Appl. Sci. 2023, 13, x. https://doi.org/10.3390/xxxxx  www.mdpi.com/journal/applsci 
Article  1  
Multi-factor highway freight volume prediction based on BP  2  
neural network  3  
Yanshuang Zhang 1  ， Caixia Tian 2 ,  *， Baohua Guo 1 ， 3  ，Meixia Wang 1， Zhezhe Zhang 1  and Morobeni-Kgaugelo 1     4  
1   School of Energy Science and Engineering, Henan Polytechnic University, Jiaozuo, Henan 454000, China;  5  
<PRESIDIO_ANONYMIZED_EMAIL_ADDRESS>; <PRESIDIO_ANONYMIZED_EMAIL_ADDRESS>; <PRESIDIO_ANONYMIZED_EMAIL_ADDRESS>; <PRESIDIO_ANONYMIZED_EMAIL_ADDRESS>  6  
2   School of Resources and Environment, Henan Polytechnic University, Jiaozuo, Henan 454000, China;  7  
<PRESIDIO_ANONYMIZED_EMAIL_ADDRESS>  8  
3   Jiaozuo Engineering Research Center of Road Traffic and Transportation, Henan Polytechnic University,  9  
Jiaozuo, Henan 454000, China; <PRESIDIO_ANONYMIZED_EMAIL_ADDRESS>  10  
*  Correspondence: <PRESIDIO_ANONYMIZED_EMAIL_ADDRESS>    11  
  12  
Abstract: With the development of the times, the traditional single factor time series prediction can- 13  
not meet the needs of actual prediction. It is necessary to comprehensively consider the influence of  14  
various variables on the prediction results. Therefore, we use MATLAB to predict the highway  15  
freight volume of multiple factors. According to the relevant data of highway freight volume in  16  
Chinese history, the BP neural network prediction model of highway freight volume is established,  17  
coded and calculated in the MATLAB software environment. Through repeated training of the data,  18  
the predicted value is finally obtained. To prove the validity of the highway freight volume predic- 19  
tion model based on BP neural network, the example analysis of China’s highway freight volume is  20  
used and the original data is accurately fitted. The investment in the infrastructure construction is  21  
also improved through the prediction of the freight volume to promote the development of trans- 22  
portation industry and the progress of the social economy.  23  
Keywords: BP neural network; highway freight volume; multi-factor prediction  24  
  25  
1. Introduction  26  
Since the reform and opening up, the rapid development of the national economy  27  
has promoted the rapid development of various industries. For example, it has promoted  28  
the rapid development of road freight transportation. With the rise of online shopping, it  29  
has promoted the growth of China's logistics industry to an extent that has led to the de- 30  
velopment of China's freight transportation. The increase in the investment share of social  31  
fixed assets has promoted the development of trucks. In the ' Twelfth Five-Year Plan ', the  32  
state  clearly  proposed  to  vigorously  develop  road  freight  transportation,  improve  the  33  
level of standardization and intensification, promote the development and improvement  34  
of freight transportation methods, and expand the radiation range of less-than-truckload  35  
and fast-operating business networks. With the completion of a well-off society in an all- 36  
round way, China 's poverty alleviation has achieved great results. The economy has de- 37  
veloped steadily, the income level of urban and rural residents has been continuously  38  
improved and consumer demand has been increasing. In addition, China 's highway net- 39  
work has been continuously improved. For instance,  the structure of the highway has  40  
been continuously rationalized, the connection between urban and rural areas has been  41  
strengthened and the highway network has been gradually built and improved. The pro- 42  
gress of informatization technology will promote the development of highway transpor- 43  
tation, improve the quality of transportation, promote the transformation and upgrading  44  
of transportation mode while promoting the development of transportation industry.  45  
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ativecommons.org/licenses/by/4.0/). Appl. Sci. 2023, 13, x FOR PEER REVIEW  2  of  12 
 
