# Application of BP Neural Network Model in Risk Evaluation of Railway Construction

Authors: Yang Changwei; Li Zonghao; Guo Xueyan; Yu Wenying; Jin Jing; Zhu Liang
Journal: Complexity
 (2019)

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## Abstract

Chinese railway construction project is an important part of the implementation of the “Belt and Road” strategy, and the risk evaluation of overseas railway construction is the primary link of the project. Firstly, this paper mainly analyzes the Asian and European countries along the railway construction project, establishes a railway construction project risk evaluation system, and synthesizes various risk factors. Secondly, it establishes two independent BP neural network models by using different training algorithms because of the different political, economic, and cultural elements between the two continents.


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## Body

## 1. Introduction

Since the “the Belt and Road” cooperation initiative was put forward, China is committed to the construction of overseas railways. Railways are the key means of forming crucial international channels and achieving interconnection [1–3]. At the same time, China's railway technology is technologically advanced, safe and reliable, compatible, and cost-effective. These advantages make this line a hot project which attract the countries involved in the Belt and Road. However, since “the Belt and Road” involves many countries, the national conditions and needs of different countries vary, which makes it necessary to design different policies according to different conditions. Besides, a railway project needs a large investment, a long construction period that involves many links. Therefore, the various risk factors are complex and need to be treated differently according to differently countries, aiming to assess project risks and provide decision support for railway construction in order to avoid and control risks [4, 5]. The traditional risk evaluation method cannot meet the current complicated situation, so it is of great practical significance to seek a new method suitable for overseas railway investment and construction risk evaluation. Figure 1 shows the overall trend of "the Belt and Road" Eurasia region railway [6, 7].Figure 1
“The Belt and Road” railway roadmap.This paper mainly analyzes countries along “the Belt and Road” strategic line in Asia and Europe, establish a risk evaluation index system, and use the BP neural network toolbox in MATLAB under this risk evaluation index system to process the data to build a risk prediction model.


## 2. Railway Construction Risk Evaluation Method

### 2.1. Evaluation Index System

The railway construction technology expert resource and investment should be integrated based on the national conditions of Asian and European countries, the factors needed to be considered for railway construction, and the principles of being scientifically, systematically, typically, and feasibly practical. The opinions of experts, market operation experts, and venture capital experts establish an evaluation index system, as shown in Figure2 [8, 9].Figure 2
Railway construction project risk evaluation index system.The risk is roughly divided into several aspects.(1) Economic Risk. The risk refers to the risk that may be brought about by changes in the social economic situation of the country where the project is located, including the country’s import and export volume, per capital GDP, the turnover of foreign contracted projects, inflation rate, and economic prospects. It affects willingness and ability to pay of a country to some extent.(2) Population Risk. The risk is analyzed according to the average quality of people’s life of the target country, including population density, population growth rate, average life expectancy, infectious disease mortality, and the number of refugees. It reflects the living standards of the people in that country to a certain extent.(3) Traffic Risk. The risk is analyzed based on the current national overall traffic level of the target country. It includes elements such as transportation services, power coverage, and traffic accident rate, which reflect the current development of the country's transportation industry to a certain extent.(4) Political Risk. The risk is analyzed based on the current domestic policies and regulations of the target country, including the cooperative relationship with China, the law, civil political freedom, and political stability. The unstable political situation of Central Asia and the Middle East is quite dangerous. If there is any big change, there will be huge impact on the project, even Casualties.


### 2.2. Comprehensive Evaluation Criteria

Among the 17 factors that affect the evaluation index of railway investment and construction project risks, there is no direct relationship between each factor, and the dimensions are very different. Therefore, before the neural network model being established, the data should be normalized. That is to say, the data is limited to a certain range and classified by the expert after the data is processed. When scoring, it should be fully reviewed by experts; the specific results are shown in Table1.Table 1
Experts' criteria for risk.
Risk Grade High Mid-High Medium Mid-Low Low Expert Grading 0~0.2 0.2~0.4 0.4~0.6 0.6~0.8 0.8~1.0Due to the large social and cultural differences between Asia and Europe, as well as the large gap in economic development, this paper will use the same system for evaluation in Asia and Europe but score and model independently, which means the criteria for judging in Asia and Europe are independent. Experts will score 17 factors according to different environments in Asia and Europe and work out the final score based on the final comprehensive opinions and the scores of each factor, which also satisfies the scoring standard of Table1; that is, the higher the value the lower the risk of building a railway in that country and vice versa.


## 2.1. Evaluation Index System

The railway construction technology expert resource and investment should be integrated based on the national conditions of Asian and European countries, the factors needed to be considered for railway construction, and the principles of being scientifically, systematically, typically, and feasibly practical. The opinions of experts, market operation experts, and venture capital experts establish an evaluation index system, as shown in Figure2 [8, 9].Figure 2
Railway construction project risk evaluation index system.The risk is roughly divided into several aspects.(1) Economic Risk. The risk refers to the risk that may be brought about by changes in the social economic situation of the country where the project is located, including the country’s import and export volume, per capital GDP, the turnover of foreign contracted projects, inflation rate, and economic prospects. It affects willingness and ability to pay of a country to some extent.(2) Population Risk. The risk is analyzed according to the average quality of people’s life of the target country, including population density, population growth rate, average life expectancy, infectious disease mortality, and the number of refugees. It reflects the living standards of the people in that country to a certain extent.(3) Traffic Risk. The risk is analyzed based on the current national overall traffic level of the target country. It includes elements such as transportation services, power coverage, and traffic accident rate, which reflect the current development of the country's transportation industry to a certain extent.(4) Political Risk. The risk is analyzed based on the current domestic policies and regulations of the target country, including the cooperative relationship with China, the law, civil political freedom, and political stability. The unstable political situation of Central Asia and the Middle East is quite dangerous. If there is any big change, there will be huge impact on the project, even Casualties.


## 2.2. Comprehensive Evaluation Criteria

Among the 17 factors that affect the evaluation index of railway investment and construction project risks, there is no direct relationship between each factor, and the dimensions are very different. Therefore, before the neural network model being established, the data should be normalized. That is to say, the data is limited to a certain range and classified by the expert after the data is processed. When scoring, it should be fully reviewed by experts; the specific results are shown in Table1.Table 1
Experts' criteria for risk.
Risk Grade High Mid-High Medium Mid-Low Low Expert Grading 0~0.2 0.2~0.4 0.4~0.6 0.6~0.8 0.8~1.0Due to the large social and cultural differences between Asia and Europe, as well as the large gap in economic development, this paper will use the same system for evaluation in Asia and Europe but score and model independently, which means the criteria for judging in Asia and Europe are independent. Experts will score 17 factors according to different environments in Asia and Europe and work out the final score based on the final comprehensive opinions and the scores of each factor, which also satisfies the scoring standard of Table1; that is, the higher the value the lower the risk of building a railway in that country and vice versa.


## 3. Establish BP Neural Network Model

### 3.1. Introduction to BP Neural Network

Artificial neural network is a model based on human brain [10–13]. It has a neuron system composed of many neurons, which has the advantages of massive parallelism, distributed processing, self-organization, and self-learning. Among these models, multilayer forward BP network is the most widely used neural network form. It has the universal advantages of all neural networks, self-learning and self-adaptive ability, nonlinear mapping ability, and high fault tolerance rate. Many problems that cannot be solved by traditional information processing methods have made some progress after using neural networks. For example, the risk evaluation of this paper and BP neural network can play a vital role.Figure3 is a typical BP neural network flow chart, which shows the whole process of BP neural network for data processing: firstly, input the variables (input layer), then deal with the data through the processing of the function, adjust the weight of each inputted variable, and finally compare the output value with the target value. If the satisfied accuracy is not met, then readjust the weight until the output value meets the error requirement. In this case, the scores of the 17 risk evaluation factor are the input values; the synthesized score of each country is the target value. By inputting 17 risk scores and synthesized scores of each country, the BP neural network functions like experts who can give an overall score; thus it forms a railway construction risk evaluation model.Figure 3
Typical 3-layer BP network flow chart.


