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

This paper analyzed the model of swinging oscillation a solid circular sector arising in hydrodynamical machines, electrical engineering, heat transfer applications, and civil engineering. Nonlinear differential equations govern mathematical for frequency system. Furthermore, computational strength Cascade neural networks (CNNs) is utilized with backpropagated Levenberg–Marquardt (BLM) algorithm to study oscillations angular displacement θ , velocity id="M2"> ′ acceleration id="M3"> ″ . A data set supervised learning CNN-BLM different angles id="M4"> α radius id="M5"> R are generated by Runge–Kutta (RK-4) method. The BLM further interprets dataset log-sigmoid as an activation function solutions’ validation, testing, training. results obtained design scheme compared Akbari–Ganji’s (AG) rapid convergence quality solutions validated through performance indicators such mean absolute deviations (MAD), root means square error, error Nash–Sutcliffe efficiency (ENSE). statistics demonstrate scheme’s applicability highly singular nonlinear problems.