CN101924718B

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

Info

Publication number: CN101924718B
Application number: CN 201010267951
Authority: CN
Inventors: 郭业才; 王丽华
Original assignee: Nanjing University of Information Science and Technology
Current assignee: Nanjing University of Information Science and Technology
Priority date: 2010-08-30
Filing date: 2010-08-30
Publication date: 2013-07-03
Anticipated expiration: 2030-08-30
Also published as: CN101924718A

Abstract

The present invention discloses a mixed wavelet neural network blind equalization method controlled by a fuzzy neural network. The method of the present invention includes the following steps: a.) Obtaining a channel output vector b(n) through a transmission signal x(n) through an impulse response channel; b .) using channel noise N(n) and the channel output vector b(n) described in step a to obtain the input sequence of the blind equalizer; c.) the input sequence y(n) of the blind equalizer described in step b sequentially The output signal is obtained by the improved hybrid wavelet neural network

Use the fuzzy neural network (FNN) to adjust the iterative step size of the translation factor and scale factor in the neuron wavelet function in the improved hybrid wavelet neural network, and use the mean square error E(n)=MSE(n) and the mean square error Deviation ΔE (n) = MSE (n) - MSE (n-1) as the input of the fuzzy neural network controller. The system of the invention has high flexibility and avoids the predicament of easily falling into local minimum.

Description

Hybrid wavelet neural network blind equalization method controlled by fuzzy neural network

技术领域 technical field

本发明涉及一种模糊神经网络控制的混合小波神经网络盲均衡方法，属于多小波模糊神经网络盲均衡方法的技术领域。The invention relates to a mixed wavelet neural network blind equalization method controlled by a fuzzy neural network, belonging to the technical field of multi-wavelet fuzzy neural network blind equalization methods.

背景技术 Background technique

在水声通信系统中，信道的多径衰落和畸变产生的码间干扰(ISI，Inter-SymbolInterference)，降低了系统的性能，影响着通信质量。抑制码间干扰的有效方法是采用不需训练序列的盲均衡技术。盲均衡技术的本质是通过设计性能优越的算法来调整均衡器参数，是一个求逆系统的非线性逼近问题；而小波神经网络(WNN，Wavelet NeuralNetwork)将神经网络的自学习功能和小波的时频局域化性质结合起来，具有自适应分辨性和良好的容错能力(见文献[1]：Zhang Q H，Benveniste A.Wavelet networks[J].IEEETransactions on Neural Networks，1992，3(6)：889-898.)。而采用传统WNN的盲均衡算法，仍然存在收敛速度慢和容易陷入局部极小值的缺陷(见文献[2]：Rahib H.Abiyev.Neuro-fuuzy system for equalization channel distortion[J].International Journal of Computati-onal Intelligence，2005，Fall：229-232；文献[3]：刘国军，唐降龙，黄剑华，刘家峰。基于模糊小波的图像对比度增强算法[J].电子学报，2005，33(4)：643-647；文献[4]：桂延宁，焦李成，张福顺。基于小波和BP神经网络的无线电探测目标识别技术[J].电子学报，2003，31(12)：1811-1814.)。模糊神经网络(FNN，Fuzzy Neural Network)汇集了模糊理论与神经网络的优点，集学习、联想、识别、自适应及模糊信息处理于一体，具有计算简便、容错能力强、处理信息范围大、学习速度快等优点(见文献[5]：张晓琴.基于模糊神经网络盲均衡算法的研究[D].沈阳太原：太原理工大学，2008；文献[6]：徐小来，雷英杰，谢文彪。基于UKF的自组织直觉模糊神经网络[J].电子学报，2010，28(3)：638-645.)。因此，将FNN与WNN相结合应用于盲均衡方法中，将是有研究意义的课题。In the underwater acoustic communication system, inter-symbol interference (ISI, Inter-SymbolInterference) generated by channel multipath fading and distortion reduces system performance and affects communication quality. An effective way to suppress intersymbol interference is to use blind equalization techniques that do not require training sequences. The essence of blind equalization technology is to adjust the equalizer parameters by designing an algorithm with superior performance. Combined with the frequency localization properties, it has adaptive resolution and good fault tolerance (see literature [1]: Zhang Q H, Benveniste A. Wavelet networks [J]. IEEE Transactions on Neural Networks, 1992, 3 (6): 889-898.). However, the traditional WNN blind equalization algorithm still has the defects of slow convergence speed and easy to fall into local minimum (see literature [2]: Rahib H.Abiyev.Neuro-fuuzy system for equalization channel distortion[J].International Journal of Computati-onal Intelligence, 2005, Fall: 229-232; Literature [3]: Liu Guojun, Tang Jianglong, Huang Jianhua, Liu Jiafeng. Image contrast enhancement algorithm based on fuzzy wavelet [J]. Electronic Journal, 2005, 33(4): 643- 647; Literature [4]: Gui Yanning, Jiao Licheng, Zhang Fushun. Radio detection target recognition technology based on wavelet and BP neural network [J]. Electronic Journal, 2003, 31(12): 1811-1814.). Fuzzy Neural Network (FNN, Fuzzy Neural Network) brings together the advantages of fuzzy theory and neural network, and integrates learning, association, recognition, self-adaptation and fuzzy information processing. Fast speed and other advantages (see literature [5]: Zhang Xiaoqin. Research on blind equalization algorithm based on fuzzy neural network [D]. Shenyang Taiyuan: Taiyuan University of Technology, 2008; literature [6]: Xu Xiaolai, Lei Yingjie, Xie Wenbiao. Based on UKF Self-organizing intuitionistic fuzzy neural network [J]. Electronic Journal, 2010, 28(3): 638-645.). Therefore, combining FNN and WNN in the blind equalization method will be a subject of research significance.

混合小波神经网络(HWNN)盲均衡方法是在WNN输入层之前级联一个横向滤波器(见文献[7]：肖瑛，董玉华。一种级联混合小波神经网络盲均衡算法[J].信息与控制，2009，38(4)：479-483.)，其不足之处有：①横向滤波器各节点输出直接作为WNN输入层相应神经元的输入，即WNN输入层各神经元的输入之间没有任何联系；②没有把信号的实部与虚部分开考虑，不适用于PSK、QAM等复数调制系统；③对小波函数中尺度因子和平移因子的迭代步长没有进行模糊控制与调整，从而影响了系统处理信息的灵活性和速度，均衡性能较差。The hybrid wavelet neural network (HWNN) blind equalization method is to cascade a transverse filter before the WNN input layer (see literature [7]: Xiao Ying, Dong Yuhua. A cascaded hybrid wavelet neural network blind equalization algorithm [J]. Information and Control, 2009, 38(4): 479-483.), its disadvantages are: ①The output of each node of the transversal filter is directly used as the input of the corresponding neuron in the WNN input layer, that is, the input of each neuron in the WNN input layer There is no connection between them; ②The real part and the imaginary part of the signal are not considered separately, and it is not suitable for complex modulation systems such as PSK and QAM; ③There is no fuzzy control and adjustment of the iterative step size of the scale factor and translation factor in the wavelet function, As a result, the flexibility and speed of system processing information are affected, and the equalization performance is poor.

发明内容 Contents of the invention

本发明目的是针对现有技术存在的缺陷提供一种模糊神经网络控制的混合小波神经网络盲均衡方法。The object of the present invention is to provide a blind equalization method of mixed wavelet neural network controlled by fuzzy neural network aiming at the defects existing in the prior art.

本发明为实现上述目的，采用如下技术方案：In order to achieve the above object, the present invention adopts the following technical solutions:

本发明模糊神经网络控制的混合小波神经网络盲均衡方法，其特征在于包括如下步骤：The hybrid wavelet neural network blind equalization method controlled by fuzzy neural network of the present invention is characterized in that comprising the following steps:

a.)将发射信号x(n)经过脉冲响应信道得到信道输出向量b(n)，其中n为正整数，表示时间序列，下同；a.) Pass the transmitted signal x(n) through the impulse response channel to obtain the channel output vector b(n), where n is a positive integer representing a time sequence, the same below;

b.)采用信道噪声N(n)和步骤a所述的信道输出向量b(n)得到盲均衡器的输入序列：y(n)＝b(n)+N(n)；b.) adopt the channel noise N(n) and the channel output vector b(n) described in step a to obtain the input sequence of the blind equalizer: y(n)=b(n)+N(n);

c.)将步骤b所述的盲均衡器的输入序列y(n)依次经过改进的混合小波神经网络得到输出信号

c.) The input sequence y(n) of the blind equalizer described in step b is sequentially passed through the improved mixed wavelet neural network to obtain the output signal

利用模糊神经网络(FNN)来调整改进的混合小波神经网络中神经元小波函数中平移因子和尺度因子的迭代步长，并以均方误差E(n)＝MSE(n)与均方误差的偏差ΔE(n)＝MSE(n)-MSE（n-1)作为模糊神经网络控制器的输入。Use the fuzzy neural network (FNN) to adjust the iterative step size of the translation factor and scale factor in the neuron wavelet function in the improved hybrid wavelet neural network, and use the mean square error E(n)=MSE(n) and the mean square error Deviation ΔE (n) = MSE (n) - MSE (n-1) as the input of the fuzzy neural network controller.

