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%% Chaotic Time Series Prediction 
% Chaotic time series prediction using ANFIS. 
% 
% Copyright 1994-2002 The MathWorks, Inc.  
% $Revision: 1.15 $ 
 
%% 
% The Mackey-Glass time-delay differential equation is defined by 
%  
%  dx(t)/dt = 0.2x(t-tau)/(1+x(t-tau)^10) - 0.1x(t) 
%  
% When x(0) = 1.2 and tau = 17, we have a non-periodic and 
% non-convergent time series that is very sensitive to 
% initial conditions. (We assume x(t) = 0 when t < 0.) 
clc 
clear 
close all 
load mackeyclass.dat 
a=mackeyclass; 
time = a(:, 1); 
ts = a(:, 2); 
plot(time, ts); 
xlabel('Time (sec)'); ylabel('x(t)'); 
title('Mackey-Glass Chaotic Time Series'); 
 
%% 
% Now we want to build an ANFIS that can predict x(t+6) from 
% the past values of this time series, that is, x(t-18), x(t-12), 
% x(t-6), and x(t). Therefore the training data format is 
% 
%  [x(t-18), x(t-12), x(t-6), x(t); x(t+6] 
% 
% From t = 118 to 1117, we collect 1000 data pairs of the above 
% format. The first 500 are used for training while the others 
% are used for checking. The plot shows the segment of the time 
% series where data pairs were extracted from. 
 
trn_data = zeros(100, 5); 
chk_data = zeros(40, 5); 
 
% prepare training data 
start = 101; 
trn_data(:, 1) = ts(start:start+100-1); 
start = start + 6; 
trn_data(:, 2) = ts(start:start+100-1); 
start = start + 6; 
trn_data(:, 3) = ts(start:start+100-1); 
start = start + 6; 
trn_data(:, 4) = ts(start:start+100-1); 
start = start + 6; 
trn_data(:, 5) = ts(start:start+100-1); 
 
% prepare checking data 
start = 201; 
chk_data(:, 1) = ts(start:start+40-1); 
start = start + 6; 
chk_data(:, 2) = ts(start:start+40-1); 
start = start + 6; 
chk_data(:, 3) = ts(start:start+40-1); 
start = start + 6; 
chk_data(:, 4) = ts(start:start+40-1); 
start = start + 6; 
chk_data(:, 5) = ts(start:start+40-1); 
 
index = 118:257+1; % ts starts with t = 0 
plot(time(index), ts(index)); 
axis([min(time(index)) max(time(index)) min(ts(index)) max(ts(index))]); 
xlabel('Time (sec)'); ylabel('x(t)'); 
title('Mackey-Glass Chaotic Time Series'); 
 
%% 
% We use GENFIS1 to generate an initial FIS matrix from training 
% data. The command is quite simple since default values for 
% MF number (2) and MF type ('gbellmf') are used: 
  
fismat = genfis1(trn_data); 
 
% The initial MFs for training are shown in the plots. 
figure 
for input_index=1:4, 
    subplot(2,2,input_index) 
    [x,y]=plotmf(fismat,'input',input_index); 
    plot(x,y) 
    axis([-inf inf 0 1.2]); 
    xlabel(['Input ' int2str(input_index)]); 
end 
 
%% 
% There are 2^4 = 16 rules in the generated FIS matrix and the 
% number of fitting parameters is 108, including 24 nonlinear 
% parameters and 80 linear parameters. This is a proper balance 
% between number of fitting parameters and number of training 
% data (500). The ANFIS command looks like this: 
%  
%  >> [trn_fismat,trn_error] = anfis(trn_data, fismat,[],[],chk_data) 
%  
% To save time, we will load the training results directly. 
% 
% After ten epochs of training, the final MFs are shown in the 
% plots. Note that these MFs after training do not change 
% drastically. Obviously most of the fitting is done by the linear 
% parameters while the nonlinear parameters are mostly for fine- 
% tuning for further improvement. 
 
% load training results 
load mganfis 
 
% plot final MF's on x, y, z, u 
% for input_index=1:4, 
    % subplot(2,2,input_index) 
    % [x,y]=plotmf(trn_fismat,'input',input_index); 
   %  plot(x,y) 
   %  axis([-inf inf 0 1.2]); 
   %  xlabel(['Input ' int2str(input_index)]); 
% end 
 
%% Error curves  
% This plot displays error curves for both training and 
% checking data. Note that the training error is higher than the 
% checking error. This phenomenon is not uncommon in ANFIS 
% learning or nonlinear regression in general; it could indicate 
% that the training process is not close to finished yet. 
 
% error curves plot 
% epoch_n = 10; 
% tmp = [trn_error chk_error]; 
% subplot(1,1,1) 
% plot(tmp); 
% hold on; plot(tmp, 'o'); hold off; 
% xlabel('Epochs'); 
% ylabel('RMSE (Root Mean Squared Error)'); 
% title('Error Curves'); 
% axis([0 epoch_n min(tmp(:)) max(tmp(:))]); 
 
%% Comparisons 
% This plot shows the original time series and the one predicted 
% by ANFIS. The difference is so tiny that it is impossible to tell 
% one from another by eye inspection. That is why you probably 
% see only the ANFIS prediction curve. The prediction errors 
% must be viewed on another scale. 
figure 
input = [trn_data(:, 1:4); chk_data(:, 1:4)]; 
anfis_output = evalfis(input, trn_fismat); 
index = 125:264; 
plot(time(index), ts(index),'b'); 
text(210,1.25,'原始数据(蓝色)'); 
text(210,1.3,'预测数据(红色)'); 
hold on 
plot(time(index), anfis_output,'r+'); 
xlabel('Time (sec)'); 
hold off 
%% Prediction errors of ANFIS 
% Prediction error of ANFIS is shown here. Note that the scale 
% is about a hundredth of the scale of the previous plot. 
% Remember that we have only 10 epochs of training in this case; 
% better performance is expected if we have extensive training. 
 
diff = ts(index)-anfis_output; 
figure 
plot(time(index), diff); 
xlabel('Time (sec)'); 
title('ANFIS Prediction Errors'); 
RMSE=sum(sqrt(mean(diff.*diff)));%均方根误差 
MAE=sum(mean(abs(diff)));%平均绝对误差 
MAPE=sum(mean(abs((diff)./ts(index))));%平均相对百分比误差