### 3.2. Basic Principle of BP Neural Network

There are many training functions in BP neural network; the most common ones are traind (gradient descent method), traindm (momentum gradient descent method), trainda (adaptive learning rate gradient descent method), traindx (adaptive learning rate and momentum gradient descent method), traincgf/traincgp/traincgb (three conjugate gradient methods), etc. Each one of them has different parameters and different training methods that are based on the basic principles of BP neural network [14–16]. The basic principles are as follows.The essence of neural networks is the following function:(1)y→=fnetworkx→In the input layer, the input node spreads the inputted information to the hidden layer node through activating functionf(u). There are two kinds of activation functions: Sigmoid and Purein. They are nonlinear for either nonlinear data or linear data. Thus, this model is nonlinear; the expression of sigmoid is(2)fu=1+exp⁡-u-1Supposing thatw is the input layer and the hidden layer, the random weight between the hidden layer and the output layer, the vector is w→, the output of the hidden layer node is represented by O, and then there is(3)O=sigmoidw→T·x→Similarly, the output of the output layer node is represented byP, (4)P=sigmoidw→T·O→After the output is figured out, the node output errorδ can be calculated as follows:(5)δ=P1-PT-PT is the target value of the output node, and for hidden layer nodes,(6)δi=ai1-ai∑k∈outputswkiδkwhereδi is the error term of the hidden layer node i, ai is the output of the hidden layer node i, and wki is the weight of the node i to the next layer node k. And δk is the error term of the node k also the next layer of the node i. Finally, the weight on each link is updated:(7)wji←wji+ηδjxjiIn this expression,wji is the weight of node i to node j,η is the learning rate constant,δj is the error term of nodej, andxji is the input passed by nodei to nodej.The content above is the calculation of the error term of each node of the BP neural network and the weight update method. To calculate the error term of a node, it is necessary to firstly calculate the error term of each node connected to it. This requires to begin with calculating the error terms of the output layer, then the error terms of each hidden layer are calculated reversely until the hidden layer connected to the input layer. This is the meaning of the name of the reverse propagation (BP) algorithm.