2. Literature review  46  
Zhang [1] established a PB neural network model and analyzed the influencing fac- 47  
tors of freight volume in Xinjiang. Through the training and fitting of the model, historical  48  
data were selected as the test samples of the network model, which proved that the pre- 49  
diction of BP neural network was more accurate than other prediction methods. Taking  50  
the national railway freight volume as the research object, Luo [3] uses the methods of  51  
multiple linear regression and BP neural network to obtain a more suitable prediction  52  
method for the national railway and conducts research on the prediction of national rail- 53  
way  freight  volume  based  on  multiple  factors.  Practice  shows  that  the  two  prediction  54  
methods have their own advantages and the combination of the two can improve the pre- 55  
diction accuracy. Chen [8] analyzed the characteristics of Shandong's freight volume while  56  
using several prediction models to make quantitative predictions under the influence of  57  
relevant factors and qualitatively corrected the prediction results to obtain the final com- 58  
prehensive prediction results. Yang [7] established a PSO-SVM prediction model using a  59  
particle swarm support vector machine model, and predicted the road freight volume un- 60  
der the influence of industrial transfer in the Yangtze River transport corridor to verify  61  
the effectiveness of the model. An [11] used the GM ( 1,1 ) model direct modeling method  62  
to improve and analyze the unbiased grey Verhulst model and the traditional grey Ver- 63  
hulst model. Through the simulation and prediction of Lanzhou highway freight volume,  64  
the superiority of GM ( 1,1 ), traditional grey Verhulst and unbiased grey Verhulst model  65  
is analyzed and the feasibility as well as the applicability of the improved model unbiased  66  
grey Verhulst model were illustrated. On the basis of qualitative and quantitative analysis  67  
of the influencing factors of railway transportation, Wu [23] selected some factors affect- 68  
ing China 's freight volume to carry out BP neural network prediction research based on  69  
multi-factor  railway  freight  volume.  Both  prediction  fitting  and  the  algorithm  conver- 70  
gence are good. The complex nonlinear mapping between the influencing factors and the  71  
railway freight volume is realized and the prediction results are excellent.    72  
Whether it is for the study of highway freight volume, or for the study of railway  73  
freight volume, we can get inspiration from it, so as to apply it to the study of highway  74  
freight volume. The application of research methods does not distinguish between fields,  75  
but focuses on reliability. Based on the research of the above scholars, we can find that  76  
multiple regression and multi-factor prediction have a good effect on the prediction of  77  
freight volume. In summary, based on the comprehensive consideration of the impact in- 78  
dicators of freight volume, this paper selects relevant indicators and collects data. The  79  
multi-factor prediction based on BP neural network is used to predict China 's freight vol- 80  
ume and compare it with the actual China 's highway freight volume. The predicted re- 81  
sults and reliability are obtained.  82  
3. Neural network theory  83  
3.1. MATLAB multivariate prediction theory  84  
In this paper, we mainly use the neural network regression prediction. MATLAB is  85  
a powerful tool for data analysis and numerical calculation. It can use a variety of func- 86  
tions and toolboxes for multivariate prediction. Multivariate prediction generally predicts  87  
the value of one or more output variables through a variety of input variables. The steps  88  
of multivariate prediction are shown in Figure 1-1. In MATLAB, we can use a variety of  89  
multivariate prediction algorithms to predict. For example, through the construction of  90  
multiple decision trees, their results are averaged or voted by random forest regression  91  
prediction ; to predict the relationship between independent variables and dependent var- 92  
iables and establish multiple linear regression prediction of linear model ; the weighted  93  
average  is  performed  according  to  the  nearest  neighbor  weight  to  find  the  K-nearest  94  
neighbor regression prediction of the nearest sample point ; support vector regression  95  
prediction using support vector machine idea by finding the optimal hyperplane ; the  96  Appl. Sci. 2023, 13, x FOR PEER REVIEW  3  of  12 
 
