A novel univariate Legendre polynomial method for probabilistic failure load prediction in composite open-hole laminate

A novel univariate Legendre polynomial method for probabilistic failure load prediction in composite open-hole laminate | 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 A novel univariate Legendre polynomial method for probabilistic failure load prediction in composite open-hole laminate Mingxuan Li, Ben Yuan, Fugui Li, Yuan Fang, Xiaolei Zhu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6933117/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 30 Dec, 2025 Read the published version in Scientific Reports → Version 1 posted 10 You are reading this latest preprint version Abstract A novel univariate Legendre polynomial method for probabilistic failure load prediction in composite open-hole laminate based on the dimension-reduction method and Legendre polynomial. First, an n-dimensional response function about the ultimate load of composite open-hole laminate is reduced in dimension. The original response function was converted to the sum of univariate functions of all random variables. Legendre polynomial was used to fit all univariate functions, and the univariate Legendre approximate model (ULAM) of the response function was obtained. To verify the correctness of the model, static tensile experiments were carried out on composite open-hole laminates, and the ultimate loads were obtained. The predicted results were compared with the experimental results to verify the effectiveness of the method. The errors of the results are all less than 13%, indicating the new method can effectively predict the ultimate load value of composite open-hole laminate with probability. In addition, ULAM was analyzed in comparison with RSM and Kriging model to verify the superiority of the model. Finally, the effect of the order on the prediction accuracy of ULAM was studied. If the order is too low, underfitting will occur. Increasing the order can improve the prediction accuracy of ULAM. If the order is too high, overfitting will occur, resulting in a decline in the prediction accuracy of the model. Physical sciences/Materials science Physical sciences/Engineering/Mechanical engineering composite open-hole laminate Legendre polynomial dimension reduction method probabilistic prediction Full Text Additional Declarations No competing interests reported. Supplementary Files DeclarationofInterestStatement.docx Cite Share Download PDF Status: Published Journal Publication published 30 Dec, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 07 Sep, 2025 Reviews received at journal 03 Aug, 2025 Reviews received at journal 28 Jul, 2025 Reviewers agreed at journal 21 Jul, 2025 Reviewers agreed at journal 20 Jul, 2025 Reviewers invited by journal 04 Jul, 2025 Editor assigned by journal 04 Jul, 2025 Editor invited by journal 04 Jul, 2025 Submission checks completed at journal 04 Jul, 2025 First submitted to journal 19 Jun, 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-6933117","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":481631867,"identity":"ddf52546-f3c4-4aa4-bfdd-e8adbf68cca7","order_by":0,"name":"Mingxuan Li","email":"","orcid":"","institution":"Nanjing Tech University","correspondingAuthor":false,"prefix":"","firstName":"Mingxuan","middleName":"","lastName":"Li","suffix":""},{"id":481631868,"identity":"bce5d1be-e31c-4080-adac-02fa800ce8eb","order_by":1,"name":"Ben Yuan","email":"","orcid":"","institution":"Nanjing Tech 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First, an n-dimensional response function about the ultimate load of composite open-hole laminate is reduced in dimension. The original response function was converted to the sum of univariate functions of all random variables. Legendre polynomial was used to fit all univariate functions, and the univariate Legendre approximate model (ULAM) of the response function was obtained. To verify the correctness of the model, static tensile experiments were carried out on composite open-hole laminates, and the ultimate loads were obtained. The predicted results were compared with the experimental results to verify the effectiveness of the method. The errors of the results are all less than 13%, indicating the new method can effectively predict the ultimate load value of composite open-hole laminate with probability. In addition, ULAM was analyzed in comparison with RSM and Kriging model to verify the superiority of the model. Finally, the effect of the order on the prediction accuracy of ULAM was studied. If the order is too low, underfitting will occur. Increasing the order can improve the prediction accuracy of ULAM. 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