### 3.3. Model and Algorithmic Principles for Asia

As mentioned earlier in this article, the railway construction project spans the Eurasian continent and passes through dozens of countries; each country has different national conditions. The regional differences between the two continents are obvious. Therefore, the target countries are divided into Asian district and European district. Thus, different learning functions and separate training models are applied.In general, the number of hidden layers increases, complicating the network, thereby increasing the training time of the network and the tendency of “overfitting”. After many tests and extensive statistical analysis, the neural network is designed to be 3 layers containing one hidden layer based on the calculate accuracy requirement and training time, which is the same as other research results [17–21].From a view of the overall situation in Asia, the economic development of some country is relatively backward, the political situation of some country is turbulent, and the overall situation is even more complicated. This paper adopts the traindx (adaptive learning rate momentum gradient descent method) algorithm that is attached to the most basic gradient descent method. The momentum and automatic adjustment of the learning rate: the standard BP algorithm is essentially a simple steepest descent static optimization method, which does not consider the direction of the error gradient descent, so that the learning process is often oscillated, the convergence is slow, and the additional momentum is the part of the last weight adjustment. It is added to the weight adjustment amount calculated according to the current error. As the actual weight adjustment amount, the essence of this is the influence of the last weight change, which is transmitted by a momentum factor. The weight adjustment formula with an additional momentum factor is(8)Wk+1-Wk=ΔWk+1=1-mcη×δiOj×Wk-Wk-1In this expression,W is the weight, ΔW is the weight increment,k is the training number,mc is the momentum factor,η is the learning rate,δi is the error of the output nodei, andOj is the input of the input nodej. The role of momentum is to remember the direction of the change of the last connection weight (positive and negative values), so that you can use a higher learning rate to improve learning speed.Based on the additional momentum, the traindx algorithm also uses the adaptive learning rate method. An important reason for the slow convergence rate of the standard BP algorithm is that the learning rate is not properly selected, and the rate cannot be changed after the rate is determined. When the learning rate is low, the training time will be long and the convergence will be slow. If the learning rate is too high, the overfitting will be caused and the data oscillation finally will diverge, so the adaptive learning rate method is used to solve this problem. The principle is as follows: check whether the modification of each weight changes the error. It means that the selected learning rate value is small if the error becomes smaller, and an appropriate amount can be added to it; if the error increases, then it should be reduced. The value of the learning rate can be expressed by the following equation:(9)ηK+1=aηkEWK+1<EWKbηkEWK+1<kEWKηkOtherwhereη is the learning rate,K is the number of trainings, andE is the error function, E=∑i=1n(yi-yi∧)2, i=1,2,…,n, yi is the actual output value after network training,y^i is the expected output value of the learning sample, andn is the number of learning samples.Additional momentum can help to find better solutions, and adaptive learning can shorten the network training time. The combination of the two is the traindx training algorithm. There are many countries in Asia which have complicated situations. The traindx algorithm is relatively suitable for these countries. The sample set of the training network should be the authoritative evaluation result with high credibility, which can be obtained by experts in some Asian countries. The trained model is stored, and the risk prediction is performed on the project that needs to be predicted. If the corresponding risk evaluation value is input, the neural network system can calculate the comprehensive risk evaluation value of the project through the previously calculated weights and thresholds. And outputting the output layer as a network result, you can get the final evaluation result.For the confirmation of the number of neurons in the hidden layer, the formulam=n+l+a is used in this manuscript (m is the number of neurons in the hidden layer, n is the number of neurons in the input layer,l is the number of neurons in the output layer, and a is an arbitrary integer from 0 to 5), which also is used in other researches [22–26]. In order to avoid “overfitting” during training and ensure high enough network performance and generalization ability, the basic principle for determining the number of hidden layer neurons is using the most compact structure while satisfying the accuracy requirements. That is, take as few hidden layer neurons as possible. When a=0, m=4.24, take 5, and then the number (5,6,7,8,9,10,11) of hidden layer neurons is used to verify the error rate until the best error rate is obtained. Table 1 shows the error rate of each selected hidden layer neuron, and the error meets accuracy requirement (error < 5%) when the number of hidden layer neurons is 6. Therefore, 6 neurons in the hidden layer are selected in this paper.Based on the above BP neural network model and risk evaluation system, the macrorisks of 36 Asian countries along “the Belt and Road” were evaluated; Table2 shows these countries. First, based on the expert experience method, the 17 risks of each country are evaluated, and then the 17 scores are combined to evaluate the risk of railway construction in each country. The results are shown in Table 3. In the model for Asian countries, the data for training set comes from United Arab Emirates/Oman/Azerbaijan/Pakistan/Bahrain/Bhutan/ Philippines/Georgia/Hassackstein/Korea/Qatar/Kuwait/ Laos/Lebanon/Maldives/Malaysia/Mongolia/Bangladesh/ Saudi Arabia/Sri Lanka/Turkey/Iran. The training function uses traindx to adjust the training parameters until the error requirements of the training set are met, as shown in Table 4. The parameters are selected as follows: 6000 cycles of maximum epochs, 0.001 for training accuracy, and 0.05 for learning rate (lr), the learning rate growth ratio is 1.05 (lr_inc), the learning rate reduction ratio (lr_dec) is 0.7, the maximum performance increment (max_perf_inc) is 1.04, the momentum factor (mc) is 0.9, and the rest are default values. The training results are shown in Table 5.Table 2
Number 36 countries in Asia.
