{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T23:14:35Z","timestamp":1773443675885,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,12,25]],"date-time":"2020-12-25T00:00:00Z","timestamp":1608854400000},"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>Indirect measurement can be used as an alternative to obtain a desired quantity, whose physical positioning or use of a direct sensor in the plant is expensive or not possible. This procedure can been improved by means of feedback control strategies of a secondary variable, which can be measured and controlled. Its main advantage is a new form of dynamic response, with improvements in the response time of the measurement of the quantity of interest. In water pumping networks, this methodology can be employed for measuring the flow indirectly, which can be advantageous due to the high price of flow sensors and the operational complexity to install them in pipelines. In this work, we present the use of artificial intelligence techniques in the implementation of the feedback system for indirect flow measurement. Among the contributions of this new technique is the design of the pressure controller using the Fuzzy logic theory, which rules out the need for knowing the plant model, as well as the use of an artificial neural network for the construction of nonlinear models with the purpose of indirectly estimating the flow. The validation of the proposed approach was carried out through experimental tests in a water pumping system, fully automated and installed at the Laboratory of Hydraulic and Energy Efficiency in Sanitation at the Federal University of Paraiba (LENHS\/UFPB). The results were compared with an electromagnetic flow sensor present in the system, obtaining a maximum relative error of 10%.<\/jats:p>","DOI":"10.3390\/s21010075","type":"journal-article","created":{"date-parts":[[2020,12,25]],"date-time":"2020-12-25T09:30:19Z","timestamp":1608888619000},"page":"75","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Indirect Feedback Measurement of Flow in a Water Pumping Network Employing Artificial Intelligence"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2808-8529","authenticated-orcid":false,"given":"Thommas Kevin Sales","family":"Flores","sequence":"first","affiliation":[{"name":"Renewable and Alternatives Energies Center (CEAR), Electrical Engineering Department (DEE), Campus I, Federal University of Paraiba (UFPB), Joao Pessoa 58058-600, PB, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8760-9390","authenticated-orcid":false,"given":"Juan Moises Mauricio","family":"Villanueva","sequence":"additional","affiliation":[{"name":"Renewable and Alternatives Energies Center (CEAR), Electrical Engineering Department (DEE), Campus I, Federal University of Paraiba (UFPB), Joao Pessoa 58058-600, PB, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8374-1469","authenticated-orcid":false,"given":"Heber P.","family":"Gomes","sequence":"additional","affiliation":[{"name":"Technology Center (CT), Department of Civil and Environmental Engineering (DECV), Campus I, Federal University of Paraiba (UFPB), Joao Pessoa 58058-600, PB, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9599-9552","authenticated-orcid":false,"given":"Sebastian Y. C.","family":"Catunda","sequence":"additional","affiliation":[{"name":"Computer and Automation Engineering Department (DCA), Federal University of Rio Grande do Norte, Natal 59078-970, RN, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.engappai.2014.01.008","article-title":"Combining learning in model space fault diagnosis with data validation\/reconstruction: Application to the Barcelona water network","volume":"30","author":"Quevedo","year":"2014","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"87","DOI":"10.2166\/aqua.2019.043","article-title":"Estimation of costs for monitoring urban water and wastewater networks","volume":"68","author":"Cabral","year":"2019","journal-title":"J. Water Supply Res. Technol. Aqua"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1051\/e3sconf\/20184400051","article-title":"Analysis of the water meter management of the urban-rural water supply system","volume":"44","year":"2018","journal-title":"E3S Web Conf."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.enbuild.2016.02.003","article-title":"TDevelopment of a virtual pump water flow meter with a flow rate function of motor power and pump head","volume":"117","author":"Wang","year":"2016","journal-title":"Energy Build."},{"key":"ref_5","first-page":"142","article-title":"Mathematical model for efficient water flow management. Nonlinear Analysis: Real World Applications","volume":"10","author":"Vladimir","year":"2008","journal-title":"J. Abbr."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1016\/j.measurement.2017.03.040","article-title":"Measurement plus observation\u2014A new structure in metrology","volume":"126","author":"Ruhm","year":"2018","journal-title":"Measurement"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"148","DOI":"10.4314\/njt.v36i1.19","article-title":"Water demand prediction using artificial neural network for supervisory control","volume":"36","author":"Gwaivangmin","year":"2017","journal-title":"Niger. J. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"01004","DOI":"10.1051\/matecconf\/201929501004","article-title":"Prediction of water consumption using Artificial Neural Networks modelling (ANN)","volume":"295","author":"Farah","year":"2019","journal-title":"MATEC Web Conf."