drydemo.html

模糊控制工具箱,很好用的,有相应的说明文件,希望对大家有用!

tmp = x(:, ones(1, 3))';
X = tmp(:);
tmp = [zeros(anfis_n, 1) max(trn_error, chk_error) nan*ones(anfis_n, 1)]';
Y = tmp(:);
hold <span class="string">on</span>;
plot(X, Y, <span class="string">'g'</span>);
hold <span class="string">off</span>;
axis([1 anfis_n -inf inf]);
set(gca, <span class="string">'xticklabel'</span>, []);

<span class="comment">% ====== Add text of input variables</span>
<span class="keyword">for</span> k = 1:anfis_n,
    text(x(k), 0, <span class="keyword">...</span>
        [input_name(index(k,1), :) <span class="string">' '</span> <span class="keyword">...</span>
            input_name(index(k,2), :) <span class="string">' '</span> <span class="keyword">...</span>
            input_name(index(k,3), :)]);
<span class="keyword">end</span>
h = findobj(gcf, <span class="string">'type'</span>, <span class="string">'text'</span>);
set(h, <span class="string">'rot'</span>, 90, <span class="string">'fontsize'</span>, 11, <span class="string">'hori'</span>, <span class="string">'right'</span>);
drawnow

<span class="comment">% ====== Generate input_index for bjtrain.m</span>
[a b] = min(trn_error);
input_index = index(b,:);
title(<span class="string">'Training (Circles) and Checking (Asterisks) Errors'</span>);
ylabel(<span class="string">'RMSE'</span>);
</pre><pre class="codeoutput">
Train 36 ANFIS models, each with 3 inputs selected from 10 candidates...

ANFIS model = 1: y(k-1) y(k-2) u(k-1) --&gt; trn=0.0990, chk=0.0962
ANFIS model = 2: y(k-1) y(k-2) u(k-2) --&gt; trn=0.0852, chk=0.0862
ANFIS model = 3: y(k-1) y(k-2) u(k-3) --&gt; trn=0.0474, chk=0.0485
ANFIS model = 4: y(k-1) y(k-2) u(k-4) --&gt; trn=0.0808, chk=0.0822
ANFIS model = 5: y(k-1) y(k-2) u(k-5) --&gt; trn=0.1023, chk=0.0991
ANFIS model = 6: y(k-1) y(k-2) u(k-6) --&gt; trn=0.1021, chk=0.0974
ANFIS model = 7: y(k-1) y(k-3) u(k-1) --&gt; trn=0.1231, chk=0.1206
ANFIS model = 8: y(k-1) y(k-3) u(k-2) --&gt; trn=0.1047, chk=0.1085
ANFIS model = 9: y(k-1) y(k-3) u(k-3) --&gt; trn=0.0587, chk=0.0626
ANFIS model = 10: y(k-1) y(k-3) u(k-4) --&gt; trn=0.0806, chk=0.0836
ANFIS model = 11: y(k-1) y(k-3) u(k-5) --&gt; trn=0.1261, chk=0.1311
ANFIS model = 12: y(k-1) y(k-3) u(k-6) --&gt; trn=0.1210, chk=0.1151
ANFIS model = 13: y(k-1) y(k-4) u(k-1) --&gt; trn=0.1420, chk=0.1353
ANFIS model = 14: y(k-1) y(k-4) u(k-2) --&gt; trn=0.1224, chk=0.1229
ANFIS model = 15: y(k-1) y(k-4) u(k-3) --&gt; trn=0.0700, chk=0.0765
ANFIS model = 16: y(k-1) y(k-4) u(k-4) --&gt; trn=0.0817, chk=0.0855
ANFIS model = 17: y(k-1) y(k-4) u(k-5) --&gt; trn=0.1337, chk=0.1405
ANFIS model = 18: y(k-1) y(k-4) u(k-6) --&gt; trn=0.1421, chk=0.1333
ANFIS model = 19: y(k-2) y(k-3) u(k-1) --&gt; trn=0.2393, chk=0.2264
ANFIS model = 20: y(k-2) y(k-3) u(k-2) --&gt; trn=0.2104, chk=0.2077
ANFIS model = 21: y(k-2) y(k-3) u(k-3) --&gt; trn=0.1452, chk=0.1497
ANFIS model = 22: y(k-2) y(k-3) u(k-4) --&gt; trn=0.0958, chk=0.1047
ANFIS model = 23: y(k-2) y(k-3) u(k-5) --&gt; trn=0.2048, chk=0.2135
ANFIS model = 24: y(k-2) y(k-3) u(k-6) --&gt; trn=0.2388, chk=0.2326
ANFIS model = 25: y(k-2) y(k-4) u(k-1) --&gt; trn=0.2756, chk=0.2574
ANFIS model = 26: y(k-2) y(k-4) u(k-2) --&gt; trn=0.2455, chk=0.2400
ANFIS model = 27: y(k-2) y(k-4) u(k-3) --&gt; trn=0.1726, chk=0.1797
ANFIS model = 28: y(k-2) y(k-4) u(k-4) --&gt; trn=0.1074, chk=0.1157
ANFIS model = 29: y(k-2) y(k-4) u(k-5) --&gt; trn=0.2061, chk=0.2133
ANFIS model = 30: y(k-2) y(k-4) u(k-6) --&gt; trn=0.2737, chk=0.2836
ANFIS model = 31: y(k-3) y(k-4) u(k-1) --&gt; trn=0.3842, chk=0.3605
ANFIS model = 32: y(k-3) y(k-4) u(k-2) --&gt; trn=0.3561, chk=0.3358
ANFIS model = 33: y(k-3) y(k-4) u(k-3) --&gt; trn=0.2719, chk=0.2714
ANFIS model = 34: y(k-3) y(k-4) u(k-4) --&gt; trn=0.1763, chk=0.1808
ANFIS model = 35: y(k-3) y(k-4) u(k-5) --&gt; trn=0.2132, chk=0.2240
ANFIS model = 36: y(k-3) y(k-4) u(k-6) --&gt; trn=0.3460, chk=0.3601
</pre><img vspace="5" hspace="5" src="drydemo_05.png"> <p>The popped window shows ANFIS predictions on both training and checking data sets.  Obviously the performance is better than
            those of the ARX model.
         </p><pre class="codeinput"><span class="keyword">if</span> ishandle(winH1), delete(winH1); <span class="keyword">end</span>

