CN101924718B - Hybrid wavelet neural network blind equalization method controlled by fuzzy neutral network - Google Patents

Abstract

The invention discloses a hybrid wavelet neural network blind equalization method controlled by a fuzzy neutral network, and the method comprises the following steps: a. emission signals x (n) go through a pulse response channel, thus obtaining channel output vectors b (n); b. input sequences of a blind equalizer is obtained by adopting channel noise N (n) and the channel output vectors b (n) in Step a; and c. the input sequences y (n) of the blind equalizer in Step b go through an improved hybrid wavelet neural network sequentially, thus obtaining output signals, then iteration steps of a shift factor and a scale factor in a neuron wavelet function in the improved hybrid wavelet neural network are regulated by utilizing the fuzzy neural network (FNN), and a mean-square error E (n)=MSE (n) and the deviation of the mean-square error delta E (n) =MSE (n)-MSE (n-1) serve as input of a controller of the fuzzy neural network. The system has high flexibility and can avoid getting into dilemmas of local minimum.

Description

The hybrid wavelet neural net blind balance method of Fuzzy Neural-network Control

Technical field

The present invention relates to a kind of hybrid wavelet neural net blind balance method of Fuzzy Neural-network Control, belong to the technical field of many wavelet fuzzy neural network blind balance method.

Background technology

In underwater sound communication system, the intersymbol interference (ISI, Inter-Symbol Interference) that the multipath fading of channel and distortion produce has reduced the performance of system, affects communication quality.The effective ways that suppress intersymbol interference are to adopt the Blind Equalization Technique that does not need training sequence.The essence of Blind Equalization Technique is to adjust parametric equalizer by the superior algorithm of design performance, is the non-linear approximation problem of the system of inverting; And wavelet neural network (WNN, Wavelet Neural Network) self-learning function of neural net and the time-frequency localization character of small echo are combined, have self adaptation distinguishing and good fault-tolerant ability and (see document [1]: Zhang Q H, Benveniste A.Wavelet networks[J] .IEEE Transactions on Neural Networks, 1992,3 (6): 889-898.).And adopt the blind equalization algorithm of traditional WNN, still exist convergence rate be absorbed in slowly and easily local minimum defective (see document [2]: Rahib H.Abiyev.Neuro-fuuzy system for equalization channel distortion[J] .International Journal of Computati-onal Intelligence, 2005, Fall:229-232; Document [3]: Liu Guojun, Tang Jianglong, Huang Jianhua, Liu Jiafeng.Picture contrast based on fuzzy wavelet strengthens algorithm [J]. electronic letters, vol, 2005,33 (4): 643-647; Document [4]: Gui Yanning, Jiao Licheng, Zhang Fushun.Radio detection target identification technology [J] based on small echo and BP neural net. electronic letters, vol, 2003,31 (12): 1811-1814.).Fuzzy neural network (FNN, Fuzzy Neural Network) compiled the advantage of fuzzy theory and neural net, integrating study, association, identification, self adaptation and fuzzy information handles, have calculate advantage such as easy, that fault-tolerant ability strong, the process information scope is big, pace of learning is fast (see document [5]: Zhang Xiaoqin. based on fuzzy neural network Study on Blind Equalization [D]. Taiyuan, Shenyang: Institutes Of Technology Of Taiyuan, 2008; Document [6]: Xu Xiaolai, thunder hero, Xie Wenbiao.Self-organizing intuitionistic fuzzy reasoning neural networks [J] based on UKF. electronic letters, vol, 2010,28 (3): 638-645.).Therefore, FNN combined with WNN to be applied in the blind balance method, will be the problem that Research Significance is arranged.

Hybrid wavelet neural net (HWNN) blind balance method is that transversal filter of cascade before the WNN input layer (is seen document [7]: Xiao Ying, Dong Yuhua.A kind of cascade hybrid wavelet neural net blind equalization algorithm [J]. information and control, 2009,38 (4): 479-483.), its weak point has: 1. the output of each node of transversal filter is directly as the corresponding neuronic input of WNN input layer, i.e. between each neuronic input of WNN input layer without any contact; 2. not the worry that sets the exam of the real part of signal and imaginary component, be not suitable for complex modulation systems such as PSK, QAM; 3. the iteration step length to the wavelet function mesoscale factor and shift factor does not carry out fuzzy control and adjustment, thereby has influenced flexibility and the speed of system handles information, and equalization performance is relatively poor.

Summary of the invention

The present invention seeks to provide at the defective that prior art exists a kind of hybrid wavelet neural net blind balance method of Fuzzy Neural-network Control.

The present invention adopts following technical scheme for achieving the above object:

The hybrid wavelet neural net blind balance method of Fuzzy Neural-network Control of the present invention is characterized in that comprising the steps:

A.) x (n) that will transmit obtains channel output vector b (n) through the impulse response channel, and wherein n is positive integer, the expression time series, down with;

B.) adopt interchannel noise N (n) and the described channel output vector of step a b (n) to obtain the list entries of blind equalizer: y (n)=b (n)+N (n);

C.) the list entries y (n) of the described blind equalizer of step b improved hybrid wavelet neural net is successively obtained output signal

Utilize fuzzy neural network (FNN) to adjust in the improved hybrid wavelet neural net iteration step length of shift factor and scale factor in the neuron wavelet function, and with deviation delta E (the n)=MSE (n)-MSE(n-1) of mean square error E (n)=MSE (n) and the mean square error input as fuzzy neural network controller.

Preferably, the construction method of described improved hybrid wavelet neural net is as follows:

Transversal filter has constituted the linear segment of improved hybrid wavelet neural net, and wavelet neural network (WNN) has constituted non-linear partial; I tap coefficient of transversal filter is c _i(n), i=1,2 ..., m, m are the number of hybrid wavelet neural net (HWNN) input layer, down together; Improved hybrid wavelet neural net input layer i the neuronic T that is input as _i(n), hidden layer k neuronic u that is input as _k(n), be output as Q _k(n), k=1,2 ..., p, p are the number of HWNN hidden neuron, down together; Output layer be input as g (n), be output as

I neuron of input layer to hidden layer k neuronic connection weight is w _Ik(n), k neuron of hidden layer to the connection weight of output layer is v _k(n);

The signal of network, channel, weights etc. are decomposed into real part and imaginary part two parts, and then the state equation of network is

c _i(n)＝c _i，R(n)+jc _i，I(n) (1)

In the formula, c _{I, R}(n) be c _i(n) real part, c _{I, I}(n) be c _i(n) imaginary part,

Expression imaginary unit, down together;

w _ik(n)＝w _ik，R(n)+jw _ik，I(n) (2)

v _k(n)＝v _k，R(n)+jv _k，I(n) (3)

y(n)＝y _R(n)+jy _I(n) (4)

$T_i\left(n\right)=\underset{t=1}{\overset{i}{\mathrm{\Σ}}}{c}_t\left(n\right)y(n+1-t)=\underset{t=1}{\overset{i}{\mathrm{\Σ}}}(c_{t,R}\left(n\right)y_R(n+1-t)-c_{t,I}\left(n\right)y_I(n+1-t))$