principal component regression prediction of the principal component analysis of the in- 97  
dependent  variables  and  the  principal  component  regression  analysis  of  the  principal  98  
component ; the partial least squares regression prediction of the linear model is estab- 99  
lished after the dimension reduction of the independent variable and the dependent var- 100  
iable. The neural network model is used to establish the neural network regression pre- 101  
diction of the nonlinear mapping relationship between input and output.  102  
  103  
  104  
Figure 1. Multivariate flow chart.  105  
First item;  106  
Data preparation: Collect and organize input and output data. Ensure that the data  107  
is clean and complete and perform the necessary preprocessing, such as removing outli- 108  
ers, filling missing values, etc.    109  
Second item;  110  
Feature selection: According to the characteristics of the problem and data, select the  111  
appropriate input variables as features. Correlation analysis, principal component analy- 112  
sis and other methods can be used to assist selection.    113  
Third item;  114  
Data partitioning: The data set is divided into training set and test set. Usually, most  115  
of the data is used to train the model, and the remaining part is used to evaluate the per- 116  
formance of the model.    117  
Fourth item;  118  
Model training: Select the appropriate algorithm and use the training set to train the  119  
model. In MATLAB, functions such as fitlm, svmtrain and trainlm can be used to train the  120  
model.    121  
Fifth item;  122  
Model evaluation: Use the test set to evaluate the performance of the model. Various  123  
indicators, such as mean square error and coefficient of determination, can be used to  124  
evaluate the accuracy and generalization ability of the model.    125  
Sixth item;  126  
Model optimization: According to the evaluation results, the model is adjusted and  127  
optimized. Different parameter settings and feature combinations can be tried to improve  128  
the performance of the model.    129  
Seventh item;  130  
Prediction: Use the trained model to predict. Input new data and get the correspond- 131  
ing output through the model.  132  
3.2. BP neural network theory  133  
3.2.1. Algorithm flow    134  Appl. Sci. 2023, 13, x FOR PEER REVIEW  4  of  12 
 
The characteristic of BP neural network is to improve signal propagation according  135  
to the reverse feedback of error. The topology of BP neural network model is generally  136  
composed of three aspects: input layer, hidden layer and output layer, as shown in Figure  137  
2.1 below.  138  
  139  
  140  
Figure 2. 1 Topological structure of BP neural network model.  141  
The output layers 
1
, , , ,
j i
y y y   denote information output, that is, the target re- 142  
sult.    143  
The hidden layers 
1 2
, , , , ,
h q
b b b b   denote data processing, you can set the number  144  
of layers.    145  
The input layers 
1
, , , ,
j d
x x x   denote information input, read data    146  
w is the black path between b and y.    147  
w represents the weight from hidden layer to input layer.    148  
v is the black path between b and x.    149  
v represents the weight of the input layer to the hidden layer.  150  
3.2.2. Working process  151  
In the working process, the weight and bias from the hidden layer to the output layer  152  
are adjusted in turn, and the weight and bias from the input layer to the hidden layer are  153  
adjusted in turn. The working process of the BP neural network is shown in Figure 2.2.  154  
  155  Appl. Sci. 2023, 13, x FOR PEER REVIEW  5  of  12 
 
Figure 2. 2 Working process diagram of BP neural network.  156  
3.2.3. Propagation process    157  
First item;  158  
Forward propagation    159  
The information enters the network from the input layer and passes through each  160  
layer in turn, and the process of obtaining the final output layer result is shown in Figure  161  
2.3.  162  
  163  
Figure 2. 3 Forward propagation graph.  164  
The  calculation  process  mainly  involves  matrix  multiplication,  using  the  value  of  165  
each layer multiplied by the corresponding weight + bias variable (activation function).    166  
From the input layer to the hidden layer:  167  
1
d
h ih i
i
v x
=
= 
                                                                    (1)  168  
The activation function through the hidden layer is:  169  
( ) h h h
b f = −
 
