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within 1 minute. Regretfully, the precision of
traingdm, traingda, traingdx, trainrp can not meet the
minimum precision which means the failure of the network..
Comparatively, the trainlm shows its priority in the training
speed and precision, thus the trainlm is an ideal choice of the
network. Settings of the training parameters are shown as
follows.
net=newcf(minmax(p),[4,11,1],{'logsig','logsig','purelin'
},'trainlm');
net.trainParam.show=10;
net.trainParam.time=60;
net.trainParam.epochs=1000;
net.trainParam.goal=1e-12;
net.trainParam.min_grad=1e-10;
net.trainParam.mu=1000;
net.trainParam.mu_max=1e+10;
net.trainParam.mu_dec=0.5;
net.trainParam.mu_inc=2;
net=train(net,p,t);
Where net.trainParam.mu is the initial value of
u; net.trainParam.mu_dec is the reduction rate of
u; net.trainParam.mu_inc is the growth rate of u,
net.trainParam.mu_max is the maximum value of
u;
Large numbers of trainings are tried and a network is
found to be adequate for the training standard, shown as in
TABLE 􀄉.
TABLE I. THE COMPARISION OF THE PREDICTED DATA AND
THE DATA USED FOR TESTING
Year Actual data Predicted data Errors (%)
2001 0.4235 0.4031 -4.82
2002 0.4220 0.4194 -0.62
2003 0.4608 0.4693 1.84
The training process of the BP neutral network is shown in
Figure 3. As can be seen, the network needs 57 epochs of
training to meet the performance goal.
0 10 20 30 40 50
10-14
10-12
10-10
10-8
10-6
10-4
10-2
100
57 Epochs
Training-Blue Goal-Black
Performance is 9.90636e-015, Goal is 1e-012
Figure 3. The training process of the BP neutral network
The detail of the approximation process of the BP
network is shown as follows.
TRAINLM, Epoch 0/1000, Time 0.0%, MSE
1.77204/1e-012, Gradient 129.919/1e-010
TRAINLM, Epoch 10/1000, Time 0.2%, MSE
0.0075568/1e-012, Gradient 0.452695/1e-010
TRAINLM, Epoch 20/1000, Time 0.6%, MSE
0.000406175/1e-012, Gradient 0.253839/1e-010
TRAINLM, Epoch 30/1000, Time 0.9%, MSE
0.000263977/1e-012, Gradient 0.324352/1e-010
TRAINLM, Epoch 40/1000, Time 1.2%, MSE
4.95865e-005/1e-012, Gradient 0.0990928/1e-010
TRAINLM, Epoch 50/1000, Time 1.5%, MSE
1.61868e-005/1e-012, Gradient 0.117101/1e-010
TRAINLM, Epoch 57/1000, Time 1.6%, MSE
9.90636e-015/1e-012, Gradient 9.016e-007/1e-010
TRAINLM, Performance goal met.
Figure 4 show a failure of the training process by using
the traingda as the training method. It can be discovered that
when the maximum epoch reached, performance goal was not
met. The similar results was found in using the traingdm,
traingda, traingdx, trainrp as the training method.
0 100 200 300 400 500 600 700 800 900 1000
10-12
10-10
10-8
10-6
10-4
10-2
100
1000 Epochs
Training-Blue Goal-Black
Performance is 0.00127767, Goal is 1e-012
Figure 4. A failure of the training process by using the traingda as the training
method
220
C. Prediction Results
The trained network is used to predict the solar radiation of
Guangzhou in the following years and the result is shown in
TABLE􀀃􀄊.
TABLE􀀃􀄊. THE PREDICTION OF YEARLY SOLAR RADIATIONS IN THE
FOLLOWING YEARS OF GUANGZHOU
Year PRPSR PRSR(MJ/m2) Year PRPSR PRSR(MJ/m2)
2004 0.3905 3905 2008 0.4600 4600
2005 0.4254 4254 2009 0.4459 4459
2006 0.4199 4199 2010 0.3634 3634