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layer is the linear
function purelin. The performance function of the network is
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only to reflect the performance situation of the network,
without any influence to it, thus the mse is used in this
proposed network.
C. Determination of the Neurons
1) The number of neurons at the input and output layers
Considering that the each input vector is the solar radiation
data of the adjacent 4 years, the number of input neurons is set
to be 4. Simultaneously, there is only one output parameter of
the network, which is the solar radiation of the following
year, thus the number of the output neurons is set to be 1.
2) The number of neurons at the hidden layer
In the BP neutral network, the determination of the hidden
layer is very important since it has a great influence on the
establishment of the neutral network, but till now there are no
definite ways to determine the number of it. The number of
the hidden nodes has a relation with the input and output
nodes, and it also depends on the complexity of the network
and the type of the transfer function. Equation (11) proposes a
generally used way to specify the number of hidden layer
neurons [12].
n = n + m + a 1 (11)
Where n is the number of neurons at the input layer; m is the
number of neurons at the output layer; n1 is the number of
neurons at the hidden layer; a is a constant between 1 and 10.
The basic method for determining the number of neurons
at the hidden layer is to compare with the different values of
n1 by choosing different values of a and find which is the
optimum one. In this proposed network, the network is
trained from the minimum value of 4 to the maximum value
of 13. If the number of the hidden neurons is set to be too
small, the network will be enable to be trained or the errors
will be too large. The number of the hidden neurons is also
limited to a value since too many neurons will cause prolong
of the training time and cause the over similarity between the
training results and the used data since the training process
will easily lapse into the local minimum point, not the
minimum point. In this proposed network, much training is
done and it is discovered that when n1 is set to be 11, the
network reaches its best performance. At the same time, the
number of the hidden nodes must be less than N-1, while N is
the number of the samples, or the systematic error of the
network has no relevance of the characteristic of samples,
which is equal to say that the network has no generalization
ability thus have no practical value.
D. Data Processing
In order to get a reliable network, the number of the
samples must be 2-10 times larger than the number of the
connection weight of the network, or the samples must be
divided to several different parts to be trained alternatively.
As the input layer is always the Sigmoid, all the input data
will be compressed to a relative small data range. In order to
improve the training speed and the sensitivity of the network
and avoid the saturation region of the Sigmoid function, the
data range must be restricted to be from 0 to 1, and [0.2, 0.8]
is preferred to ensure the extrapolation capacity of the
network. In this proposed system, all the input data are solar
radiation that is a very large figure, thus it must be divided be
a constant before training of the network