$+j\underset{t=1}{\overset{i}{\mathrm{\Σ}}}(c_{t,R}\left(n\right)y_I(n+1-t)+c_{i,I}\left(n\right)y_R(n+1-t))---\left(5\right)$

$u_k\left(n\right)=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{w}_{\mathrm{ik}}\left(n\right)T_i\left(n\right)=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}[w_{\mathrm{ik},R}\left(n\right)T_{i,R}\left(n\right)-w_{\mathrm{ik},I}\left(n\right)T_{i,I}\left(n\right)]$

$+j\underset{i=1}{\overset{m}{\mathrm{\Σ}}}[w_{\mathrm{ik},R}\left(n\right)T_{i,I}\left(n\right)-w_{\mathrm{ik},I}\left(n\right)T_{i,R}\left(n\right)]---\left(6\right)$

Q _k(n)＝ψ _a，b(u _k，R(n))+jψ _a，b(u _k，I(n)) (7)

In the formula, ψ _{A, b}() expression is carried out wavelet transformation to the hidden layer input signal, selects the Morlet wavelet mother function here, then

${\mathrm{\ψ}}_{a,b}\left(u_{k,R}\left(n\right)\right)={\left|a\right|}^{-\frac{1}{2}}\mathrm{\ψ}\left(\frac{u_{k,R}\left(n\right)-b}{a}\right)={\left|a\right|}^{-\frac{1}{2}}\left(\frac{u_{k,R}\left(n\right)-b}{a}\right)e^{-\frac{1}{2}{\left(\frac{u_{k,R}\left(n\right)-b}{a}\right)}^2}---\left(8\right)$

In the formula, b is shift factor, and a is scale factor; With u in the formula (8) _{K, R}(n) change u into _{K, I}(n) just obtain ψ _{A, b}(u _{K, I}(n)) expression formula, wavelet neural network is output as:

${\tilde{x}}_2\left(n\right)=\underset{k=1}{\overset{p}{\mathrm{\Σ}}}[v_{k,R}\left(n\right)Q_{k,R}\left(n\right)-v_{k,I}\left(n\right)Q_{k,I}\left(n\right)]+j\underset{k=1}{\overset{p}{\mathrm{\Σ}}}[v_{k,R}\left(n\right)Q_{k,I}\left(n\right)+v_{k,I}\left(n\right)Q_{k,R}\left(n\right)]---\left(9\right)$

Transversal filter is output as:

${\tilde{x}}_1\left(n\right)=c_i^T\left(n\right)y(n+1-i),i=\mathrm{1,2},\·\·\·,m---\left(10\right)$

Will With

Weighting is merged:

$g\left(n\right)=\mathrm{\α}{\tilde{x}}_1\left(n\right)+\mathrm{\β}{\tilde{x}}_2\left(n\right)---\left(11\right)$

In the formula, 0≤α, β≤1 is weighted factor, and satisfies alpha+beta=1, improved HWNN finally is output as:

$\tilde{x}\left(n\right)=f\left(g\left(n\right)\right)=g\left(n\right)+\mathrm{\λ}\sin \left(\mathrm{\πg}\left(n\right)\right)---\left(12\right)$

In the formula, f () is the transfer function between the input and output of output layer, and wherein λ sin (π g (n)) is to be the non-linear correction term of independent variable with g (n), and it makes that the pendulum signal is drawn close to original signal about near the original signal central point.

Preferably, described hidden layer to the update method of output layer connection weight is:

$v_k(n+1)=v_k\left(n\right)+{\mathrm{\μ}}_{1}K\left(n\right)Q_k^{*}\left(n\right),$

K(n)＝-2βe(n)[f(g _R(n))f′(g _R(n))+jf(g _I(n))f′(g _I(n))]，

μ in the formula ₁Be iteration step length, * is conjugation, and j represents imaginary number, subscript " ' " expression differentiate, down together.

Preferably, the weight that connects of described input layer to hidden layer more new formula be:

$w_{\mathrm{ik}}(n+1)=w_{\mathrm{ik}}\left(n\right)+{\mathrm{\μ}}_2{K}_0\left(n\right)T_i^{*}\left(n\right),$

$K_0\left(n\right)=\mathrm{\βe}\left(n\right){\mathrm{\ψ}}_{a,b}^{\′}\left(u_{k,R}\left(n\right)\right)\mathrm{Re}\left\{\right[f\left(g_R\left(n\right)\right)\·f^{\′}\left(g_R\left(n\right)\right)+\mathrm{jf}\left(g_I\left(n\right)\right)f^{\′}\left(g_I\left(n\right)\right)]v_k^{*}\left(n\right)\}$

$+\mathrm{j\βe}\left(n\right){\mathrm{\ψ}}_{a,b}^{\′}\left(u_{k,I}\left(n\right)\right)\mathrm{Im}\left\{\right[f\left(g_R\left(n\right)\right)\·f^{\′}\left(g_R\left(n\right)\right)+\mathrm{jf}\left(g_I\left(n\right)\right)f^{\′}\left(g_I\left(n\right)\right)\left]v_k^{*}\left(n\right)\right\},$

In the formula, μ ₂Be iteration step length.

Preferably, the update method of described scale factor a and shift factor b is:

$a(n+1)=a\left(n\right)-{\mathrm{\μ}}_3\frac{\∂J\left(n\right)}{\∂a\left(n\right)},$

$b(n+1)=b\left(n\right)-{\mathrm{\μ}}_4\frac{\∂J\left(n\right)}{\∂b\left(n\right)},$

$\frac{\∂J\left(n\right)}{\∂a\left(n\right)}=2\mathrm{\βe}\left(n\right)|{\tilde{x}}_R\left(n\right)+j{\tilde{x}}_I\left(n\right)|\·(\frac{\∂\left|{\tilde{x}}_R\left(n\right)\right|}{\∂a\left(n\right)}+j\frac{\∂\left|{\tilde{x}}_I\left(n\right)\right|}{\∂a\left(n\right)}),$

In the formula

$\frac{\∂\left|{\tilde{x}}_R\left(n\right)\right|}{\∂a\left(n\right)}=\frac{1}{\left|\tilde{x}\left(n\right)\right|}[f\left(g_R\left(n\right)\right)f^{\′}\left(g_R\left(n\right)\right)\frac{\∂g_R\left(n\right)}{\∂a\left(n\right)}+f\left(g_I\left(n\right)\right)f^{\′}\left(g_I\left(n\right)\right)\frac{\∂g_I\left(n\right)}{\∂a\left(n\right)}],$

$\frac{{\∂g}_R\left(n\right)}{\∂a\left(n\right)}=v_{k,R}\left(n\right)\frac{\∂{\mathrm{\ψ}}_{a,b}\left(u_{k,R}\left(n\right)\right)}{\∂a\left(n\right)}-v_{k,I}\left(n\right)\frac{\∂{\mathrm{\ψ}}_{a,b}\left(u_{k,I}\left(n\right)\right)}{\∂a\left(n\right)},$

$\frac{{\∂g}_I\left(n\right)}{\∂a\left(n\right)}=v_{k,R}\left(n\right)\frac{{\∂\mathrm{\ψ}}_{a,b}\left(u_{k,I}\left(n\right)\right)}{\∂a\left(n\right)}+v_{k,I}\left(n\right)\frac{{\∂\mathrm{\ψ}}_{a,b}\left(u_{k,R}\left(n\right)\right)}{\∂a\left(n\right)},$

