gasdemo.html

交流 模糊控制 交流 模糊控制

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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">Car mileage prediction with ANFIS</p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">This slide show addresses the use of ANFIS function in the Fuzzy Logic
Toolbox for predicting the MPG (miles per gallon) of a given automobile.
</p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">Copyright 1994-2002 The MathWorks, Inc.
$Revision: 1.9 $
</p><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">Automobile MPG (miles per gallon)  prediction is a typical nonlinear
regression problem, in which several attributes of an automobile's
profile information are used to predict another continuous attribute,
that is, the fuel consumption in MPG. The training data is available from
the UCI (Univ. of California at Irvine) Machine Learning Repository
(<a href="http://www.ics.uci.edu/~mlearn/MLRepository.html).">http://www.ics.uci.edu/~mlearn/MLRepository.html).</a> It contains data
collected from automobiles of various manufactures and models, as shown
in the next slide.
</p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">The table shown above is several tuples from the MPG data set.  The six
input attributes are no. of cylinders, displacement, horsepower, weight,
acceleration, and model year; the output variable to be predicted is the
fuel consumption in MPG. (The automobile's manufacturers and models in
the first column of the table are not used for prediction.  The data set
is obtained from the original data file 'auto-gas.dat'. Then we partition
the data set into a training set (odd-indexed tuples) and a checking set
(even-indexed tuples), and use the function 'exhsrch' to find the input
attributes that have better prediction power for ANFIS modeling.
</p><pre xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="position: relative; left:30px">a=imread(<span style="color:#B20000">'gasdata.jpg'</span>, <span style="color:#B20000">'jpg'</span>);
image(a); colormap(gray); axis image;
axis off
[data, input_name] = loadgas;
trn_data = data(1:2:end, :);
chk_data = data(2:2:end, :);</pre><img xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" src="gasdemo_img02.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">To select the best input attribute, 'exhsrch' constructs six ANFIS, each
with a single input attribute. Here the result
after executing exhsrch(1, trn_data, chk_data, input_name). Obviously,
'Weight' is the most influential input attribute and 'Disp' is the second
one, etc.  The training and checking errors are comparable in size, which
implies that there is no overfitting and we can select more input
variables. Intuitively, we can simply select 'Weight' and 'Disp'
directly.  However, this will not necessarily lead to a two-ANFIS model
with the minimal training error.  To verify this, we can issue the
command exhsrch(2, trn_data, chk_data, input_name) to select the best two
inputs from all possible combinations.
</p><pre xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="position: relative; left:30px">exhsrch(1, trn_data, chk_data, input_name);
win1 = gcf;</pre><pre xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="color:gray; font-style:italic;">
Train 6 ANFIS models, each with 1 inputs selected from 6 candidates...

ANFIS model 1: Cylinder --&gt; trn=4.6400, chk=4.7255
ANFIS model 2: Disp --&gt; trn=4.3106, chk=4.4316
ANFIS model 3: Power --&gt; trn=4.5399, chk=4.1713
ANFIS model 4: Weight --&gt; trn=4.2577, chk=4.0863
ANFIS model 5: Acceler --&gt; trn=6.9789, chk=6.9317
ANFIS model 6: Year --&gt; trn=6.2255, chk=6.1693
</pre><img xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" src="gasdemo_img03.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">Demonstrate the result of selecting two inputs. 'Weight' and 'Year' are
selected as the best two input variables, which is quite reasonable.  The
training and checking errors are getting distinguished, indicating the
outset of overfitting.  As a comparison, let us use exhsrch to select
three inputs
</p><pre xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="position: relative; left:30px">input_index = exhsrch(2, trn_data, chk_data, input_name);
new_trn_data = trn_data(:, [input_index, size(trn_data,2)]);
new_chk_data = chk_data(:, [input_index, size(chk_data,2)]);
win2 = gcf;</pre><pre xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="color:gray; font-style:italic;">
Train 15 ANFIS models, each with 2 inputs selected from 6 candidates...

ANFIS model 1: Cylinder Disp --&gt; trn=3.9320, chk=4.7920
ANFIS model 2: Cylinder Power --&gt; trn=3.7364, chk=4.8683
ANFIS model 3: Cylinder Weight --&gt; trn=3.8741, chk=4.6763
ANFIS model 4: Cylinder Acceler --&gt; trn=4.3287, chk=5.9625
ANFIS model 5: Cylinder Year --&gt; trn=3.7129, chk=4.5946
ANFIS model 6: Disp Power --&gt; trn=3.8087, chk=3.8594
ANFIS model 7: Disp Weight --&gt; trn=4.0271, chk=4.6350
ANFIS model 8: Disp Acceler --&gt; trn=4.0782, chk=4.4890
ANFIS model 9: Disp Year --&gt; trn=2.9565, chk=3.3905
ANFIS model 10: Power Weight --&gt; trn=3.9310, chk=4.2976
ANFIS model 11: Power Acceler --&gt; trn=4.2740, chk=3.8738
ANFIS model 12: Power Year --&gt; trn=3.3796, chk=3.3505
ANFIS model 13: Weight Acceler --&gt; trn=4.0875, chk=4.0095
ANFIS model 14: Weight Year --&gt; trn=2.7657, chk=2.9953
ANFIS model 15: Acceler Year --&gt; trn=5.6242, chk=5.6481
</pre><img xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" src="gasdemo_img04.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">The popped figure demonstrates the result of selecting three inputs, in
which 'Weight', 'Year', and 'Acceler' are selected as the best three
input variables.  However, the minimal training (and checking) error do
not reduce significantly from that of the best 2-input model, which
indicates that the newly added attribute 'Acceler' does not improve the
prediction too much.  For better generalization, we always prefer a model
with a simple structure. Therefore we will stick to the two-input ANFIS
for further exploration
</p><pre xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="position: relative; left:30px">exhsrch(3, trn_data, chk_data, input_name);
win3 = gcf;</pre><pre xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="color:gray; font-style:italic;">
Train 20 ANFIS models, each with 3 inputs selected from 6 candidates...