Number 1 2 3 4 5 6 7 8 9 Country United Arab Emirates Oman Azerbaijan Pakistan Bahrain Bhutan Philippines Georgia Kazakhstan  Number 10 11 12 13 14 15 16 17 18  Country Korea Qatar Kuwait Laos Lebanon Maldives Malaysia Mongolia Bangladesh  Number 19 20 21 22 23 24 25 26 27  Country Saudi Arabia Sri Lanka Turkey Iran Thailand Turkmenistan Brunei Uzbekistan Singapore  Number 28 29 30 31 32 33 34 35 36  Country Syria Armenia Yemen Iraq Israel India Indonesia Jordan VietnamTable 3
Risk scores for railway construction projects in 36 countries in Asia.
Country Risk R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12 R13 R14 R15 R16 R17 score 1 0.78 0.90 0.62 0.80 0.90 0.52 0.78 0.67 0.50 0.71 0.70 0.37 0.61 0.62 0.01 0.81 0.86 0.819 2 0.65 0.71 0.44 0.86 0.79 0.81 0.56 0.71 0.14 0.98 0.75 0.37 0.78 0.27 0.82 0.71 0.78 0.792 3 0.19 0.61 0.34 0.72 0.45 0.41 0.32 0.45 0.50 0.48 0.45 0.79 0.53 0.37 0.74 0.39 0.42 0.545 4 0.61 0.22 0.91 0.29 0.40 0.38 0.56 0.39 0.64 0.77 0.39 0.11 0.04 0.77 0.97 0.41 0.12 0.491 5 0.21 0.77 0.04 0.82 0.87 0.88 0.23 0.70 0.86 0.67 0.78 0.78 0.70 0.37 0.28 0.59 0.29 0.602 6 0.03 0.39 0.00 0.52 0.62 0.67 0.46 0.67 0.16 0.56 0.67 0.26 0.28 0.13 0.83 0.82 0.86 0.505 7 0.72 0.41 0.62 0.79 0.61 0.67 0.76 0.63 0.66 0.59 0.58 0.32 0.77 0.63 0.32 0.66 0.32 0.663 8 0.15 0.52 0.38 0.70 0.84 0.87 0.41 0.71 0.31 0.23 0.78 0.95 0.57 0.27 0.49 0.76 0.45 0.674 9 0.70 0.69 0.79 0.33 0.51 0.59 0.53 0.56 0.06 0.53 0.55 0.75 0.58 0.88 0.67 0.44 0.59 0.612 10 0.99 0.80 0.37 0.83 0.95 0.95 0.86 0.72 0.75 0.27 0.87 0.62 0.38 0.77 0.76 0.75 0.71 0.691 11 0.53 0.99 0.62 0.82 0.91 0.90 0.75 0.72 0.55 0.90 0.87 0.31 0.79 0.63 0.92 0.73 0.95 0.733 12 0.61 0.92 0.57 0.87 0.71 0.75 0.65 0.69 0.59 0.89 0.60 0.65 0.61 0.37 0.85 0.68 0.67 0.773 13 0.33 0.30 0.74 0.73 0.35 0.29 0.35 0.39 0.21 0.61 0.23 0.09 0.99 0.89 0.82 0.36 0.69 0.535 14 0.33 0.62 0.07 0.77 0.48 0.43 0.41 0.47 0.76 0.91 0.49 0.86 0.06 0.27 0.53 0.28 0.18 0.542 15 0.07 0.61 0.22 0.51 0.51 0.45 0.65 0.51 0.87 0.80 0.50 0.55 0.98 0.49 0.67 0.56 0.70 0.503 16 0.95 0.69 0.81 0.80 0.88 0.89 0.78 0.71 0.42 0.54 0.80 0.35 0.29 0.89 0.39 0.70 0.66 0.791 17 0.52 0.53 0.53 0.38 0.52 0.58 0.63 0.58 0.03 0.67 0.56 0.59 0.90 0.89 0.61 0.67 0.78 0.651 18 0.57 0.13 0.68 0.52 0.34 0.29 0.32 0.38 0.86 0.43 0.31 0.23 0.19 0.77 0.52 0.49 0.25 0.563 19 0.84 0.78 0.99 0.85 0.73 0.76 0.69 0.69 0.14 0.82 0.67 0.37 0.62 0.88 0.55 0.71 0.50 0.743 20 0.43 0.45 0.71 0.61 0.64 0.69 0.58 0.65 0.67 0.34 0.61 0.66 0.67 0.63 0.72 0.66 0.46 0.635 21 0.65 0.68 0.58 0.43 0.79 0.81 0.63 0.70 0.43 0.54 0.76 0.85 0.05 0.63 0.62 0.61 0.27 0.714 22 0.73 0.61 0.72 0.16 0.41 0.51 0.52 0.47 0.26 0.46 0.53 0.65 0.12 0.89 0.04 0.52 0.27 0.536 23 0.87 0.54 0.63 0.82 0.73 0.77 0.41 0.69 0.54 0.27 0.68 0.35 0.23 0.88 0.18 0.55 0.28 0.635 24 0.52 0.61 0.57 0.70 0.18 0.01 0.32 0.21 0.09 0.47 0.03 0.44 0.86 0.63 0.66 0.03 0.67 0.442 25 0.22 0.89 0.17 0.85 0.92 0.90 0.68 0.72 0.35 0.54 0.85 0.77 0.99 0.63 0.21 0.72 0.94 0.406 26 0.42 0.31 0.46 0.18 0.30 0.50 0.36 0.40 0.35 0.74 0.44 0.58 0.77 0.62 0.30 0.25 0.45 0.457 27 0.91 0.94 0.81 0.83 0.99 0.99 0.81 0.71 0.99 0.65 0.99 0.68 0.92 0.48 0.10 0.93 0.92 0.865 28 0.19 0.30 0.12 0.17 0.26 0.50 0.12 0.39 0.51 0.23 0.45 0.37 0.13 0.27 0.51 0.15 0.01 0.135 29 0.13 0.46 0.14 0.72 0.62 0.69 0.42 0.67 0.51 0.26 0.60 0.93 0.32 0.38 0.17 0.61 0.61 0.442 30 0.45 0.22 0.33 0.23 0.30 0.21 0.36 0.34 0.26 0.83 0.18 0.17 0.17 0.13 0.53 0.13 0.06 0.263 31 0.70 0.56 0.87 0.82 0.21 0.14 0.06 0.25 0.35 0.86 0.04 0.20 0.22 0.63 0.08 0.17 0.15 0.314 32 0.55 0.86 0.22 0.79 0.96 0.95 0.58 0.71 0.74 0.76 0.92 0.87 0.30 0.49 0.31 0.76 0.28 0.741 33 0.88 0.29 0.98 0.59 0.60 0.66 0.75 0.66 0.74 0.45 0.59 0.19 0.21 0.63 0.91 0.68 0.28 0.736 34 0.83 0.44 0.95 0.62 0.57 0.63 0.36 0.61 0.55 0.48 0.56 0.36 0.41 0.88 0.62 0.64 0.42 0.743 35 0.38 0.52 0.24 0.67 0.77 0.79 0.62 0.67 0.42 0.86 0.69 0.54 0.01 0.62 0.43 0.68 0.43 0.577 36 0.88 0.32 0.89 0.35 0.51 0.50 0.45 0.57 0.65 0.39 0.53 0.49 0.68 0.89 0.75 0.63 0.68 0.683Table 4
Asian model error corresponding to the number of neurons in different hidden layers.
Country Neurons 5 6 7 8 9 10 11 1 5.76% 0.23% 3.96% 7.30% 8.17% 7.09% 6.94% 2 1.68% 4.52% 2.09% 4.40% 3.85% 5.65% 13.55% 3 1.75% 0.39% 4.36% 2.29% 5.11% 4.45% 6.79% 4 4.58% 4.37% 3.24% 1.47% 8.47% 5.44% 2.16% 5 3.38% 0.77% 3.50% 1.58% 3.91% 3.55% 6.48% 6 3.97% 4.78% 4.90% 4.36% 8.70% 4.52% 11.33% 7 5.00% 4.88% 4.19% 2.12% 7.08% 16.59% 14.55% 8 3.55% 2.24% 3.47% 0.33% 5.61% 6.87% 2.17% 9 3.12% 0.75% 2.96% 5.29% 2.26% 1.45% 12.32% 10 2.06% 3.99% 4.43% 9.33% 4.76% 4.29% 7.69% 11 2.98% 1.90% 3.20% 6.13% 5.90% 7.19% 7.29% 12 4.17% 3.44% 2.41% 4.54% 6.86% 5.35% 14.23% 13 1.27% 1.28% 3.82% 2.82% 7.02% 6.57% 0.39% 14 1.89% 2.40% 3.24% 2.20% 0.29% 6.25% 12.37% 15 5.39% 4.24% 3.32% 5.37% 1.85% 3.79% 15.91% 16 1.97% 3.15% 4.46% 5.29% 0.84% 3.38% 14.56% 17 2.69% 1.11% 3.69% 1.61% 5.40% 0.89% 11.06% 18 2.75% 1.22% 4.76% 4.08% 5.57% 7.74% 7.56% 19 2.58% 4.22% 4.27% 4.80% 11.97% 11.60% 0.81% 20 4.70% 4.65% 4.20% 6.97% 1.85% 10.02% 3.82% 21 3.91% 2.80% 0.32% 5.02% 1.39% 0.05% 7.49% 22 5.18% 2.10% 2.17% 4.40% 2.08% 6.89% 16.78%Table 5
BP neural network results of training on railway construction risks in 22 Asian countries.
NO. 1 2 3 4 5 6 7 8 9 10 11 Expert mark 0.819 0.792 0.545 0.491 0.602 0.505 0.663 0.674 0.612 0.691 0.733  Training results 0.817 0.756 0.542 0.512 0.597 0.480 0.695 0.689 0.616 0.718 0.747  Error(%) 0.23 4.52 0.39 4.37 0.77 4.78 4.88 2.24 0.75 3.99 1.90  NO. 12 13 14 15 16 17 18 19 20 21 22  Expert mark 0.773 0.535 0.542 0.503 0.791 0.651 0.563 0.743 0.635 0.714 0.536  Training results 0.746 0.541 0.529 0.524 0.766 0.658 0.556 0.774 0.664 0.694 0.524  Error(%) 3.44 1.28 2.40 4.24 3.15 1.11 1.22 4.22 4.65 2.80 2.10It can be seen from Table5 that the average relative error of the 22 training data in the Asian training set countries is 2.70%, and the maximum error in the sample set is 4.88% which satisfies the accuracy requirement of 5%; this means the model training learning result is good. Then the verification samples are replaced by the remaining 14 countries to verify whether the model is valid; eventually the results will be compared with the expert score results. The results are shown in Table 6.Table 6
Validation results of BP neural network on construction risk of railways in 14 Asian countries.
NO. 23 24 25 26 27 28 29 30 31 32 33 34 35 36 Expert mark 0.635 0.442 0.406 0.457 0.865 0.135 0.442 0.263 0.314 0.741 0.736 0.743 0.577 0.683 Training results 0.612 0.452 0.390 0.451 0.833 0.129 0.451 0.274 0.322 0.711 0.709 0.729 0.575 0.656 Error (%) 3.62 2.47 3.92 1.31 3.64 4.15 2.16 4.22 2.55 4.05 3.65 1.88 0.35 3.95It can be seen from Table6 that the average relative error of the verification data set is 2.99% and the maximum relative error of the prediction set is 4.22%, which meets the accuracy requirement of 5%, indicating that the neural network model can achieve the accuracy required by the project and can be used for risk assessment and prediction of Asian countries in railway construction projects.


