Abstract
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.
Highlights
In the fields of engineering technology, economic management, natural sciences and social sciences, there are complex systems and non-linear phenomena that change with time
Gene expression programming (GEP) is a structure-based evolutionary algorithm based on genetic algorithm (GA) and genetic programming (GP), which owns the advantages of GA and GP, and has stronger the ability of problem solving [21]
The two artificial complex-valued function approximation problems and non-minimum phase equalization problem are utilized to test the performance of our proposed algorithm
Summary
In the fields of engineering technology, economic management, natural sciences and social sciences, there are complex systems and non-linear phenomena that change with time. Yang et al.: CSE: Complex-Valued System With Evolutionary Algorithm the intricate external phenomena These can be demonstrated with the mathematical forms, including equations or other similar methods. In order to express the internal mechanism of complex-value system more clearly, a novel hybrid evolutionary algorithm is proposed to optimize complex-valued mathematical expression model (CEM) in order to identify nonlinear complex-valued systems. In this hybrid algorithm, complex-valued gene expression programming (CVGEP) is proposed to optimize the architectures of CEM. The two artificial complex-valued functions and one real system are utilized to test the performance of our proposed algorithm
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