【LMS时间序列预测】基于matlab LMS麦基玻璃时间序列预测【含Matlab源码 1443期】.zip

%% Mackey Glass Time Series Prediction Using Least Mean Square (LMS) % clc clear all close all %% Loading Time series data % I generated a series y(t) for t = 0,1, . . . ,3000, using % mackey glass series equation with the following configurations: % b = 0.1, a = 0.2, Tau = 20, and the initial conditions y(t - Tau) = 0. load Dataset\Data.mat time_steps=2; teacher_forcing=1; % recurrent ARMA modelling with forced desired input after defined time steps %% Training and Testing datasets % For training Tr=Data(100:2500,1); % Selecting a Interval of series data t = 100~2500 Yr(Tr)=Data(Tr,2); % Selecting a chuck of series data y(t) % For testing Ts=Data(2500:3000,1); % Selecting a Interval of series data t = 2500~3000 Ys(Ts)=Data(Ts,2); % Selecting a chuck of series data y(t) %% LMS Parameters eta=5e-3; % Learning rate M=1; % Order of LMS filter U=zeros(M+1,1); % Initial values of taps W=zeros(M+1,1); % Initial weight of LMS MSE=[]; % Initial mean squared error (MSE) %% Learning weights of LMS (Training) tic % start for t=Tr(1):Tr(end)-time_steps U(1:end-1)=U(2:end); % Shifting of tap window if (teacher_forcing==1) if rem(t,time_steps)==0 || (t==Tr(1)) U(end)=Yr(t); % Input (past/current samples) else U(end)=Yp(t-1); % Input (past/current samples) end else U(end)=Yr(t); % Input (past/current samples) end Yp(t)=W'*U; % Predicted output e(t)=Yr(t+time_steps)-Yp(t); % Error in predicted output W=W+eta*e(t)*U; % Weight update rule of LMS E(t)=e(t).^2; % Current mean squared error (MSE) end training_time=toc; % total time including training and calculation of MSE %% Prediction of a next outcome of series using previous samples (Testing) tic % start U=U*0; % Reinitialization of taps (optional) for t=Ts(1):Ts(end)-time_steps+1 U(1:end-1)=U(2:end); % Shifting of tap window if (teacher_forcing==1) if rem(t,time_steps)==0 || (t==Ts(1)) U(end)=Ys(t); % Input (past/current samples) else U(end)=Yp(t-1); % Input (past/current samples) end else U(end)=Ys(t); % Input (past/current samples) end Yp(t)=W'*U; % Calculating output (future value) e(t)=Ys(t+time_steps-1)-Yp(t); % Error in predicted output E(t)=e(t).^2; % Current mean squared error (MSE) end testing_time=toc; % total time including testing and calculation of MSE %% Results figure(1) plot(Tr,10*log10(E(Tr))); % MSE curve hold on plot(Ts(1:end-time_steps+1),10*log10(E(Ts(1:end-time_steps+1))),'r'); % MSE curve grid minor title('Cost Function'); xlabel('Iterations (samples)'); ylabel('Mean Squared Error (MSE)'); legend('Training Phase','Test Phase'); figure(2) plot(Tr(2*M:end),Yr(Tr(2*M:end))); % Actual values of mackey glass series hold on plot(Tr(2*M:end),Yp(Tr(2*M:end))','r') % Predicted values during training plot(Ts,Ys(Ts),'--b'); % Actual unseen data plot(Ts(1:end-time_steps+1),Yp(Ts(1:end-time_steps+1))','--r'); % Predicted values of mackey glass series (testing) xlabel('Time: t'); ylabel('Output: Y(t)'); title('Mackey Glass Time Series Prediction Using Least Mean Square (LMS)') ylim([min(Ys)-0.5, max(Ys)+0.5]) legend('Training Phase (desired)','Training Phase (predicted)','Test Phase (desired)','Test Phase (predicted)'); mitr=10*log10(mean(E(Tr))); % Minimum MSE of training mits=10*log10(mean(E(Ts(1:end-time_steps+1)))); % Minimum MSE of testing display(sprintf('Total training time is %.5f, \nTotal testing time is %.5f \nMSE value during training %.3f (dB),\nMSE value during testing %.3f (dB)', ... training_time,testing_time,mitr,mits));