$\frac{{\∂\mathrm{\ψ}}_{a,b}\left(u_{k,R}\left(n\right)\right)}{\∂a\left(n\right)}=-{\left|a\right|}^{-\frac{1}{2}}\frac{(u_{k,R}\left(n\right)-b)}{a^2}{e}^{-\frac{1}{2}{\left(\frac{u_{k,R}\left(n\right)-b}{a}\right)}^2}$

$+{\left|a\right|}^{-\frac{1}{2}}{\left(\frac{u_{k,R}\left(n\right)-b}{a}\right)}^2\left(\frac{u_{k,R}\left(n\right)-b}{a^2}\right)e^{-\frac{1}{2}{\left(\frac{u_{k,R}\left(n\right)-b}{a}\right)}^2}$

$-\frac{1}{2}{\left|a\right|}^{-3/2}\left(\frac{u_{k,R}\left(n\right)-b}{a}\right)e^{-\frac{1}{2}{\left(\frac{u_{k,R}\left(n\right)-b}{a}\right)}^2},$

In the formula, μ ₃, μ ₄Be iteration step length.

Preferably, the construction method of described fuzzy neural network controller is as follows:

The fuzzy rule of this fuzzy neural network (FNN) is:

Rule 1: if Δ E (n) for just and E (n) greatly, then Δ μ is honest;

Rule 2: if Δ E (n) for just and among the E (n), then Δ μ is zero;

Rule 3: if Δ E (n) for just and E (n) little, then Δ μ bears little;

Rule 4: if Δ E (n) be zero and E (n) big, then Δ μ is just little;

Rule 5: if Δ E (n) is among zero and the E (n), then Δ μ zero;

Rule 6: if Δ E (n) be zero and E (n) little, then Δ μ is negative little;

Rule 7: if Δ E (n) for negative and E (n) big, then Δ μ is just little;

Rule 8: if Δ E (n) is among negative and the E (n), then Δ μ zero;

Rule 9: if Δ E (n) for negative and E (n) is little, then Δ μ is negative big.

The processing procedure of each layer of FNN controller is as follows:

Ground floor: input layer, with E (n) and Δ E (n) the controller input variable as step-length.

$I_1^{\left(1\right)}\left(n\right)=\mathrm{\ΔE}\left(n\right)=\mathrm{MSE}\left(n\right)-\mathrm{MSE}(n-1),$

$I_2^{\left(1\right)}\left(n\right)=E\left(n\right)=\mathrm{MSE}\left(n\right),$

$O_{\mathrm{ql}}^{\left(1\right)}\left(n\right)=I_q^{\left(1\right)}\left(n\right),$

In the formula, q=1,2 is the input number of FNN, l=1,2,3 is fuzzy field, I ^(t), O ^(t)Be respectively input and the output of FNN t layer, t=1,2 ..., 5 times together;

The second layer: obfuscation layer

$I_{\mathrm{ql}}^{\left(2\right)}\left(n\right)=O_{\mathrm{ql}}^{\left(1\right)}\left(n\right),$

$O_{\mathrm{ql}}^{\left(2\right)}\left(n\right)=\exp [-{\left(\frac{I_{\mathrm{ql}}^{\left(2\right)}\left(n\right)-m_{\mathrm{ql}}^{\left(2\right)}\left(n\right)}{{\mathrm{\σ}}_{\mathrm{ql}}^{\left(2\right)}\left(n\right)}\right)}^2],$

In the formula, With

Expectation and the variance of representing input space fuzzy field respectively;

The 3rd layer: rules layer

$I_{\mathrm{ql}}^{\left(3\right)}\left(n\right)=O_{\mathrm{ql}}^{\left(2\right)}\left(n\right),$

$O_r^{\left(3\right)}=\mathrm{\Π}{I}_{\mathrm{ql}}^{\left(3\right)}\left(n\right),$

In the formula, r=1,2 ..., the preceding number of packages of 9 expression fuzzy rules.

The 4th layer: select layer, namely from the output of the 3rd floor, select the value of one tunnel maximum as the output of this layer, namely

$O^{\left(4\right)}=\max \left(O_r^{\left(3\right)}\right),$

Layer 5: normalization layer

O ⁽⁵⁾＝O ⁽⁴⁾·δ(i)，

In the formula, δ (i) controlled quentity controlled variable is mainly used to adjust the output of this layer, finishes the rear section of rule;

Layer 6: ambiguity solution layer

Δμ＝O ⁽⁶⁾＝O ⁽⁵⁾·MSE(n)。

On the basis that takes full advantage of WNN and FNN network advantage, the present invention the hybrid wavelet neural net blind balance method of Fuzzy Neural-network Control (FHWNN, FNN controller based Hybrid WNN).This method replaces neuron with small echo unit, sets up relation between wavelet transformation and the network parameter by affine transformation; With the compensation of the realization of the forward direction transversal filter in hybrid wavelet neural net (HWNN, the Hybrid WNN) structure to the channel linearity characteristic, with the compensation of WNN realization to non-linear characteristics of channel; With the FNN controller scale factor in the wavelet function and shift factor are adjusted; Thereby improved the flexibility of system, avoided easily being absorbed in the predicament of local minimum.The simulation result of underwater acoustic channel has been verified the validity of FHWNN method.

Description of drawings

Fig. 1: FHWNN theory diagram of the present invention

Fig. 2: the improved HWNN structure of the present invention;

Fig. 3: fuzzy neural network of the present invention (FNN) controller architecture;

Fig. 4: embodiment result, (a) mean square error curve, (b) WTCMA output, (c) output of WNN, (d) HWNN output, (e) FHWNN output.

Embodiment

The wavelet neural network blind equalization algorithm of Fuzzy Neural-network Control

Advantage according to WNN and FNN, the present invention utilizes FNN to adjust the iteration step length of shift factor and scale factor in the network neuron wavelet function, and with deviation delta E (n)=MSE (the n)-MSE (n-1) of mean square error E (n)=MSE (n) (MSE (n) is n mean square error constantly) and the mean square error input as fuzzy neural network controller.The FHWNN principle, as shown in Figure 1.

Among Fig. 1, x (n) is for sending burst, and h (n) is Unknown Channel, and N (n) is the additive white Gaussian noise of channel, and y (n) is the input of improved hybrid wavelet neural net,

Judgement output for decision device.Blind equalization algorithm relies on observation sequence y (n) exactly and realizes sending the undistorted recovery of signal x (n).Binding constant mould blind equalization algorithm, then the cost function of WNN blind equalization algorithm is

$J=\frac{1}{2}{({\left|\tilde{x}\left(n\right)\right|}^2-R_{\mathrm{CM}})}^2---\left(1\right)$

In the formula, R _CM=E[|x (n) | ⁴]/E[|x (n) | ²].

Among Fig. 1, improved hybrid wavelet neural net is determining the input of neural net in the blind equalization algorithm; Fuzzy neural network controller is controlled the iteration step length of the wavelet function mesoscale factor and shift factor in the improved hybrid wavelet neural net.Below this two parts will be discussed respectively.

