A New Method for Dynamical System Identification by Optimizing the Control Parameters of Legendre Multiwavelet Neural Network
Xiaoyang Zheng,
Shiyu Liu,
Zejiang Yu (zjyu@stu.cqut.edu.cn) and
Chengyou Luo
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Xiaoyang Zheng: School of Artificial Intelligence, Chongqing University of Technology, Chongqing 400054, China
Shiyu Liu: School of Artificial Intelligence, Chongqing University of Technology, Chongqing 400054, China
Zejiang Yu: School of Artificial Intelligence, Chongqing University of Technology, Chongqing 400054, China
Chengyou Luo: School of Artificial Intelligence, Chongqing University of Technology, Chongqing 400054, China
Mathematics, 2023, vol. 11, issue 24, 1-26
Abstract:
Wavelet neural networks have been widely applied to dynamical system identification fields. The most difficult issue lies in selecting the optimal control parameters (the wavelet base type and corresponding resolution level) of the network structure. This paper utilizes the advantages of Legendre multiwavelet (LW) bases to construct a Legendre multiwavelet neural network (LWNN), whose simple structure consists of an input layer, hidden layer, and output layer. It is noted that the activation functions in the hidden layer are adopted as LW bases. This selection if based on the its rich properties of LW bases, such as piecewise polynomials, orthogonality, various regularities, and more. These properties contribute to making LWNNs more effective in approximating the complex characteristics exhibited by uncertainties, step, nonlinear, and ramp in the dynamical systems compared to traditional wavelet neural networks. Then, the number of selection LW bases and the corresponding resolution level are effectively optimized by the simple Genetic Algorithm, and the improved gradient descent algorithm is implemented to learn the weight coefficients of LWNN. Finally, four nonlinear dynamical system identification problems are applied to validate the efficiency and feasibility of the proposed LWNN-GA method. The experiment results indicate that the LWNN-GA method achieves better identification accuracy with a simpler network structure than other existing methods.
Keywords: wavelet neural networks; Legendre multiwavelet; Legendre multiwavelet neural network; Nonlinear dynamical system identification; genetic algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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