优选地，所述改进的混合小波神经网络的构建方法如下：Preferably, the construction method of the improved hybrid wavelet neural network is as follows:

横向滤波器构成了改进的混合小波神经网络的线性部分，而小波神经网络(WNN)构成了非线性部分；横向滤波器第i个抽头系数为c_i(n)，i＝1，2，…，m，m为混合小波神经网络(HWNN)输入层神经元的个数，下同；改进的混合小波神经网络输入层第i个神经元的输入为T_i(n)，隐层第k个神经元的输入为u_k(n)，输出为Q_k(n)，k＝1，2，…，p，p为HWNN隐层神经元的个数，下同；输出层的输入为g(n)，输出为

输入层第i个神经元至隐层第k个神经元的连接权重为w_ik(n)，隐层第k个神经元至输出层的连接权重为v_k(n)；The transversal filter constitutes the linear part of the improved hybrid wavelet neural network, and the wavelet neural network (WNN) constitutes the nonlinear part; the i-th tap coefficient of the transversal filter is c _i (n), i=1, 2, ... , m, m is the number of neurons in the input layer of the hybrid wavelet neural network (HWNN), the same below; the input of the neuron i in the input layer of the improved hybrid wavelet neural network is T _i (n), and the kth neuron in the hidden layer The input of the neuron is u _k (n), the output is Q _k (n), k=1, 2, ..., p, p is the number of neurons in the hidden layer of HWNN, the same below; the input of the output layer is g( n), the output is

The connection weight from the i-th neuron in the input layer to the k-th neuron in the hidden layer is w _ik (n), and the connection weight from the k-th neuron in the hidden layer to the output layer is v _k (n);

将网络的信号、信道、权值等分解为实部和虚部两部分，则网络的状态方程为Decompose the network signal, channel, weight, etc. into two parts, the real part and the imaginary part, then the state equation of the network is

c_i(n)＝c_i，R(n)+jc_i，I(n) (1)c _i (n) = c _{i, R} (n) + jc _{i, I} (n) (1)

式中，c_i，R(n)为c_i(n)的实部，c_i，I(n)为c_i(n)的虚部，

表示虚数单位，下同；In the formula, c _{i, R} (n) is the real part of c _i (n), and c _{i, I} (n) is the imaginary part of c _i (n),

Indicates the imaginary unit, the same below;

w_ik(n)＝w_ik，R(n)+jw_ik，I(n) (2)w _ik (n)=wi _{ik, R} (n)+jw _{ik, I} (n) (2)

v_k(n)＝v_k，R(n)+jv_k，I(n) (3)v _k (n) = v _{k, R} (n) + jv _{k, I} (n) (3)

y(n)＝y_R(n)+jy_I(n) (4)y(n)=y _R (n)+jy _I (n) (4)

${T T}_{i i} ((n no)) = = {Σ Σ}_{t t = = 11}^{i i} {c c}_{t t} ((n no)) y the y ((n no + + 11 - - t t)) = = {Σ Σ}_{t t = = 11}^{i i} (({c c}_{t t,, R R} ((n no)) {y the y}_{R R} ((n no + + 11 - - t t)) - - {c c}_{t t,, I I} ((n no)) {y the y}_{I I} ((n no + + 11 - - t t))))$

$+ + j j {Σ Σ}_{t t = = 11}^{i i} (({c c}_{t t,, R R} ((n no)) {y the y}_{I I} ((n no + + 11 - - t t)) + + {c c}_{i i,, I I} ((n no)) {y the y}_{R R} ((n no + + 11 - - t t)))) - - - - - - ((55))$

${u u}_{k k} ((n no)) = = {Σ Σ}_{i i = = 11}^{m m} {w w}_{ik ik} ((n no)) {T T}_{i i} ((n no)) = = {Σ Σ}_{i i = = 11}^{m m} [[{w w}_{ik ik,, R R} ((n no)) {T T}_{i i,, R R} ((n no)) - - {w w}_{ik ik,, I I} ((n no)) {T T}_{i i,, I I} ((n no))]]$

$+ + j j {Σ Σ}_{i i = = 11}^{m m} [[{w w}_{ik ik,, R R} ((n no)) {T T}_{i i,, I I} ((n no)) - - {w w}_{ik ik,, I I} ((n no)) {T T}_{i i,, R R} ((n no))]] - - - - - - ((66))$

Q_k(n)＝ψ_a，b(u_k，R(n))+jψ_a，b(u_k，I(n)) (7)Q _k (n) = ψ _{a, b} ( _{uk, R} (n)) + jψ _{a, b} (u _{k, I} (n)) (7)

式中，ψ_a，b(·)表示对隐层输入信号进行小波变换，这里选择Morlet小波母函数，则In the formula, ψ _{a, b} ( ) represents the wavelet transform of the input signal of the hidden layer. Here, the Morlet wavelet mother function is selected, then

${ψ ψ}_{a a,, b b} (({u u}_{k k,, R R} ((n no)))) = = {| | a a | |}^{- - \frac{11}{22}} ψ ψ ((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{a a})) = = {| | a a | |}^{- - \frac{11}{22}} ((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{a a})) {e e}^{- - \frac{11}{22} {((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{a a}))}^{22}} - - - - - - ((88))$

式中，b为平移因子，a为尺度因子；将式(8)中u_k，R(n)换成u_k，I(n)就得到ψ_a，b(u_k，I(n))的表达式，小波神经网络的输出为：In the formula, b is the translation factor, a is the scale factor; in formula (8) u _{k, R} (n) is replaced by u _{k, I} (n) to get ψ _{a, b} (u _{k, I} (n)) The expression of the wavelet neural network output is:

${\overset{~ ~}{x x}}_{22} ((n no)) = = {Σ Σ}_{k k = = 11}^{p p} [[{v v}_{k k,, R R} ((n no)) {Q Q}_{k k,, R R} ((n no)) - - {v v}_{k k,, I I} ((n no)) {Q Q}_{k k,, I I} ((n no))]] + + j j {Σ Σ}_{k k = = 11}^{p p} [[{v v}_{k k,, R R} ((n no)) {Q Q}_{k k,, I I} ((n no)) + + {v v}_{k k,, I I} ((n no)) {Q Q}_{k k,, R R} ((n no))]] - - - - - - ((99))$

横向滤波器的输出为：The output of the transversal filter is:

${\overset{~ ~}{x x}}_{11} ((n no)) = = {c c}_{i i}^{T T} ((n no)) y the y ((n no + + 11 - - i i)),, i i = = 1,2 1,2,, \cdot &Center Dot; \cdot \cdot \cdot \cdot,, m m - - - - - - ((1010))$

将和

加权融合，得：Will and

Weighted fusion, get:

$g g ((n no)) = = α α {\overset{~ ~}{x x}}_{11} ((n no)) + + β β {\overset{~ ~}{x x}}_{22} ((n no)) - - - - - - ((1111))$

式中，0≤α，β≤1，为加权因子，并且满足α+β＝1，改进的HWNN最终输出为：In the formula, 0≤α, β≤1, is the weighting factor, and satisfies α+β=1, the final output of the improved HWNN is:

$\overset{~ ~}{x x} ((n no)) = = f f ((g g ((n no)))) = = g g ((n no)) + + λ λ sin sin ((πg πg ((n no)))) - - - - - - ((1212))$

式中，f(·)为输出层的输入和输出之间的传递函数，其中λsin(πg(n))是以g(n)为自变量的非线性修正项，它使得在原信号中心点附近左右摆信号向原信号靠拢。In the formula, f( ) is the transfer function between the input and output of the output layer, where λsin(πg(n)) is a nonlinear correction term with g(n) as the independent variable, which makes The left and right swing signals are close to the original signal.

优选地，所述隐层到输出层连接权重的更新方法为：Preferably, the method for updating the connection weights from the hidden layer to the output layer is:

${v v}_{k k} ((n no + + 11)) = = {v v}_{k k} ((n no)) + + {μ μ}_{11} K K ((n no)) {Q Q}_{k k}^{* *} ((n no)),,$

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

式中μ₁为迭代步长，*为共轭，j表示虚数，上标“′”表示求导，下同。In the formula, μ ₁ is the iterative step size, * is the conjugate, j is an imaginary number, and the superscript "'" means derivation, the same below.

优选地，所述输入层至隐层连接的权重更新公式为：Preferably, the weight update formula for the connection between the input layer and the hidden layer is:

${w w}_{ik ik} ((n no + + 11)) = = {w w}_{ik ik} ((n no)) + + {μ μ}_{22} {K K}_{00} ((n no)) {T T}_{i i}^{* *} ((n no)),,$

${K K}_{00} ((n no)) = = βe βe ((n no)) {ψ ψ}_{a a,, b b}^{' '} (({u u}_{k k,, R R} ((n no)))) Re Re {{[[f f (({g g}_{R R} ((n no)))) \cdot \cdot {f f}^{' '} (({g g}_{R R} ((n no)))) + + jf jf (({g g}_{I I} ((n no)))) {f f}^{' '} (({g g}_{I I} ((n no))))]] {v v}_{k k}^{* *} ((n no))}}$

$+ + jβe jβe ((n no)) {ψ ψ}_{a a,, b b}^{' '} (({u u}_{k k,, I I} ((n no)))) Im Im {{[[f f (({g g}_{R R} ((n no)))) \cdot &Center Dot; {f f}^{' '} (({g g}_{R R} ((n no)))) + + jf jf (({g g}_{I I} ((n no)))) {f f}^{' '} (({g g}_{I I} ((n no))))]] {v v}_{k k}^{* *} ((n no))}},,$

式中，μ₂为迭代步长。In the formula, μ ₂ is the iteration step size.