1. improved hybrid wavelet neural net blind balance method

Hybrid wavelet neural net (HWNN) blind balance method is that transversal filter of cascade before the WNN input layer (is seen document [10]: Xiao Ying, Dong Yuhua.A kind of cascade hybrid wavelet neural net blind equalization algorithm [J]. information and control, 2009,38 (4): 479-483.), its weak point has: 1. the output of each node of transversal filter is directly as the corresponding neuronic input of WNN input layer, i.e. between each neuronic input of WNN input layer without any contact; 2. not the worry that sets the exam of the real part of signal and imaginary component, be not suitable for complex modulation systems such as PSK, QAM; 3. the iteration step length to the wavelet function mesoscale factor and shift factor does not carry out fuzzy control and adjustment, thereby has influenced flexibility and the speed of system handles information, and equalization performance is relatively poor.Therefore, this paper proposes a kind of improved HWNN structure, as shown in Figure 2 at the defective of HWNN.

Among Fig. 2, transversal filter has constituted the linear segment of network, and WNN has constituted non-linear partial.If i tap coefficient of transversal filter is c _i(n) (i=1,2 ..., m, m are the number of HWNN input layer, down together); HWNN input layer i the neuronic T that is input as _i(n), hidden layer k neuronic u that is input as _k(n), be output as Q _k(n) (k=1,2 ..., p, p are the number of HWNN hidden neuron, down together); Output layer be input as g (n), be output as

I neuron of input layer to hidden layer k neuronic connection weight is w _Ik(n), k neuron of hidden layer to the connection weight of output layer is v _k(n).In order to make this algorithm be applicable to plural system, the signal of network, channel, weights etc. are decomposed into real part and imaginary part two parts, then the state equation of network is

c _i(n)＝c _i，R(n)+jc _i，I(n) (2)

In the formula, c _{I, R}(n) be c _i(n) real part, c _{I, I}(n) be c _i(n) imaginary part, down together.

w _ik(n)＝w _ik，R(n)+jw _ik，I(n) (3)

v _k(n)＝v _k，R(n)+jv _k，I(n) (4)

y(n)＝y _R(n)+jy _I(n) (5)

$T_i\left(n\right)=\underset{t=1}{\overset{i}{\mathrm{\Σ}}}{c}_t\left(n\right)y(n+1-t)=\underset{t=1}{\overset{i}{\mathrm{\Σ}}}(c_{t,R}\left(n\right)y_R(n+1-t)-c_{t,I}\left(n\right)y_I(n+1-t))$

$+j\underset{t=1}{\overset{i}{\mathrm{\Σ}}}(c_{t,R}\left(n\right)y_I(n+1-t)+c_{i,I}\left(n\right)y_R(n+1-t))---\left(6\right)$

$u_k\left(n\right)=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{w}_{\mathrm{ik}}\left(n\right)T_i\left(n\right)=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}[w_{\mathrm{ik},R}\left(n\right)T_{i,R}\left(n\right)-w_{\mathrm{ik},I}\left(n\right)T_{i,I}\left(n\right)]$

$+j\underset{i=1}{\overset{m}{\mathrm{\Σ}}}[w_{\mathrm{ik},R}\left(n\right)T_{i,I}\left(n\right)-w_{\mathrm{ik},I}\left(n\right)T_{i,R}\left(n\right)]---\left(7\right)$

Q _k(n)＝ψ _a，b(u _k，R(n))+jψ _a，b(u _k，I(n)) (8)

In the formula, ψ _{A, b}() expression is carried out wavelet transformation to the hidden layer input signal, selects the Morlet wavelet mother function here, then

${\mathrm{\ψ}}_{a,b}\left(u_{k,R}\left(n\right)\right)={\left|a\right|}^{-\frac{1}{2}}\mathrm{\ψ}\left(\frac{u_{k,R}\left(n\right)-b}{a}\right)={\left|a\right|}^{-\frac{1}{2}}\left(\frac{u_{k,R}\left(n\right)-b}{a}\right)e^{-\frac{1}{2}{\left(\frac{u_{k,R}\left(n\right)-b}{a}\right)}^2}---\left(9\right)$

In the formula, b is shift factor, and a is scale factor.With u in the formula (9) _{K, R}(n) change u into _{K, I}(n) just obtain ψ _{A, b}(u _{K, I}(n)) expression formula.Wavelet neural network is output as

${\tilde{x}}_2\left(n\right)=\underset{k=1}{\overset{p}{\mathrm{\Σ}}}[v_{k,R}\left(n\right)Q_{k,R}\left(n\right)-v_{k,I}\left(n\right)Q_{k,I}\left(n\right)]+j\underset{k=1}{\overset{p}{\mathrm{\Σ}}}[v_{k,R}\left(n\right)Q_{k,I}\left(n\right)+v_{k,I}\left(n\right)Q_{k,R}\left(n\right)]---\left(10\right)$

Transversal filter is output as

${\tilde{x}}_1\left(n\right)=c_i^T\left(n\right)y(n+1-i),i=\mathrm{1,2},\·\·\·,m---\left(11\right)$

Will

With

Weighting is merged,

$g\left(n\right)=\mathrm{\α}{\tilde{x}}_1\left(n\right)+\mathrm{\β}{\tilde{x}}_2\left(n\right)---\left(12\right)$

In the formula, 0≤α, β≤1 is weighted factor, and satisfies alpha+beta=1.Improved HWNN finally is output as

$\tilde{x}\left(n\right)=f\left(g\left(n\right)\right)=g\left(n\right)+\mathrm{\λ}\sin \left(\mathrm{\πg}\left(n\right)\right)---\left(13\right)$

In the formula, f () is the transfer function between the input and output of output layer, is controlling the output of whole network, have level and smooth, asymptotic, dull characteristics, and be conducive to list entries is differentiated.The effect of f () is that signal value is revised within the specific limits, make it more close to original signal g (n), wherein λ sin (π g (n)) is to be the non-linear correction term of independent variable with g (n), and it makes that the pendulum signal is drawn close to original signal about near the original signal central point.The value of λ affects f () regulating the speed to output signal.In the application of reality, different signals and channel, the selection of λ should be different.

According to error back propagation algorithm and at random gradient descent algorithm realize renewal adjustment to the wavelet network parameter, can obtain after the derivation wavelet neural network hidden layer to the connection weight of output layer more new formula be

$v_k(n+1)=v_k\left(n\right)-{\mathrm{\μ}}_1\frac{\∂J\left(n\right)}{\∂v_k\left(n\right)}---\left(14\right)$

In the formula, μ ₁Be iteration step length.

$\frac{\∂J\left(n\right)}{\∂v_k\left(n\right)}=2\mathrm{\βe}\left(n\right)|{\tilde{x}}_R\left(n\right)+j{\tilde{x}}_I\left(n\right)|\·(\frac{\∂\tilde{x}\left(n\right)}{\∂v_{k,R}\left(n\right)}+j\frac{\∂\tilde{x}\left(n\right)}{\∂v_{k,I}\left(n\right)})---\left(15\right)$

$\frac{\∂\tilde{x}\left(n\right)}{\∂v_{k,R}\left(n\right)}=\frac{1}{\left|\tilde{x}\left(n\right)\right|}[f\left(g_R\left(n\right)\right)f^{\′}\left(g_R\left(n\right)\right)Q_{k,R}\left(n\right)+f\left(g_I\left(n\right)\right)f^{\′}\left(g_I\left(n\right)\right)Q_{k,I}\left(n\right)]---\left(16\right)$

In the formula, f ' () is derivative, down together.

