{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T00:32:32Z","timestamp":1760401952375,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2020,4,30]],"date-time":"2020-04-30T00:00:00Z","timestamp":1588204800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012639","name":"Prince Sultan University","doi-asserted-by":"publisher","award":["TBA"],"award-info":[{"award-number":["TBA"]}],"id":[{"id":"10.13039\/501100012639","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, a gradient descent algorithm is proposed for the parameter estimation of multi-input and multi-output (MIMO) total non-linear dynamic models. Firstly, the MIMO total non-linear model is mapped to a non-completely connected feedforward neural network, that is, the parameters of the total non-linear model are mapped to the connection weights of the neural network. Then, based on the minimization of network error, a weight-updating algorithm, that is, an estimation algorithm of model parameters, is proposed with the convergence conditions of a non-completely connected feedforward network. In further determining the variables of the model set, a method of model structure detection is proposed for selecting a group of important items from the whole variable candidate set. In order to verify the usefulness of the parameter identification process, we provide a virtual bench test example for the numerical analysis and user-friendly instructions for potential applications.<\/jats:p>","DOI":"10.3390\/e22050510","type":"journal-article","created":{"date-parts":[[2020,5,4]],"date-time":"2020-05-04T03:29:39Z","timestamp":1588562979000},"page":"510","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Neural Computing Enhanced Parameter Estimation for Multi-Input and Multi-Output Total Non-Linear Dynamic Models"],"prefix":"10.3390","volume":"22","author":[{"given":"Longlong","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Ocean University of China, Qingdao 266000, China"}]},{"given":"Di","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Ocean University of China, Qingdao 266000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7869-6373","authenticated-orcid":false,"given":"Ahmad Taher","family":"Azar","sequence":"additional","affiliation":[{"name":"Robotics and Internet-of-Things Lab (RIOTU), Prince Sultan University, Riyadh 11586, Saudi Arabia"},{"name":"Faculty of Computers and Artificial Intelligence, Benha University, 13511 Benha, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8173-1179","authenticated-orcid":false,"given":"Quanmin","family":"Zhu","sequence":"additional","affiliation":[{"name":"Department of Engineering Design and Mathematics, University of the West of England, Frenchy Campus Coldharbour Lane, Bristol BS16 1QY, UK"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1080\/00207728908910143","article-title":"Identification of non-linear rational systems using a prediction-error estimation algorithm","volume":"20","author":"Billings","year":"1989","journal-title":"Int. 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