优选地，所述尺度因子a和平移因子b的更新方法为：Preferably, the update method of the scale factor a and the translation factor b is:

$a a ((n no + + 11)) = = a a ((n no)) - - {μ μ}_{33} \frac{&PartialD; &PartialD; J J ((n no))}{&PartialD; &PartialD; a a ((n no))},,$

$b b ((n no + + 11)) = = b b ((n no)) - - {μ μ}_{44} \frac{&PartialD; &PartialD; J J ((n no))}{&PartialD; &PartialD; b b ((n no))},,$

$\frac{&PartialD; &PartialD; J J ((n no))}{&PartialD; &PartialD; a a ((n no))} = = 22 βe βe ((n no)) | | {\overset{~ ~}{x x}}_{R R} ((n no)) + + j j {\overset{~ ~}{x x}}_{I I} ((n no)) | | \cdot &Center Dot; ((\frac{&PartialD; &PartialD; | | {\overset{~ ~}{x x}}_{R R} ((n no)) | |}{&PartialD; &PartialD; a a ((n no))} + + j j \frac{&PartialD; &PartialD; | | {\overset{~ ~}{x x}}_{I I} ((n no)) | |}{&PartialD; &PartialD; a a ((n no))})),,$

式中In the formula

$\frac{&PartialD; &PartialD; | | {\overset{~ ~}{x x}}_{R R} ((n no)) | |}{&PartialD; &PartialD; a a ((n no))} = = \frac{11}{| | \overset{~ ~}{x x} ((n no)) | |} [[f f (({g g}_{R R} ((n no)))) {f f}^{' '} (({g g}_{R R} ((n no)))) \frac{&PartialD; &PartialD; {g g}_{R R} ((n no))}{&PartialD; &PartialD; a a ((n no))} + + f f (({g g}_{I I} ((n no)))) {f f}^{' '} (({g g}_{I I} ((n no)))) \frac{&PartialD; &PartialD; {g g}_{I I} ((n no))}{&PartialD; &PartialD; a a ((n no))}]],,$

$\frac{{&PartialD; &PartialD; g g}_{R R} ((n no))}{&PartialD; &PartialD; a a ((n no))} = = {v v}_{k k,, R R} ((n no)) \frac{&PartialD; &PartialD; {ψ ψ}_{a a,, b b} (({u u}_{k k,, R R} ((n no))))}{&PartialD; &PartialD; a a ((n no))} - - {v v}_{k k,, I I} ((n no)) \frac{&PartialD; &PartialD; {ψ ψ}_{a a,, b b} (({u u}_{k k,, I I} ((n no))))}{&PartialD; &PartialD; a a ((n no))},,$

$\frac{{&PartialD; &PartialD; g g}_{I I} ((n no))}{&PartialD; &PartialD; a a ((n no))} = = {v v}_{k k,, R R} ((n no)) \frac{{&PartialD; &PartialD; ψ ψ}_{a a,, b b} (({u u}_{k k,, I I} ((n no))))}{&PartialD; &PartialD; a a ((n no))} + + {v v}_{k k,, I I} ((n no)) \frac{{&PartialD; &PartialD; ψ ψ}_{a a,, b b} (({u u}_{k k,, R R} ((n no))))}{&PartialD; &PartialD; a a ((n no))},,$

$\frac{{&PartialD; &PartialD; ψ ψ}_{a a,, b b} (({u u}_{k k,, R R} ((n no))))}{&PartialD; &PartialD; a a ((n no))} = = - - {| | a a | |}^{- - \frac{11}{22}} \frac{(({u u}_{k k,, R R} ((n no)) - - b b))}{{a a}^{22}} {e e}^{- - \frac{11}{22} {((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{a a}))}^{22}}$

$+ + {| | a a | |}^{- - \frac{11}{22}} {((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{a a}))}^{22} ((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{{a a}^{22}})) {e e}^{- - \frac{11}{22} {((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{a a}))}^{22}}$

$- - \frac{11}{22} {| | a a | |}^{- - 33 / / 22} ((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{a a})) {e e}^{- - \frac{11}{22} {((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{a a}))}^{22}},,$

式中，μ₃，μ₄为迭代步长。In the formula, μ ₃ and μ ₄ are the iteration step size.

优选地，所述模糊神经网络控制器的构建方法如下：Preferably, the construction method of the fuzzy neural network controller is as follows:

此模糊神经网络(FNN)的模糊规则为：The fuzzy rules of this fuzzy neural network (FNN) are:

规则1：如果ΔE(n)为正且E(n)大，则Δμ正大；Rule 1: If ΔE(n) is positive and E(n) is large, then Δμ is positive;

规则2：如果ΔE(n)为正且E(n)中，则Δμ零；Rule 2: If ΔE(n) is positive and E(n) is neutral, then Δμ is zero;

规则3：如果ΔE(n)为正且E(n)小，则Δμ负小；Rule 3: If ΔE(n) is positive and E(n) is small, then Δμ is negatively small;

规则4：如果ΔE(n)为零且E(n)大，则Δμ正小；Rule 4: If ΔE(n) is zero and E(n) is large, then Δμ is positively small;

规则5：如果ΔE(n)为零且E(n)中，则Δμ零；Rule 5: If ΔE(n) is zero and E(n) is in, then Δμ is zero;

规则6：如果ΔE(n)为零且E(n)小，则Δμ负小；Rule 6: If ΔE(n) is zero and E(n) is small, then Δμ is negatively small;

规则7：如果ΔE(n)为负且E(n)大，则Δμ正小；Rule 7: If ΔE(n) is negative and E(n) is large, then Δμ is positively small;

规则8：如果ΔE(n)为负且E(n)中，则Δμ零；Rule 8: If ΔE(n) is negative and E(n) is neutral, then Δμ is zero;

规则9：如果ΔE(n)为负且E(n)小，则Δμ负大。Rule 9: If ΔE(n) is negative and E(n) is small, then Δμ is negatively large.

FNN控制器各层的处理过程如下：The processing of each layer of the FNN controller is as follows:

第一层：输入层，以E(n)和ΔE(n)作为步长的控制器输入量。The first layer: the input layer, with E(n) and ΔE(n) as the controller input of the step size.

${I I}_{11}^{((11))} ((n no)) = = ΔE ΔE ((n no)) = = MSE MSE ((n no)) - - MSE MSE ((n no - - 11)),,$

${I I}_{22}^{((11))} ((n no)) = = E E. ((n no)) = = MSE MSE ((n no)),,$

${O o}_{ql ql}^{((11))} ((n no)) = = {I I}_{q q}^{((11))} ((n no)),,$

式中，q＝1，2为FNN的输入个数，l＝1，2，3为模糊域，I^(t)、O^(t)分别为FNN第t层的输入与输出，t＝1，2，…，5下同；In the formula, q=1, 2 is the input number of FNN, l=1, 2, 3 is the fuzzy domain, I ^(t) and O ^(t) are the input and output of FNN layer t respectively, t=1, 2, ..., 5 the same below;

第二层：模糊化层The second layer: fuzzy layer

${I I}_{ql ql}^{((22))} ((n no)) = = {O o}_{ql ql}^{((11))} ((n no)),,$

${O o}_{ql ql}^{((22))} ((n no)) = = exp exp [[- - {((\frac{{I I}_{ql ql}^{((22))} ((n no)) - - {m m}_{ql ql}^{((22))} ((n no))}{{σ σ}_{ql ql}^{((22))} ((n no))}))}^{22}]],,$

式中，和

分别表示输入空间模糊域的期望与方差；In the formula, and

represent the expectation and variance of the input space fuzzy domain, respectively;

第三层：规则层The third layer: rule layer

${I I}_{ql ql}^{((33))} ((n no)) = = {O o}_{ql ql}^{((22))} ((n no)),,$

${O o}_{r r}^{((33))} = = Π Π {I I}_{ql ql}^{((33))} ((n no)),,$

式中，r＝1，2，…，9表示模糊规则的前件数。In the formula, r=1, 2, ..., 9 represent the number of antecedents of fuzzy rules.

第四层：选择层，即从第三层的输出中选择一路最大的值作为该层的输出，即The fourth layer: the selection layer, that is, select the largest value from the output of the third layer as the output of this layer, that is,

${O o}^{((44))} = = max max (({O o}_{r r}^{((33))})),,$

第五层：归一化层The fifth layer: normalization layer

O⁽⁵⁾＝O⁽⁴⁾·δ(i)，O ⁽⁵⁾ = O ⁽⁴⁾ ·δ(i),

式中，δ(i)控制量，主要用来调整该层的输出，完成规则的后部分；In the formula, the δ(i) control amount is mainly used to adjust the output of this layer and complete the latter part of the rule;

第六层：解模糊层The sixth layer: defuzzification layer

Δμ＝O⁽⁶⁾＝O⁽⁵⁾·MSE(n)。Δμ=O ⁽⁶⁾ =O ⁽⁵⁾ ·MSE(n).

