Echo State Wavelet-sigmoid Networks and Their Application to Nonlinear System Identification
نویسندگان
چکیده
Wavelet theory has become popular in modeling echo state network. One of the most promising directions is usage of the wavelets as membership activation functions of its reservoir. However, only Symlets wavelet seems to be suitable for hybrid wavelet-sigmoid activation functions. To enhance a systematic study of the field, we concentrate on developing more wavelets towards the typical ESN representation, and ask: What are the more outstanding wavelets of reservoir structure for obtaining competitive models and what is the memory capacity of such reservoirs for obtaining competitive models? In the paper, three echo state wavelet-sigmoid networks (ESWNs) are proposed, considering Shannon wavelet, frequency B-spline wavelet and impulse response wavelet, respectively. The corresponding wavelet functions are instead of sigmoid one in part to construct wavelet-sigmoid reservoirs. On three widely used system nonlinear approximation tasks of different origin and characteristics, as well as by conducting a theoretical analysis we show that the proposed ESWNs are superior to the popular echo state network with build-in Symlets wavelet.
منابع مشابه
Neural Network Sensitivity to Inputs and Weights and its Application to Functional Identification of Robotics Manipulators
Neural networks are applied to the system identification problems using adaptive algorithms for either parameter or functional estimation of dynamic systems. In this paper the neural networks' sensitivity to input values and connections' weights, is studied. The Reduction-Sigmoid-Amplification (RSA) neurons are introduced and four different models of neural network architecture are proposed and...
متن کاملNonlinear System Identification Using Hammerstein-Wiener Neural Network and subspace algorithms
Neural networks are applicable in identification systems from input-output data. In this report, we analyze theHammerstein-Wiener models and identify them. TheHammerstein-Wiener systems are the simplest type of block orientednonlinear systems where the linear dynamic block issandwiched in between two static nonlinear blocks, whichappear in many engineering applications; the aim of nonlinearsyst...
متن کاملEcho State Networks in Audio Processing
In this article echo state networks, a special form of recurrent neural networks, are discussed in the area of nonlinear audio signal processing. Echo state networks are a novel approach in recurrent neural networks with a very easy (linear) training algorithm. Signal processing examples in nonlinear system identification (valve distortion, clipping), inverse modeling (quality enhancement) and ...
متن کاملThe Sine-Cosine Wavelet and Its Application in the Optimal Control of Nonlinear Systems with Constraint
In this paper, an optimal control of quadratic performance index with nonlinear constrained is presented. The sine-cosine wavelet operational matrix of integration and product matrix are introduced and applied to reduce nonlinear differential equations to the nonlinear algebraic equations. Then, the Newton-Raphson method is used for solving these sets of algebraic equations. To present ability ...
متن کاملVerification of an Evolutionary-based Wavelet Neural Network Model for Nonlinear Function Approximation
Nonlinear function approximation is one of the most important tasks in system analysis and identification. Several models have been presented to achieve an accurate approximation on nonlinear mathematics functions. However, the majority of the models are specific to certain problems and systems. In this paper, an evolutionary-based wavelet neural network model is proposed for structure definiti...
متن کامل