Investigation of Nonlinear Vibrational Analysis of Circular Sector Oscillator by Using Cascade Learning

Abstract

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 $\left(\theta \right)$ , velocity $\left({\theta }^{\prime }\right)$ , and acceleration $\left({\theta }^{″}\right)$ . A data set for the supervised learning of the CNN-BLM algorithm for different angles $\left(\alpha \right)$ and radius $\left(R\right)$ 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.