在充分利用WNN和FNN络优点的基础上，本发明了模糊神经网络控制的混合小波神经网络盲均衡方法(FHWNN，FNN controller based Hybrid WNN)。该方法用小波元代替神经元，通过仿射变换建立起小波变换和网络参数之间的关系；用混合小波神经网络(HWNN，Hybrid WNN)结构中的前向横向滤波器实现对信道线性特性的补偿，用WNN实现对信道非线性特性的补偿；用FNN控制器对小波函数中的尺度因子和平移因子进行调整；从而提高了系统的灵活性，避免了易陷入局部极小值的困境。水声信道的仿真结果，验证了FHWNN方法的有效性。On the basis of making full use of the advantages of WNN and FNN networks, the present invention proposes a hybrid wavelet neural network blind equalization method (FHWNN, FNN controller based Hybrid WNN) controlled by a fuzzy neural network. In this method, wavelet elements are used to replace neurons, and the relationship between wavelet transformation and network parameters is established through affine transformation; the forward transversal filter in the hybrid wavelet neural network (HWNN, Hybrid WNN) structure is used to realize the linear characteristics of the channel. Compensation, using WNN to realize the compensation of the nonlinear characteristics of the channel; using the FNN controller to adjust the scale factor and translation factor in the wavelet function; thus improving the flexibility of the system and avoiding the dilemma of being easily trapped in local minimum values. The simulation results of the underwater acoustic channel verify the effectiveness of the FHWNN method.

附图说明 Description of drawings

图1：本发明FHWNN原理框图Figure 1: Block diagram of FHWNN of the present invention

图2：本发明改进的HWNN结构；Figure 2: The improved HWNN structure of the present invention;

图3：本发明模糊神经网络(FNN)控制器结构；Fig. 3: fuzzy neural network (FNN) controller structure of the present invention;

图4：实施实例结果，(a)均方误差曲线，(b)WTCMA输出，(c)WNN的输出，(d)HWNN输出，(e)FHWNN输出。Figure 4: Implementation example results, (a) mean square error curve, (b) WTCMA output, (c) WNN output, (d) HWNN output, (e) FHWNN output.

具体实施方式 Detailed ways

模糊神经网络控制的小波神经网络盲均衡算法Wavelet Neural Network Blind Equalization Algorithm Controlled by Fuzzy Neural Network

根据WNN和FNN的优点，本发明利用FNN来调整网络神经元小波函数中平移因子和尺度因子的迭代步长，并以均方误差E(n)＝MSE(n)(MSE(n)为n时刻的均方误差)与均方误差的偏差ΔE(n)＝MSE(n)-MSE(n-1)作为模糊神经网络控制器的输入。FHWNN原理，如图1所示。According to the advantages of WNN and FNN, the present invention utilizes FNN to adjust the iterative step size of translation factor and scale factor in the network neuron wavelet function, and with mean square error E (n)=MSE (n) (MSE (n) is n Time mean square error) and mean square error deviation ΔE (n) = MSE (n) - MSE (n-1) as the input of the fuzzy neural network controller. FHWNN principle, as shown in Figure 1.

图1中，x(n)为发送信号序列，h(n)为未知信道，N(n)为信道的加性高斯白噪声，y(n)为改进的混合小波神经网络的输入，

为判决器的判决输出。盲均衡算法就是依赖观测序列y(n)实现对发送信号x(n)的无失真恢复。结合常数模盲均衡算法，则WNN盲均衡算法的代价函数为In Figure 1, x(n) is the transmitted signal sequence, h(n) is the unknown channel, N(n) is the additive white Gaussian noise of the channel, y(n) is the input of the improved hybrid wavelet neural network,

is the decision output of the decider. The blind equalization algorithm relies on the observation sequence y(n) to realize the distortion-free restoration of the transmitted signal x(n). Combined with the constant modulus blind equalization algorithm, the cost function of the WNN blind equalization algorithm is

$J J = = \frac{11}{22} {(({| | \overset{~ ~}{x x} ((n no)) | |}^{22} - - {R R}_{CM CM}))}^{22} - - - - - - ((11))$

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

图1中，改进的混合小波神经网络决定着盲均衡算法中神经网络的输入；模糊神经网络控制器控制改进的混合小波神经网络中小波函数中尺度因子和平移因子的迭代步长。下面将分别讨论这两部分。In Figure 1, the improved hybrid wavelet neural network determines the input of the neural network in the blind equalization algorithm; the fuzzy neural network controller controls the iterative step size of the wavelet function in the improved hybrid wavelet neural network. These two parts will be discussed separately below.

1.改进的混合小波神经网络盲均衡方法1. Improved hybrid wavelet neural network blind equalization method

混合小波神经网络(HWNN)盲均衡方法是在WNN输入层之前级联一个横向滤波器(见文献[10]：肖瑛，董玉华。一种级联混合小波神经网络盲均衡算法[J].信息与控制，2009，38(4)：479-483.)，其不足之处有：①横向滤波器各节点输出直接作为WNN输入层相应神经元的输入，即WNN输入层各神经元的输入之间没有任何联系；②没有把信号的实部与虚部分开考虑，不适用于PSK、QAM等复数调制系统；③对小波函数中尺度因子和平移因子的迭代步长没有进行模糊控制与调整，从而影响了系统处理信息的灵活性和速度，均衡性能较差。因此，本文针对HWNN的缺陷，提出一种改进的HWNN结构，如图2所示。The hybrid wavelet neural network (HWNN) blind equalization method is to cascade a transversal filter before the WNN input layer (see literature [10]: Xiao Ying, Dong Yuhua. A cascaded hybrid wavelet neural network blind equalization algorithm [J]. Information and Control, 2009, 38(4): 479-483.), its disadvantages are: ①The output of each node of the transversal filter is directly used as the input of the corresponding neuron in the WNN input layer, that is, the input of each neuron in the WNN input layer There is no connection between them; ②The real part and the imaginary part of the signal are not considered separately, and it is not suitable for complex modulation systems such as PSK and QAM; ③There is no fuzzy control and adjustment of the iterative step size of the scale factor and translation factor in the wavelet function, As a result, the flexibility and speed of system processing information are affected, and the equalization performance is poor. Therefore, aiming at the defects of HWNN, this paper proposes an improved HWNN structure, as shown in Figure 2.

图2中，横向滤波器构成了网络的线性部分，而WNN构成了非线性部分。设横向滤波器第i个抽头系数为c_i(n)(i＝1，2，…，m，m为HWNN输入层神经元的个数，下同)；HWNN输入层第i个神经元的输入为T_i(n)，隐层第k个神经元的输入为u_k(n)，输出为Q_k(n)(k＝1，2，…，p，p为HWNN隐层神经元的个数，下同)；输出层的输入为g(n)，输出为

输入层第i个神经元至隐层第k个神经元的连接权重为w_ik(n)，隐层第k个神经元至输出层的连接权重为v_k(n)。为了使该算法适用于复数系统，将网络的信号、信道、权值等分解为实部和虚部两部分，则网络的状态方程为In Figure 2, the transversal filter constitutes the linear part of the network, while the WNN constitutes the nonlinear part. Let the i-th tap coefficient of the transversal filter be c _i (n) (i=1, 2, ..., m, m is the number of neurons in the HWNN input layer, the same below); the i-th neuron in the HWNN input layer The input is T _i (n), the input of the kth neuron in the hidden layer is u _k (n), and the output is Q _k (n) (k=1, 2,..., p, p is the neuron in the hidden layer of HWNN number, the same below); the input of the output layer is g(n), and the output is

The connection weight from the i-th neuron in the input layer to the k-th neuron in the hidden layer is w _ik (n), and the connection weight from the k-th neuron in the hidden layer to the output layer is v _k (n). In order to make the algorithm suitable for complex systems, the network signal, channel, weight, etc. are decomposed into two parts, real part and imaginary part, then the state equation of the network is

c_i(n)＝c_i，R(n)+jc_i，I(n) (2)c _i (n) = c _{i, R} (n) + jc _{i, I} (n) (2)

式中，c_i，R(n)为c_i(n)的实部，c_i，I(n)为c_i(n)的虚部，下同。In the formula, ci _{, R} (n) is the real part of ci ₍ n), ci _{, I} (n) is the imaginary part of _ci (n), the same below.

w_ik(n)＝w_ik，R(n)+jw_ik，I(n) (3)w _ik (n)=wi _{ik, R} (n)+jw _{ik, I} (n) (3)

v_k(n)＝v_k，R(n)+jv_k，I(n) (4)v _k (n) = v _{k, R} (n) + jv _{k, I} (n) (4)

y(n)＝y_R(n)+jy_I(n) (5)y(n)=y _R (n)+jy _I (n) (5)

$+ + j j {Σ Σ}_{t t = = 11}^{i i} (({c c}_{t t,, R R} ((n no)) {y the y}_{I I} ((n no + + 11 - - t t)) + + {c c}_{i i,, I I} ((n no)) {y the y}_{R R} ((n no + + 11 - - t t)))) - - - - - - ((66))$

$+ + j j {Σ Σ}_{i i = = 11}^{m m} [[{w w}_{ik ik,, R R} ((n no)) {T T}_{i i,, I I} ((n no)) - - {w w}_{ik ik,, I I} ((n no)) {T T}_{i i,, R R} ((n no))]] - - - - - - ((77))$

Q_k(n)＝ψ_a，b(u_k，R(n))+jψ_a，b(u_k，I(n)) (8)Q _k (n) = ψ _{a, b} ( _{uk, R} (n)) + jψ _{a, b} (u _{k, I} (n)) (8)

