[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-123438-en":3,"doc-seo-123438-105":30,"detail-sidebar-cat-0-en-105":83},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},123438,1374391974564,"Clementine","https://ap-avatar.wpscdn.com/avatar/14000253aa45c000a9e?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779874745381141002",8,"Research & Report","Machine learning aided uncertainty quantification for engineering structures involving material-geometric randomness and data imperfection","Real-world engineering applications face pervasive uncertainty in material properties, structural geometry, and loading conditions, which can significantly distort estimates of structural performance. Practical datasets also commonly include imperfections such as noise, outliers, or missing information, while numerical simulation can introduce additional errors and modeling inaccuracies. A machine learning-aided stochastic analysis framework is proposed to quantify the combined effects of material and geometric randomness and to jointly mitigate data imperfection impacts on structural behavior estimation through the proposed Capped Extended Support Vector Regression (CX-SVR).","Computer Methods in Applied Mechanics and Engineering 423 (2024) 116868  \nContents lists available at ScienceDirect  \nComputer Methods in Applied Mechanics and Engineering  \njournal [homepage: www.elsevier.com/locate/cma](homepage: www.elsevier.com/locate/cma)  \n| Machine learning aided uncertainty quantification for engineering   structures involving material-geometric randomness and\u003Cbr>data imperfection\u003Cbr>Qihan Wang a, Di Wu b, Guoyin Li c, Zhenyu Liud, Jingzhong Tong e, Xiaojun Chen a, Wei Gao a, *\u003Cbr>a Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW 2052, Australia\u003Cbr>b School of Civil and Environmental Engineering, University of Technology Sydney, Sydney, NSW 2007, Australia c School of Mathematics and Statistics, The University of New South Wales, Sydney, NSW, Australia\u003Cbr>d State Key Lab of CAD&CG, School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China e College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China |\n| --- |\n| H I G H L I G H T S |\n| • A machine learning-aided uncertainty quantification framework is proposed for engineering structures.\u003Cbr>• The effects of material and geometric randomness on structural performance are quantified simultaneously.\u003Cbr>• Data imperfections, i.e., noise and outliers within observations, are considered within the proposed framework.\u003Cbr>• A novel machine learning technique is developed to handle the datasets with imperfection.\u003Cbr>• The applicability and computational efficiency of the proposed approach are well demonstrated. |\n\nA R T I C L E I N F O  \nKeywords:  \nMaterial and geometric uncertainty  \nData imperfection  \nCapped extended support vector regression Machine learning  \nEngineering application  \nA B S T R A C T  \nIn real-world engineering, uncertainty is ubiquitous within material properties, structural geometry, load conditions, and the like. These uncertainties have substantial impacts on the estimation of structural performance. Furthermore, information or datasets in real life commonly contain imperfections, e.g., noise, outliers, or missing data. To quantify these impacts induced by uncertainties on structural behaviours and reduce the effects of data imperfections simultaneously, a machine learning-aided stochastic analysis framework is proposed. A novel supervised machine learning technique, namely the Capped Extended Support Vector Regression (CX-SVR) technique, is developed to effectively suppress the effects of outliers and noise in datasets. Its inherent convexity in optimization and capped strategy theoretically supports the accuracy of CXSVR, especially in handling datasets with imperfections. Once the effective surrogate model is established, subsequent analyses, like sampling-based methods, can circumvent the cumbersome physical model, which is potentially the nest of computational burden and errors in engineering applications. The high robustness of the proposed approach can be summarized in four main aspects: unrestrictive selection of the system inputs and their statistical information,‘perfect’ or‘imperfect’ data, enough statistical information (including statistical moments, probability  \n* Corresponding author.  \n[E-mail address:](E-mail address: w.gao@unsw.edu.au)[ w.gao@unsw.edu.au](E-mail address: w.gao@unsw.edu.au) (W. Gao).  \n[https://doi.org/10.1016/j.cma.2024.116868](https://doi.org/10.1016/j.cma.2024.116868)  \nReceived 18 April 2023; Received in revised form 12 November 2023; Accepted 18 February 2024 Available online 26 February 2024  \n0045-7825/© 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license  \n([http://creativecommons.org/licenses/by/4.0/](http://creativecommons.org/licenses/by/4.0/)).  \nQ. Wang et al.  \nComputer Methods in Applied Mechanics and Engineering 423 (2024) 116868  \ndensity functions, and cumulative distribution functions) of th","cbCairt1p3YCHKaZ","https://ap.wps.com/l/cbCairt1p3YCHKaZ","pdf",3576871,1,20,"English","en",105,"# Highlights\n## Proposed machine learning-aided uncertainty quantification framework\n## Quantifying material and geometric randomness effects\n## Handling noise, outliers, and missing data with CX-SVR\n# Article details\n## Keywords\n## Abstract\n## 1. Introduction","[{\"question\":\"Why is the CX-SVR surrogate model useful for subsequent stochastic analyses?\",\"answer\":\"After training an effective surrogate model, later analyses (e.g., sampling-based methods) can avoid using the cumbersome physical model, reducing computational burden and modeling-induced errors.\"}]","Machine learning aided uncertainty quantification for engineering structures involving material-geometric randomness and data imperfection | PDF",1785816484,50,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":78,"head_meta":80,"extra_data":82,"updated_unix":28},"machine-learning-aided-uncertainty-quantification-for-engineering-structures-involving-material-geometric-randomness-and-data-imperfection","",{"@graph":36,"@context":77},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/machine-learning-aided-uncertainty-quantification-for-engineering-structures-involving-material-geometric-randomness-and-data-imperfection/123438/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-04",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71],{"name":72,"@type":73,"acceptedAnswer":74},"Why is the CX-SVR surrogate model useful for subsequent stochastic analyses?","Question",{"text":75,"@type":76},"After training an effective surrogate model, later analyses (e.g., sampling-based methods) can avoid using the cumbersome physical model, reducing computational burden and modeling-induced errors.","Answer","https://schema.org",{"og:url":52,"og:type":79,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":81,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":84},[85,89,93,97,102,106,111,114,118,121,125],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":86,"show_sort_weight":87,"slug":88},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":90,"show_sort_weight":91,"slug":92},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Exam",70,"exam",{"id":98,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},5,"Comic",60,"comic",{"id":103,"doc_module":4,"doc_module_name":46,"category_name":104,"show_sort_weight":29,"slug":105},6,"Technology","technology",{"id":107,"doc_module":4,"doc_module_name":46,"category_name":108,"show_sort_weight":109,"slug":110},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":112,"slug":113},30,"research-report",{"id":115,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":21,"slug":117},9,"Religion & Spirituality","religion-spirituality",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":119,"show_sort_weight":21,"slug":120},"World Cup","world-cup",{"id":122,"doc_module":4,"doc_module_name":46,"category_name":123,"show_sort_weight":122,"slug":124},10,"Lifestyle","lifestyle",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":127,"show_sort_weight":98,"slug":128},19,"General","general"]