                                                          （2）  170  
Among them, the weight between the first neuron of the input layer and the first  171  
neuron of the hidden layer is the threshold of the first neuron of the hidden layer.    172  
From the hidden layer to the output layer:  173  
1
q
j hj h j
h
w b
=
= + 
                                                    （3）  174  
Among them, the weight between the first neuron in the hidden layer and the first  175  
neuron in the output layer is the threshold of the first neuron in the output layer.  176  
In the machine learning model, the parameters we start with are random, so the cal- 177  
culation results may have a large error with the real values. In order to reduce this error,  178  
we need to adjust the parameters according to the error, and this process requires the back  179  
propagation algorithm of the model.  180  
Second item;  181  
Back propagation  182  
The core idea of the back propagation algorithm is to calculate the error between the  183  
output layer and the expected value, and then propagate the error back to each layer of  184  
the network, and then adjust the parameters in the network. In this process, each neuron  185  
adjusts its own weight and bias according to the error, so that the output of the network  186  
is closer to the expected value. This process is an iterative process, which needs to be re- 187  
peated until the error reaches the minimum or meets the preset stop condition. The error  188  
is usually measured by calculating the square sum of the difference between the true value  189  
and the neural network training result. Of course, other calculation methods can also be  190  
selected. This error value will be used to guide the parameter adjustment in the back prop- 191  
agation process, so that the network can better fit the real data.  192  
4. Case analysis of highway freight volume forecasting based on neural network  193  
4.1. Data source  194  Appl. Sci. 2023, 13, x FOR PEER REVIEW  6  of  12 
 
According to the strong nonlinear mapping and other characteristics of the neural  195  
network, only the input and output data of the object are given. Through the learning  196  
function of the network itself, the characteristics of the mapping relationship between in- 197  
put and output can be achieved. By using the strong nonlinear mapping and other char- 198  
acteristics of the neural network, that is, through the input and output data of the given  199  
object, the mapping relationship between input and output can be achieved through the  200  
learning function of the network itself. Through the analysis of the relevant data over the  201  
years and the review of the relevant literature. Finally, five indicators such as road diesel  202  
consumption, population, GDP, road freight turnover, and road freight volume were se- 203  
lected as influencing factors. The data were derived from the China Statistical Yearbook,  204  
and the relevant data from 1997 to 2021 were mainly queried and summarized. The ex- 205  
ample analysis proves that the freight volume prediction model based on BP neural net- 206  
work is effective, which provides a new prediction idea and method for highway freight  207  
volume prediction. The data over the years are shown in Table 1.  208  
Table 1. Data source.  209  
particular year 
Diesel consump-
tion (million tons) 
Population (ten 
thousand people) 
Gross domestic 
product (billion 
yuan) 
Freight turnover 
(billions of tons of 
kilometers) 
Freight volume (mil-
lion tons) 
1997  1379.53  123626  78802.9  5271.5  976536 
1998  1901.93  124761  83817.6  5483.4  976004 
1999  2221.65  125768  89366.5  5724.3  990444 
2000  2543.81  126743  99066.1  6129.4  1038813 
2001  2754.31  127627  109276.2  6330.4  1056312 
2002  2964.80  128453  120480.4  6782.5  1116324 
2003  34485.2  129227  136576.3  7099.5  1159957 
2004  4182.24  129988  161415.4  7840.9  1244990 
2005  4964.78  130756  185998.9  8693.2  1341778 
2006  5747.32  131448  219028.5  9754.2  1466347 
2007  6794.36  132129  270704.0  11354.7  1639432 
2008  7343.16  132802  321229.5  32868.2  1916759 
2009  7891.96  133450  347934.9  37188.8  2127834 
2010  8518.56  134091  410354.1  43389.7  2448052 
2011  9485.2  134916  483392.8  51374.7  2820100 
2012  10727.03  135922  537329.0  59534.9  3188475 
2013  10920.53  136726  588141.2  55738.1  3076648 
2014  11042.8  137646  644380.2  56846.9  3113334 
2015  11162.8  138326  685571.2  57955.7  3150019 
2016  11068.48  139232  742694.1  61080.1  3341259 
2017  11253.69  140011  830945.7  66771.5  3686858 
2018  11167  140541  915243.5  71249.2  3956871 
2019  9867  141008  983751.2  59636.4  3435480 
2020  9532  141212  1005451.3  60171.8  3426413 
2021  9984  141260  1141230.8  69087.7  3913889 
  210  
4.2. MATLAB running process  211  
Based on the analysis of historical data and the influencing factors of highway freight  212  
volume, BP neural network is used to predict the highway freight volume in China. The  213  
specific operation process is as follows, and the neural network view is shown in Figure  214  
3.1.  215  
  216  Appl. Sci. 2023, 13, x FOR PEER REVIEW  7  of  12 
 
