Sparse Magnetic Array for the Imaging of Defects in Multilayer Metals
This study presents a novel eddy current sensing method for imaging defect distribution in multilayered nonferrous metal plates using an array of magnetic sensors. This method involves dividing the metal plate into small voxels to facilitate reconstruction and uses multifrequency to excite the coil....
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Veröffentlicht in: | IEEE sensors journal 2024-05, Vol.24 (9), p.14082-14092 |
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description | This study presents a novel eddy current sensing method for imaging defect distribution in multilayered nonferrous metal plates using an array of magnetic sensors. This method involves dividing the metal plate into small voxels to facilitate reconstruction and uses multifrequency to excite the coil. For each frequency, reconstructing defects from magnetic flux density (MFD) measurements is formulated as a linear inverse problem. The absence or presence of a defect strongly suggests that the solution to the linear inverse problem is binary. This study develops an algorithm under a statistical framework to solve the linear inverse problem with binary constraints. The algorithm introduces a Bernoulli prior over the hidden variables and uses a variational Bayesian inference (VBI) to analytically approximate the posterior probability of the hidden variables conditioned on the observed data. The effectiveness of the proposed method is demonstrated using numerically simulated data and a prototype consisting of a coil and an 8\times8 array of magnetic sensors with 4 mm intervals. The results demonstrate that the method is feasible for imaging defects of 2 mm with a depth resolution of 0.5 mm. |
doi_str_mv | 10.1109/JSEN.2024.3381623 |
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This method involves dividing the metal plate into small voxels to facilitate reconstruction and uses multifrequency to excite the coil. For each frequency, reconstructing defects from magnetic flux density (MFD) measurements is formulated as a linear inverse problem. The absence or presence of a defect strongly suggests that the solution to the linear inverse problem is binary. This study develops an algorithm under a statistical framework to solve the linear inverse problem with binary constraints. The algorithm introduces a Bernoulli prior over the hidden variables and uses a variational Bayesian inference (VBI) to analytically approximate the posterior probability of the hidden variables conditioned on the observed data. The effectiveness of the proposed method is demonstrated using numerically simulated data and a prototype consisting of a coil and an <inline-formula> <tex-math notation="LaTeX">8\times8 </tex-math></inline-formula> array of magnetic sensors with 4 mm intervals. The results demonstrate that the method is feasible for imaging defects of 2 mm with a depth resolution of 0.5 mm.</description><identifier>ISSN: 1530-437X</identifier><identifier>EISSN: 1558-1748</identifier><identifier>DOI: 10.1109/JSEN.2024.3381623</identifier><identifier>CODEN: ISJEAZ</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Algorithms ; Bayesian analysis ; Bernoulli Bayesian learning (BBL) ; Coils ; Conditional probability ; defect imaging ; Defects ; eddy current testing (ECT) ; Eddy currents ; Flux density ; Image reconstruction ; Imaging ; Inverse problems ; Magnetic flux ; Magnetic sensors ; Metal plates ; Metals ; Multilayers ; Nonferrous metals ; Sensor arrays ; Sensors ; Statistical analysis ; Statistical inference</subject><ispartof>IEEE sensors journal, 2024-05, Vol.24 (9), p.14082-14092</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2024</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c246t-e2f2bbe6c93b668f17792b7b7bdb066b4b8049a96611c0e16ab9c75197fcfd683</cites><orcidid>0009-0005-9899-3753 ; 0000-0003-4585-5881</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/10487644$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27903,27904,54737</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/10487644$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Li, Wei-Chen</creatorcontrib><creatorcontrib>Lin, Chun-Yeon</creatorcontrib><title>Sparse Magnetic Array for the Imaging of Defects in Multilayer Metals</title><title>IEEE sensors journal</title><addtitle>JSEN</addtitle><description>This study presents a novel eddy current sensing method for imaging defect distribution in multilayered nonferrous metal plates using an array of magnetic sensors. This method involves dividing the metal plate into small voxels to facilitate reconstruction and uses multifrequency to excite the coil. For each frequency, reconstructing defects from magnetic flux density (MFD) measurements is formulated as a linear inverse problem. The absence or presence of a defect strongly suggests that the solution to the linear inverse problem is binary. This study develops an algorithm under a statistical framework to solve the linear inverse problem with binary constraints. The algorithm introduces a Bernoulli prior over the hidden variables and uses a variational Bayesian inference (VBI) to analytically approximate the posterior probability of the hidden variables conditioned on the observed data. The effectiveness of the proposed method is demonstrated using numerically simulated data and a prototype consisting of a coil and an <inline-formula> <tex-math notation="LaTeX">8\times8 </tex-math></inline-formula> array of magnetic sensors with 4 mm intervals. The results demonstrate that the method is feasible for imaging defects of 2 mm with a depth resolution of 0.5 mm.