In like manner

$\frac{\∂\tilde{x}\left(n\right)}{{\∂v}_{k,I}\left(n\right)}=\frac{1}{\left|\tilde{x}\left(n\right)\right|}[-f\left(g_R\left(n\right)\right)f^{\′}\left(g_R\left(n\right)\right)Q_{k,I}\left(n\right)+f\left(g_I\left(n\right)\right)f^{\′}\left(g_I\left(n\right)\right)Q_{k,R}\left(n\right)]---\left(17\right)$

In wushu (15)～(17) substitution formula (14), get final product to such an extent that the wavelet network hidden layer to the more new formula of output layer connection weight is

$v_k(n+1)=v_k\left(n\right)+{\mathrm{\μ}}_{1}K\left(n\right)Q_k^{*}\left(n\right)---\left(18\right)$

K(n)＝-2βe(n)[f(g _R(n))f′(g _R(n))+jf(g _I(n))f′(g _I(n))] (19)

In the formula, μ ₁Be iteration step length, * is conjugation.

In like manner, the weight that connects of input layer to hidden layer more new formula be

$w_{\mathrm{ik}}(n+1)=w_{\mathrm{ik}}\left(n\right)+{\mathrm{\μ}}_2{K}_0\left(n\right)T_i^{*}\left(n\right)---\left(20\right)$

In the formula, μ ₂Be iteration step length.

$K_0\left(n\right)=\mathrm{\βe}\left(n\right){\mathrm{\ψ}}_{a,b}^{\′}\left(u_{k,R}\left(n\right)\right)\mathrm{Re}\left\{\right[f\left(g_R\left(n\right)\right)\·f^{\′}\left(g_R\left(n\right)\right)+\mathrm{jf}\left(g_I\left(n\right)\right)f^{\′}\left(g_I\left(n\right)\right)]v_k^{*}\left(n\right)\}$

$+\mathrm{j\βe}\left(n\right){\mathrm{\ψ}}_{a,b}^{\′}\left(u_{k,I}\left(n\right)\right)\mathrm{Im}\left\{\right[f\left(g_R\left(n\right)\right)\·f^{\′}\left(g_R\left(n\right)\right)+\mathrm{jf}\left(g_I\left(n\right)\right)f^{\′}\left(g_I\left(n\right)\right)\left]v_k^{*}\left(n\right)\right\}---\left(21\right)$

The more new formula of scale factor a and shift factor b is

$a(n+1)=a\left(n\right)-{\mathrm{\μ}}_3\frac{\∂J\left(n\right)}{\∂a\left(n\right)}---\left(22\right)$

$b(n+1)=b\left(n\right)-{\mathrm{\μ}}_4\frac{\∂J\left(n\right)}{\∂b\left(n\right)}---\left(23\right)$

In the formula, μ ₃, μ ₄Be iteration step length.

$\frac{\∂J\left(n\right)}{\∂a\left(n\right)}=2\mathrm{\βe}\left(n\right)|{\tilde{x}}_R\left(n\right)+j{\tilde{x}}_I\left(n\right)|\·(\frac{\∂\left|{\tilde{x}}_R\left(n\right)\right|}{\∂a\left(n\right)}+j\frac{\∂\left|{\tilde{x}}_I\left(n\right)\right|}{\∂a\left(n\right)})---\left(24\right)$

In the formula

$\frac{\∂\left|{\tilde{x}}_R\left(n\right)\right|}{\∂a\left(n\right)}=\frac{1}{\left|\tilde{x}\left(n\right)\right|}[f\left(g_R\left(n\right)\right)f^{\′}\left(g_R\left(n\right)\right)\frac{\∂g_R\left(n\right)}{\∂a\left(n\right)}+f\left(g_I\left(n\right)\right)f^{\′}\left(g_I\left(n\right)\right)\frac{\∂g_I\left(n\right)}{\∂a\left(n\right)}]---\left(25\right)$

$\frac{{\∂g}_R\left(n\right)}{\∂a\left(n\right)}=v_{k,R}\left(n\right)\frac{\∂{\mathrm{\ψ}}_{a,b}\left(u_{k,R}\left(n\right)\right)}{\∂a\left(n\right)}-v_{k,I}\left(n\right)\frac{\∂{\mathrm{\ψ}}_{a,b}\left(u_{k,I}\left(n\right)\right)}{\∂a\left(n\right)}---\left(26\right)$

$\frac{{\∂g}_I\left(n\right)}{\∂a\left(n\right)}=v_{k,R}\left(n\right)\frac{{\∂\mathrm{\ψ}}_{a,b}\left(u_{k,I}\left(n\right)\right)}{\∂a\left(n\right)}+v_{k,I}\left(n\right)\frac{{\∂\mathrm{\ψ}}_{a,b}\left(u_{k,R}\left(n\right)\right)}{\∂a\left(n\right)}---\left(27\right)$

$\frac{{\∂\mathrm{\ψ}}_{a,b}\left(u_{k,R}\left(n\right)\right)}{\∂a\left(n\right)}=-{\left|a\right|}^{-\frac{1}{2}}\frac{(u_{k,R}\left(n\right)-b)}{a^2}{e}^{-\frac{1}{2}{\left(\frac{u_{k,R}\left(n\right)-b}{a}\right)}^2}+{\left|a\right|}^{-\frac{1}{2}}{\left(\frac{u_{k,R}\left(n\right)-b}{a}\right)}^2\left(\frac{u_{k,R}\left(n\right)-b}{a^2}\right)e^{-\frac{1}{2}{\left(\frac{u_{k,R}\left(n\right)-b}{a}\right)}^2}$

$-\frac{1}{2}{\left|a\right|}^{-3/2}\left(\frac{u_{k,R}\left(n\right)-b}{a}\right)e^{-\frac{1}{2}{\left(\frac{u_{k,R}\left(n\right)-b}{a}\right)}^2}---\left(28\right)$

With the u in the formula (28) _{K, R}(n) change u into _{K, I}(n) can obtain

Expression formula; According to the derivation of formula (25), can get

Expression formula (as space is limited, these expression formulas omit).Wushu (24)～(28) substitution formula (22) namely gets the iterative formula of scale factor a.

In like manner, can obtain iterative formula about shift factor b.According to above formula, finished the renewal to wavelet function scale factor and shift factor in the wavelet neural network, thereby carried out blind equalization.

2. fuzzy neural network controller

In fuzzy neural network controller, the controller with an input variable and an output variable is called the single argument fuzzy neural network controller, and its input variable number is called the dimension of fuzzy controller.Dimension is more high, control is more meticulous; But dimension is too high, and fuzzy control rule is just more complicated, and the realization of controller is just more difficult.This paper adopts the two-dimensional fuzzy controller in the single argument structure of fuzzy controller, and its input variable is mean square error E (n)=MSE (n) and its variation delta E (n)=MSE (n)-MSE (n-1).As output variable, it is more effective than the control of a D controller, and is easy to computer realization with the changing value Δ μ of step size mu.Its structure as shown in Figure 3.

