Investigation of Nonlinear Vibrational Analysis of Circular Sector Oscillator by Using Cascade Learning
This paper analyzed the model of swinging oscillation of a solid circular sector arising in hydrodynamical machines, electrical engineering, heat transfer applications, and civil engineering. Nonlinear differential equations govern the mathematical model for frequency oscillation of the system. Furt...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Advances in Materials Science and Engineering |
| Online Access: | http://dx.doi.org/10.1155/2022/1898124 |
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| author | Naveed Ahmad Khan Muhammad Sulaiman Jamel Seidu Fahad Sameer Alshammari |
| author_facet | Naveed Ahmad Khan Muhammad Sulaiman Jamel Seidu Fahad Sameer Alshammari |
| author_sort | Naveed Ahmad Khan |
| collection | DOAJ |
| description | This paper analyzed the model of swinging oscillation of a solid circular sector arising in hydrodynamical machines, electrical engineering, heat transfer applications, and civil engineering. Nonlinear differential equations govern the mathematical model for frequency oscillation of the system. Furthermore, a computational strength of Cascade neural networks (CNNs) is utilized with backpropagated Levenberg–Marquardt (BLM) algorithm to study the oscillations in angular displacement θ, velocity θ′, and acceleration θ″. A data set for the supervised learning of the CNN-BLM algorithm for different angles α and radius R are generated by Runge–Kutta (RK-4) method. The BLM algorithm further interprets the dataset with log-sigmoid as an activation function for the solutions’ validation, testing, and training. The results obtained by the design scheme are compared with Akbari–Ganji’s (AG) method. The rapid convergence and quality of the solutions are validated through performance indicators such as mean absolute deviations (MAD), root means square error, and error in Nash–Sutcliffe efficiency (ENSE). The statistics demonstrate the design scheme’s applicability and efficiency to highly singular nonlinear problems. |
| format | Article |
| id | doaj-art-df55698e461149c89f3dae6e889af9fa |
| institution | Kabale University |
| issn | 1687-8442 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Materials Science and Engineering |
| spelling | doaj-art-df55698e461149c89f3dae6e889af9fa2025-02-03T05:49:21ZengWileyAdvances in Materials Science and Engineering1687-84422022-01-01202210.1155/2022/1898124Investigation of Nonlinear Vibrational Analysis of Circular Sector Oscillator by Using Cascade LearningNaveed Ahmad Khan0Muhammad Sulaiman1Jamel Seidu2Fahad Sameer Alshammari3Department of MathematicsDepartment of MathematicsSchool of Railways and Infrastructure DevelopmentDepartment of MathematicsThis paper analyzed the model of swinging oscillation of a solid circular sector arising in hydrodynamical machines, electrical engineering, heat transfer applications, and civil engineering. Nonlinear differential equations govern the mathematical model for frequency oscillation of the system. Furthermore, a computational strength of Cascade neural networks (CNNs) is utilized with backpropagated Levenberg–Marquardt (BLM) algorithm to study the oscillations in angular displacement θ, velocity θ′, and acceleration θ″. A data set for the supervised learning of the CNN-BLM algorithm for different angles α and radius R are generated by Runge–Kutta (RK-4) method. The BLM algorithm further interprets the dataset with log-sigmoid as an activation function for the solutions’ validation, testing, and training. The results obtained by the design scheme are compared with Akbari–Ganji’s (AG) method. The rapid convergence and quality of the solutions are validated through performance indicators such as mean absolute deviations (MAD), root means square error, and error in Nash–Sutcliffe efficiency (ENSE). The statistics demonstrate the design scheme’s applicability and efficiency to highly singular nonlinear problems.http://dx.doi.org/10.1155/2022/1898124 |
| spellingShingle | Naveed Ahmad Khan Muhammad Sulaiman Jamel Seidu Fahad Sameer Alshammari Investigation of Nonlinear Vibrational Analysis of Circular Sector Oscillator by Using Cascade Learning Advances in Materials Science and Engineering |
| title | Investigation of Nonlinear Vibrational Analysis of Circular Sector Oscillator by Using Cascade Learning |
| title_full | Investigation of Nonlinear Vibrational Analysis of Circular Sector Oscillator by Using Cascade Learning |
| title_fullStr | Investigation of Nonlinear Vibrational Analysis of Circular Sector Oscillator by Using Cascade Learning |
| title_full_unstemmed | Investigation of Nonlinear Vibrational Analysis of Circular Sector Oscillator by Using Cascade Learning |
| title_short | Investigation of Nonlinear Vibrational Analysis of Circular Sector Oscillator by Using Cascade Learning |
| title_sort | investigation of nonlinear vibrational analysis of circular sector oscillator by using cascade learning |
| url | http://dx.doi.org/10.1155/2022/1898124 |
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