  217  
Figure 3. 1 Neural network view.  218  
First item;  219  
Emptying environment variables. Delete the defined variables and start building our  220  
code again.    221  
Second item;  222  
Import data. The data of five indicators such as road diesel consumption, population,  223  
gross domestic product, road freight turnover and road freight volume in China from 1997  224  
to 2018 were selected as import data. A total of 22 sets of data were collected from the  225  
national statistical yearbook.    226  
Third item;  227  
Divide the training set and test set. Partitioning training set and test set is an im- 228  
portant task in machine learning and data analysis, which is used to evaluate the perfor- 229  
mance and generalization ability of the model. Here we select the first 17 sets of data, that  230  
is, 1997-2013 data as the divided training set, and select the last 5 sets of data, that is, 2014- 231  
2018 data as the divided test set.  232  
Fourth item;  233  
Data normalization. The data is scaled to a certain range according to a certain pro- 234  
portion to improve the accuracy and efficiency of subsequent data processing or analysis,  235  
accelerate the speed of gradient descent to find the optimal solution, and improve the  236  
training efficiency of the model.    237  
Fifth item;  238  
Create a network. In MATLAB, a new feedforward neural network is created, where  239  
p _ train is the training input data, t _ train is the training target data, and 5 represents the  240  
number of neurons in the hidden layer of the network.  241  
Sixth item;  242  
Set training parameters. The maximum number of iterations of training is set to 1000  243  
times. The training algorithm will try to minimize the error by adjusting the weight and  244  
deviation of the network, and perform up to 1000 iterations. If the set error threshold is  245  
reached within this number of iterations or other stop conditions are met, the training may  246  
end early. The training error threshold is set to 1e-6. The training algorithm will try to  247  
make the output error of the network less than or equal to this threshold. When the thresh- 248  
old is reached or lower than this threshold, the training will stop, even if the maximum  249  
number of iterations has not been reached. The learning rate is set to 0.01, which deter- 250  
mines the magnitude of network weight and bias update in each iteration. High learning  251  
rate may lead to fast or unstable training, and low learning rate may lead to more stable  252  
training.  253  
Seventh item;  254  
Training network. The train function is called to train the neural network net, using  255  
the input data p _ train and the target data t _ train.    256  
Eighth item;  257  Appl. Sci. 2023, 13, x FOR PEER REVIEW  8  of  12 
 
