{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:32:38Z","timestamp":1760232758217,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2022,11,30]],"date-time":"2022-11-30T00:00:00Z","timestamp":1669766400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003246","name":"Dutch Technology Foundation STW","doi-asserted-by":"publisher","award":["15031"],"award-info":[{"award-number":["15031"]}],"id":[{"id":"10.13039\/501100003246","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Bronkhorst","award":["15031"],"award-info":[{"award-number":["15031"]}]},{"name":"KROHNE","award":["15031"],"award-info":[{"award-number":["15031"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Ultrasonic flow meters (UFMs) based on transducer arrays offer several advantages. With electronic beam steering, it is possible to tune the steering angle of the beam for optimal signal-tonoise ratio (SNR) upon reception. Moreover, multiple beams can be generated to propagate through different travel paths, covering a wider section of the flow profile. Furthermore, in a clamp-on configuration, UFMs based on transducer arrays can perform self-calibration. In this manner, userinput is minimized and measurement repeatability is increased. In practice, transducer array elements may break down. This could happen due to aging, exposure to rough environments, and\/or rough mechanical contact. As a consequence of inactive array elements, the measured transit time difference contains two offsets. One offset originates from non-uniform spatial sampling of the generated wavefield. Another offset originates from the ill-defined beam propagating through a travel path different from the intended one. In this paper, an algorithm is proposed that corrects for both of these offsets. The algorithm also performs a filtering operation in the frequency-wavenumber domain of all spurious (i.e., flow-insensitive) wave modes. The advantage of implementing the proposed algorithm is demonstrated on simulations and measurements, showing improved accuracy and precision of the transit time differences compared to the values obtained when the algorithm is not applied. The proposed algorithm can be implemented in both in-line and clamp-on configuration of UFMs based on transducer arrays.<\/jats:p>","DOI":"10.3390\/s22239317","type":"journal-article","created":{"date-parts":[[2022,11,30]],"date-time":"2022-11-30T08:46:41Z","timestamp":1669798001000},"page":"9317","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Algorithm to Correct Measurement Offsets Introduced by Inactive Elements of Transducer Arrays in Ultrasonic Flow Metering"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3905-1206","authenticated-orcid":false,"given":"Jack","family":"Massaad","sequence":"first","affiliation":[{"name":"Laboratory of Medical Imaging, Department of Imaging Physics, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands"},{"name":"KROHNE New Technologies B.V., Kerkeplaat 12, 3313 LC Dordrecht, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4199-4374","authenticated-orcid":false,"given":"Paul L. M. J.","family":"van Neer","sequence":"additional","affiliation":[{"name":"Laboratory of Medical Imaging, Department of Imaging Physics, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands"},{"name":"Netherlands Organisation for Applied Scientific Research (TNO), Oude Waalsdorperweg 63, 2597 AK The Hague, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2297-4370","authenticated-orcid":false,"given":"Douwe M.","family":"van Willigen","sequence":"additional","affiliation":[{"name":"Netherlands Organisation for Applied Scientific Research (TNO), Oude Waalsdorperweg 63, 2597 AK The Hague, The Netherlands"},{"name":"Electronic Instrumentation Laboratory, Department of Microelectronics, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9891-4374","authenticated-orcid":false,"given":"Michiel A. P.","family":"Pertijs","sequence":"additional","affiliation":[{"name":"Electronic Instrumentation Laboratory, Department of Microelectronics, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8902-0099","authenticated-orcid":false,"given":"Nicolaas","family":"de Jong","sequence":"additional","affiliation":[{"name":"Laboratory of Medical Imaging, Department of Imaging Physics, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands"},{"name":"Erasmus MC, Thorax Center, Department of Biomedical Engineering, Doctor Molewaterplein 40, 3015 GD Rotterdam, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7441-7218","authenticated-orcid":false,"given":"Martin D.","family":"Verweij","sequence":"additional","affiliation":[{"name":"Laboratory of Medical Imaging, Department of Imaging Physics, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands"},{"name":"Erasmus MC, Thorax Center, Department of Biomedical Engineering, Doctor Molewaterplein 40, 3015 GD Rotterdam, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,30]]},"reference":[{"key":"ref_1","unstructured":"Baker, R.C. 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