${ψ ψ}_{a a,, b b} (({u u}_{k k,, R R} ((n no)))) = = {| | a a | |}^{- - \frac{11}{22}} ψ ψ ((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{a a})) = = {| | a a | |}^{- - \frac{11}{22}} ((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{a a})) {e e}^{- - \frac{11}{22} {((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{a a}))}^{22}} - - - - - - ((99))$

式中，b为平移因子，a为尺度因子。将式(9)中u_k，R(n)换成u_k，I(n)就得到ψ_a，b(u_k，I(n))的表达式。小波神经网络的输出为In the formula, b is the translation factor, and a is the scale factor. Replace u _{k, R} (n) in formula (9) with u _{k, I} (n) to get the expression of ψ _{a, b} (u _{k, I} (n)). The output of the wavelet neural network is

${\overset{~ ~}{x x}}_{22} ((n no)) = = {Σ Σ}_{k k = = 11}^{p p} [[{v v}_{k k,, R R} ((n no)) {Q Q}_{k k,, R R} ((n no)) - - {v v}_{k k,, I I} ((n no)) {Q Q}_{k k,, I I} ((n no))]] + + j j {Σ Σ}_{k k = = 11}^{p p} [[{v v}_{k k,, R R} ((n no)) {Q Q}_{k k,, I I} ((n no)) + + {v v}_{k k,, I I} ((n no)) {Q Q}_{k k,, R R} ((n no))]] - - - - - - ((1010))$

横向滤波器的输出为The output of the transversal filter is

${\overset{~ ~}{x x}}_{11} ((n no)) = = {c c}_{i i}^{T T} ((n no)) y the y ((n no + + 11 - - i i)),, i i = = 1,2 1,2,, \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot;,, m m - - - - - - ((1111))$

将

和

加权融合，得Will

and

Weighted fusion, get

$g g ((n no)) = = α α {\overset{~ ~}{x x}}_{11} ((n no)) + + β β {\overset{~ ~}{x x}}_{22} ((n no)) - - - - - - ((1212))$

式中，0≤α，β≤1，为加权因子，并且满足α+β＝1。改进的HWNN最终输出为In the formula, 0≤α and β≤1 are weighting factors and satisfy α+β=1. The final output of the improved HWNN is

$\overset{~ ~}{x x} ((n no)) = = f f ((g g ((n no)))) = = g g ((n no)) + + λ λ sin sin ((πg πg ((n no)))) - - - - - - ((1313))$

式中，f(·)为输出层的输入和输出之间的传递函数，控制着整个网络的输出，要具有平滑、渐近、单调特点，并有利于对输入序列进行判别。f(·)的作用是对信号值在一定范围内进行修正，使其更接近于原信号g(n)，其中λsin(πg(n))是以g(n)为自变量的非线性修正项，它使得在原信号中心点附近左右摆信号向原信号靠拢。λ的取值影响着f(·)对输出信号的调整速度。在实际的应用中，不同的信号和信道，λ的选择应不同。In the formula, f(·) is the transfer function between the input and output of the output layer, which controls the output of the entire network, and should have smooth, asymptotic, and monotonic characteristics, and it is beneficial to discriminate the input sequence. The function of f( ) is to modify the signal value within a certain range to make it closer to the original signal g(n), where λsin(πg(n)) is a nonlinear correction with g(n) as the independent variable item, which makes the left and right pendulum signals close to the original signal near the center point of the original signal. The value of λ affects the adjustment speed of f(·) to the output signal. In practical applications, the choice of λ should be different for different signals and channels.

根据误差反传算法和随机梯度下降算法实现对小波网络参数的更新调整，推导后可以得到小波神经网络隐层到输出层的连接权重更新公式为According to the error backpropagation algorithm and the stochastic gradient descent algorithm, the wavelet network parameters are updated and adjusted. After derivation, the connection weight update formula from the hidden layer to the output layer of the wavelet neural network can be obtained as follows:

${v v}_{k k} ((n no + + 11)) = = {v v}_{k k} ((n no)) - - {μ μ}_{11} \frac{&PartialD; &PartialD; J J ((n no))}{&PartialD; &PartialD; {v v}_{k k} ((n no))} - - - - - - ((1414))$

式中，μ₁为迭代步长。In the formula, μ ₁ is the iteration step size.

$\frac{&PartialD; &PartialD; J J ((n no))}{&PartialD; &PartialD; {v v}_{k k} ((n no))} = = 22 βe βe ((n no)) | | {\overset{~ ~}{x x}}_{R R} ((n no)) + + j j {\overset{~ ~}{x x}}_{I I} ((n no)) | | \cdot &Center Dot; ((\frac{&PartialD; &PartialD; \overset{~ ~}{x x} ((n no))}{&PartialD; &PartialD; {v v}_{k k,, R R} ((n no))} + + j j \frac{&PartialD; &PartialD; \overset{~ ~}{x x} ((n no))}{&PartialD; &PartialD; {v v}_{k k,, I I} ((n no))})) - - - - - - ((1515))$

$\frac{&PartialD; &PartialD; \overset{~ ~}{x x} ((n no))}{&PartialD; &PartialD; {v v}_{k k,, R R} ((n no))} = = \frac{11}{| | \overset{~ ~}{x x} ((n no)) | |} [[f f (({g g}_{R R} ((n no)))) {f f}^{' '} (({g g}_{R R} ((n no)))) {Q Q}_{k k,, R R} ((n no)) + + f f (({g g}_{I I} ((n no)))) {f f}^{' '} (({g g}_{I I} ((n no)))) {Q Q}_{k k,, I I} ((n no))]] - - - - - - ((1616))$

式中，f′(·)为导数，下同。In the formula, f′(·) is the derivative, the same below.

同理in the same way

$\frac{&PartialD; &PartialD; \overset{~ ~}{x x} ((n no))}{{&PartialD; &PartialD; v v}_{k k,, I I} ((n no))} = = \frac{11}{| | \overset{~ ~}{x x} ((n no)) | |} [[- - f f (({g g}_{R R} ((n no)))) {f f}^{' '} (({g g}_{R R} ((n no)))) {Q Q}_{k k,, I I} ((n no)) + + f f (({g g}_{I I} ((n no)))) {f f}^{' '} (({g g}_{I I} ((n no)))) {Q Q}_{k k,, R R} ((n no))]] - - - - - - ((1717))$

把式(15)～(17)代入式(14)中，即可得小波网络隐层到输出层连接权重的更新公式为Substituting equations (15)-(17) into equation (14), the update formula of the connection weight from the hidden layer to the output layer of the wavelet network can be obtained as

${v v}_{k k} ((n no + + 11)) = = {v v}_{k k} ((n no)) + + {μ μ}_{11} K K ((n no)) {Q Q}_{k k}^{* *} ((n no)) - - - - - - ((1818))$

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

式中，μ₁为迭代步长，*为共轭。In the formula, μ ₁ is the iteration step size, * is the conjugate.

同理，输入层至隐层连接的权重更新公式为Similarly, the weight update formula for the connection between the input layer and the hidden layer is

${w w}_{ik ik} ((n no + + 11)) = = {w w}_{ik ik} ((n no)) + + {μ μ}_{22} {K K}_{00} ((n no)) {T T}_{i i}^{* *} ((n no)) - - - - - - ((2020))$

$+ + jβe jβe ((n no)) {ψ ψ}_{a a,, b b}^{' '} (({u u}_{k k,, I I} ((n no)))) Im Im {{[[f f (({g g}_{R R} ((n no)))) \cdot &Center Dot; {f f}^{' '} (({g g}_{R R} ((n no)))) + + jf jf (({g g}_{I I} ((n no)))) {f f}^{' '} (({g g}_{I I} ((n no))))]] {v v}_{k k}^{* *} ((n no))}} - - - - - - ((21 twenty one))$

尺度因子a和平移因子b的更新公式为The update formulas of scale factor a and translation factor b are

$a a ((n no + + 11)) = = a a ((n no)) - - {μ μ}_{33} \frac{&PartialD; &PartialD; J J ((n no))}{&PartialD; &PartialD; a a ((n no))} - - - - - - ((22 twenty two))$

$b b ((n no + + 11)) = = b b ((n no)) - - {μ μ}_{44} \frac{&PartialD; &PartialD; J J ((n no))}{&PartialD; &PartialD; b b ((n no))} - - - - - - ((23 twenty three))$

$\frac{&PartialD; &PartialD; J J ((n no))}{&PartialD; &PartialD; a a ((n no))} = = 22 βe βe ((n no)) | | {\overset{~ ~}{x x}}_{R R} ((n no)) + + j j {\overset{~ ~}{x x}}_{I I} ((n no)) | | \cdot &Center Dot; ((\frac{&PartialD; &PartialD; | | {\overset{~ ~}{x x}}_{R R} ((n no)) | |}{&PartialD; &PartialD; a a ((n no))} + + j j \frac{&PartialD; &PartialD; | | {\overset{~ ~}{x x}}_{I I} ((n no)) | |}{&PartialD; &PartialD; a a ((n no))})) - - - - - - ((24 twenty four))$

式中In the formula

$\frac{&PartialD; &PartialD; | | {\overset{~ ~}{x x}}_{R R} ((n no)) | |}{&PartialD; &PartialD; a a ((n no))} = = \frac{11}{| | \overset{~ ~}{x x} ((n no)) | |} [[f f (({g g}_{R R} ((n no)))) {f f}^{' '} (({g g}_{R R} ((n no)))) \frac{&PartialD; &PartialD; {g g}_{R R} ((n no))}{&PartialD; &PartialD; a a ((n no))} + + f f (({g g}_{I I} ((n no)))) {f f}^{' '} (({g g}_{I I} ((n no)))) \frac{&PartialD; &PartialD; {g g}_{I I} ((n no))}{&PartialD; &PartialD; a a ((n no))}]] - - - - - - ((2525))$

