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⛄ 内容介绍
基于时间反向传播 (BPTT)递归神经网络实现非线性系统识别附matlab完整代码
⛄ 完整代码
%% Non-Linear System Identification using Backpropagation Throught Time (BPTT)
clc;
clear all;
close all;
%% Training method
BPTT_type='Epochwise';
% BPTT_type='Truncated';
%% system configuration
ts=0.001;
if (strcmp(BPTT_type,'Epochwise'))
a=20;
eta = 0.001; %%%%%% Learning Rate 0-1 eg .01, .05, .005
t = 0:ts:a;
l=length(t);
u = square(pi*t);
else
a=20;
eta = 0.05; %%%%%% Learning Rate 0-1 eg .01, .05, .005
t = 0:ts:a;
l=length(t);
u = square(pi*t);
end
% u = awgn(u,30);
plant=[1 -0.25 0.1045 0.0902]; % Minimum Phase Plant
y(1:2)=0;
for i=3:length(t)
ph=[y(i-1) y(i-2) cos(2*u(i))+exp(-10*abs(u(i))) u(i-1)];
y(i)=ph*plant'+.001*randn(1,1);
end
%% RNN architecture
inp=6; % Input Layer Neurons (2 nodes for u(i) and u(i-1), 2 for y(i-1) and y(i-2) for state 1 feedback + 1 bias
N1=3; % Middle Layer Neurons
N2=1; % Output Layer Neurons
window_length=3;
epoch=(length(t)-2)/window_length;
w1=ones(N1,inp);
w2=ones(N2,N1);
y_NN = 0.*y;
j=2;
a1=zeros(N1,length(t));
e = ones(window_length,1);
%% RNN configuration
for k=1:epoch
for i=1:window_length
j=j+1;
Input_Vec(:,i)=[-y_NN(j-1) -y_NN(j-2) u(j) u(j-1) a1(1,j-1) 1]';
n1 = w1*Input_Vec(:,i);
a1(:,j)=tansig(n1); %%%% Hidden Layer Activation Function % tansig for [-1,+1] % logsig for [0,1]
n2 = w2*a1(:,j);
a2=tansig(n2); %%%% Output Layer Activation Function
y_NN(j) = a2;
e(i) = y(j) - y_NN(j);
if(strcmp(BPTT_type,'Epochwise'))
%% Epochwise BBTT
Y2(:,i) = 2*dtansig(n2,a2)*e(i); %%%% For Output Layer Equation (15.40) for n=n1
Y1(:,i) = diag(dtansig(n1,a1(:,j)),0)*[e + w2'*Y2(:,i)]; %%%% For Hidden Layer
elseif(strcmp(BPTT_type,'Truncated'))
%% Truncated BPTT
Y2(:,i) = 2*dtansig(n2,a2)*e(i); %%%% For Output Layer
Y1(:,i) = diag(dtansig(n1,a1(:,j)),0)*w2'*Y2(:,i); %%%% For Hidden Layer
end
end
MSE(k) = mse(e);
w1 = w1 + eta*Y1*Input_Vec'; % Equation (15.41) and (15.44)
w2 = w2 + eta*Y2(:,i)*a1(:,j)';
% w2 = w2 + eta*Y2*a1(:,j-i+1:j)';
end
for n=1:length(MSE)
MSE_trend(n)=mean(MSE(1:n));
end
10*log10(MSE_trend(n))
figure
semilogy(MSE);
hold on
semilogy(MSE_trend,'r')
title('Objective Function');
figure
plot(t,y,'r')
hold on
plot(t,y_NN,'b')
%% Testing
a=10;
ts=0.001;
t = 0:ts:a;
l=length(t);
u = square(pi*t);
u = awgn(u,30);
plant=[1 -0.25 0.1045 0.0902]; % Minimum Phase Plant
epoch=(length(t)-2)/window_length;
y=0;
y(1:2)=0;
for i=3:length(t)
ph=[y(i-1) y(i-2) cos(2*u(i))+exp(-10*abs(u(i))) u(i-1)];
y(i)=ph*plant';
end
y_NN = 0.*y;
j=2;
a1=zeros(N1,length(t));
for k=1:epoch
for i=1:window_length
j=j+1;
Input_Vec(:,i)=[-y_NN(j-1) -y_NN(j-2) u(j) u(j-1) a1(1,j-1) 1]';
n1 = w1*Input_Vec(:,i);
a1(:,j)=tansig(n1); %%%% Hidden Layer Activation Function % tansig for [-1,+1] % logsig for [0,1]
n2 = w2*a1(:,j);
a2=tansig(n2); %%%% Output Layer Activation Function
y_NN(j) = a2;
e(i) = y(j) - y_NN(j);
end
MSE(k) = mse(e);
end
for n=1:length(MSE)
MSE_trend(n)=mean(MSE(1:n));
end
10*log10(MSE_trend(n))
figure
semilogy(MSE);
hold on
semilogy(MSE_trend,'r')
title('Objective Function');
figure
plot(t,y,'m')
hold on
plot(t,y_NN,'b')
legend('Actual Output','RNN');
⛄ 运行结果
⛄ 参考文献
[1]TANG Meili, HU Qiong, MA Tinghuai. 基于循环神经网络的语音识别研究[J]. 现代电子技术, 2019, 42(14):5.
