{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,30]],"date-time":"2025-11-30T09:19:09Z","timestamp":1764494349058,"version":"build-2065373602"},"reference-count":46,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,8,21]],"date-time":"2024-08-21T00:00:00Z","timestamp":1724198400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Fahd University of Petroleum &amp; Minerals"},{"name":"Interdisciplinary Research Center for Sustainable Energy Systems (IRC-SES)"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this paper, we aimed to identify the dynamics of a crude distillation unit (CDU) using closed-loop data with NARX\u2212NN and the Koopman operator in both linear (KL) and bilinear (KB) forms. A comparative analysis was conducted to assess the performance of each method under different experimental conditions, such as the gain, a delay and time constant mismatch, tight constraints, nonlinearities, and poor tuning. Although NARX\u2212NN showed good training performance with the lowest Mean Squared Error (MSE), the KB demonstrated better generalization and robustness, outperforming the other methods. The KL observed a significant decline in performance in the presence of nonlinearities in inputs, yet it remained competitive with the KB under other circumstances. The use of the bilinear form proved to be crucial, as it offered a more accurate representation of CDU dynamics, resulting in enhanced performance.<\/jats:p>","DOI":"10.3390\/a17080368","type":"journal-article","created":{"date-parts":[[2024,8,22]],"date-time":"2024-08-22T06:28:51Z","timestamp":1724308131000},"page":"368","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Identification of Crude Distillation Unit: A Comparison between Neural Network and Koopman Operator"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8777-5401","authenticated-orcid":false,"given":"Abdulrazaq Nafiu","family":"Abubakar","sequence":"first","affiliation":[{"name":"Control and Instrumentation Engineering Department, King Fahd University of Petroleum and Minerals, P.O. Box 5067, Dhahran 31261, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7064-0458","authenticated-orcid":false,"given":"Mustapha Kamel","family":"Khaldi","sequence":"additional","affiliation":[{"name":"Control and Instrumentation Engineering Department, King Fahd University of Petroleum and Minerals, P.O. Box 5067, Dhahran 31261, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8441-2146","authenticated-orcid":false,"given":"Mujahed","family":"Aldhaifallah","sequence":"additional","affiliation":[{"name":"Control and Instrumentation Engineering Department, King Fahd University of Petroleum and Minerals, P.O. Box 5067, Dhahran 31261, Saudi Arabia"}]},{"given":"Rohit","family":"Patwardhan","sequence":"additional","affiliation":[{"name":"Process & Control Systems Department, Saudi Aramco, Dhahran 31311, Saudi Arabia"}]},{"given":"Hussain","family":"Salloum","sequence":"additional","affiliation":[{"name":"Process & Control Systems Department, Saudi Aramco, Dhahran 31311, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Achaw, O.-W., and Danso-Boateng, E. (2021). Crude Oil Refinery and Refinery Products, Springer International Publishing.","DOI":"10.1007\/978-3-030-79139-1_9"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"e0001","DOI":"10.1111\/roie.12383","article-title":"The impact of oil prices on trade","volume":"27","author":"Nanovsky","year":"2019","journal-title":"Rev. Int. 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