5.1 Data Selection and Analysis
Regional gross domestic product (regional GDP) refers to the total final result of all units in this region to carry out production activities at a certain period of time (usually a year or a quarter) and the value of the labor. Regional GDP has great significance and it is deemed as a criterion to evaluate the development level and economic conditions of a region at this period of time. This paper collects valid data and uses Matlab software platform for BP neural network model simulation for a certain regional GDP.
We have chosen household consumption level, permanent population, average wage, registered urban unemployment rate, cargo volume, passenger volume, and data of medical and health institutions as the input samples of BP neural network and the regional GDP as the predicted output of the model.
5.2 Result and Analysis of Experiment Simulation
(1) Layers of network
It has bias and at least one S-shaped hidden layer and a linear output layer and it can approximate any rational number. To increase layers can further reduce errors and improve accuracy, but meanwhile it also makes the network more complex and increase the training time of network weight.
(2) Neurons in the hidden layer
In order to avoid the “over-fitting” phenomena as many as possible, and ensure sufficient network performance and generalization ability, the most fundamental principle to identify the number of nodes in the hidden layer is as follows: take as compact a structure as possible while meeting the accuracy demand, in other words, take as few nodes in the hidden layer as possible. Research shows that the number of nodes in the hidden layer are related to not only the nodes of the input/output layer, but also the factors such as the complexity of the problem to be solved, the type of the transfer function, and the property of sample data.
(3) Selection of initial weight
As the system is non-linear, the initial value is closely related to whether the learning can reach the local minimum, whether it can converge and the length of training time. Generally, it is hope that the output value of every neuron after initial weight is close to zero. In this way, the weight of each neuron is ensured that it is adjusted within the maximum change of their activation functions. So, the initial weight is a random number between (-1, 1).
(4) Learning rate
Learning rate decides the change of weight generated in every cyclic training. A big learning rate may result in uncertain system, but a small one may lead to a longer training time and a slow convergence. So it tends to choose a small learning rate to ensure the stability of the system. The value range of learning rate is (0.01, 0.8).
According to the number of input data, the number of nodes in the input layer is 7. According to the output data, the number of nodes in the output layer is set as 1. The number of nodes in the hidden layer is 10. The empirical equation for the number of nodes in the hidden layer is as follows:
See formulas 5 and 6 in the supplementary files.
In Fig. 3, X-axis is the number of training and the Y-axis is the Mean Squared Error (MSE). The curve shows the error change of the network model with the increase of trainings, and the dotted line reflects the error goal we set. It can be seen that after several trainings, the error has achieved the expected goal. As shown in Fig. 4, the functional relationship between the expected output and theactual output basically fluctuates around a straight line with good fitting effect and ideal training effect. Fig. 5 shows the change of gradient in the training process of the entire network. The prediction results is shown in the Tab.1.
Table 1. The prediction results
Year
|
Real value (RMB 100 million)
|
Predicted value (RMB 100 million)
|
Error value (RMB 100 million)
|
Accuracy (%)
|
Error rate (%)
|
2000
|
2975.63
|
3399.66
|
424.03
|
85.75
|
14.25
|
2001
|
3528.81
|
3198.51
|
330.30
|
90.64
|
9.36
|
2002
|
4633.56
|
5169.66
|
536.10
|
88.43
|
11.57
|
2003
|
5236.17
|
4823.04
|
413.13
|
92.11
|
7.89
|
2004
|
5941.82
|
5191.96
|
749.86
|
87.38
|
12.62
|
2005
|
7069.34
|
7996.13
|
926.79
|
86.89
|
13.11
|
2006
|
8308.25
|
6834.37
|
1473.88
|
82.26
|
17.74
|
2007
|
9934.37
|
8757.15
|
1177.22
|
88.15
|
11.85
|
2008
|
11595.68
|
10401.32
|
1194.36
|
89.7
|
10.3
|
2009
|
12542.23
|
14428.58
|
1886.35
|
84.96
|
15.04
|
2010
|
14206.45
|
12263.01
|
1943.44
|
86.32
|
13.68
|
2011
|
16020.8
|
17545.98
|
1525.18
|
90.48
|
9.52
|
2012
|
17658.34
|
20236.46
|
2578.12
|
85.4
|
14.6
|
2013
|
18842.2
|
21274.73
|
2432.53
|
87.09
|
12.91
|
2014
|
20431.66
|
23588.35
|
3156.69
|
84.55
|
15.45
|
As can be seen from Tab.1, the prediction accuracy is 87.34%, and the average error is 12.66%. The comparison results between the predicted value and the actual value are shown in Fig. 6.
In Fig. 6, the abscissa is the year and the ordinate is the output value. Among them, the output of the neural network is very close to the predicted output, and the predicted GDP is consistent with the actual GDP. The output result of neural network is very close to the expected output. The expected regional GDP basically coincides with the actual Regional GDP, as demonstrated in the Fig. 7 and Fig. 8.
After training, we have got the necessary network model, according to the design principle of additional momentum method, when a revised weight leads to a too big increase result in the error, the new weight shall be cancelled and shall not be adopted and the role of momentum shall be stopped so as to prevent the network from entering big error curved surface. When the new change rate of error exceeds the previously-set maximum change rate of error, the change of weight calculated shall also be cancelled. The maximum change rate of error can be any value bigger than or equal to 1. In BP neural network training of additional momentum method, conditions shall be be added to determine the use of its weight revision equation correctly.