# Multi-Factor Highway Freight Volume Prediction Based on Backpropagation Neural Network
## 4 Case Analysis of Highway Freight Volume Forecasting Based on Neural Network
### Model Construction  
According to the strong nonlinear mapping characteristics of the neural network, only the input and output data of the object are given, and the characteristics of the mapping relationship between input and output can be achieved through the learning function of the network itself. By using the strong nonlinear mapping characteristics of the neural network, that is, through the input and output data of a given object, the mapping relationship between input and output can be achieved through the learning function of the network itself. The BP neural network includes input layer, hidden layer, and output layer. The input layer contains four factors, namely, road diesel consumption, road mileage, road operating truck ownership, and gross domestic product. For independent variables, the output layer is road freight volume, and the number of hidden layers is five. The effect is better. This is obtained through multiple tests. Finally, a 4-5-1 network is determined, and the structure is shown in Figure 4. The maximum number of iterations of the training is set to 1000 times, and the error threshold of the training is set to 10\({}^{-6}\). Three sets of data are selected from the collated data to test the model. The first 17 sets of data, namely the data from 1997 to 2013, are selected as the divided training set, and the last five sets of data, namely the data from 2014 to 2018, are selected as the divided test set. In general, we use 70% to 80% of the data as the training set and the remaining data are used for the division of the test set. Therefore, the ratio of the divided training set to the test set is 7:2, and the size of the data set is divided according to the amount of data and the data studied. After determining the network structure and data grouping, Matlab R2022a software is used for network training and analysis [24; 25; 26; 27; 28]. The BP neural network model consists of input layer, hidden layer, and output layer. Each layer contains one or more neuron nodes. Based on the multi-layer feedforward neural network trained by the error back propagation algorithm, the mapping relationship between the input value and the output value is established by continuously training and learning the data. The number of hidden layers is determined by Formula (5). \[l=\sqrt{\text{m}+\text{n}}+\text{a} \tag{5}\]  
\begin{table}
\begin{tabular}{l l l l l l} \hline \hline \multirow{2}{*}{**Particular Year**} & **Road Diesel** & **Gross Domestic** & **Highway Mileage** & **The Number of Road** & **Volume of Road** \\  & **Consumption (Ten** & **Product** & **(Ten Thousand** & **Operating Trucks** & **Haulage (Ten** \\  & **Thousand Tons)** & **(Billion Yuan)** & **Kilometers)** & **(Ten Thousand)** & **Thousand Tons)** \\ \hline
2002 & 2965 & 120,480 & 177 & 537 & 1,116,324 \\
2003 & 34,485 & 136,576 & 181 & 592 & 1,159,957 \\
2004 & 4182 & 161,415 & 187 & 648 & 1,244,990 \\
2005 & 4965 &  
In the formula: m is the number of neurons in the output layer; n is the number of neurons in the input layer; a is a constant between 1 and 12; and \(l\) is the number of neurons in the hidden layer, \(l\in[4,15]\). The reference activation function is sigmoid (logistic), also known as the S-shaped growth curve. The input signal from negative infinity to positive infinity can be transformed into output between 0 and 1. The activation function is shown in the following Figure 5.  
The properties of the activation function are very good:  
\[f(x)=\frac{1}{1+e^{-x}} \tag{6}\]  
\[f^{\prime}(x)=f(x)(1-f(x)) \tag{7}\]  
Figure 4: Model structure. Figure 5: Activation function. The BP neural network model was evaluated by the coefficient of determination (R\({}^{2}\)), the mean absolute error (MAE), the mean deviation (MBE), and the root mean square error (RMSE) between the estimated value and the true value.