Simulation test. The trained neural network net is used to simulate (predict) the train- 258  
ing data p _ train and the test data p _ test, and the simulated outputs t _ sim1 and t _ sim2  259  
are obtained respectively.    260  
Ninth item;  261  
Data denormalization. The map minmax function is used to normalize the input data  262  
P _ train and P _ test and the target data T _ train and T _ test. Scales the data to a specific  263  
range (between 0 and 1) for better neural network training.  264  
Tenth item;  265  
Root mean square error. Calculate the error between the neural network prediction  266  
result and the actual target value. The calculation method of root mean square error RMSE  267  
is used.    268  
Eleventh item;  269  
Drawing. The comparison diagram between the neural network prediction results  270  
and the actual target values is drawn, and the root mean square error (RMSE) of each data  271  
set is displayed. The comparison diagram of the training set prediction results and the  272  
comparison diagram of the test set prediction results can be obtained.    273  
Twelfth item;  274  
Calculation of relevant indicators. Several key indicators of the neural network pre- 275  
diction results are calculated, R2 (determination coefficient), MAE (mean absolute error),  276  
MBE (mean deviation) and RMSE (root mean square error).    277  
Thirteenth item;  278  
Draw scatter plot. By drawing the scatter plot to visualize the relationship between  279  
the predicted value and the true value of the training set and the test set, the training set  280  
scatter plot and the test set scatter plot are drawn.  281  
Fourteenth item;  282  
Read the predicted data. Read data from Excel files and read data on four indicators  283  
of China 's road diesel consumption, population, gross domestic product, and road freight  284  
turnover from 2019 to 2021.    285  
Fifteenth item;  286  
Data transpose. The kes matrix is transposed, and the transposed  matrix is re-as- 287  
signed to kes.  288  
Sixteenth item;  289  
Data normalization. Each value in the original data is mapped to the specified range  290  
by linear transformation.    291  
Seventeenth item;  292  
Simulation test. Perform neural network simulation tests.    293  
Eighteenth item;  294  
Data denormalization. The denormalized data is stored in T _ sim3, and it is directly  295  
compared with the original output data to evaluate the performance of the model.    296  
Nineteenth item;  297  
Save the results. Save the data as an Excel file, and open and view these results when  298  
needed.  299  
4.3. Analysis of output results  300  
First item;  301  
The prediction results of the training set are compared with the prediction results of  302  
the test set, as shown in Figure 3.1.  303  Appl. Sci. 2023, 13, x FOR PEER REVIEW  9  of  12 
 
  304  
Figure 3. 1 Comparison of training set prediction results and test set prediction results.  305  
The comparison of the prediction results of the training set: RMSE = 15101.9604, the  306  
comparison of the prediction results of the test set: RMSE = 73520.6683 .The virtual depic- 307  
tion shows that that the difference between the two is large. The data shows that the model  308  
performs better in the training set and performs relatively poorly in the test set.  309  
Second item;  310  
Analysis and comparison of the training set and the prediction set fitting graph, as  311  
shown in Figure 3.2.  312  
  313  
  314  
Figure 3. 2 Comparison of training set and prediction set fitting.  315  
From the figure, we can see that in the predicted value image of the training set and  316  
the prediction set, in the fitting relationship between the scatter points of the predicted  317  
value and the real value of the training set as well as the prediction set and the linear  318  
fitting line, we can compare and observe that the fitting effect of the training set is very  319  
significant, and the scatter points are in or very close to the linear fitting line, which indi- 320  
cates that the model is very accurate in the prediction results of the training set and poor  321  
in the structure of the test set prediction.  322  
Third item;  323  
Output analysis of prediction results of training set and test set. The prediction re- 324  
sults of the training set and test set are shown in Table 3.1.  325  
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 2 4 6 8 10 12 14 16
forecasting results
prediction samples
Predicted Value
True Value
0
1
2
3
4
0 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
prediction samples
predicted samples
True Value
Predicted Value
0
0.5
1
1.5
2
2.5
3
3.5
4
0 1 2 3 4
Prediction value of training set
The real value of training set 
The predicted value of the training set vs. the 
true value of the training set
0
0.5
1
1.5
2
2.5
3
3.5
0 1 2 3 4
Predict ed value of test set
The true value of the test set
Test set predicted value vs. test set true valueAppl. Sci. 2023, 13, x FOR PEER REVIEW  10  of  12 
 