### 3.4. Modeling and Algorithmic Principles for Europe

In Europe, the gap between various factors in various countries is not very large, the situation is relatively stable, the economy is more developed, and traindx is suitable for networks that have more complex and more data and may be used for smaller models. The error is increased so that trainda (adaptive learning rate algorithm) is selected; that is, no momentum is added except that the adaptive learning rate is added. The principle is shown in the previous section, Table7 shows these countries; the expert risk evaluation in Europe is shown in Table 8. In the model for European countries, the data for training set comes from Albania/Estonia/Belarus/Bulgaria/Bosnia/Poland/Russia/ Montenegro/Croatia/Latvia/Lithuania/Romania/Macedonia/ Czech/Moldova. Trainda is chosen as the training function; then adjusting the training parameters should be done until the error requirements of the training set are met. The parameter selection is as follows: the European model hidden layer neurons are determined in the same way as the Asian model. Table 9 shows the error of the number of neurons, and the error meets accuracy requirement (error < 5%) when the number of hidden layer neurons is 6. Therefore, 6 neurons in the hidden layer are selected in this manuscript. The maximum number of cycles (epochs) is 5000 times, the training accuracy (goal) is 0.001, the learning rate (lr) takes 0.01, learning rate growth ratio (lr_inc) is 1.05, the learning rate reduction ratio (lr_dec) is 0.8, and the maximum performance increment (max_perf_inc) is 1.04. The rest are taken as default values. The training results are shown in Table 10.Table 7
Number 20 countries in Europe.
Number 1 2 3 4 5 6 7 8 9 10 Country Albania Estonia Belarus Bulgaria Bosnia Poland Russia Montenegro Czech Croatia  Number 11 12 13 14 15 16 17 18 19 20  Country Latvia Lithuania Romania Macedonia Moldova Serbia Slovakia Slovenia Ukraine HungaryTable 8
Risk scores for railway construction projects in 20 countries in Europe.
NO. R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12 R13 R14 R15 R16 R17 score 1 0.33 0.27 0.35 0.66 0.32 0.40 0.36 0.68 0.73 0.47 0.34 0.50 0.91 0.38 0.45 0.41 0.47 0.525 2 0.51 0.87 0.23 0.52 0.96 0.98 0.56 0.35 0.24 0.43 0.89 0.66 0.95 0.18 0.45 0.85 0.71 0.563 3 0.46 0.48 0.79 0.36 0.16 0.36 0.63 0.78 0.33 0.66 0.43 0.33 0.63 0.90 0.72 0.55 0.44 0.532 4 0.53 0.56 0.15 0.26 0.75 0.72 0.62 0.32 0.44 0.25 0.97 0.90 0.32 0.58 0.28 0.57 0.54 0.623 5 0.11 0.40 0.76 0.63 0.34 0.33 0.36 0.74 0.67 0.51 0.31 0.79 0.37 0.33 0.57 0.42 0.25 0.543 6 0.88 0.72 0.44 0.62 0.79 0.80 0.76 0.43 0.87 0.61 0.73 0.47 0.23 0.90 0.52 0.72 0.88 0.811 7 0.85 0.73 0.77 0.39 0.42 0.27 0.82 0.76 0.19 0.92 0.26 0.42 0.04 0.90 0.15 0.38 0.33 0.802 8 0.16 0.49 0.78 0.66 0.56 0.54 0.42 0.56 0.33 0.58 0.53 0.90 0.45 0.38 0.40 0.55 0.60 0.621 9 0.84 0.90 0.42 0.63 0.94 0.93 0.75 0.29 0.93 0.82 0.85 0.62 0.49 0.72 0.38 0.69 0.93 0.767 10 0.42 0.68 0.73 0.72 0.66 0.64 0.62 0.50 0.52 0.34 0.63 0.73 0.70 0.43 0.68 0.62 0.69 0.621 11 0.42 0.75 0.13 0.58 0.85 0.83 0.65 0.39 0.26 0.16 0.80 0.55 0.83 0.18 0.67 0.66 0.63 0.602 12 0.48 0.77 0.11 0.62 0.89 0.86 0.56 0.34 0.35 0.10 0.81 0.41 0.62 0.18 0.36 0.74 0.79 0.654 13 0.66 0.60 0.58 0.51 0.60 0.57 0.81 0.54 0.63 0.31 0.59 0.70 0.51 0.58 0.87 0.61 0.50 0.625 14 0.23 0.37 0.57 0.58 0.55 0.52 0.31 0.58 0.63 0.86 0.51 0.96 0.58 0.38 0.76 0.46 0.31 0.571 15 0.09 0.12 0.09 0.44 0.37 0.35 0.42 0.71 0.85 0.56 0.39 0.43 0.76 0.38 0.08 0.34 0.36 0.455 16 0.35 0.40 0.62 0.46 0.49 0.47 0.45 0.64 0.61 0.27 0.44 0.97 0.16 0.90 0.35 0.46 0.41 0.620 17 0.73 0.83 0.20 0.69 0.73 0.71 0.68 0.45 0.79 0.77 0.68 0.52 0.66 0.38 0.58 0.65 0.93 0.725 18 0.59 0.99 0.04 0.66 0.85 0.82 0.62 0.38 0.71 0.84 0.77 0.30 0.77 0.18 0.80 0.81 0.84 0.651 19 0.83 0.20 0.68 0.35 0.21 0.21 0.82 0.79 0.54 0.39 0.20 0.36 0.45 0.72 0.83 0.39 0.17 0.589 20 0.79 0.70 0.33 0.55 0.71 0.70 0.52 0.44 0.77 0.36 0.70 0.83 0.42 0.38 0.92 0.59 0.75 0.713Table 9
Europe model error corresponding to the number of neurons in different hidden layers.
Country Neurons 5 6 7 8 9 10 11 1 1.44% 4.22% 4.31% 3.58% 6.85% 2.67% 4.94% 2 4.73% 4.14% 3.00% 8.54% 4.49% 14.19% 8.70% 3 6.48% 2.29% 3.78% 7.36% 1.99% 10.95% 10.09% 4 7.05% 4.08% 6.23% 1.94% 6.62% 3.82% 4.45% 5 2.18% 2.94% 2.40% 8.07% 4.55% 5.03% 1.36% 6 2.68% 3.73% 5.04% 4.71% 5.29% 16.39% 9.16% 7 7.91% 4.77% 8.36% 0.22% 4.77% 5.95% 9.87% 8 4.08% 4.11% 2.31% 5.98% 3.27% 7.28% 2.45% 9 1.80% 3.56% 0.55% 6.61% 1.88% 14.33% 2.11% 10 1.74% 0.12% 4.44% 3.07% 8.49% 5.57% 5.64% 11 3.56% 4.15% 4.57% 2.27% 8.56% 4.15% 10.01% 12 4.57% 4.46% 1.52% 7.78% 5.83% 3.82% 5.41% 13 2.22% 4.36% 1.78% 5.51% 7.02% 6.27% 0.27% 14 2.67% 3.92% 2.72% 10.75% 7.89% 0.13% 0.69% 15 3.99% 4.56% 8.37% 6.01% 6.85% 7.86% 15.18%Table 10
BP neural network results of training on railway construction risks in 15 European countries.
NO 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Expert mark 0.525 0.563 0.532 0.623 0.543 0.811 0.802 0.621 0.767 0.621 0.602 0.654 0.625 0.571 0.455 Training results 0.547 0.586 0.544 0.648 0.559 0.781 0.764 0.595 0.794 0.620 0.577 0.625 0.652 0.549 0.476 Error (%) 4.22 4.14 2.29 4.08 2.94 3.73 4.77 4.11 3.56 0.12 4.15 4.46 4.36 3.92 4.56It can be seen from Table10 that the average relative error of the 15 training data in Europe is 3.69%, and the maximum error in the sample set is 4.77% which meets the accuracy requirement of 5%; that is to say, the model training learning result is better. Then the verification sample is replaced by the remaining 5 countries to verify whether the model is valid or not; lastly compare the results with the expert score results. The results are shown in Table 11.Table 11
Validation results of BP neural network on construction risk of railways in 5 European countries.
NO. 16 17 18 19 20 Expert mark 0.620 0.725 0.651 0.589 0.713 Training results 0.590 0.761 0.682 0.569 0.686 Error (%) 4.91 4.97 4.76 3.44 3.76It can be seen from Table11 that the average relative error of the verification data set is 4.37% and the maximum relative error of the prediction set is 4.97%, indicating that the neural network model has been able to achieve the accuracy required by the project and can be used for railway outbuilding projects in European national risk evaluation forecast.


### 3.5. Model Robustness Test

It can be seen from the above training and testing that the accuracy of the model is good, and for machine learning, robustness is also an important feature, and the artificial neural network itself is robust [27–29]. The following is a robust test using the European model as an example: it is assumed that some data in the first 10 countries are randomly interfered and the data is shown in Table 12. The interference data is substituted into the model for simulation calculation, and the error between the verification result and the score given by the expert is shown in Table 13. The error between the verification result and the model score is shown in Table 14.Table 12
Interfered data in the top 10 countries in Europe.
NO 1 2 3 4 5 6 7 8 9 10 R1 0.35 0.51 0.46 0.53 0.19 0.88 0.85 0.16 0.84 0.42 R2 0.27 0.79 0.48 0.56 0.40 0.72 0.73 0.49 0.86 0.68 R3 0.35 0.23 0.79 0.24 0.76 0.46 0.86 0.78 0.42 0.73 R4 0.66 0.52 0.36 0.26 0.63 0.62 0.39 0.72 0.63 0.72 R5 0.32 0.96 0.25 0.75 0.34 0.79 0.42 0.56 0.94 0.62 R6 0.40 0.98 0.36 0.72 0.33 0.80 0.27 0.54 0.93 0.64 R7 0.36 0.56 0.63 0.62 0.36 0.76 0.82 0.42 0.75 0.62 R8 0.68 0.43 0.78 0.32 0.74 0.48 0.76 0.56 0.29 0.50 R9 0.64 0.24 0.33 0.44 0.67 0.87 0.19 0.46 0.93 0.52 R10 0.47 0.43 0.61 0.25 0.59 0.61 0.82 0.58 0.75 0.34 R11 0.34 0.89 0.43 0.97 0.31 0.73 0.26 0.53 0.85 0.58 R12 0.50 0.66 0.33 0.81 0.79 0.47 0.42 0.90 0.62 0.73 R13 0.91 0.87 0.63 0.32 0.37 0.23 0.13 0.45 0.49 0.70 R14 0.38 0.18 0.90 0.58 0.28 0.85 0.90 0.27 0.68 0.43 R15 0.58 0.45 0.85 0.28 0.57 0.52 0.15 0.40 0.38 0.59 R16 0.41 0.85 0.55 0.64 0.42 0.72 0.38 0.55 0.69 0.62 R17 0.47 0.71 0.44 0.54 0.25 0.88 0.33 0.60 0.93 0.69Table 13
Error test of interference data score and expert score.
NO 1 2 3 4 5 6 7 8 9 10 Expert score 0.525 0.563 0.532 0.623 0.543 0.811 0.802 0.621 0.767 0.621 Interference data score 0.541 0.589 0.549 0.609 0.545 0.773 0.782 0.593 0.762 0.652 Error (%) 3.05 4.64 3.15 2.32 0.43 4.68 2.55 4.46 0.66 4.96Table 14
Error test of interference data score and model score.
NO 1 2 3 4 5 6 7 8 9 10 Model score 0.547 0.586 0.544 0.648 0.559 0.781 0.764 0.595 0.794 0.620 Interference data score 0.541 0.589 0.549 0.609 0.545 0.773 0.782 0.593 0.762 0.652 Error (%) 1.14 0.46 0.88 6.47 2.57 1.01 2.33 0.42 4.24 4.87It can be seen from the data in the table that even if the input sample data is partially interfered with the data, the model can guarantee the result that the accuracy requirement (error < 5%) is met after the network is running; that means the robustness test result is good.