</description><subject>Algorithms</subject><subject>Bayesian analysis</subject><subject>Bernoulli Bayesian learning (BBL)</subject><subject>Coils</subject><subject>Conditional probability</subject><subject>defect imaging</subject><subject>Defects</subject><subject>eddy current testing (ECT)</subject><subject>Eddy currents</subject><subject>Flux density</subject><subject>Image reconstruction</subject><subject>Imaging</subject><subject>Inverse problems</subject><subject>Magnetic flux</subject><subject>Magnetic sensors</subject><subject>Metal plates</subject><subject>Metals</subject><subject>Multilayers</subject><subject>Nonferrous metals</subject><subject>Sensor arrays</subject><subject>Sensors</subject><subject>Statistical analysis</subject><subject>Statistical inference</subject><issn>1530-437X</issn><issn>1558-1748</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNpNkE9PAjEQxRujiYh-ABMPTTwv9t-22yNBVAzoAU28NW2Z4hLYxbYc-PbuBg9mDm8O7828_BC6pWREKdEPr8vp24gRJkacV1QyfoYGtCyrgipRnfc7J4Xg6usSXaW0IYRqVaoBmi73NibAC7tuINcej2O0RxzaiPM34NnOrutmjduAHyGAzwnXDV4ctrne2iNEvIBst-kaXYRO4OZPh-jzafoxeSnm78-zyXheeCZkLoAF5hxIr7mTsgpUKc2c6mbliJROuIoIbbWUlHoCVFqnvSq7qsGHlaz4EN2f7u5j-3OAlM2mPcSme2l4lxSacUU7Fz25fGxTihDMPtY7G4-GEtPTMj0t09Myf7S6zN0pUwPAP7-olBSC_wLSPmUz</recordid><startdate>20240501</startdate><enddate>20240501</enddate><creator>Li, Wei-Chen</creator><creator>Lin, Chun-Yeon</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SP</scope><scope>7U5</scope><scope>8FD</scope><scope>L7M</scope><orcidid>https://orcid.org/0009-0005-9899-3753</orcidid><orcidid>https://orcid.org/0000-0003-4585-5881</orcidid></search><sort><creationdate>20240501</creationdate><title>Sparse Magnetic Array for the Imaging of Defects in Multilayer Metals</title><author>Li, Wei-Chen ; Lin, Chun-Yeon</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c246t-e2f2bbe6c93b668f17792b7b7bdb066b4b8049a96611c0e16ab9c75197fcfd683</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Algorithms</topic><topic>Bayesian analysis</topic><topic>Bernoulli Bayesian learning (BBL)</topic><topic>Coils</topic><topic>Conditional probability</topic><topic>defect imaging</topic><topic>Defects</topic><topic>eddy current testing (ECT)</topic><topic>Eddy currents</topic><topic>Flux density</topic><topic>Image reconstruction</topic><topic>Imaging</topic><topic>Inverse problems</topic><topic>Magnetic flux</topic><topic>Magnetic sensors</topic><topic>Metal plates</topic><topic>Metals</topic><topic>Multilayers</topic><topic>Nonferrous metals</topic><topic>Sensor arrays</topic><topic>Sensors</topic><topic>Statistical analysis</topic><topic>Statistical inference</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Li, Wei-Chen</creatorcontrib><creatorcontrib>Lin, Chun-Yeon</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005–Present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998–Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>CrossRef</collection><collection>Electronics & Communications Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>IEEE sensors journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Li, Wei-Chen</au><au>Lin, Chun-Yeon</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Sparse Magnetic Array for the Imaging of Defects in Multilayer Metals</atitle><jtitle>IEEE sensors journal</jtitle><stitle>JSEN</stitle><date>2024-05-01</date><risdate>2024</risdate><volume>24</volume><issue>9</issue><spage>14082</spage><epage>14092</epage><pages>14082-14092</pages><issn>1530-437X</issn><eissn>1558-1748</eissn><coden>ISJEAZ</coden><abstract>This study presents a novel eddy current sensing method for imaging defect distribution in multilayered nonferrous metal plates using an array of magnetic sensors. This method involves dividing the metal plate into small voxels to facilitate reconstruction and uses multifrequency to excite the coil. For each frequency, reconstructing defects from magnetic flux density (MFD) measurements is formulated as a linear inverse problem. The absence or presence of a defect strongly suggests that the solution to the linear inverse problem is binary. This study develops an algorithm under a statistical framework to solve the linear inverse problem with binary constraints. The algorithm introduces a Bernoulli prior over the hidden variables and uses a variational Bayesian inference (VBI) to analytically approximate the posterior probability of the hidden variables conditioned on the observed data. The effectiveness of the proposed method is demonstrated using numerically simulated data and a prototype consisting of a coil and an <inline-formula> <tex-math notation="LaTeX">8\times8 </tex-math></inline-formula> array of magnetic sensors with 4 mm intervals. The results demonstrate that the method is feasible for imaging defects of 2 mm with a depth resolution of 0.5 mm.</abstract><cop>New York</cop><pub>IEEE</pub><doi>10.1109/JSEN.2024.3381623</doi><tpages>11</tpages><orcidid>https://orcid.org/0009-0005-9899-3753</orcidid><orcidid>https://orcid.org/0000-0003-4585-5881</orcidid></addata></record> |
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subjects | Algorithms Bayesian analysis Bernoulli Bayesian learning (BBL) Coils Conditional probability defect imaging Defects eddy current testing (ECT) Eddy currents Flux density Image reconstruction Imaging Inverse problems Magnetic flux Magnetic sensors Metal plates Metals Multilayers Nonferrous metals Sensor arrays Sensors Statistical analysis Statistical inference |
title | Sparse Magnetic Array for the Imaging of Defects in Multilayer Metals |
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