  326  
Table 3. 1 Test results of training set and prediction set.  327  
  R2  MAE  MBE  RMSE 
training sets  0.99977  9473.3095  -2629.6813  15101.9604 
testing set  0.99437  39126.4915  39126.4915  73520.6683 
（4）R 2 ( coefficient of determination ), in the training set R 2 = 0.99977, the test set R 2 =  328  
0.99437, we can see that both the training set and the test set, their test results are very  329  
close to 1, which shows that the model has a good fitting effect on road freight volume.  330  
Compared with the test set, the performance of the training set is more prominent.  331  
Fourth item;  332  
Analysis and forecast of freight volume in the past three years. The forecast results  333  
of China 's freight volume in the past three years are shown in Table 3.2.  334  
Table 3. 2 Prediction results of China 's freight volume in the three years.  335  
Freight volume of China  2019  2020  2021 
Prediction value  3099695.178  3131698.189  3534316.054 
Actual value  3435480  3426413  3913889 
We use the data from 1997 to 2013 as the training set, and select the data from 2014  336  
to 2018 as the test set to predict the freight volume of China from 2019 to 2021. It is pre- 337  
dicted that the freight volume of China 's highways in 2019 will be 3099695.178 million  338  
tons. In 2020, the freight volume of China 's highways will be 3131698.189 million tons. In  339  
2021, the freight volume of China 's highways will be 3534316.054 million tons. The actual  340  
freight volume of China 's highways will be 34354.8 million tons in 2019. In 2020, China 's  341  
road freight volume will be 3426413 million tons, and in 2021, China 's freight volume will  342  
be 3913889 million tons. It can be seen from the comparison that the predicted Chinese  343  
road freight volume in 2019-2021 is lower than the actual Chinese road freight volume.  344  
Since 2019 to 2021 it is in the period of the new coronavirus epidemic. There are many  345  
reasons why the actual freight volume is higher than the predicted highway freight vol- 346  
ume. On the one hand, it is due to the national policy, the state is coordinating a series of  347  
measures to promote epidemic prevention and control and social and economic develop- 348  
ment. Strengthen the service guarantee of road freight employees, provide free nucleic  349  
acid detection for them, provide guarantee for their commuting, and provide help for  350  
truck drivers with difficulties in life. Make every effort to smooth the transportation chan- 351  
nel, ensure the smooth flow of the main traffic lines, coordinate and linkage between var- 352  
ious regions, solve the problem of road network disconnection in time and strengthen the  353  
monitoring and dispatching of the road network. Furthermore, accelerate the establish- 354  
ment of material transfer stations, connection points or distribution sites and make every  355  
effort to organize emergency material transfer. Accurate management policies should be  356  
implemented as well to optimize the epidemic management measures according to the  357  
itinerary and whether the epidemic is involved and truck traffic should not be arbitrarily  358  
restricted. With the gradual relaxation of prevention and control policies in various re- 359  
gions, various restrictions on freight vehicles and epidemic prevention checkpoints have  360  
been  lifted,  enabling  freight  vehicles  to  carry  out  cross-regional  transportation  more  361  
freely. This has enabled truck drivers and logistics companies, which were originally lim- 362  
ited due to the epidemic, to resume road operations, which has led to a recovery in road  363  
freight volume. On the other hand, during the epidemic, the transportation of epidemic  364  
prevention materials and the transfer of materials needed to ensure people 's production  365  
and life also promoted the increase of highway freight volume to a certain extent. During  366  
the period when the epidemic situation was controlled and gradually stabilized, the pro- 367  
duction and consumption demand of various industries began to rebound, and the circu- 368  
lation of goods needed to be completed by road transportation. The rapid development  369  
of the commercial industry made online shopping a choice for more and more people,  370  Appl. Sci. 2023, 13, x FOR PEER REVIEW  11  of  12 
 