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1016\/j.proeng.2014.02.045","article-title":"Using artificial neural network models to assess water quality in water distribution networks","volume":"70","author":"Cordoba","year":"2014","journal-title":"Procedia Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"23","DOI":"10.3233\/IDA-2001-5103","article-title":"A neural network-based software sensor for coagulation control in a water treatment plant","volume":"5","author":"Valentin","year":"2001","journal-title":"Intell. Data Anal."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/j.ifacol.2018.06.376","article-title":"A machine learning approach for virtual flow metering and forecasting","volume":"51","author":"Andrianov","year":"2018","journal-title":"IFAC-PapersOnLine"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1204","DOI":"10.1109\/JSEN.2018.2882239","article-title":"Recent advances in multifunctional sensing technology on a perspective of multi-sensor system: A review","volume":"19","author":"Majumder","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"212018","DOI":"10.1088\/1742-6596\/1065\/21\/212018","article-title":"Dynamic measurement and its relation to metrology, mathematical theory and signal processing: A review","volume":"1065","author":"Ruhm","year":"2018","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1109\/19.293425","article-title":"Unified approach to measurand reconstruction","volume":"43","author":"Morawski","year":"1994","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_15","first-page":"1","article-title":"Optimization methods for water supply SCADA system","volume":"7","author":"Babunski","year":"2018","journal-title":"Mediterr. Conf. Embed. Comput."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Roman, R.C., Precup, R.E., and Petriu, E.M. (2020). Hybrid data-driven Fuzzy active disturbance rejection control for tower crane systems. Eur. J. Control.","DOI":"10.1016\/j.ejcon.2020.08.001"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Kim, D., Lee, J., Chung, W.Y., and Lee, J. (2020). Artificial Intelligence-Based Optimal Grasping Control. Sensors, 20.","DOI":"10.3390\/s20216390"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Gonz\u00e1lez, B., Jim\u00e9nez, F.J., and De Frutos, J. (2020). A virtual instrument for road vehicle classification based on piezoelectric transducers. Sensors, 20.","DOI":"10.3390\/s20164597"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"864","DOI":"10.1109\/19.779191","article-title":"Feedback control method for estimating the oxygen uptake rate in activated sludge systems","volume":"48","author":"Catunda","year":"1999","journal-title":"J. IEEE Trans. Instrum. Meas."},{"key":"ref_20","first-page":"1746","article-title":"Flow meter data validation and reconstruction using neural networks: Application to the Barcelona water network","volume":"1","author":"Rodriguez","year":"2016","journal-title":"Eur. Control Conf. (ECC)"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1080\/1573062X.2014.988733","article-title":"Water distribution systems flow monitoring and anomalous event detection: A practical approach","volume":"13","author":"Loureiro","year":"2016","journal-title":"Urban Water J."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"161904","DOI":"10.1063\/1.4802799","article-title":"Graphene based piezoresistive pressure sensor","volume":"102","author":"Zhu","year":"2013","journal-title":"Appl. Phys. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1007\/s11269-014-0836-3","article-title":"ydropower potential in water distribution networks: Pressure control by PATs","volume":"29","author":"Fecarotta","year":"2015","journal-title":"Water Resour. Manag."},{"key":"ref_24","first-page":"142","article-title":"TImplementation of Fuzzy and PID controller to water level system using LabView","volume":"116","author":"Sabri","year":"2015","journal-title":"Int. J. Comput. Appl."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Camboim, M.M., Villanueva, J.M.M., and de Souza, C.P. (2020). Fuzzy Controller Applied to a Remote Energy Harvesting Emulation Platform. Sensors, 20.","DOI":"10.3390\/s20205874"},{"key":"ref_26","first-page":"148","article-title":"Fuzzy logic with engineering applications","volume":"Volume 2","author":"Ross","year":"2004","journal-title":"Fuzzy Logic with Engineering Applications"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/s12053-014-9292-4","article-title":"Dynamic modeling and simulation of a water supply system with applications for improving energy efficiency","volume":"8","author":"Diniz","year":"2015","journal-title":"Energy Effic."},{"key":"ref_28","unstructured":"Barker, G.B. (2017). The Engineer\u2019s Guide to Plant Layout and Piping Design for the Oil and Gas Industries, Gulf Professional Publishing."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.ifacol.2015.09.162","article-title":"Water distribution network modeling based on NARX","volume":"48","author":"Xu","year":"2015","journal-title":"IFAC-PapersOnLine"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"989","DOI":"10.1109\/72.329697","article-title":"Training feedforward networks with the Marquardt algorithm","volume":"5","author":"Hagan","year":"1994","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Liu, H. (2010, January 10\u201312). On the Levenberg-Marquardt training method for feed-forward neural networks. Proceedings of the 2010 Sixth International Conference on Natural Computation, Yantai, China.","DOI":"10.1109\/ICNC.2010.5583151"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/1\/75\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:46:01Z","timestamp":1760179561000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/1\/75"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,25]]},"references-count":31,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["s21010075"],"URL":"https:\/\/doi.org\/10.3390\/s21010075","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12,25]]}}}