{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T14:56:06Z","timestamp":1781621766339,"version":"3.54.5"},"reference-count":35,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2019,8,29]],"date-time":"2019-08-29T00:00:00Z","timestamp":1567036800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Wavenumber imaging with Green\u2019s function reconstruction of ultrasonic diffuse fields is used to realize fast imaging of near-surface defects in rails. Ultrasonic phased array has been widely used in industries because of its high sensitivity and strong flexibility. However, the directly measured signal is always complicated by noise caused by physical limitations of the acquisition system. To overcome this problem, the cross-correlations of the diffuse field signals captured by the probe are performed to reconstruct the Green\u2019s function. These reconstructed signals can restore the early time information from the noise. Experiments were conducted on rails with near-surface defects. The results confirm the effectiveness of the cross-correlation method to reconstruct the Green\u2019s function for the detection of near-surface defects. Different kinds of ultrasonic phased array probes were applied to collect experimental data on the surface of the rails. The Green\u2019s function recovery is related to the number of phased array elements and the excitation frequency. In addition, the duration and starting time of the time-windowed diffuse signals were explored in order to achieve high-quality defect images.<\/jats:p>","DOI":"10.3390\/s19173744","type":"journal-article","created":{"date-parts":[[2019,8,29]],"date-time":"2019-08-29T11:26:22Z","timestamp":1567077982000},"page":"3744","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Wavenumber Imaging of Near-Surface Defects in Rails using Green\u2019s Function Reconstruction of Ultrasonic Diffuse Fields"],"prefix":"10.3390","volume":"19","author":[{"given":"Hui","family":"Zhang","sequence":"first","affiliation":[{"name":"School Institute for Advanced Communication and Data Science, School of Communication and Information Engineering, Shanghai University, Shanghai 200444, China"},{"name":"School of Urban Railway Transportation, Shanghai University of Engineering Science, Shanghai 201620, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haiyan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School Institute for Advanced Communication and Data Science, School of Communication and Information Engineering, Shanghai University, Shanghai 200444, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiayan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School Institute for Advanced Communication and Data Science, School of Communication and Information Engineering, Shanghai University, Shanghai 200444, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianquan","family":"Liu","sequence":"additional","affiliation":[{"name":"School Institute for Advanced Communication and Data Science, School of Communication and Information Engineering, Shanghai University, Shanghai 200444, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenfa","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Urban Railway Transportation, Shanghai University of Engineering Science, Shanghai 201620, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7828-8054","authenticated-orcid":false,"given":"Guopeng","family":"Fan","sequence":"additional","affiliation":[{"name":"School Institute for Advanced Communication and Data Science, School of Communication and Information Engineering, Shanghai University, Shanghai 200444, China"},{"name":"School of Urban Railway Transportation, Shanghai University of Engineering Science, Shanghai 201620, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qi","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Mechatronic and Automation Engineering, Shanghai University, Shanghai 200444, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,29]]},"reference":[{"key":"ref_1","unstructured":"Rose, J.L. 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