{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T19:42:32Z","timestamp":1777664552055,"version":"3.51.4"},"reference-count":17,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2018,8,1]],"date-time":"2018-08-01T00:00:00Z","timestamp":1533081600000},"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>This research put forward an exogenous liquid level measurement method based on continuous sound wave amplitude. The distribution of round piston transducers in the sound field of a metal solid was analyzed by building 15 Multi-Gaussian Beam superposition models; the calculation method for echo sound pressure was worked out according to the reflection and refraction properties of ultrasonic wave. The continuous wave with three amplitudes was used as the driving source of ultrasonic sensor, and two single-crystal sensors with the same diameter were used as the transmitting terminal and receiving terminal of ultrasonic waves to carry out experiments for four groups of containers of different wall thickness and to compare the characteristics of echo energy of driving sources with three amplitudes above and below the liquid levels with different wall thickness. Two groups of sensors of different diameters were used to measure the liquid levels of experimental models, and the measuring errors of the two groups of sensors were analyzed and compared. The experimental result shows that the measuring error of the model is less than 5 mm, so it is applicable to the level measurement of liquids or liquid mixtures in many sectors.<\/jats:p>","DOI":"10.3390\/s18082516","type":"journal-article","created":{"date-parts":[[2018,8,1]],"date-time":"2018-08-01T11:22:34Z","timestamp":1533122554000},"page":"2516","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Liquid Level Measurement Model Outside of Closed Containers Based on Continuous Sound Wave Amplitude"],"prefix":"10.3390","volume":"18","author":[{"given":"Yanjun","family":"Zhang","sequence":"first","affiliation":[{"name":"Key Laboratory of Instrumentation Science &amp; Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, China"},{"name":"Science and Technology on Electronic Test &amp; Measurement Laboratory, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bin","family":"Zhang","sequence":"additional","affiliation":[{"name":"Software School of North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0570-4683","authenticated-orcid":false,"given":"Liang","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Instrumentation Science &amp; Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, China"},{"name":"Science and Technology on Electronic Test &amp; Measurement Laboratory, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yunchao","family":"Li","sequence":"additional","affiliation":[{"name":"Key Laboratory of Instrumentation Science &amp; Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, China"},{"name":"Science and Technology on Electronic Test &amp; Measurement Laboratory, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaolong","family":"Gao","sequence":"additional","affiliation":[{"name":"Key Laboratory of Instrumentation Science &amp; Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, China"},{"name":"Science and Technology on Electronic Test &amp; Measurement Laboratory, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhaojun","family":"Liu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Instrumentation Science &amp; Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, China"},{"name":"Science and Technology on Electronic Test &amp; Measurement Laboratory, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,8,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Schmerr, L.W. (1998). Fundamentals of Ultrasonic Nondestructive Evaluation: A Modeling Approach, Plenum Press.","DOI":"10.1007\/978-1-4899-0142-2"},{"key":"ref_2","first-page":"366","article-title":"Research on Ultrasonic Liquid Level Non-contact Measurement in Sealed Vessel","volume":"133","author":"Zhang","year":"2009","journal-title":"Piezoelectric Acoust."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.sna.2006.03.008","article-title":"Reduction of blind zone in ultrasonic transmitter\/receiver sensors","volume":"133","author":"Hernandez","year":"2007","journal-title":"Sens. Actuators A Phys."},{"key":"ref_4","first-page":"58","article-title":"A detecting scope of supersonic wave is expanded with AD603","volume":"4","author":"Liu","year":"2005","journal-title":"J. Zhejiang Bus. Technol. 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