{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T08:16:27Z","timestamp":1770279387835,"version":"3.49.0"},"reference-count":44,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2019,12,5]],"date-time":"2019-12-05T00:00:00Z","timestamp":1575504000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Research and Development Program of Shandong","award":["2019GGX104037"],"award-info":[{"award-number":["2019GGX104037"]}]},{"name":"Shandong Provincial Natural Science Foundation of China","award":["ZR2017MF064"],"award-info":[{"award-number":["ZR2017MF064"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, normalized mutual information feature selection (NMIFS) and tabu search (TS) are integrated to develop a new variable selection algorithm for soft sensors. NMIFS is applied to select influential variables contributing to the output variable and avoids selecting redundant variables by calculating mutual information (MI). A TS based strategy is designed to prevent NMIFS from falling into a local optimal solution. The proposed algorithm performs the variable selection by combining the entropy information and MI and validating error information of artificial neural networks (ANNs); therefore, it has advantages over previous MI-based variable selection algorithms. Several simulation datasets with different scales, correlations and noise parameters are implemented to demonstrate the performance of the proposed algorithm. A set of actual production data from a power plant is also used to check the performance of these algorithms. The experiments showed that the developed variable selection algorithm presents better model accuracy with fewer selected variables, compared with other state-of-the-art methods. The application of this algorithm to soft sensors can achieve reliable results.<\/jats:p>","DOI":"10.3390\/s19245368","type":"journal-article","created":{"date-parts":[[2019,12,5]],"date-time":"2019-12-05T11:16:23Z","timestamp":1575544583000},"page":"5368","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["An Improved Normalized Mutual Information Variable Selection Algorithm for Neural Network-Based Soft Sensors"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9482-470X","authenticated-orcid":false,"given":"Kai","family":"Sun","sequence":"first","affiliation":[{"name":"School of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China"}]},{"given":"Pengxin","family":"Tian","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China"}]},{"given":"Huanning","family":"Qi","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China"}]},{"given":"Fengying","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China"}]},{"given":"Genke","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Automation, Shanghai Jiao Tong University, Shanghai 200240, China"},{"name":"Ningbo Artificial Intelligence Institute, Shanghai Jiao Tong University, Ningbo 315000, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"17864","DOI":"10.3390\/s141017864","article-title":"A soft sensor for bioprocess control based on sequential filtering of metabolic heat signals","volume":"14","author":"Paulsson","year":"2014","journal-title":"Sensors"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Chen, K., Liang, Y., Gao, Z., and Liu, Y. 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