## 3.1. Introduction to BP Neural Network

Artificial neural network is a model based on human brain [10–13]. It has a neuron system composed of many neurons, which has the advantages of massive parallelism, distributed processing, self-organization, and self-learning. Among these models, multilayer forward BP network is the most widely used neural network form. It has the universal advantages of all neural networks, self-learning and self-adaptive ability, nonlinear mapping ability, and high fault tolerance rate. Many problems that cannot be solved by traditional information processing methods have made some progress after using neural networks. For example, the risk evaluation of this paper and BP neural network can play a vital role.Figure3 is a typical BP neural network flow chart, which shows the whole process of BP neural network for data processing: firstly, input the variables (input layer), then deal with the data through the processing of the function, adjust the weight of each inputted variable, and finally compare the output value with the target value. If the satisfied accuracy is not met, then readjust the weight until the output value meets the error requirement. In this case, the scores of the 17 risk evaluation factor are the input values; the synthesized score of each country is the target value. By inputting 17 risk scores and synthesized scores of each country, the BP neural network functions like experts who can give an overall score; thus it forms a railway construction risk evaluation model.Figure 3
Typical 3-layer BP network flow chart.


## 3.2. Basic Principle of BP Neural Network

There are many training functions in BP neural network; the most common ones are traind (gradient descent method), traindm (momentum gradient descent method), trainda (adaptive learning rate gradient descent method), traindx (adaptive learning rate and momentum gradient descent method), traincgf/traincgp/traincgb (three conjugate gradient methods), etc. Each one of them has different parameters and different training methods that are based on the basic principles of BP neural network [14–16]. The basic principles are as follows.The essence of neural networks is the following function:(1)y→=fnetworkx→In the input layer, the input node spreads the inputted information to the hidden layer node through activating functionf(u). There are two kinds of activation functions: Sigmoid and Purein. They are nonlinear for either nonlinear data or linear data. Thus, this model is nonlinear; the expression of sigmoid is(2)fu=1+exp⁡-u-1Supposing thatw is the input layer and the hidden layer, the random weight between the hidden layer and the output layer, the vector is w→, the output of the hidden layer node is represented by O, and then there is(3)O=sigmoidw→T·x→Similarly, the output of the output layer node is represented byP, (4)P=sigmoidw→T·O→After the output is figured out, the node output errorδ can be calculated as follows:(5)δ=P1-PT-PT is the target value of the output node, and for hidden layer nodes,(6)δi=ai1-ai∑k∈outputswkiδkwhereδi is the error term of the hidden layer node i, ai is the output of the hidden layer node i, and wki is the weight of the node i to the next layer node k. And δk is the error term of the node k also the next layer of the node i. Finally, the weight on each link is updated:(7)wji←wji+ηδjxjiIn this expression,wji is the weight of node i to node j,η is the learning rate constant,δj is the error term of nodej, andxji is the input passed by nodei to nodej.The content above is the calculation of the error term of each node of the BP neural network and the weight update method. To calculate the error term of a node, it is necessary to firstly calculate the error term of each node connected to it. This requires to begin with calculating the error terms of the output layer, then the error terms of each hidden layer are calculated reversely until the hidden layer connected to the input layer. This is the meaning of the name of the reverse propagation (BP) algorithm.