The fuzzy rule of this fuzzy neural network (FNN) is designed to

Rule 1: if Δ E (n) for just and E (n) greatly, then Δ μ is honest;

Rule 2: if Δ E (n) for just and among the E (n), then Δ μ is zero;

Rule 3: if Δ E (n) for just and E (n) little, then Δ μ bears little;

Rule 4: if Δ E (n) be zero and E (n) big, then Δ μ is just little;

Rule 5: if Δ E (n) is among zero and the E (n), then Δ μ zero;

Rule 6: if Δ E (n) be zero and E (n) little, then Δ μ is negative little;

Rule 7: if Δ E (n) for negative and E (n) big, then Δ μ is just little;

Rule 8: if Δ E (n) is among negative and the E (n), then Δ μ zero;

Rule 9: if Δ E (n) for negative and E (n) is little, then Δ μ is negative big.

The processing procedure of each layer of FNN controller is as follows:

Ground floor: input layer, with E (n) and Δ E (n) the controller input variable as step-length.

$I_1^{\left(1\right)}\left(n\right)=\mathrm{\ΔE}\left(n\right)=\mathrm{MSE}\left(n\right)-\mathrm{MSE}(n-1)---\left(29\right)$

$I_2^{\left(1\right)}\left(n\right)=E\left(n\right)=\mathrm{MSE}\left(n\right)---\left(30\right)$

$O_{\mathrm{ql}}^{\left(1\right)}\left(n\right)=I_q^{\left(1\right)}\left(n\right)---\left(31\right)$

In the formula, q=1,2 is the input number of FNN, l=1,2,3 is fuzzy field, I ^(t), O ^(t)Be respectively FNN t (t=1,2 ..., 5) input and the output of layer, down with.

The second layer: obfuscation layer

$I_{\mathrm{ql}}^{\left(2\right)}\left(n\right)=O_{\mathrm{ql}}^{\left(1\right)}\left(n\right)---\left(32\right)$

$O_{\mathrm{ql}}^{\left(2\right)}\left(n\right)=\exp [-{\left(\frac{I_{\mathrm{ql}}^{\left(2\right)}\left(n\right)-m_{\mathrm{ql}}^{\left(2\right)}\left(n\right)}{{\mathrm{\σ}}_{\mathrm{ql}}^{\left(2\right)}\left(n\right)}\right)}^2]---\left(33\right)$

In the formula,

With

Expectation and the variance of representing input space fuzzy field respectively.For convenience of calculation, adopt fixing center (m in this article _QlAnd width (σ (n)) _Ql(n)).

The 3rd layer: rules layer.

$I_{\mathrm{ql}}^{\left(3\right)}\left(n\right)=O_{\mathrm{ql}}^{\left(2\right)}\left(n\right)---\left(34\right)$

$O_l^{\left(3\right)}=\mathrm{\Π}{I}_{\mathrm{ij}}^{\left(3\right)}\left(n\right)---\left(35\right)$

In the formula, r=1,2 ..., the preceding number of packages of 9 expression fuzzy rules.

The 4th layer: select layer, namely from the output of the 3rd floor, select the value of one tunnel maximum as the output of this layer, namely

$O^{\left(4\right)}=\max \left(O_r^{\left(3\right)}\right)---\left(36\right)$

Layer 5: normalization layer

O ⁽⁵⁾＝O ⁽⁴⁾·δ(i) (37)

In the formula, δ (i) controlled quentity controlled variable is mainly used to adjust the output of this layer, finishes the rear section of rule.

Layer 6: ambiguity solution layer

Δμ＝O ⁽⁶⁾＝O ⁽⁵⁾·MSE(n) (38)

Iteration step length in formula (22), (23) will become μ respectively ₃+ Δ μ, μ ₄+ Δ μ.This has just constituted the blind equalization algorithm of controlling the wavelet function mesoscale factor and shift factor iteration step length with the FNN controller, and the introducing of MSE (n) makes the change amount of step-length corresponding with mean square error.

In sum, utilize the advantage of FNN aspect control, control the shift factor of neural net hidden neuron wavelet function and the iteration step length of scale factor.Its main thought is to utilize neural net to adjust membership function and the adjustment inference rule of fuzzy logic inference system, utilizes the formal construction propagated forward structure of fuzzy inference rule, thereby can give full play to characteristics separately, realizes having complementary functions.Embodiment and analysis

In order to verify the validity of FHWNN method, utilize underwater acoustic channel to carry out emulation experiment, and compare with wavelet transformation constant modeling method (WTCMA), WNN and HWNN method.In the experiment, the transfer function of underwater acoustic channel is c=zeros (1,1001); C (1)=0.076; C (2)=0.122; C (1001)=1; Transmitting is that 16QAM, signal to noise ratio are 20dB, and the power length of equalizer is 32.To the WTCMA equalizer, the 7th tap initialization is 1, step size mu _WTCMA=0.003, adopt the DB2 wavelet decomposition, decomposing the number of plies is 2, power is initialized as 4; To the WNN equalizer, adopt 1/4 tap, λ _WNN=0.52, the wavelet function mesoscale factor and shift factor be initialized as a _WNN=5.5, b _WNN=0.0075; To the HWNN equalizer, adopt 1/4 tap, transversal filter also adopts 1/4 tap, step size mu=0.0001, the initialization a of the wavelet function mesoscale factor and shift factor _HWNN=7.5, b _HWNN=0.0098, weighted factor is α _HWNN=0.98, β _HWNN=0.02, λ _HWNN=3.8; To the FHWNN equalizer, adopt 1/4 tap, transversal filter also adopts 1/4 tap, step size mu _FHWNN=0.0001, the wavelet function mesoscale factor and shift factor be initialized as a _FHWNN=7.5, b _FHWNN=0.0098, weighted factor is α _FHWNN=0.95, β _FHWNN=0.05, λ _FHWNN=3.65.The simulation result of 500 Meng Te Kanos, as shown in Figure 4.

Fig. 4 shows, compares with HWNN with WTCMA, WNN, and the FHW-NN convergence rate has been accelerated 100 steps, 3000 steps and 300 steps respectively; Steady-state error has reduced 12dB, 3dB and 1.5dB respectively; The output planisphere is more clear, compact.

In addition, compare with traditional blind equalization method for wavelet neural network, on the computational efficiency of method: on time complexity, the each iterative process of hybrid wavelet neural net (FHWNN) blind balance method of Fuzzy Neural-network Control has only increased L multiplying (wherein L is the exponent number of transversal filter, equals the input unit number of wavelet network); On space complexity, only increased L+1 memory cell.