ANFIS model 1: Cylinder Disp Power --&gt; trn=3.4446, chk=11.5329
ANFIS model 2: Cylinder Disp Weight --&gt; trn=3.6686, chk=4.8922
ANFIS model 3: Cylinder Disp Acceler --&gt; trn=3.6610, chk=5.2384
ANFIS model 4: Cylinder Disp Year --&gt; trn=2.5463, chk=4.9001
ANFIS model 5: Cylinder Power Weight --&gt; trn=3.4797, chk=9.3761
ANFIS model 6: Cylinder Power Acceler --&gt; trn=3.5432, chk=4.4804
ANFIS model 7: Cylinder Power Year --&gt; trn=2.6300, chk=3.6300
ANFIS model 8: Cylinder Weight Acceler --&gt; trn=3.5708, chk=4.8378
ANFIS model 9: Cylinder Weight Year --&gt; trn=2.4951, chk=4.0435
ANFIS model 10: Cylinder Acceler Year --&gt; trn=3.2698, chk=6.2616
ANFIS model 11: Disp Power Weight --&gt; trn=3.5879, chk=7.4948
ANFIS model 12: Disp Power Acceler --&gt; trn=3.5395, chk=3.9953
ANFIS model 13: Disp Power Year --&gt; trn=2.4607, chk=3.3563
ANFIS model 14: Disp Weight Acceler --&gt; trn=3.6075, chk=4.2318
ANFIS model 15: Disp Weight Year --&gt; trn=2.5617, chk=3.7865
ANFIS model 16: Disp Acceler Year --&gt; trn=2.4149, chk=3.2480
ANFIS model 17: Power Weight Acceler --&gt; trn=3.7884, chk=4.0480
ANFIS model 18: Power Weight Year --&gt; trn=2.4371, chk=3.2852
ANFIS model 19: Power Acceler Year --&gt; trn=2.7276, chk=3.2580
ANFIS model 20: Weight Acceler Year --&gt; trn=2.3603, chk=2.9152
</pre><img xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" src="gasdemo_img05.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">The input-output surface of the best two-input ANFIS model for MPG
prediction is shown above. It is a nonlinear and monotonic surface, in
which the predicted MPG increases with the increase in 'Weight' and
decrease in 'Year'. The training RMSE (root mean squared error) is 2.766;
the checking RMSE is 2.995. In comparison, a simple linear regression
using all input candidates results in a training RMSE of 3.452, and a
checking RMSE of 3.444.
</p><pre xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="position: relative; left:30px"><span style="color:blue">if</span> ishandle(win1), delete(win1); <span style="color:blue">end</span>
<span style="color:blue">if</span> ishandle(win2), delete(win2); <span style="color:blue">end</span>
<span style="color:blue">if</span> ishandle(win3), delete(win3); <span style="color:blue">end</span>

in_fis=genfis1(new_trn_data);
mf_n = 2;
mf_type = <span style="color:#B20000">'gbellmf'</span>;
epoch_n = 1;
ss = 0.01;
ss_dec_rate = 0.5;
ss_inc_rate = 1.5;
in_fismat = genfis1(new_trn_data, mf_n, mf_type);
[trn_out_fismat trn_error step_size chk_out_fismat chk_error] = anfis(new_trn_data, in_fismat, [epoch_n nan ss ss_dec_rate ss_inc_rate], nan, new_chk_data, 1);
<span style="color:blue">for</span> i=1:length(input_index),
    chk_out_fismat = setfis(chk_out_fismat, <span style="color:#B20000">'input'</span>, i, <span style="color:#B20000">'name'</span>, deblank(input_name(input_index(i), :)));
<span style="color:blue">end</span>
chk_out_fismat = setfis(chk_out_fismat, <span style="color:#B20000">'output'</span>, 1, <span style="color:#B20000">'name'</span>, deblank(input_name(size(input_name, 1), :)));
gensurf(chk_out_fismat); colormap(<span style="color:#B20000">'default'</span>);
set(gca, <span style="color:#B20000">'box'</span>, <span style="color:#B20000">'on'</span>);
view(-22, 36);
fprintf(<span style="color:#B20000">'\nLinear regression with parameters:\n'</span>);
param= size(trn_data,2)
A_trn = [trn_data(:, 1:size(data,2)-1) ones(size(trn_data,1), 1)];
B_trn = trn_data(:, size(data,2));
coef = A_trn\B_trn;
trn_error = norm(A_trn*coef-B_trn)/sqrt(size(trn_data,1));
A_chk = [chk_data(:, 1:size(data,2)-1) ones(size(chk_data,1), 1)];
B_chk = chk_data(:, size(data,2));
chk_error = norm(A_chk*coef-B_chk)/sqrt(size(chk_data,1));
fprintf(<span style="color:#B20000">'\nRMSE for training data: '</span>);
RMSE=trn_error
fprintf(<span style="color:#B20000">'\nRMSE for checking data: '</span>);
RMSE = chk_error</pre><pre xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="color:gray; font-style:italic;">
ANFIS info: 
	Number of nodes: 21
	Number of linear parameters: 12
	Number of nonlinear parameters: 12
	Total number of parameters: 24
	Number of training data pairs: 196
	Number of checking data pairs: 196
	Number of fuzzy rules: 4


Start training ANFIS ...

   1 	 2.7657 	 2.99534

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


Linear regression with parameters:

param =

     7


RMSE for training data: 
RMSE =

    3.4527