## 3.3. Model and Algorithmic Principles for Asia

As mentioned earlier in this article, the railway construction project spans the Eurasian continent and passes through dozens of countries; each country has different national conditions. The regional differences between the two continents are obvious. Therefore, the target countries are divided into Asian district and European district. Thus, different learning functions and separate training models are applied.In general, the number of hidden layers increases, complicating the network, thereby increasing the training time of the network and the tendency of “overfitting”. After many tests and extensive statistical analysis, the neural network is designed to be 3 layers containing one hidden layer based on the calculate accuracy requirement and training time, which is the same as other research results [17–21].From a view of the overall situation in Asia, the economic development of some country is relatively backward, the political situation of some country is turbulent, and the overall situation is even more complicated. This paper adopts the traindx (adaptive learning rate momentum gradient descent method) algorithm that is attached to the most basic gradient descent method. The momentum and automatic adjustment of the learning rate: the standard BP algorithm is essentially a simple steepest descent static optimization method, which does not consider the direction of the error gradient descent, so that the learning process is often oscillated, the convergence is slow, and the additional momentum is the part of the last weight adjustment. It is added to the weight adjustment amount calculated according to the current error. As the actual weight adjustment amount, the essence of this is the influence of the last weight change, which is transmitted by a momentum factor. The weight adjustment formula with an additional momentum factor is(8)Wk+1-Wk=ΔWk+1=1-mcη×δiOj×Wk-Wk-1In this expression,W is the weight, ΔW is the weight increment,k is the training number,mc is the momentum factor,η is the learning rate,δi is the error of the output nodei, andOj is the input of the input nodej. The role of momentum is to remember the direction of the change of the last connection weight (positive and negative values), so that you can use a higher learning rate to improve learning speed.Based on the additional momentum, the traindx algorithm also uses the adaptive learning rate method. An important reason for the slow convergence rate of the standard BP algorithm is that the learning rate is not properly selected, and the rate cannot be changed after the rate is determined. When the learning rate is low, the training time will be long and the convergence will be slow. If the learning rate is too high, the overfitting will be caused and the data oscillation finally will diverge, so the adaptive learning rate method is used to solve this problem. The principle is as follows: check whether the modification of each weight changes the error. It means that the selected learning rate value is small if the error becomes smaller, and an appropriate amount can be added to it; if the error increases, then it should be reduced. The value of the learning rate can be expressed by the following equation:(9)ηK+1=aηkEWK+1<EWKbηkEWK+1<kEWKηkOtherwhereη is the learning rate,K is the number of trainings, andE is the error function, E=∑i=1n(yi-yi∧)2, i=1,2,…,n, yi is the actual output value after network training,y^i is the expected output value of the learning sample, andn is the number of learning samples.Additional momentum can help to find better solutions, and adaptive learning can shorten the network training time. The combination of the two is the traindx training algorithm. There are many countries in Asia which have complicated situations. The traindx algorithm is relatively suitable for these countries. The sample set of the training network should be the authoritative evaluation result with high credibility, which can be obtained by experts in some Asian countries. The trained model is stored, and the risk prediction is performed on the project that needs to be predicted. If the corresponding risk evaluation value is input, the neural network system can calculate the comprehensive risk evaluation value of the project through the previously calculated weights and thresholds. And outputting the output layer as a network result, you can get the final evaluation result.For the confirmation of the number of neurons in the hidden layer, the formulam=n+l+a is used in this manuscript (m is the number of neurons in the hidden layer, n is the number of neurons in the input layer,l is the number of neurons in the output layer, and a is an arbitrary integer from 0 to 5), which also is used in other researches [22–26]. In order to avoid “overfitting” during training and ensure high enough network performance and generalization ability, the basic principle for determining the number of hidden layer neurons is using the most compact structure while satisfying the accuracy requirements. That is, take as few hidden layer neurons as possible. When a=0, m=4.24, take 5, and then the number (5,6,7,8,9,10,11) of hidden layer neurons is used to verify the error rate until the best error rate is obtained. Table 1 shows the error rate of each selected hidden layer neuron, and the error meets accuracy requirement (error < 5%) when the number of hidden layer neurons is 6. Therefore, 6 neurons in the hidden layer are selected in this paper.Based on the above BP neural network model and risk evaluation system, the macrorisks of 36 Asian countries along “the Belt and Road” were evaluated; Table2 shows these countries. First, based on the expert experience method, the 17 risks of each country are evaluated, and then the 17 scores are combined to evaluate the risk of railway construction in each country. The results are shown in Table 3. In the model for Asian countries, the data for training set comes from United Arab Emirates/Oman/Azerbaijan/Pakistan/Bahrain/Bhutan/ Philippines/Georgia/Hassackstein/Korea/Qatar/Kuwait/ Laos/Lebanon/Maldives/Malaysia/Mongolia/Bangladesh/ Saudi Arabia/Sri Lanka/Turkey/Iran. The training function uses traindx to adjust the training parameters until the error requirements of the training set are met, as shown in Table 4. The parameters are selected as follows: 6000 cycles of maximum epochs, 0.001 for training accuracy, and 0.05 for learning rate (lr), the learning rate growth ratio is 1.05 (lr_inc), the learning rate reduction ratio (lr_dec) is 0.7, the maximum performance increment (max_perf_inc) is 1.04, the momentum factor (mc) is 0.9, and the rest are default values. The training results are shown in Table 5.Table 2
Number 36 countries in Asia.
Number 1 2 3 4 5 6 7 8 9 Country United Arab Emirates Oman Azerbaijan Pakistan Bahrain Bhutan Philippines Georgia Kazakhstan  Number 10 11 12 13 14 15 16 17 18  Country Korea Qatar Kuwait Laos Lebanon Maldives Malaysia Mongolia Bangladesh  Number 19 20 21 22 23 24 25 26 27  Country Saudi Arabia Sri Lanka Turkey Iran Thailand Turkmenistan Brunei Uzbekistan Singapore  Number 28 29 30 31 32 33 34 35 36  Country Syria Armenia Yemen Iraq Israel India Indonesia Jordan VietnamTable 3
Risk scores for railway construction projects in 36 countries in Asia.
