CSE: Complex-Valued System With Evolutionary Algorithm

Complex-valued system identification has the ability to provide the basis for system analysis. So as to demonstrate the potential and internal mechanism of the complex-valued system, this paper proposes a novel complex-valued hybrid evolutionary (CSE) algorithm to optimize the complex-valued expression model (CEM). Complex-valued gene expression programming (CVGEP) is proposed to optimize the architectures of the CEM. Complex-valued water wave optimization (CVWWO) is first proposed to optimize complex-valued coefficients and constants of the CEM. The two artificial complex-valued function approximation problems and non-minimum phase equalization problem are utilized to test the performance of the proposed algorithm. The results demonstrate that this method could identify complex-valued systems more correctly than complex-valued neural networks, which could obtain above 90% smaller mean-squared error (MSE) performance than other complex-valued models. With 10% Gaussian white noise, the CSE could identify accurate complex-valued structure and parameters containing coefficients and constants. The CVWWO has better convergence performance than complex-valued particle swarm optimization and crow search algorithm.