further promoting the growth of road freight volume. In addition, in order to stimulate  371  
consumption and promote economic recovery, the state has also introduced a series of  372  
policies to support the development of the logistics industry. These policies include re- 373  
ducing logistics costs, improving logistics efficiency, optimizing logistics networks, etc.,  374  
which provide a strong guarantee for the development of the road freight industry. Fi- 375  
nally, the advancement of digital reform has also injected new impetus into the develop- 376  
ment of the road freight industry. Through the wide application of digital means such as  377  
electronic licenses, the road freight industry has been able to achieve more efficient and  378  
convenient services, improve transportation efficiency and quality, and further promote  379  
the growth of road freight volume. In summary, the reasons for the increase in road freight  380  
volume during the epidemic mainly include policy relaxation, demand recovery, policy  381  
support and digital reform. These factors work together to make the road freight industry  382  
maintain a steady development trend during the epidemic.  383  
5. Conclusion  384  
This study comprehensively considers a variety of factors, such as road diesel con- 385  
sumption, population, gross domestic product, and road freight turnover on China 's road  386  
freight volume. It fully considers the influence of independent variables on dependent  387  
variables, and has certain operability. In the future, we can try to enrich the influencing  388  
factors of freight volume and increase the spatial dimension characteristics, so as to enrich  389  
the influencing factors of China 's road freight volume. In this study, through the estab- 390  
lishment of BP neural network, the multi-factor prediction method is used to accurately  391  
fit the original data and finally the predicted value of China 's highway freight volume is  392  
obtained, which has achieved high prediction accuracy. After testing, the model has a  393  
small error, which meets the prediction requirements of future freight volume, meets the  394  
needs of economic development, meets the needs of regional and social development, and  395  
provides  a  certain  reference  for  correctly  predicting  the  development  trend  of  future  396  
freight volume.  397  
The significance of highway freight volume prediction involves many aspects. It is  398  
conducive to enterprises to grasp the development trend of the market, understand the  399  
changes in demand, and correctly formulate development strategies to cope with market  400  
changes, reduce operating costs, improve transportation efficiency, and gain a foothold in  401  
the market. Through the prediction of highway freight volume, it is conducive to the ra- 402  
tional planning of highway operation lines, strengthening the planning and management  403  
of highway vehicles, and rational planning of traffic flow.  404  
For the case analysis of road freight volume in this study, we can improve from the  405  
following aspects; increasing the vertical number of data and horizontal influencing fac- 406  
tors as well as increasing the sample size of predicted data. While selecting the influencing  407  
factors, we should consider the correlation with the freight volume. In addition, we can  408  
also adjust the number of training rounds and select the appropriate model. 

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Keep in mind it remarcs:





_"Zhang [1] established a PB neural network model and analyzed the influencing factors of freight volume in Xinjiang."_
The referenced publication, which includes *a self-citation by the author*, cannot be finded in open access. It is ambiguous whether a classic Back Propagation Neural Network (a multilayer feed-forward neural network trained using an error backpropagation algorithm) was utilized by the author in their earlier work to solve a freight volume prediction problem maximally similar to current one.


_"we can use a variety of multivariate prediction algorithms to predict"_
_" other methods can be used to assist selection."_
_" functions such as fitlm, svmtrain and trainlm can be used to train the model."_
The excessive use of declarative statements and ambiguous statements disperses attention and detracts from the core essence of the approach.




_"The data of five indicators such as road diesel consumption, population, gross domestic product, road freight turnover and road freight volume in China from 1997 to 2018 were selected as import data."_
A good practice in applying multivariate methods in machine learning is to choose a dataset where the number of records is several times greater than the number of factors/variables. Therefore, a common step in the ML workflow, such as PCA (Principal Component Analysis), cannot be applied if the dataset lacks sufficient records. Additionally, it’s worth checking your data for multicollinearity or heteroskedasticity.





_"A total of 22 sets of data were collected from the national statistical yearbook."_
_"we select ... 17 sets ... as ... training set, ... 5 sets ... test set."_
_"In this paper, we mainly use the neural network regression prediction."_
The dataset size is clearly insufficient to strike a balance between overfitting and the network's ability to generalize. Additionally, a good practice for the default function, such as the built-in function fitrnet() in MATLAB, is to split the dataset into a validation subset in addition to train and test sets. 
Consequently, on such a small dataset, it's not feasible to evaluate standard performance metrics like the confusion matrix and ROC analysis.





_"The data of five indicators such as road diesel consumption, population, gross domestic product, road freight turnover and road freight volume in China from 1997 to 2018 were selected as import data."_
Your dataset contains a variable called “particular year,” which essentially represents a multichannel/multiphactor time series. 
For forecasting such data, it is not advisable to use shallow neural networks. 
Instead, recurrent neural networks (RNNs) are commonly employed for this purpose. RNNs are better suited for handling sequential data and capturing temporal dependencies.