[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-126076-en":3,"doc-seo-126076-105":31,"detail-sidebar-cat-0-en-105":93},{"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":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},126076,962084931830,"Theodore","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","In-Plane and Out-of-Plane 2-D Microdisplacement Sensor Based on a Single Microwave Resonator - Machine Learning","Microwave displacement sensors attract strong research attention and support industrial automation and aerospace engineering, yet most existing designs primarily measure in-plane motion while treating out-of-plane displacement as constant. This work presents a 2-D microdisplacement sensing concept that experimentally captures both in-plane and out-of-plane components at the same time. A proof-of-concept system uses a custom coaxial cable resonator as the stator and a rubber-metal heterogeneous plate as the movable part. Fundamental resonant frequency monitoring detects 2-D micromovements, and machine learning analysis decouples the resonator responses for independent, accurate quantification. The approach enables multidimensional sensing using a simple 1-D microwave resonator and can extend to other 2-D physical and mechanical parameters such as vibration and acceleration.","Missouri University of Science and Technology  \nScholars' Mine  \n\n| Electrical and Computer Engineering Faculty Research & Creative Works | Electrical and Computer Engineering |\n| --- | --- |\n| 01 Jan 2024\u003Cbr>In-Plane and Out-of-Plane 2-D Microdisplacement Sensor based\u003Cbr>on a Single Microwave Resonator with Machine Learning Shiyu Li\u003Cbr>Osamah Alsalman\u003Cbr>Jie Huang\u003Cbr>Missouri University of Science and Technology, [jieh@mst.edu](jieh@mst.edu)[ ](jieh@mst.edu)Chen Zhu\u003Cbr>Follow this and additional works at: [https://scholarsmine.mst.edu/ele_comeng_facwork](https://scholarsmine.mst.edu/ele_comeng_facwork)\u003Cbr> Part of the Electrical and Computer Engineering Commons |  |\n\nRecommended Citation  \nS. Li et al., \"In-Plane and Out-of-Plane 2-D Microdisplacement Sensor based on a Single Microwave Resonator with Machine Learning,\" IEEE Transactions on Microwave Theory and Techniques, Institute of Electrical and Electronics Engineers, Jan 2024.  \nThe definitive version is available at [https://doi.org/10.1109/TMTT.2024.3510724](https://doi.org/10.1109/TMTT.2024.3510724)  \n[This Article-Journal is brought to you for free and open access by Scholars](This Article-Journal is brought to you for free and open access by Scholars)' Mine. It has been accepted for inclusion in Electrical and Computer Engineering Faculty Research & Creative Works by an authorized administrator of Scholars' Mine. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact [scholarsmine@mst.edu](scholarsmine@mst.edu).  \nThis article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.  \nIEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 1  \nIn-Plane and Out-of-Plane 2-D Microdisplacement Sensor Based on a Single Microwave Resonator  \nWith Machine Learning  \nShiyu Li, Member, IEEE, Osamah Alsalman, Jie Huang, Senior Member, IEEE,  \nand Chen Zhu, Member, IEEE  \nAbstract—Microwave displacement sensors have garnered significant research interest in recent years and have found successful applications in industrial automation and aerospace engineering. However, most microwave sensors are limited to measuring in-plane displacement, with the assumption that out-of-plane displacement remains constant during operation. In this work, we propose and experimentally demonstrate a novel concept for 2-D microdisplacement sensing that simultaneously measures both in-plane and out-of-plane displacement. We developed a proof-of-concept sensor system based on a custom-made coaxial cable resonator (CCR) serving as the stator and a rubber-metal heterogeneous plate as the movable part. The in-plane and out-of-plane micromovements of the plate relative to the CCR’s open-end plane were successfully detected by monitoring the fundamental resonant frequency of the CCR. Additionally, machine learning-based analysis was employed to decouple the CCR’s responses to the 2-D displacement, enabling independent and accurate quantification of both in-plane and outof-plane displacements. Our strategy combines the heterogeneous plate, which adds spatial information, with machine learning analysis for response decoupling, thereby paving the way for the development of multidimensional sensing systems using a simple 1-D sensor device. The resulting 2-D displacement sensor has the potential to be extended for measuring other 2-D physical and mechanical parameters, such as vibration and acceleration.  \nIndex Terms—Coaxial cable, coaxial cable resonator (CCR), displacement sensor, machine learning, microwave resonator, 2-D sensor.  \nReceived 2 October 2024; revised 11 November 2024; accepted 24 November 2024 . This work was supported in part by the Research Initiation Project of Zhejiang Laboratory under Grant 2022ME0PI01; in part by the Natural Science Foundation of Jiangsu Province under Grant BK202","cbCaioooBdr7BJHy","https://ap.wps.com/l/cbCaioooBdr7BJHy","pdf",5819695,5,1,15,"English","en",105,"# Abstract\n# Index Terms\n# Introduction\n## Background and related displacement sensing technologies","[{\"question\":\"What limitation of existing microwave displacement sensors motivates this work?\",\"answer\":\"Most microwave sensors measure only in-plane displacement and assume out-of-plane displacement remains constant during operation.\"},{\"question\":\"How does the proposed sensor measure both in-plane and out-of-plane displacement?\",\"answer\":\"It monitors the fundamental resonant frequency of a coaxial cable resonator system where the movable heterogeneous plate performs both in-plane and out-of-plane micromovements relative to the resonator plane.\"},{\"question\":\"What role does machine learning play in the sensing method?\",\"answer\":\"Machine learning-based analysis decouples the resonator’s responses to the 2-D displacement, enabling independent and accurate quantification of both components.\"}]","In-Plane and Out-of-Plane 2-D Microdisplacement Sensor Based on a Single Microwave Resonator - Machine Learning | PDF",1785902934,38,{"code":4,"msg":32,"data":33},"ok",{"site_id":25,"language":24,"slug":34,"title":13,"keywords":35,"description":14,"schema_data":36,"social_meta":88,"head_meta":90,"extra_data":92,"updated_unix":29},"in-plane-and-out-of-plane-2-d-microdisplacement-sensor-based-on-a-single-microwave-resonator-machine-learning","",{"@graph":37,"@context":87},[38,55,70],{"@type":39,"itemListElement":40},"BreadcrumbList",[41,45,49,52],{"item":42,"name":43,"@type":44,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":46,"name":47,"@type":44,"position":48},"https://docshare.wps.com/document/","Document",2,{"item":50,"name":12,"@type":44,"position":51},"https://docshare.wps.com/document/research-report/",3,{"item":53,"name":13,"@type":44,"position":54},"https://docshare.wps.com/document/in-plane-and-out-of-plane-2-d-microdisplacement-sensor-based-on-a-single-microwave-resonator-machine-learning/126076/",4,{"url":53,"name":13,"@type":56,"author":57,"headline":13,"publisher":59,"fileFormat":62,"inLanguage":24,"description":14,"dateModified":63,"datePublished":64,"encodingFormat":62,"isAccessibleForFree":65,"interactionStatistic":66},"DigitalDocument",{"name":9,"@type":58},"Person",{"url":42,"name":60,"@type":61},"DocShare","Organization","application/pdf","2026-08-21","2026-08-05",true,{"@type":67,"interactionType":68,"userInteractionCount":20},"InteractionCounter",{"@type":69},"ViewAction",{"@type":71,"mainEntity":72},"FAQPage",[73,79,83],{"name":74,"@type":75,"acceptedAnswer":76},"What limitation of existing microwave displacement sensors motivates this work?","Question",{"text":77,"@type":78},"Most microwave sensors measure only in-plane displacement and assume out-of-plane displacement remains constant during operation.","Answer",{"name":80,"@type":75,"acceptedAnswer":81},"How does the proposed sensor measure both in-plane and out-of-plane displacement?",{"text":82,"@type":78},"It monitors the fundamental resonant frequency of a coaxial cable resonator system where the movable heterogeneous plate performs both in-plane and out-of-plane micromovements relative to the resonator plane.",{"name":84,"@type":75,"acceptedAnswer":85},"What role does machine learning play in the sensing method?",{"text":86,"@type":78},"Machine learning-based analysis decouples the resonator’s responses to the 2-D displacement, enabling independent and accurate quantification of both components.","https://schema.org",{"og:url":53,"og:type":89,"og:title":13,"og:site_name":60,"og:description":14},"article",{"robots":91,"canonical":53},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":94},[95,99,103,107,111,116,121,124,129,132,136],{"id":21,"doc_module":4,"doc_module_name":47,"category_name":96,"show_sort_weight":97,"slug":98},"Story & Novel",90,"story-novel",{"id":48,"doc_module":4,"doc_module_name":47,"category_name":100,"show_sort_weight":101,"slug":102},"Literature",80,"literature",{"id":54,"doc_module":4,"doc_module_name":47,"category_name":104,"show_sort_weight":105,"slug":106},"Exam",70,"exam",{"id":20,"doc_module":4,"doc_module_name":47,"category_name":108,"show_sort_weight":109,"slug":110},"Comic",60,"comic",{"id":112,"doc_module":4,"doc_module_name":47,"category_name":113,"show_sort_weight":114,"slug":115},6,"Technology",50,"technology",{"id":117,"doc_module":4,"doc_module_name":47,"category_name":118,"show_sort_weight":119,"slug":120},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":47,"category_name":12,"show_sort_weight":122,"slug":123},30,"research-report",{"id":125,"doc_module":4,"doc_module_name":47,"category_name":126,"show_sort_weight":127,"slug":128},9,"Religion & Spirituality",20,"religion-spirituality",{"id":127,"doc_module":4,"doc_module_name":47,"category_name":130,"show_sort_weight":127,"slug":131},"World Cup","world-cup",{"id":133,"doc_module":4,"doc_module_name":47,"category_name":134,"show_sort_weight":133,"slug":135},10,"Lifestyle","lifestyle",{"id":137,"doc_module":4,"doc_module_name":47,"category_name":138,"show_sort_weight":20,"slug":139},19,"General","general"]