Echo State Wavelet-sigmoid Networks and Their Application to Nonlinear System Identification

摘要

Wavelet theory has become popular in modelingecho state network. One of the most promising directions isusage of the wavelets as membership activation functions of itsreservoir. However, only Symlets wavelet seems to be suitablefor hybrid wavelet-sigmoid activation functions. To enhance asystematic study of the field, we concentrate on developingmore wavelets towards the typical ESN representation, and ask:What are the more outstanding wavelets of reservoir structurefor obtaining competitive models and what is the memorycapacity of such reservoirs for obtaining competitive models? Inthe paper, three echo state wavelet-sigmoid networks (ESWNs)are proposed, considering Shannon wavelet, frequency B-splinewavelet and impulse response wavelet, respectively. The corresponding wavelet functions are instead of sigmoid one in partto construct wavelet-sigmoid reservoirs. On three widely usedsystem nonlinear approximation tasks of different origin andcharacteristics, as well as by conducting a theoretical analysiswe show that the proposed ESWNs are superior to the popularecho state network with build-in Symlets wavelet.