{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T08:47:49Z","timestamp":1778575669876,"version":"3.51.4"},"reference-count":93,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2024,10,9]],"date-time":"2024-10-09T00:00:00Z","timestamp":1728432000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This research focused on the helicopter turboshaft engine dynamic model, identifying task solving in unsteady and transient modes (engine starting and acceleration) based on sensor data. It is known that about 85% of helicopter turboshaft engines operate in steady-state modes, while only around 15% operate in unsteady and transient modes. Therefore, developing dynamic multi-mode models that account for engine behavior during these modes is a critical scientific and practical task. The dynamic model for starting and acceleration modes has been further developed using on-board parameters recorded by sensors (gas-generator rotor r.p.m., free turbine rotor speed, gas temperature in front of the compressor turbine, fuel consumption) to achieve a 99.88% accuracy in identifying the dynamics of these parameters. An improved Elman recurrent neural network with dynamic stack memory was introduced, enhancing the robustness and increasing the performance by 2.7 times compared to traditional Elman networks. A theorem was proposed and proven, demonstrating that the total execution time for N Push and Pop operations in the dynamic stack memory does not exceed a certain value O(N). The training algorithm for the Elman network was improved using time delay considerations and Butterworth filter preprocessing, reducing the loss function from 2.5 to 0.12% over 120 epochs. The gradient diagram showed a decrease over time, indicating the model\u2019s approach to the minimum loss function, with optimal settings ensuring the stable training.<\/jats:p>","DOI":"10.3390\/s24196488","type":"journal-article","created":{"date-parts":[[2024,10,9]],"date-time":"2024-10-09T12:22:48Z","timestamp":1728476568000},"page":"6488","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Intelligent Method of Identifying the Nonlinear Dynamic Model for Helicopter Turboshaft Engines"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8009-5254","authenticated-orcid":false,"given":"Serhii","family":"Vladov","sequence":"first","affiliation":[{"name":"Department of Scientific Work Organization and Gender Issues, Kremenchuk Flight College of Kharkiv National University of Internal Affairs, 17\/6, Peremohy Street, 39605 Kremenchuk, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4267-2783","authenticated-orcid":false,"given":"Arkadiusz","family":"Banasik","sequence":"additional","affiliation":[{"name":"Department of Mathematical Methods in Technics and Informatics, Silesian University of Technology, 44-100 Gliwice, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0907-3682","authenticated-orcid":false,"given":"Anatoliy","family":"Sachenko","sequence":"additional","affiliation":[{"name":"Research Institute for Intelligent Computer Systems, West Ukrainian National University, 11 Lvivska Street, 46009 Ternopil, Ukraine"},{"name":"Department of Teleinformatics, Kazimierz Pulaski University of Radom, 26-600 Radom, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9476-2070","authenticated-orcid":false,"given":"Wojciech M.","family":"Kempa","sequence":"additional","affiliation":[{"name":"Department of Mathematical Methods in Technics and Informatics, Silesian University of Technology, 44-100 Gliwice, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Valerii","family":"Sokurenko","sequence":"additional","affiliation":[{"name":"Department of Information Systems and Technologies, Kharkiv National University of Internal Affairs, 27, L. Landau Avenue, 61080 Kharkiv, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Oleksandr","family":"Muzychuk","sequence":"additional","affiliation":[{"name":"Department of Information Systems and Technologies, Kharkiv National University of Internal Affairs, 27, L. Landau Avenue, 61080 Kharkiv, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1348-9381","authenticated-orcid":false,"given":"Piotr","family":"Pikiewicz","sequence":"additional","affiliation":[{"name":"Department of Mathematical Methods in Technics and Informatics, Silesian University of Technology, 44-100 Gliwice, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Agnieszka","family":"Molga","sequence":"additional","affiliation":[{"name":"Department of Teleinformatics, Kazimierz Pulaski University of Radom, 26-600 Radom, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6417-3689","authenticated-orcid":false,"given":"Victoria","family":"Vysotska","sequence":"additional","affiliation":[{"name":"Information Systems and Networks Department, Lviv Polytechnic National University, 12, Bandera Street, 79013 Lviv, Ukraine"},{"name":"Institute of Computer Science, Osnabr\u00fcck University, 1, Friedrich-Janssen-Street, 49076 Osnabr\u00fcck, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"127593","DOI":"10.1016\/j.energy.2023.127593","article-title":"Exergetic, sustainability and environmental assessments of a turboshaft engine used on helicopter","volume":"276","author":"Balli","year":"2023","journal-title":"Energy"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Zhang, S., Ma, A., Zhang, T., Ge, N., and Huang, X. 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