Abstract
This paper considers a neuro-fuzzy based identification problem for Wiener model with controlled autoregressive moving average noise. The separable signal is applied to decouple the dynamic linear part and the static nonlinear part, and the correlation analysis method is adopted to estimate the parameters of the linear part. To improve the convergence rate of generalized extended stochastic gradient (GESG) algorithm, a generalized extended stochastic gradient algorithm with a forgetting factor is derived for estimating the parameters of the nonlinear part and the parameters of noise model. Examples results verify the effectiveness of the proposed method.
Highlights
Wiener model is a classic block-oriented structure which is a serial connection of linear dynamic block and static nonlinearity [1]
The Wiener model with colored noise is identified by the special input signal including independent separable signal and random signal, which leads to the identification problem of separating the linear part from the nonlinear part
The parameters of the linear part is estimated by correlation analysis method
Summary
Wiener model is a classic block-oriented structure which is a serial connection of linear dynamic block and static nonlinearity [1]. B. Lyu et al.: Parameter Estimation of Neuro-Fuzzy Wiener Model With Colored Noise Using Separable Signals. The special signal is input Wiener model with colored noise, which separates the dynamic linear part from the static nonlinear part. The separable signal is applied to identify Wiener output error model, resulting in the decoupling of dynamic linear part and static nonlinear part. Proof: If input signals are random Gaussian signals with zero mean for Wiener model with colored noise, from Eq. For the Wiener model with controlled autoregressive moving average noise η(k) colored noise is a linear combination of stochastic white noise, which is independent of internal unmeasurable variable v(k), that is, E(η(k)v(k)) = 0. Ru(τ ), we can conclude that the estimates are consistently converge to true values, namely, lim θ 1 → θ 1
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