ss = 0.01;
ss_dec_rate = 0.5;
ss_inc_rate = 1.5;

trn_data = data(1:trn_data_n, [input_index, size(data,2)]);
chk_data = data(trn_data_n+1:600, [input_index, size(data,2)]);

<span class="comment">% generate FIS matrix</span>
in_fismat = genfis1(trn_data);

[trn_out_fismat trn_error step_size chk_out_fismat chk_error] = <span class="keyword">...</span>
    anfis(trn_data, in_fismat, [1 nan ss ss_dec_rate ss_inc_rate], <span class="keyword">...</span>
    nan, chk_data, 1);

subplot(2,1,1);
index = 1:trn_data_n;
plot(index, y(index), index, yp(index), <span class="string">'.'</span>);
rmse = norm(y(index)-yp(index))/sqrt(length(index));
title([<span class="string">'(a) Training Data (Solid Line) and ARX Prediction (Dots) with RMSE = '</span> num2str(rmse)]);
disp([<span class="string">'[na nb d] = '</span> num2str(nn)]);
xlabel(<span class="string">'Time Steps'</span>);
subplot(2,1,2);
index = (trn_data_n+1):(total_data_n);
plot(index, y(index), index, yp(index), <span class="string">'.'</span>);
rmse = norm(y(index)-yp(index))/sqrt(length(index));
title([<span class="string">'(b) Checking Data (Solid Line) and ARX Prediction (Dots) with RMSE = '</span> num2str(rmse)]);
xlabel(<span class="string">'Time Steps'</span>);
</pre><pre class="codeoutput">
ANFIS info: 
	Number of nodes: 34
	Number of linear parameters: 32
	Number of nonlinear parameters: 18
	Total number of parameters: 50
	Number of training data pairs: 300
	Number of checking data pairs: 300
	Number of fuzzy rules: 8


Start training ANFIS ...

   1 	 0.0474113 	 0.0485325

Designated epoch number reached --&gt; ANFIS training completed at epoch 1.

[na nb d] = 5  10   2
</pre><img vspace="5" hspace="5" src="drydemo_06.png"> <pre class="codeinput">y_hat = evalfis(data(1:600,input_index), chk_out_fismat);

subplot(2,1,1);
index = 1:trn_data_n;
plot(index, data(index, size(data,2)), <span class="string">'-'</span>, <span class="keyword">...</span>
    index, y_hat(index), <span class="string">'.'</span>);
rmse = norm(y_hat(index)-data(index,size(data,2)))/sqrt(length(index));
title([<span class="string">'Training Data (Solid Line) and ANFIS Prediction (Dots) with RMSE = '</span> num2str(rmse)]);
xlabel(<span class="string">'Time Index'</span>); ylabel(<span class="string">''</span>);

