mgtsdemo.html

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--><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="color:#990000; font-weight:bold; font-size:x-large">Chaotic Time Series Prediction</p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">Chaotic time series prediction using ANFIS.
</p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">Copyright 1994-2002 The MathWorks, Inc.
$Revision: 1.15 $
</p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="color:#990000; font-weight:bold; font-size:medium;">Overview</p><ul xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd"><li><a href="#Error curves">Error curves</a></li><li><a href="#Comparisons">Comparisons</a></li><li><a href="#Prediction errors of ANFIS">Prediction errors of ANFIS</a></li></ul><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="color:#990000; font-weight:bold; font-size:medium; page-break-before: auto;"><a name=""></a></p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">The Mackey-Glass time-delay differential equation is defined by
</p><pre xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">dx(t)/dt = 0.2x(t-tau)/(1+x(t-tau)^10) - 0.1x(t)
</pre><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">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 &lt; 0.)
</p><pre xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="position: relative; left:30px">load mgdata.dat
a=mgdata;
time = a(:, 1);
ts = a(:, 2);
plot(time, ts);
xlabel(<span style="color:#B20000">'Time (sec)'</span>); ylabel(<span style="color:#B20000">'x(t)'</span>);
title(<span style="color:#B20000">'Mackey-Glass Chaotic Time Series'</span>);</pre><img xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" vspace="5" hspace="5" src="mgtsdemo_img_02_01.gif"><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="color:#990000; font-weight:bold; font-size:medium; page-break-before: auto;"><a name=""></a></p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">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
</p><pre xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">[x(t-18), x(t-12), x(t-6), x(t); x(t+6]
</pre><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">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.
</p><pre xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="position: relative; left:30px">trn_data = zeros(500, 5);
chk_data = zeros(500, 5);

<span style="color:green">% prepare training data</span>
start = 101;
trn_data(:, 1) = ts(start:start+500-1);
start = start + 6;
trn_data(:, 2) = ts(start:start+500-1);
start = start + 6;
trn_data(:, 3) = ts(start:start+500-1);
start = start + 6;
trn_data(:, 4) = ts(start:start+500-1);
start = start + 6;
trn_data(:, 5) = ts(start:start+500-1);

<span style="color:green">% prepare checking data</span>
start = 601;
chk_data(:, 1) = ts(start:start+500-1);
start = start + 6;
chk_data(:, 2) = ts(start:start+500-1);
start = start + 6;
chk_data(:, 3) = ts(start:start+500-1);
start = start + 6;
chk_data(:, 4) = ts(start:start+500-1);
start = start + 6;
chk_data(:, 5) = ts(start:start+500-1);

index = 118:1117+1; <span style="color:green">% ts starts with t = 0</span>
plot(time(index), ts(index));
axis([min(time(index)) max(time(index)) min(ts(index)) max(ts(index))]);
xlabel(<span style="color:#B20000">'Time (sec)'</span>); ylabel(<span style="color:#B20000">'x(t)'</span>);
title(<span style="color:#B20000">'Mackey-Glass Chaotic Time Series'</span>);</pre><img xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" vspace="5" hspace="5" src="mgtsdemo_img_03_01.gif"><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="color:#990000; font-weight:bold; font-size:medium; page-break-before: auto;"><a name=""></a></p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">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:
</p><pre xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="position: relative; left:30px"> 
fismat = genfis1(trn_data);