{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:46:56Z","timestamp":1760143616795,"version":"build-2065373602"},"reference-count":54,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,2,6]],"date-time":"2024-02-06T00:00:00Z","timestamp":1707177600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>This paper delves into precisely measuring liquid levels using a specific methodology with diverse real-world applications such as process optimization, quality control, fault detection and diagnosis, etc. It demonstrates the process of liquid level measurement by employing a chaotic observer, which senses multiple variables within a system. A three-dimensional computational fluid dynamics (CFD) model is meticulously created using ANSYS to explore the laminar flow characteristics of liquids comprehensively. The methodology integrates the system identification technique to formulate a third-order state\u2013space model that characterizes the system. Based on this mathematical model, we develop estimators inspired by Lorenz and Rossler\u2019s principles to gauge the liquid level under specified liquid temperature, density, inlet velocity, and sensor placement conditions. The estimated results are compared with those of an artificial neural network (ANN) model. These ANN models learn and adapt to the patterns and features in data and catch non-linear relationships between input and output variables. The accuracy and error minimization of the developed model are confirmed through a thorough validation process. Experimental setups are employed to ensure the reliability and precision of the estimation results, thereby underscoring the robustness of our liquid-level measurement methodology. In summary, this study helps to estimate unmeasured states using the available measurements, which is essential for understanding and controlling the behavior of a system. It helps improve the performance and robustness of control systems, enhance fault detection capabilities, and contribute to dynamic systems\u2019 overall efficiency and reliability.<\/jats:p>","DOI":"10.3390\/computation12020029","type":"journal-article","created":{"date-parts":[[2024,2,6]],"date-time":"2024-02-06T05:36:43Z","timestamp":1707197803000},"page":"29","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Accurate Liquid Level Measurement with Minimal Error: A Chaotic Observer Approach"],"prefix":"10.3390","volume":"12","author":[{"given":"Vighnesh","family":"Shenoy","sequence":"first","affiliation":[{"name":"Department of Instrumentation & Control Engg, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal 576104, India"},{"name":"Department of Artificial Intelligence and Data Science\/Machine Learning, Shri Madhwa Vadiraja Institute of Technology and Management, Bantakal 574115, India"}]},{"given":"Prathvi","family":"Shenoy","sequence":"additional","affiliation":[{"name":"Department of Electrical & Electronics Engg, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal 576104, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4394-5947","authenticated-orcid":false,"given":"Santhosh Krishnan","family":"Venkata","sequence":"additional","affiliation":[{"name":"Department of Instrumentation & Control Engg, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal 576104, India"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1016\/j.ces.2011.11.022","article-title":"Analysis of flow through an orifice meter: CFD simulation","volume":"71","author":"Shah","year":"2012","journal-title":"Chem. 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