TSK fuzzy echo state neural network: a hybrid structure for black-box nonlinear systems identification

• Published in: Neural computing & applications 2022-05, Vol.34 (9), p.7033-7051
• Main Authors: Mahmoud, Tarek A., Elshenawy, Lamiaa M.
• Format: Article
• Language: English
• Subjects: Algorithms; Artificial Intelligence; Artificial neural networks; Basis functions; Clustering; Complex systems; Complexity; Computational Biology/Bioinformatics; Computational Science and Engineering; Computer Science; Computer simulation; Data Mining and Knowledge Discovery; Fuzzy logic; Fuzzy systems; Hybrid structures; Identification methods; Image Processing and Computer Vision; Inference; Mathematical models; Neural networks; Nonlinear systems; Original Article; Parameters; Probability and Statistics in Computer Science; Singular value decomposition; System effectiveness; System identification
• ISSN: 0941-0643; 1433-3058
• DOI: 10.1007/s00521-021-06838-2

Recently, the black-box nonlinear system identification approaches have become effective methods to model complex systems. By the idea of combining the merits of reservoir computing (RC) of the Echo state network (ESN) and fuzzy inference system, a TSK fuzzy ESN for the black-box identification is proposed in this paper. The proposed network is constructed on the basis of the framework of ESN containing multiple sub-reservoirs in which each sub-reservoir is contributed with a TSK fuzzy rule. Through this hybrid structure, first, a modified structure of ESN with less complexity is provided to give an effective black-box identification method for uncertain nonlinear systems. Second, the fuzzy clustering of the training data of an application is used to define the number of sub-reservoirs; then, the singular value decomposition (SVD) is applied to randomly initialize the weight matrix of each sub-reservoir. Third, according to the characteristic of ESN, only the output weights of the sub-reservoirs are learned by the recursive least squares (RLS) algorithm without adjusting the other parameters of the network including the centers and widths of the fuzzy basis function of the TSK fuzzy inference system. Moreover, the convergence of the parameter learning based on RLS is investigated. To demonstrate the performance of the proposed TSK fuzzy ESN in the identification of nonlinear systems, three numerical simulations are given. The simulation results also involve a comparison with other structures of ESN and fuzzy neural networks to confirm the effectiveness of the proposed TSK fuzzy ESN.