{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T18:45:06Z","timestamp":1775846706747,"version":"3.50.1"},"reference-count":37,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2023,7,19]],"date-time":"2023-07-19T00:00:00Z","timestamp":1689724800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Postdoctoral Research Project of PetroChina Southwest Oil &amp; Gas Field Company","award":["20220308-08"],"award-info":[{"award-number":["20220308-08"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, a Comprehensive Diagram Method (CDM) for a Multi-Layer Perceptron Neuron Network (MLPNN) is proposed to realize natural gas energy metering using temperature, pressure, and the speed of sound from an ultrasonic flowmeter. Training and testing of the MLPNN model were performed on the basis of 1003 real data points describing the compression factors (Z-factors) and calorific values of the three main components of natural gas in Sichuan province, China. Moreover, 20 days of real tests were conducted to verify the measurements\u2019 accuracy and the adaptability of the new intelligent method. Based on the values of the Mean Relative Errors and the Root Mean Square errors for the learning and test errors calculated on the basis of the actual data, the best-quality MLP 3-5-1 network for the metering of Z-factors and the new CDM methods for the metering of calorific values were experimentally selected. The Bayesian regularized MLPNN (BR-MLPNN) 3-5-1 network showed that the Z-factors of natural gas have a maximum relative error of \u22120.44%, and the new CDM method revealed calorific values with a maximum relative error of 1.90%. In addition, three local tests revealed that the maximum relative error of the daily cumulative amount of natural gas energy was 2.39%.<\/jats:p>","DOI":"10.3390\/s23146528","type":"journal-article","created":{"date-parts":[[2023,7,19]],"date-time":"2023-07-19T21:22:58Z","timestamp":1689801778000},"page":"6528","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Research on a Hybrid Intelligent Method for Natural Gas Energy Metering"],"prefix":"10.3390","volume":"23","author":[{"given":"Jingya","family":"Dong","sequence":"first","affiliation":[{"name":"Natural Gas Research Institute, PetroChina & Southwest Oil and Gas Field Company, Chengdu 610213, China"},{"name":"School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bin","family":"Song","sequence":"additional","affiliation":[{"name":"Natural Gas Research Institute, PetroChina & Southwest Oil and Gas Field Company, Chengdu 610213, China"},{"name":"Key Laboratory of Natural Gas Quality Control & Energy Metering Measurement for State Market Regulation, Chengdu 610095, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fei","family":"He","sequence":"additional","affiliation":[{"name":"Natural Gas Research Institute, PetroChina & Southwest Oil and Gas Field Company, Chengdu 610213, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yingying","family":"Xu","sequence":"additional","affiliation":[{"name":"Natural Gas Research Institute, PetroChina & Southwest Oil and Gas Field Company, Chengdu 610213, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiang","family":"Wang","sequence":"additional","affiliation":[{"name":"Natural Gas Research Institute, PetroChina & Southwest Oil and Gas Field Company, Chengdu 610213, China"},{"name":"Key Laboratory of Natural Gas Quality Control & Energy Metering Measurement for State Market Regulation, Chengdu 610095, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wanjun","family":"Li","sequence":"additional","affiliation":[{"name":"Natural Gas Research Institute, PetroChina & Southwest Oil and Gas Field Company, Chengdu 610213, China"},{"name":"Key Laboratory of Natural Gas Quality Control & Energy Metering Measurement for State Market Regulation, Chengdu 610095, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peng","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.flowmeasinst.2015.01.006","article-title":"Uncertainty analysis of energy measurements in natural gas transmission networks","volume":"42","author":"Ficco","year":"2015","journal-title":"Flow Meas. 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