Nonlinear System Identification Using Butterfly Optimisation Algorithm and Hammerstein Model

This paper focuses on the nonlinear system identification using butterfly optimisation algorithm (BOA) optimised with adaptive Hammerstein model which is the cascade of nonlinear second-order Volterra (SOV) and linear finite impulse response (FIR) systems. Generally, gradient-based methods have been applied for solving such problems. However, these methods may face the problem of getting trapped in local minimum solution. In this paper, a novel butterfly optimisation algorithm is used to identify the nonlinear system by using three different models, namely Hammerstein model, memoryless polynomial nonlinear (MPN)-FIR model and SOV model. Furthermore, to measure the accuracy of the employed BOA, mean square error (MSE), coefficient estimation and convergence speed are considered. To prove the efficacy of the proposed BOA, the simulated results have been compared with those of the antlion optimisation algorithm and dragonfly algorithm. The simulated results confirm that Hammerstein model with SOV-FIR optimised with BOA is able to outperform the other models and algorithms.