Claims (2)

1. the hybrid wavelet neural net blind balance method of a Fuzzy Neural-network Control is characterized in that comprising the steps:

A.) x (n) that will transmit obtains channel output vector b (n) through the impulse response channel, and wherein n is positive integer, the expression time series, down with;

B.) adopt interchannel noise N (n) and the described channel vector b of step a (n) to obtain the list entries of blind equalizer: y (n)=b (n)+N (n);

C.) the list entries y (n) of the described blind equalizer of step b improved hybrid wavelet neural net is successively obtained output signal

Utilize fuzzy neural network (FNN) to adjust in the improved hybrid wavelet neural net iteration step length of shift factor and scale factor in the neuron wavelet function, and with deviation delta E (n)=MSE (the n)-MSE (n-1) of mean square error E (n)=MSE (n) and the mean square error input as fuzzy neural network controller, MSE (n) be the n mean square error in the moment;

Wherein, step c) construction method of described improved hybrid wavelet neural net is as follows:

Transversal filter has constituted the linear segment of improved hybrid wavelet neural net, and wavelet neural network (WNN) has constituted non-linear partial; If i tap coefficient of transversal filter is c _i(n), i=1,2 ..., m, m are the number of wavelet neural network hybrid wavelet neural net (HWNN) input layer, down together; Improved hybrid wavelet neural net input layer i the neuronic T that is input as _i(n), hidden layer k neuronic u that is input as _k(n), be output as Q _k(n), k=1,2 ..., p, p are the number of HWNN hidden neuron, down together; Output layer be input as g (n), be output as

I neuron of input layer to hidden layer k neuronic connection weight is w _Ik(n), k neuron of hidden layer to the connection weight of output layer is v _k(n);

Signal, channel, the weights of network are decomposed into real part and imaginary part two parts, and then the state equation of network is

c _i(n)＝c _i，R(n)+jc _i，I(n) (1)

In the formula, c _{I, R}(n) be c _i(n) real part, c _{I, I}(n) be c _i(n) imaginary part,

Be imaginary unit, down together;

w _ik(n)＝w _ik，R(n)+jw _ik，I(n) (2)

v _k(n)＝v _k，R(n)+jv _k，I(n) (3)

y(n)＝y _R(n)+jy _I(n) (4)

$T_i\left(n\right)=\underset{t=1}{\overset{i}{\mathrm{\Σ}}}{c}_t\left(n\right)y(n+1-t)=\underset{t=1}{\overset{i}{\mathrm{\Σ}}}[c_{t,R}\left(n\right)y_R(n+1-t)-c_{t,I}\left(n\right)y_I(n+1-t)]$

$+j\underset{t=1}{\overset{i}{\mathrm{\Σ}}}[c_{t,R}\left(n\right)y_I(n+1-t)+c_{i,I}\left(n\right)y_R(n+1-t)]---\left(5\right)$

In the formula, t represents delay time, gets positive integer value, and t=1,2 ..., i;

$u_k\left(n\right)=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{w}_{\mathrm{ik}}\left(n\right)T_i\left(n\right)=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}[w_{\mathrm{ik},R}\left(n\right)T_{i,R}\left(n\right)-w_{\mathrm{ik},I}\left(n\right)T_{i,I}\left(n\right)]$

$+j\underset{i=1}{\overset{m}{\mathrm{\Σ}}}[w_{\mathrm{ik},R}\left(n\right)T_{i,I}\left(n\right)-w_{\mathrm{ik},I}\left(n\right)T_{i,R}\left(n\right)]---\left(6\right)$

Q _k(n)=ψ _a,b(u _k,R(n))+jψ _a,b(u _k,I(n)) (7)

In the formula, ψ _{A, b}() expression is carried out wavelet transformation to the hidden layer input signal, selects the Morlet wavelet mother function here, then

${\mathrm{\ψ}}_{a,b}\left(u_{k,R}\left(n\right)\right)={\left|a\right|}^{-\frac{1}{2}}\mathrm{\ψ}\left(\frac{u_{k,R}\left(n\right)-b}{a}\right)={\left|a\right|}^{-\frac{1}{2}}\left(\frac{u_{k,R}\left(n\right)-b}{a}\right)e^{-\frac{1}{2}{\left(\frac{u_{k,R}\left(n\right)-b}{a}\right)}^2}---\left(8\right)$

In the formula, b is shift factor, and a is scale factor; With u in the formula (8) _{K, R}(n) change u into _{K, I}(n) just obtain ψ _{A, b}(u _{K, I}(n)) expression formula, wavelet neural network is output as:

${\tilde{x}}_2\left(n\right)=\underset{k=1}{\overset{p}{\mathrm{\Σ}}}[v_{k,R}\left(n\right)Q_{k,R}\left(n\right)-v_{k,I}\left(n\right)Q_{k,I}\left(n\right)]+j\underset{k=1}{\overset{p}{\mathrm{\Σ}}}[v_{k,R}\left(n\right)Q_{k,I}\left(n\right)+v_{k,I}\left(n\right)Q_{k,R}\left(n\right)]---\left(9\right)$

Transversal filter is output as

${\tilde{x}}_1\left(n\right)=c_i^T\left(n\right)y(n+1-i),i=\mathrm{1,2},...,m---\left(10\right)$

Will

With

Weighting is merged,

$g\left(n\right)=\mathrm{\α}{\tilde{x}}_1\left(n\right)+\mathrm{\β}{\tilde{x}}_2\left(n\right)---\left(11\right)$

In the formula, 0≤α≤1,0≤β≤1 is weighted factor, and satisfies alpha+beta=1, and improved HWNN finally is output as

$\tilde{x}\left(n\right)=f\left(g\left(n\right)\right)=g\left(n\right)+\mathrm{\λ}\sin \left(\mathrm{\πg}\left(n\right)\right)---\left(12\right)$

In the formula, f () is the transfer function between the input and output of output layer, and wherein λ sin (π g (n)) is to be the non-linear correction term of independent variable with g (n), and it makes that the pendulum signal is drawn close to original signal about near the original signal central point;

Described hidden layer to the update method of output layer connection weight is:

$v_k(n+1)=v_k\left(n\right)+{\mathrm{\μ}}_{1}K\left(n\right)Q_k^{*}\left(n\right),$

K(n)=-2βe(n)[f(g _R(n))f′(g _R(n))+jf(g _I(n))f′(g _I(n))]，

In the formula, μ ₁Be iteration step length, * is conjugation; E (n) is the error signal of equalizer;

Be imaginary unit, subscript " ' " the expression differentiate, down together;

The weight that described input layer to hidden layer connects more new formula is:

$w_{\mathrm{ik}}(n+1)=w_{\mathrm{ik}}\left(n\right)+{\mathrm{\μ}}_2{K}_0\left(n\right)T_i^{*}\left(n\right),$

$K_0\left(n\right)=\mathrm{\βe}\left(n\right){\mathrm{\ψ}}_{a,b}^{\′}\left(u_{k,R}\left(n\right)\right)\mathrm{Re}\left\{\right[f\left(g_R\left(n\right)\right)\·f^{\′}\left(g_R\left(n\right)\right)+\mathrm{jf}\left(g_I\left(n\right)\right)f^{\′}\left(g_I\left(n\right)\right)\left]v_k^{*}\left(n\right)\right\}$

$+\mathrm{j\βe}\left(n\right){\mathrm{\ψ}}_{a,b}^{\′}\left(u_{k,I}\left(n\right)\right)\mathrm{Im}\left\{\right[f\left(g_R\left(n\right)\right)\·f^{\′}\left(g_R\left(n\right)\right)+\mathrm{jf}\left(g_I\left(n\right)\right)f^{\′}\left(g_I\left(n\right)\right)\left]v_k^{*}\left(n\right)\right\},$

