":"","vorDoi":"10.1007/s40515-026-00842-6","vorDoiUrl":"https://doi.org/10.1007/s40515-026-00842-6","workflowStages":[]},"version":"v1","identity":"rs-8826415","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8826415","identity":"rs-8826415","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}