$\frac{{&PartialD; &PartialD; g g}_{R R} ((n no))}{&PartialD; &PartialD; a a ((n no))} = = {v v}_{k k,, R R} ((n no)) \frac{&PartialD; &PartialD; {ψ ψ}_{a a,, b b} (({u u}_{k k,, R R} ((n no))))}{&PartialD; &PartialD; a a ((n no))} - - {v v}_{k k,, I I} ((n no)) \frac{&PartialD; &PartialD; {ψ ψ}_{a a,, b b} (({u u}_{k k,, I I} ((n no))))}{&PartialD; &PartialD; a a ((n no))} - - - - - - ((2626))$

$\frac{{&PartialD; &PartialD; g g}_{I I} ((n no))}{&PartialD; &PartialD; a a ((n no))} = = {v v}_{k k,, R R} ((n no)) \frac{{&PartialD; &PartialD; ψ ψ}_{a a,, b b} (({u u}_{k k,, I I} ((n no))))}{&PartialD; &PartialD; a a ((n no))} + + {v v}_{k k,, I I} ((n no)) \frac{{&PartialD; &PartialD; ψ ψ}_{a a,, b b} (({u u}_{k k,, R R} ((n no))))}{&PartialD; &PartialD; a a ((n no))} - - - - - - ((2727))$

$\frac{{&PartialD; &PartialD; ψ ψ}_{a a,, b b} (({u u}_{k k,, R R} ((n no))))}{&PartialD; &PartialD; a a ((n no))} = = - - {| | a a | |}^{- - \frac{11}{22}} \frac{(({u u}_{k k,, R R} ((n no)) - - b b))}{{a a}^{22}} {e e}^{- - \frac{11}{22} {((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{a a}))}^{22}} + + {| | a a | |}^{- - \frac{11}{22}} {((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{a a}))}^{22} ((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{{a a}^{22}})) {e e}^{- - \frac{11}{22} {((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{a a}))}^{22}}$

$- - \frac{11}{22} {| | a a | |}^{- - 33 / / 22} ((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{a a})) {e e}^{- - \frac{11}{22} {((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{a a}))}^{22}} - - - - - - ((2828))$

将式(28)中的u_k，R(n)换成u_k，I(n)即可得到

的表达式；按照式(25)的推导过程，可得

的表达式(限于篇幅，这些表达式省略)。把式(24)～(28)代入式(22)即得尺度因子a的迭代公式。Replace u _{k, R} (n) in formula (28) with u _{k, I} (n) to get

The expression of ; according to the derivation process of formula (25), we can get

Expressions (limited to space, these expressions are omitted). Substitute equations (24)-(28) into equation (22) to get the iterative formula of scale factor a.

同理，可以得到关于平移因子b的迭代公式。根据以上的公式，完成了对小波神经网络中小波函数尺度因子和平移因子的更新，从而进行盲均衡。Similarly, an iterative formula for the translation factor b can be obtained. According to the above formula, the update of wavelet function scale factor and translation factor in wavelet neural network is completed, so as to carry out blind equalization.

2.模糊神经网络控制器2. Fuzzy Neural Network Controller

在模糊神经网络控制器中，具有一个输入变量和一个输出变量的控制器称为单变量模糊神经网络控制器，其输入量个数称为模糊控制器的维数。维数越高、控制越精细；但维数过高，模糊控制规则就越复杂，控制器的实现就越困难。本文采用单变量模糊控制器结构中的二维模糊控制器，其输入量是均方误差E(n)＝MSE(n)和其变化量ΔE(n)＝MSE(n)-MSE(n-1)。以步长μ的变化值Δμ作为输出量，它比一维控制器的控制效果好，且易于计算机实现。其结构如图3所示。In the fuzzy neural network controller, the controller with one input variable and one output variable is called the single-variable fuzzy neural network controller, and the number of its input quantity is called the dimension of the fuzzy controller. The higher the dimension, the finer the control; but if the dimension is too high, the fuzzy control rules will be more complicated, and the controller will be more difficult to realize. In this paper, the two-dimensional fuzzy controller in the single-variable fuzzy controller structure is adopted, and its input quantity is the mean square error E(n)=MSE(n) and its variation ΔE(n)=MSE(n)-MSE(n- 1). Taking the change value Δμ of the step size μ as the output, it has a better control effect than the one-dimensional controller and is easy to realize by computer. Its structure is shown in Figure 3.

此模糊神经网络(FNN)的模糊规则设计为The fuzzy rules of this fuzzy neural network (FNN) are designed as

${I I}_{11}^{((11))} ((n no)) = = ΔE ΔE ((n no)) = = MSE MSE ((n no)) - - MSE MSE ((n no - - 11)) - - - - - - ((2929))$

${I I}_{22}^{((11))} ((n no)) = = E E. ((n no)) = = MSE MSE ((n no)) - - - - - - ((3030))$

${O o}_{ql ql}^{((11))} ((n no)) = = {I I}_{q q}^{((11))} ((n no)) - - - - - - ((3131))$

式中，q＝1，2为FNN的输入个数，l＝1，2，3为模糊域，I^(t)、O^(t)分别为FNN第t(t＝1，2，…，5)层的输入与输出，下同。In the formula, q=1, 2 is the input number of FNN, l=1, 2, 3 is the fuzzy domain, I ^(t) and O ^(t) are the tth (t=1, 2,..., 5 ) layer input and output, the same below.

第二层：模糊化层The second layer: fuzzy layer

${I I}_{ql ql}^{((22))} ((n no)) = = {O o}_{ql ql}^{((11))} ((n no)) - - - - - - ((3232))$

${O o}_{ql ql}^{((22))} ((n no)) = = exp exp [[- - {((\frac{{I I}_{ql ql}^{((22))} ((n no)) - - {m m}_{ql ql}^{((22))} ((n no))}{{σ σ}_{ql ql}^{((22))} ((n no))}))}^{22}]] - - - - - - ((3333))$

式中，

和

分别表示输入空间模糊域的期望与方差。为了计算方便，在本文中采用固定的中心(m_ql(n))和宽度(σ_ql(n))。In the formula,

and

Denote the expectation and variance of the input space fuzzy domain, respectively. For the convenience of calculation, fixed center (m _ql (n)) and width (σ _ql (n)) are adopted in this paper.

第三层：规则层。The third layer: the rule layer.

${I I}_{ql ql}^{((33))} ((n no)) = = {O o}_{ql ql}^{((22))} ((n no)) - - - - - - ((3434))$

${O o}_{l l}^{((33))} = = Π Π {I I}_{ij ij}^{((33))} ((n no)) - - - - - - ((3535))$

${O o}^{((44))} = = max max (({O o}_{r r}^{((33))})) - - - - - - ((3636))$

第五层：归一化层The fifth layer: normalization layer

O⁽⁵⁾＝O⁽⁴⁾·δ(i) (37)O ⁽⁵⁾ = O ⁽⁴⁾ δ(i) (37)

式中，δ(i)控制量，主要用来调整该层的输出，完成规则的后部分。In the formula, the δ(i) control amount is mainly used to adjust the output of this layer to complete the latter part of the rule.

第六层：解模糊层The sixth layer: defuzzification layer

Δμ＝O⁽⁶⁾＝O⁽⁵⁾·MSE(n) (38)Δμ=O ⁽⁶⁾ ＝O ⁽⁵⁾ MSE(n) (38)

式(22)、(23)中的迭代步长将分别变为μ₃+Δμ、μ₄+Δμ。这就构成了用FNN控制器来控制小波函数中尺度因子和平移因子迭代步长的盲均衡算法，且MSE(n)的引入使步长的改变量与均方误差相对应。The iteration step size in formulas (22) and (23) will become μ ₃ +Δμ, μ ₄ +Δμ respectively. This constitutes a blind equalization algorithm that uses FNN controller to control the iterative step size of the scale factor and translation factor in the wavelet function, and the introduction of MSE(n) makes the change of the step size correspond to the mean square error.