subplot(2,1,2);
index = trn_data_n+1:600;
plot(index, data(index, size(data,2)), <span class="string">'-'</span>, index, y_hat(index), <span class="string">'.'</span>);
rmse = norm(y_hat(index)-data(index,size(data,2)))/sqrt(length(index));
title([<span class="string">'Checking Data (Solid Line) and ANFIS Prediction (Dots) with RMSE = '</span> num2str(rmse)]);
xlabel(<span class="string">'Time Index'</span>); ylabel(<span class="string">''</span>);
</pre><img vspace="5" hspace="5" src="drydemo_07.png"> <p>The above table is a comparison among various modeling approaches. The ARX modeling spends the least amount of time to reach
            the worse precision, which the ANFIS modeling via exhaustive search takes the largest amount of time to reach the best percision.
             In other words, if fast modeling is the goal, then ARX is the right choice.  But if precision is the utmost concern, then
            we can go for ANFIS that is designed for nonlinear modeling and higher precision.
         </p><pre class="codeinput">subplot(1,1,1)
a=imread(<span class="string">'drytable.jpg'</span>, <span class="string">'jpg'</span>);
image(a);
axis <span class="string">image</span>;
axis <span class="string">off</span>;
</pre><img vspace="5" hspace="5" src="drydemo_08.png"> <p class="footer">Copyright 1994-2002 The MathWorks, Inc.<br>
            Published with MATLAB&reg; 7.1<br></p>
      </div>
      <!--
##### SOURCE BEGIN #####
%% Nonlinear system identification
% This demo addresses the use of ANFIS function in the Fuzzy Logic
% Toolbox for nonlinear dynamical system identification. This demo also
% requires the System Identification Toolbox, as a comparison is made
% between a nonlinear ANFIS and a linear ARX model.
%
% Copyright 1994-2002 The MathWorks, Inc. 
% $Revision: 1.9 $

% Exit if the IDENT toolbox is not on the path
if exist('arx.m','file') == 0
  errordlg('DRYDEMO requires the System Identification Toolbox.');
  return;
end


%%
% The data set for ANFIS and ARX modeling was obtained from a laboratory
% device called Feedback's Process Trainer PT 326, as described in Chapter
% 17 of Prof. Lennart Ljung's book "System Identification, Theory for the
% User", Prentice-Hall, 1987. The device's function is like a hair dryer:
% air is fanned through a tube and heated at the inlet. The air temperature
% is measure by a thermocouple at the outlet. The input u(k) is the voltage
% over a mesh of resistor wires to heat incoming air; the output y(k) is
% the outlet air temperature. Here is a the system model

a=imread('dryblock.jpg', 'jpg');
image(a); 
axis image;
axis off;

%%
% Here are the results of the test.

load dryer2;
data_n = length(y2);
output = y2;
input = [[0; y2(1:data_n-1)] ...
        [0; 0; y2(1:data_n-2)] ...
        [0; 0; 0; y2(1:data_n-3)] ...
        [0; 0; 0; 0; y2(1:data_n-4)] ...
        [0; u2(1:data_n-1)] ...
        [0; 0; u2(1:data_n-2)] ...
        [0; 0; 0; u2(1:data_n-3)] ...
        [0; 0; 0; 0; u2(1:data_n-4)] ...
        [0; 0; 0; 0; 0; u2(1:data_n-5)] ...
        [0; 0; 0; 0; 0; 0; u2(1:data_n-6)]];
data = [input output];
data(1:6, :) = [];
input_name = str2mat('y(k-1)','y(k-2)','y(k-3)','y(k-4)','u(k-1)','u(k-2)','u(k-3)','u(k-4)','u(k-5)','u(k-6)');
trn_data_n = 300;
index = 1:100;
subplot(2,1,1);
plot(index, y2(index), '-', index, y2(index), 'o');
ylabel('y(k)');
subplot(2,1,2);
plot(index, u2(index), '-', index, u2(index), 'o');
ylabel('u(k)');

%%
% The data points was collected at a sampling time of 0.08 second. One
% thousand input-output data points were collected from the process as the
% input u(k) was chosen to be a binary random signal shifting between 3.41
% and 6.41 V. The probability of shifting the input at each sample was 0.2.
% The data set is available from the System Identification Toolbox; and the
% above plots show the output temperature y(k) and input voltage u(t) for
% the first 100 time steps.

%%
% A conventional method is to remove the means from the data and assume a
% linear model of the form:
%
% y(k)+a1*y(k-1)+...+am*y(k-m)=b1*u(k-d)+...+bn*u(k-d-n+1)
%
% where ai (i = 1 to m) and bj (j = 1 to n) are linear parameters to be
% determined by least-squares methods. This structure is called the ARX
% model and it is exactly specified by three integers [m, n, d]. To find an
% ARX model for the dryer device, the data set was divided into a training
% (k = 1 to 300) and a checking (k = 301 to 600) set.  An exhaustive search
% was performed to find the best combination of [m, n, d], where each of
% the integer is allowed to changed from 1 to 10 independently. The best
% ARX model thus found is specified by [m, n, d] = [5, 10, 2], with a
% training RMSE of 0.1122 and a checking RMSE of 0.0749. The above figure
% demonstrates the fitting results of the best ARX model.

trn_data_n = 300;
total_data_n = 600;
z = [y2 u2];
z = dtrend(z);
ave = mean(y2);
ze = z(1:trn_data_n, :);
zv = z(trn_data_n+1:total_data_n, :);