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. 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.