综上所述，利用FNN在控制方面的优势，来控制神经网络隐层神经元小波函数的平移因子和尺度因子的迭代步长。其主要思路是利用神经网络调整模糊逻辑推理系统的隶属函数和调整推理规则，利用模糊推理规则的形式构造前向传播结构，从而可以充分发挥各自的特点，实现功能互补。实施实例及分析To sum up, the advantages of FNN in control are used to control the translation factor and the iteration step size of the scale factor of the wavelet function of the hidden layer neurons of the neural network. The main idea is to use the neural network to adjust the membership function of the fuzzy logic reasoning system and adjust the reasoning rules, and use the form of fuzzy reasoning rules to construct the forward propagation structure, so that they can give full play to their respective characteristics and realize functional complementarity. Implementation examples and analysis

为了验证FHWNN方法的有效性，利用水声信道进行仿真实验，并与小波变换常数模方法(WTCMA)、WNN及HWNN方法进行比较。实验中，水声信道的传递函数为c＝zeros(1，1001)；c(1)＝0.076；c(2)＝0.122；c(1001)＝1；发射信号为16QAM，信噪比为20dB，均衡器的权长均为32。对WTCMA均衡器，第7个抽头初始化为1，步长μ_WTCMA＝0.003，采用DB2小波分解，分解层数为2，功率初始化为4；对WNN均衡器，采用1/4抽头，λ_WNN＝0.52，小波函数中尺度因子和平移因子的初始化为a_WNN＝5.5、b_WNN＝0.0075；对HWNN均衡器，采用1/4抽头，横向滤波器也采用1/4抽头，步长μ＝0.0001，小波函数中尺度因子和平移因子的初始化a_HWNN＝7.5、b_HWNN＝0.0098，加权因子为α_HWNN＝0.98，β_HWNN＝0.02，λ_HWNN＝3.8；对FHWNN均衡器，采用1/4抽头，横向滤波器也采用1/4抽头，步长μ_FHWNN＝0.0001，小波函数中尺度因子和平移因子的初始化为a_FHWNN＝7.5、b_FHWNN＝0.0098，加权因子为α_FHWNN＝0.95，β_FHWNN＝0.05，λ_FHWNN＝3.65。500次蒙特卡诺的仿真结果，如图4所示。In order to verify the effectiveness of the FHWNN method, the underwater acoustic channel is used to carry out simulation experiments, and compared with the wavelet transform constant modulus method (WTCMA), WNN and HWNN methods. In the experiment, the transfer function of the underwater acoustic channel is c=zeros(1,1001); c(1)=0.076; c(2)=0.122; c(1001)=1; the transmitted signal is 16QAM, and the signal-to-noise ratio is 20dB , the weight and length of the equalizer are both 32. For the WTCMA equalizer, the seventh tap is initialized to 1, the step size μ _WTCMA =0.003, using DB2 wavelet decomposition, the number of decomposition layers is 2, and the power is initialized to 4; for the WNN equalizer, 1/4 tap is used, λ _WNN = 0.52, the initialization of scale factor and translation factor in wavelet function is a _WNN =5.5, b _WNN =0.0075; to HWNN equalizer, adopt 1/4 tap, transversal filter also adopts 1/4 tap, step size μ=0.0001, Initialization of scale factor and translation factor in wavelet function a _HWNN = 7.5, b _HWNN = 0.0098, weighting factors are α _HWNN = 0.98, β _HWNN = 0.02, λ _HWNN = 3.8; for FHWNN equalizer, adopt 1/4 tap, horizontal The filter also adopts 1/4 taps, the step size μ _FHWNN =0.0001, the initialization of scale factor and translation factor in the wavelet function is a _FHWNN =7.5, b _FHWNN =0.0098, and the weighting factors are α _FHWNN =0.95, β _FHWNN =0.05, λ _FHWNN =3.65. The simulation results of 500 times Monte Cano are shown in FIG. 4 .

图4表明，与WTCMA、WNN和HWNN相比，FHW-NN收敛速度分别加快了100步、3000步和300步；稳态误差分别减小了12dB、3dB和1.5dB；输出星座图更加清晰、紧凑。Figure 4 shows that compared with WTCMA, WNN and HWNN, the convergence speed of FHW-NN is accelerated by 100 steps, 3000 steps and 300 steps respectively; the steady state error is reduced by 12dB, 3dB and 1.5dB respectively; the output constellation diagram is clearer, compact.

此外，与传统的小波神经网络盲均衡方法相比较，从方法的计算效率上看：在时间复杂度上，模糊神经网络控制的混合小波神经网络(FHWNN)盲均衡方法每次迭代过程仅增加了L次乘法运算(其中L为横向滤波器的阶数，等于小波网络的输入单元数)；在空间复杂度上，仅增加了L+1个存储单元。In addition, compared with the traditional wavelet neural network blind equalization method, from the calculation efficiency of the method: In terms of time complexity, the hybrid wavelet neural network (FHWNN) blind equalization method controlled by fuzzy neural network only increases L multiplication operations (where L is the order of the transversal filter, which is equal to the number of input units of the wavelet network); in terms of space complexity, only L+1 storage units are added.

Claims

1. a mixed wavelet neural network blind equalization method of fuzzy neural network control, is characterized in that comprising the steps:

a.) Pass the transmitted signal x(n) through the impulse response channel to obtain the channel output vector b(n), where n is a positive integer representing a time sequence, the same below;

b.) Obtain the input sequence of the blind equalizer by using the channel noise N(n) and the channel vector b(n) described in step a: y(n)=b(n)+N(n);

Use the fuzzy neural network (FNN) to adjust the iterative step size of the translation factor and scale factor in the neuron wavelet function in the improved hybrid wavelet neural network, and use the mean square error E(n)=MSE(n) and the mean square error Deviation ΔE(n)=MSE(n)-MSE(n-1) is used as the input of the fuzzy neural network controller, and MSE(n) is the mean square error at n moments;

Wherein, the construction method of the improved hybrid wavelet neural network described in step c.) is as follows:

The transversal filter constitutes the linear part of the improved hybrid wavelet neural network, and the wavelet neural network (WNN) constitutes the non-linear part; assuming the i-th tap coefficient of the transversal filter is c _i (n), i=1, 2, ..., m, m is the number of neurons in the input layer of the wavelet neural network hybrid wavelet neural network (HWNN), the same below; the input of the i-th neuron in the input layer of the improved hybrid wavelet neural network is T _i (n), hidden The input of the kth neuron in the layer is u _k (n), the output is Q _k (n), k=1, 2, ..., p, p is the number of neurons in the hidden layer of HWNN, the same below; the output layer The input is g(n), the output is

Decompose the signal, channel, and weight of the network into two parts, the real part and the imaginary part, then the state equation of the network is

c _i (n) = c _{i, R} (n) + jc _{i, I} (n) (1)

In the formula, c _{i, R} (n) is the real part of c _i (n), and c _{i, I} (n) is the imaginary part of c _i (n),

is the imaginary unit, the same below;

w _ik (n)=wi _{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 T}_{i i} ((n no)) = = {Σ Σ}_{t t = = 11}^{i i} {c c}_{t t} ((n no)) y the y ((n no + + 11 - - t t)) = = {Σ Σ}_{t t = = 11}^{i i} [[{c c}_{t t,, R R} ((n no)) {y the y}_{R R} ((n no + + 11 - - t t)) - - {c c}_{t t,, I I} ((n no)) {y the y}_{I I} ((n no + + 11 - - t t))]]

+ + j j {Σ Σ}_{t t = = 11}^{i i} [[{c c}_{t t,, R R} ((n no)) {y the y}_{I I} ((n no + + 11 - - t t)) + + {c c}_{i i,, I I} ((n no)) {y the y}_{R R} ((n no + + 11 - - t t))]] - - - - - - ((55))

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

{u u}_{k k} ((n no)) = = {Σ Σ}_{i i = = 11}^{m m} {w w}_{ik ik} ((n no)) {T T}_{i i} ((n no)) = = {Σ Σ}_{i i = = 11}^{m m} [[{w w}_{ik ik,, R R} ((n no)) {T T}_{i i,, R R} ((n no)) - - {w w}_{ik ik,, I I} ((n no)) {T T}_{i i,, I I} ((n no))]]

+ + j j {Σ Σ}_{i i = = 11}^{m m} [[{w w}_{ik ik,, R R} ((n no)) {T T}_{i i,, I I} ((n no)) - - {w w}_{ik ik,, I I} ((n no)) {T T}_{i i,, R R} ((n no))]] - - - - - - ((66))

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

In the formula, ψ _a,b ( ) represents the wavelet transform of the input signal of the hidden layer, here chooses the Morlet wavelet mother function, then

{ψ ψ}_{a a,, b b} (({u u}_{k k,, R R} ((n no)))) = = {| | a a | |}^{- - \frac{11}{22}} ψ ψ ((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{a a})) = = {| | a a | |}^{- - \frac{11}{22}} ((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{a a})) {e e}^{- - \frac{11}{22} {((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{a a}))}^{22}} - - - - - - ((88))

In the formula, b is the translation factor, a is the scale factor; in formula (8) u _k,R (n) is replaced by u _k,I (n) to get ψ _a,b (u _k,I (n)) The expression of the wavelet neural network output is:

{\overset{~ ~}{x x}}_{22} ((n no)) = = {Σ Σ}_{k k = = 11}^{p p} [[{v v}_{k k,, R R} ((n no)) {Q Q}_{k k,, R R} ((n no)) - - {v v}_{k k,, I I} ((n no)) {Q Q}_{k k,, I I} ((n no))]] + + j j {Σ Σ}_{k k = = 11}^{p p} [[{v v}_{k k,, R R} ((n no)) {Q Q}_{k k,, I I} ((n no)) + + {v v}_{k k,, I I} ((n no)) {Q Q}_{k k,, R R} ((n no))]] - - - - - - ((99))

The output of the transversal filter is

{\overset{~ ~}{x x}}_{11} ((n no)) = = {c c}_{i i}^{T T} ((n no)) y the y ((n no + + 11 - - i i)),, i i = = 1,2 1,2,, . . . . . .,, m m - - - - - - ((1010))

Will

and

Weighted fusion, get

g g ((n no)) = = α α {\overset{~ ~}{x x}}_{11} ((n no)) + + β β {\overset{~ ~}{x x}}_{22} ((n no)) - - - - - - ((1111))

