{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:51:18Z","timestamp":1760151078216,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,2,19]],"date-time":"2022-02-19T00:00:00Z","timestamp":1645228800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Processes"],"abstract":"<jats:p>Data-driven sensors are techniques capable of providing real-time information of unmeasured variables based on instrument measurements. They are valuable tools in several engineering fields, from car automation to chemical processes. However, they are subject to several sources of uncertainty, and in this way, they need to be able to deal with uncertainties. A way to deal with this problem is by using soft sensors and evaluating their uncertainties. On the other hand, the advent of deep learning (DL) has been providing a powerful tool for the field of data-driven modeling. The DL presents a potential to improve the soft sensor reliability. However, the uncertainty identification of the soft sensors model is a known issue in the literature. In this scenario, this work presents a strategy to identify the uncertainty of DL models prediction based on a novel Monte Carlo uncertainties training strategy. The proposed methodology is applied to identify a Soft Sensor to provide a real-time prediction of the productivity of a chemical process. The results demonstrate that the proposed methodology can yield a soft sensor based on DL that provides reliable predictions, with precision being proven by its corresponding coverage region.<\/jats:p>","DOI":"10.3390\/pr10020409","type":"journal-article","created":{"date-parts":[[2022,2,21]],"date-time":"2022-02-21T08:34:47Z","timestamp":1645432487000},"page":"409","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Mapping Uncertainties of Soft-Sensors Based on Deep Feedforward Neural Networks through a Novel Monte Carlo Uncertainties Training Process"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1397-9628","authenticated-orcid":false,"given":"Erbet A.","family":"Costa","sequence":"first","affiliation":[{"name":"Programa de P\u00f3s-Gradua\u00e7\u00e3o em Mecatr\u00f4nica, Escola Polit\u00e9cnica (Polytechnic School), Universidade Federal da Bahia, Salvador 40210-630, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0796-8116","authenticated-orcid":false,"given":"Carine M.","family":"Rebello","sequence":"additional","affiliation":[{"name":"Laboratory of Separation and Reaction Engineering, Associate Laboratory LSRE\/LCM, Department of Chemical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"},{"name":"Programa de P\u00f3s-Gradua\u00e7\u00e3o em Engenharia Industrial, Escola Polit\u00e9cnica (Polytechnic School), Universidade Federal da Bahia, Salvador 40210-630, Brazil"}]},{"given":"Vinicius V.","family":"Santana","sequence":"additional","affiliation":[{"name":"Laboratory of Separation and Reaction Engineering, Associate Laboratory LSRE\/LCM, Department of Chemical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0715-4761","authenticated-orcid":false,"given":"Al\u00edrio E.","family":"Rodrigues","sequence":"additional","affiliation":[{"name":"Laboratory of Separation and Reaction Engineering, Associate Laboratory LSRE\/LCM, Department of Chemical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4269-1420","authenticated-orcid":false,"given":"Ana M.","family":"Ribeiro","sequence":"additional","affiliation":[{"name":"Laboratory of Separation and Reaction Engineering, Associate Laboratory LSRE\/LCM, Department of Chemical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0399-6689","authenticated-orcid":false,"given":"Leizer","family":"Schnitman","sequence":"additional","affiliation":[{"name":"Programa de P\u00f3s-Gradua\u00e7\u00e3o em Mecatr\u00f4nica, Escola Polit\u00e9cnica (Polytechnic School), Universidade Federal da Bahia, Salvador 40210-630, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0963-6449","authenticated-orcid":false,"given":"Idelfonso B. R.","family":"Nogueira","sequence":"additional","affiliation":[{"name":"Laboratory of Separation and Reaction Engineering, Associate Laboratory LSRE\/LCM, Department of Chemical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"106912","DOI":"10.1016\/j.compchemeng.2020.106912","article-title":"Predictive analytics in the petrochemical industry: Research Octane Number (RON) forecasting and analysis in an industrial catalytic reforming unit","volume":"139","author":"Dias","year":"2020","journal-title":"Comput. Chem. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1016\/j.asoc.2016.05.030","article-title":"Fuzzy c-means based support vector machines classifier for perfume recognition","volume":"46","author":"Esme","year":"2016","journal-title":"Appl. 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