In the formula, μ ₂Be iteration step length;

The update method of described scale factor a and shift factor b is:

$a(n+1)=a\left(n\right)-{\mathrm{\μ}}_3\frac{\∂J\left(n\right)}{\∂a\left(n\right)},$

$b(n+1)=b\left(n\right)-{\mathrm{\μ}}_4\frac{\∂J\left(n\right)}{\∂b\left(n\right)},$

$\frac{\∂J\left(n\right)}{\∂a\left(n\right)}=2\mathrm{\β}\·e\left(n\right)|{\tilde{x}}_R\left(n\right)+j{\tilde{x}}_I\left(n\right)|\·[\frac{\∂\left|{\tilde{x}}_R\left(n\right)\right|}{\∂a\left(n\right)}+j\frac{\∂\left|{\tilde{x}}_I\left(n\right)\right|}{\∂a\left(n\right)}]$

In the formula

$\frac{\∂\left|{\tilde{x}}_R\left(n\right)\right|}{\∂a\left(n\right)}=\frac{1}{\left|\tilde{x}\left(n\right)\right|}\left[(f\left(g_R\left(n\right)\right)f^{\′}\left(g_R\left(n\right)\right)\frac{\∂g_R\left(n\right)}{\∂a\left(n\right)}+f\left(g_I\left(n\right)\right)f^{\′}\left(g_I\left(n\right)\right)\frac{\∂g_I\left(n\right)}{\∂a\left(n\right)})\right],$

$\frac{\∂g_R\left(n\right)}{\∂a\left(n\right)}{=v}_{k,R}\left(n\right)\frac{\∂{\mathrm{\ψ}}_{a,b}\left(u_{k,R}\left(n\right)\right)}{\∂a\left(n\right)}-v_{k,I}\left(n\right)\frac{\∂{\mathrm{\ψ}}_{a,b}\left(u_{k,I}\left(n\right)\right)}{\∂a\left(n\right)},$

$\frac{\∂g_I\left(n\right)}{\∂a\left(n\right)}=v_{k,R}\left(n\right)\frac{\∂{\mathrm{\ψ}}_{a,b}\left(u_{k,I}\left(n\right)\right)}{\∂a\left(n\right)}+v_{k,I}\left(n\right)\frac{\∂{\mathrm{\ψ}}_{a,b}\left(u_{k,R}\left(n\right)\right)}{\∂a\left(n\right)},$ $\frac{\∂{\mathrm{\ψ}}_{a,b}\left(u_{k,R}\left(n\right)\right)}{\∂a\left(n\right)}=-{\left|a\right|}^{-\frac{1}{2}}\frac{(u_{k,R}\left(n\right)-b)}{a^2}{e}^{-\frac{1}{2}{\left(\frac{u_{k,R}\left(n\right)-b}{a}\right)}^2}$

$+{\left|a\right|}^{-\frac{1}{2}}{\left(\frac{u_{k,R}\left(n\right)-b}{a}\right)}^2\left(\frac{u_{k,R}\left(n\right)-b}{a^2}\right)e^{-\frac{1}{2}{\left(\frac{u_{k,R}\left(n\right)-b}{a}\right)}^2}$

$-\frac{1}{2}{\left|a\right|}^{-3/2}\left(\frac{u_{k,R}\left(n\right)-b}{a}\right)e^{-\frac{1}{2}{\left(\frac{u_{k,R}\left(n\right)-b}{a}\right)}^2},$

In the formula, μ ₃, μ ₄Be iteration step length.

2. the hybrid wavelet neural net blind balance method of Fuzzy Neural-network Control according to claim 1 is characterized in that the construction method of described fuzzy neural network controller is as follows:

The fuzzy rule of this fuzzy neural network (FNN) is:

Rule 1: if Δ E (n) for just and E (n) greatly, then Δ μ is honest;

Rule 2: if Δ E (n) for just and among the E (n), then Δ μ is zero;

Rule 3: if Δ E (n) for just and E (n) little, then Δ μ bears little;

Rule 4: if Δ E (n) be zero and E (n) big, then Δ μ is just little;

Rule 5: if Δ E (n) is among zero and the E (n), then Δ μ zero;

Rule 6: if Δ E (n) be zero and E (n) little, then Δ μ is negative little;

Rule 7: if Δ E (n) for negative and E (n) big, then Δ μ is just little;

Rule 8: if Δ E (n) is among negative and the E (n), then Δ μ zero;

Rule 9: if Δ E (n) for negative and E (n) is little, then Δ μ is negative big;

Wherein, Δ μ represents the changing value of step size mu;

The processing procedure of each layer of FNN controller is as follows:

Ground floor: input layer, with E (n) and Δ E (n) the controller input variable as step-length;

$I_1^{\left(1\right)}\left(n\right)=\mathrm{\ΔE}\left(n\right)=\mathrm{MSE}\left(n\right)-\mathrm{MSE}(n-1),$

$I_2^{\left(1\right)}\left(n\right)=E\left(n\right)=\mathrm{MSE}\left(n\right),$

$O_{\mathrm{ql}}^{\left(1\right)}\left(n\right)=I_q^{\left(1\right)}\left(n\right),$

In the formula, q=1,2 is the input number of FNN, l=1,2,3 is fuzzy field, I ^(t), O ^(t)Be respectively the input of FNN t layer and output, t=1,2 ..., 5, down together;

The second layer: obfuscation layer

$I_{\mathrm{ql}}^{\left(2\right)}\left(n\right)=O_{\mathrm{ql}}^{\left(1\right)}\left(n\right),$

$O_{\mathrm{ql}}^{\left(2\right)}\left(n\right)=\exp [-{\left(\frac{I_{\mathrm{ql}}^{\left(2\right)}\left(n\right)-m_{\mathrm{ql}}^{\left(2\right)}\left(n\right)}{{\mathrm{\σ}}_{\mathrm{ql}}^{\left(2\right)}\left(n\right)}\right)}^2]$

In the formula,

With

Expectation and the variance of representing input space fuzzy field respectively;

The 3rd layer: rules layer

$I_{\mathrm{ql}}^{\left(3\right)}\left(n\right)=O_{\mathrm{ql}}^{\left(2\right)}\left(n\right),$

$O_r^{\left(3\right)}=\mathrm{\Π}{I}_{\mathrm{ql}}^{\left(3\right)}\left(n\right),$

In the formula, r=1,2 ..., the preceding number of packages of 9 expression fuzzy rules;

The 4th layer: select layer, namely from the output of the 3rd floor, select the value of one tunnel maximum as the output of this layer, namely

$O^{\left(4\right)}=\max \left(O_r^{\left(3\right)}\right),$

Layer 5: normalization layer

O ⁽⁵⁾=O ⁽⁴⁾·δ(i)，

In the formula, δ (i) controlled quentity controlled variable is mainly used to adjust the output of this layer, finishes the rear section of rule;

Layer 6: ambiguity solution layer

Δμ=O ⁽⁶⁾=O ⁽⁵⁾·MSE(n)。

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