In the formula, 0≤α≤1, 0≤β≤1, are weighting factors, and satisfy α+β=1, the final output of the improved HWNN is

\overset{~ ~}{x x} ((n no)) = = f f ((g g ((n no)))) = = g g ((n no)) + + λ λ sin sin ((πg πg ((n no)))) - - - - - - ((1212))

In the formula, f(·) is the transfer function between the input and output of the output layer, where λsin(πg(n)) is a nonlinear correction term with g(n) as the independent variable, which makes The left and right swing signals are close to the original signal;

The update method of the connection weights from the hidden layer to the output layer is:

{v v}_{k k} ((n no + + 11)) = = {v v}_{k k} ((n no)) + + {μ μ}_{11} K K ((n no)) {Q Q}_{k k}^{* *} ((n no)),,

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

In the formula, μ ₁ is the iteration step size, * is the conjugate; e(n) is the error signal of the equalizer;

It is an imaginary unit, and the superscript "'" means derivation, the same below;

The weight update formula for the connection between the input layer and the hidden layer is:

{w w}_{ik ik} ((n no + + 11)) = = {w w}_{ik ik} ((n no)) + + {μ μ}_{22} {K K}_{00} ((n no)) {T T}_{i i}^{* *} ((n no)),,

{K K}_{00} ((n no)) = = βe βe ((n no)) {ψ ψ}_{a a,, b b}^{' '} (({u u}_{k k,, R R} ((n no)))) Re Re {{[[f f (({g g}_{R R} ((n no)))) \cdot &Center Dot; {f f}^{' '} (({g g}_{R R} ((n no)))) + + jf jf (({g g}_{I I} ((n no)))) {f f}^{' '} (({g g}_{I I} ((n no))))]] {v v}_{k k}^{* *} ((n no))}}

+ + jβe jβe ((n no)) {ψ ψ}_{a a,, b b}^{' '} (({u u}_{k k,, I I} ((n no)))) Im Im {{[[f f (({g g}_{R R} ((n no)))) \cdot &Center Dot; {f f}^{' '} (({g g}_{R R} ((n no)))) + + jf jf (({g g}_{I I} ((n no)))) {f f}^{' '} (({g g}_{I I} ((n no))))]] {v v}_{k k}^{* *} ((n no))}},,

In the formula, μ ₂ is the iteration step size;

The update method of the scale factor a and translation factor b is:

a a ((n no + + 11)) = = a a ((n no)) - - {μ μ}_{33} \frac{&PartialD; &PartialD; J J ((n no))}{&PartialD; &PartialD; a a ((n no))},,

b b ((n no + + 11)) = = b b ((n no)) - - {μ μ}_{44} \frac{&PartialD; &PartialD; J J ((n no))}{&PartialD; &PartialD; b b ((n no))},,

\frac{&PartialD; &PartialD; J J ((n no))}{&PartialD; &PartialD; a a ((n no))} = = 22 β β \cdot &Center Dot; e e ((n no)) | | {\overset{~ ~}{x x}}_{R R} ((n no)) + + j j {\overset{~ ~}{x x}}_{I I} ((n no)) | | \cdot &Center Dot; [[\frac{&PartialD; &PartialD; | | {\overset{~ ~}{x x}}_{R R} ((n no)) | |}{&PartialD; &PartialD; a a ((n no))} + + j j \frac{&PartialD; &PartialD; | | {\overset{~ ~}{x x}}_{I I} ((n no)) | |}{&PartialD; &PartialD; a a ((n no))}]]

In the formula

\frac{&PartialD; &PartialD; | | {\overset{~ ~}{x x}}_{R R} ((n no)) | |}{&PartialD; &PartialD; a a ((n no))} = = \frac{11}{| | \overset{~ ~}{x x} ((n no)) | |} [[((f f (({g g}_{R R} ((n no)))) {f f}^{' '} (({g g}_{R R} ((n no)))) \frac{&PartialD; &PartialD; {g g}_{R R} ((n no))}{&PartialD; &PartialD; a a ((n no))} + + f f (({g g}_{I I} ((n no)))) {f f}^{' '} (({g g}_{I I} ((n no)))) \frac{&PartialD; &PartialD; {g g}_{I I} ((n no))}{&PartialD; &PartialD; a a ((n no))}))]],,

\frac{&PartialD; &PartialD; {g g}_{R R} ((n no))}{&PartialD; &PartialD; a a ((n no))} {= = v v}_{k k,, R R} ((n no)) \frac{&PartialD; &PartialD; {ψ ψ}_{a a,, b b} (({u u}_{k k,, R R} ((n no))))}{&PartialD; &PartialD; a a ((n no))} - - {v v}_{k k,, I I} ((n no)) \frac{&PartialD; &PartialD; {ψ ψ}_{a a,, b b} (({u u}_{k k,, I I} ((n no))))}{&PartialD; &PartialD; a a ((n no))},,

\frac{&PartialD; &PartialD; {g g}_{I I} ((n no))}{&PartialD; &PartialD; a a ((n no))} = = {v v}_{k k,, R R} ((n no)) \frac{&PartialD; &PartialD; {ψ ψ}_{a a,, b b} (({u u}_{k k,, I I} ((n no))))}{&PartialD; &PartialD; a a ((n no))} + + {v v}_{k k,, I I} ((n no)) \frac{&PartialD; &PartialD; {ψ ψ}_{a a,, b b} (({u u}_{k k,, R R} ((n no))))}{&PartialD; &PartialD; a a ((n no))},,

\frac{&PartialD; &PartialD; {ψ ψ}_{a a,, b b} (({u u}_{k k,, R R} ((n no))))}{&PartialD; &PartialD; a a ((n no))} = = - - {| | a a | |}^{- - \frac{11}{22}} \frac{(({u u}_{k k,, R R} ((n no)) - - b b))}{{a a}^{22}} {e e}^{- - \frac{11}{22} {((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{a a}))}^{22}}

+ + {| | a a | |}^{- - \frac{11}{22}} {((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{a a}))}^{22} ((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{{a a}^{22}})) {e e}^{- - \frac{11}{22} {((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{a a}))}^{22}}

- - \frac{11}{22} {| | a a | |}^{- - 33 / / 22} ((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{a a})) {e e}^{- - \frac{11}{22} {((\frac{{u u}_{k k,, R R} ((n no)) - - b b}{a a}))}^{22}},,

In the formula, μ ₃ and μ ₄ are the iteration step size.

2. the hybrid wavelet neural network blind equalization 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 rules of this fuzzy neural network (FNN) are:

Rule 1: If ΔE(n) is positive and E(n) is large, then Δμ is positive;

Rule 2: If ΔE(n) is positive and E(n) is neutral, then Δμ is zero;

Rule 3: If ΔE(n) is positive and E(n) is small, then Δμ is negatively small;

Rule 4: If ΔE(n) is zero and E(n) is large, then Δμ is positively small;

Rule 5: If ΔE(n) is zero and E(n) is in, then Δμ is zero;

Rule 6: If ΔE(n) is zero and E(n) is small, then Δμ is negatively small;

Rule 7: If ΔE(n) is negative and E(n) is large, then Δμ is positively small;

Rule 8: If ΔE(n) is negative and E(n) is neutral, then Δμ is zero;

Rule 9: If ΔE(n) is negative and E(n) is small, then Δμ is negative;

Among them, Δμ represents the change value of the step size μ;

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

The first layer: the input layer, with E(n) and ΔE(n) as the controller input of the step size;

{I I}_{11}^{((11))} ((n no)) = = ΔE ΔE ((n no)) = = MSE MSE ((n no)) - - MSE MSE ((n no - - 11)),,

{I I}_{22}^{((11))} ((n no)) = = E E. ((n no)) = = MSE MSE ((n no)),,

{O o}_{ql ql}^{((11))} ((n no)) = = {I I}_{q q}^{((11))} ((n no)),,

In the formula, q=1,2 is the input number of FNN, l=1,2,3 is the fuzzy domain, I ^(t) and O ^(t) are the input and output of FNN layer t respectively, t=1,2 ,...,5, the same below;

The second layer: fuzzy layer

{I I}_{ql ql}^{((22))} ((n no)) = = {O o}_{ql ql}^{((11))} ((n no)),,

{O o}_{ql ql}^{((22))} ((n no)) = = exp exp [[- - {((\frac{{I I}_{ql ql}^{((22))} ((n no)) - - {m m}_{ql ql}^{((22))} ((n no))}{{σ σ}_{ql ql}^{((22))} ((n no))}))}^{22}]]

In the formula,

and

The third layer: rule layer

{I I}_{ql ql}^{((33))} ((n no)) = = {O o}_{ql ql}^{((22))} ((n no)),,

{O o}_{r r}^{((33))} = = Π Π {I I}_{ql ql}^{((33))} ((n no)),,

In the formula, r=1,2,...,9 represent the number of previous items of the fuzzy rule;

The fourth layer: the selection layer, that is, select the largest value from the output of the third layer as the output of this layer, that is,

{O o}^{((44))} = = max max (({O o}_{r r}^{((33))})),,

The fifth layer: normalization layer

O ⁽⁵⁾ =O ⁽⁴⁾ ·δ(i),

In the formula, the δ(i) control amount is mainly used to adjust the output of this layer and complete the latter part of the rule;

The sixth layer: defuzzification layer

Δμ=O ⁽⁶⁾ =O ⁽⁵⁾ MSE(n).