Country Risk R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12 R13 R14 R15 R16 R17 score 1 0.78 0.90 0.62 0.80 0.90 0.52 0.78 0.67 0.50 0.71 0.70 0.37 0.61 0.62 0.01 0.81 0.86 0.819 2 0.65 0.71 0.44 0.86 0.79 0.81 0.56 0.71 0.14 0.98 0.75 0.37 0.78 0.27 0.82 0.71 0.78 0.792 3 0.19 0.61 0.34 0.72 0.45 0.41 0.32 0.45 0.50 0.48 0.45 0.79 0.53 0.37 0.74 0.39 0.42 0.545 4 0.61 0.22 0.91 0.29 0.40 0.38 0.56 0.39 0.64 0.77 0.39 0.11 0.04 0.77 0.97 0.41 0.12 0.491 5 0.21 0.77 0.04 0.82 0.87 0.88 0.23 0.70 0.86 0.67 0.78 0.78 0.70 0.37 0.28 0.59 0.29 0.602 6 0.03 0.39 0.00 0.52 0.62 0.67 0.46 0.67 0.16 0.56 0.67 0.26 0.28 0.13 0.83 0.82 0.86 0.505 7 0.72 0.41 0.62 0.79 0.61 0.67 0.76 0.63 0.66 0.59 0.58 0.32 0.77 0.63 0.32 0.66 0.32 0.663 8 0.15 0.52 0.38 0.70 0.84 0.87 0.41 0.71 0.31 0.23 0.78 0.95 0.57 0.27 0.49 0.76 0.45 0.674 9 0.70 0.69 0.79 0.33 0.51 0.59 0.53 0.56 0.06 0.53 0.55 0.75 0.58 0.88 0.67 0.44 0.59 0.612 10 0.99 0.80 0.37 0.83 0.95 0.95 0.86 0.72 0.75 0.27 0.87 0.62 0.38 0.77 0.76 0.75 0.71 0.691 11 0.53 0.99 0.62 0.82 0.91 0.90 0.75 0.72 0.55 0.90 0.87 0.31 0.79 0.63 0.92 0.73 0.95 0.733 12 0.61 0.92 0.57 0.87 0.71 0.75 0.65 0.69 0.59 0.89 0.60 0.65 0.61 0.37 0.85 0.68 0.67 0.773 13 0.33 0.30 0.74 0.73 0.35 0.29 0.35 0.39 0.21 0.61 0.23 0.09 0.99 0.89 0.82 0.36 0.69 0.535 14 0.33 0.62 0.07 0.77 0.48 0.43 0.41 0.47 0.76 0.91 0.49 0.86 0.06 0.27 0.53 0.28 0.18 0.542 15 0.07 0.61 0.22 0.51 0.51 0.45 0.65 0.51 0.87 0.80 0.50 0.55 0.98 0.49 0.67 0.56 0.70 0.503 16 0.95 0.69 0.81 0.80 0.88 0.89 0.78 0.71 0.42 0.54 0.80 0.35 0.29 0.89 0.39 0.70 0.66 0.791 17 0.52 0.53 0.53 0.38 0.52 0.58 0.63 0.58 0.03 0.67 0.56 0.59 0.90 0.89 0.61 0.67 0.78 0.651 18 0.57 0.13 0.68 0.52 0.34 0.29 0.32 0.38 0.86 0.43 0.31 0.23 0.19 0.77 0.52 0.49 0.25 0.563 19 0.84 0.78 0.99 0.85 0.73 0.76 0.69 0.69 0.14 0.82 0.67 0.37 0.62 0.88 0.55 0.71 0.50 0.743 20 0.43 0.45 0.71 0.61 0.64 0.69 0.58 0.65 0.67 0.34 0.61 0.66 0.67 0.63 0.72 0.66 0.46 0.635 21 0.65 0.68 0.58 0.43 0.79 0.81 0.63 0.70 0.43 0.54 0.76 0.85 0.05 0.63 0.62 0.61 0.27 0.714 22 0.73 0.61 0.72 0.16 0.41 0.51 0.52 0.47 0.26 0.46 0.53 0.65 0.12 0.89 0.04 0.52 0.27 0.536 23 0.87 0.54 0.63 0.82 0.73 0.77 0.41 0.69 0.54 0.27 0.68 0.35 0.23 0.88 0.18 0.55 0.28 0.635 24 0.52 0.61 0.57 0.70 0.18 0.01 0.32 0.21 0.09 0.47 0.03 0.44 0.86 0.63 0.66 0.03 0.67 0.442 25 0.22 0.89 0.17 0.85 0.92 0.90 0.68 0.72 0.35 0.54 0.85 0.77 0.99 0.63 0.21 0.72 0.94 0.406 26 0.42 0.31 0.46 0.18 0.30 0.50 0.36 0.40 0.35 0.74 0.44 0.58 0.77 0.62 0.30 0.25 0.45 0.457 27 0.91 0.94 0.81 0.83 0.99 0.99 0.81 0.71 0.99 0.65 0.99 0.68 0.92 0.48 0.10 0.93 0.92 0.865 28 0.19 0.30 0.12 0.17 0.26 0.50 0.12 0.39 0.51 0.23 0.45 0.37 0.13 0.27 0.51 0.15 0.01 0.135 29 0.13 0.46 0.14 0.72 0.62 0.69 0.42 0.67 0.51 0.26 0.60 0.93 0.32 0.38 0.17 0.61 0.61 0.442 30 0.45 0.22 0.33 0.23 0.30 0.21 0.36 0.34 0.26 0.83 0.18 0.17 0.17 0.13 0.53 0.13 0.06 0.263 31 0.70 0.56 0.87 0.82 0.21 0.14 0.06 0.25 0.35 0.86 0.04 0.20 0.22 0.63 0.08 0.17 0.15 0.314 32 0.55 0.86 0.22 0.79 0.96 0.95 0.58 0.71 0.74 0.76 0.92 0.87 0.30 0.49 0.31 0.76 0.28 0.741 33 0.88 0.29 0.98 0.59 0.60 0.66 0.75 0.66 0.74 0.45 0.59 0.19 0.21 0.63 0.91 0.68 0.28 0.736 34 0.83 0.44 0.95 0.62 0.57 0.63 0.36 0.61 0.55 0.48 0.56 0.36 0.41 0.88 0.62 0.64 0.42 0.743 35 0.38 0.52 0.24 0.67 0.77 0.79 0.62 0.67 0.42 0.86 0.69 0.54 0.01 0.62 0.43 0.68 0.43 0.577 36 0.88 0.32 0.89 0.35 0.51 0.50 0.45 0.57 0.65 0.39 0.53 0.49 0.68 0.89 0.75 0.63 0.68 0.683Table 4
Asian model error corresponding to the number of neurons in different hidden layers.
Country Neurons 5 6 7 8 9 10 11 1 5.76% 0.23% 3.96% 7.30% 8.17% 7.09% 6.94% 2 1.68% 4.52% 2.09% 4.40% 3.85% 5.65% 13.55% 3 1.75% 0.39% 4.36% 2.29% 5.11% 4.45% 6.79% 4 4.58% 4.37% 3.24% 1.47% 8.47% 5.44% 2.16% 5 3.38% 0.77% 3.50% 1.58% 3.91% 3.55% 6.48% 6 3.97% 4.78% 4.90% 4.36% 8.70% 4.52% 11.33% 7 5.00% 4.88% 4.19% 2.12% 7.08% 16.59% 14.55% 8 3.55% 2.24% 3.47% 0.33% 5.61% 6.87% 2.17% 9 3.12% 0.75% 2.96% 5.29% 2.26% 1.45% 12.32% 10 2.06% 3.99% 4.43% 9.33% 4.76% 4.29% 7.69% 11 2.98% 1.90% 3.20% 6.13% 5.90% 7.19% 7.29% 12 4.17% 3.44% 2.41% 4.54% 6.86% 5.35% 14.23% 13 1.27% 1.28% 3.82% 2.82% 7.02% 6.57% 0.39% 14 1.89% 2.40% 3.24% 2.20% 0.29% 6.25% 12.37% 15 5.39% 4.24% 3.32% 5.37% 1.85% 3.79% 15.91% 16 1.97% 3.15% 4.46% 5.29% 0.84% 3.38% 14.56% 17 2.69% 1.11% 3.69% 1.61% 5.40% 0.89% 11.06% 18 2.75% 1.22% 4.76% 4.08% 5.57% 7.74% 7.56% 19 2.58% 4.22% 4.27% 4.80% 11.97% 11.60% 0.81% 20 4.70% 4.65% 4.20% 6.97% 1.85% 10.02% 3.82% 21 3.91% 2.80% 0.32% 5.02% 1.39% 0.05% 7.49% 22 5.18% 2.10% 2.17% 4.40% 2.08% 6.89% 16.78%Table 5
BP neural network results of training on railway construction risks in 22 Asian countries.
NO. 1 2 3 4 5 6 7 8 9 10 11 Expert mark 0.819 0.792 0.545 0.491 0.602 0.505 0.663 0.674 0.612 0.691 0.733  Training results 0.817 0.756 0.542 0.512 0.597 0.480 0.695 0.689 0.616 0.718 0.747  Error(%) 0.23 4.52 0.39 4.37 0.77 4.78 4.88 2.24 0.75 3.99 1.90  NO. 12 13 14 15 16 17 18 19 20 21 22  Expert mark 0.773 0.535 0.542 0.503 0.791 0.651 0.563 0.743 0.635 0.714 0.536  Training results 0.746 0.541 0.529 0.524 0.766 0.658 0.556 0.774 0.664 0.694 0.524  Error(%) 3.44 1.28 2.40 4.24 3.15 1.11 1.22 4.22 4.65 2.80 2.10It can be seen from Table5 that the average relative error of the 22 training data in the Asian training set countries is 2.70%, and the maximum error in the sample set is 4.88% which satisfies the accuracy requirement of 5%; this means the model training learning result is good. Then the verification samples are replaced by the remaining 14 countries to verify whether the model is valid; eventually the results will be compared with the expert score results. The results are shown in Table 6.Table 6
Validation results of BP neural network on construction risk of railways in 14 Asian countries.
NO. 23 24 25 26 27 28 29 30 31 32 33 34 35 36 Expert mark 0.635 0.442 0.406 0.457 0.865 0.135 0.442 0.263 0.314 0.741 0.736 0.743 0.577 0.683 Training results 0.612 0.452 0.390 0.451 0.833 0.129 0.451 0.274 0.322 0.711 0.709 0.729 0.575 0.656 Error (%) 3.62 2.47 3.92 1.31 3.64 4.15 2.16 4.22 2.55 4.05 3.65 1.88 0.35 3.95It can be seen from Table6 that the average relative error of the verification data set is 2.99% and the maximum relative error of the prediction set is 4.22%, which meets the accuracy requirement of 5%, indicating that the neural network model can achieve the accuracy required by the project and can be used for risk assessment and prediction of Asian countries in railway construction projects.


## 3.4. Modeling and Algorithmic Principles for Europe

In Europe, the gap between various factors in various countries is not very large, the situation is relatively stable, the economy is more developed, and traindx is suitable for networks that have more complex and more data and may be used for smaller models. The error is increased so that trainda (adaptive learning rate algorithm) is selected; that is, no momentum is added except that the adaptive learning rate is added. The principle is shown in the previous section, Table7 shows these countries; the expert risk evaluation in Europe is shown in Table 8. In the model for European countries, the data for training set comes from Albania/Estonia/Belarus/Bulgaria/Bosnia/Poland/Russia/ Montenegro/Croatia/Latvia/Lithuania/Romania/Macedonia/ Czech/Moldova. Trainda is chosen as the training function; then adjusting the training parameters should be done until the error requirements of the training set are met. The parameter selection is as follows: the European model hidden layer neurons are determined in the same way as the Asian model. Table 9 shows the error of the number of neurons, and the error meets accuracy requirement (error < 5%) when the number of hidden layer neurons is 6. Therefore, 6 neurons in the hidden layer are selected in this manuscript. The maximum number of cycles (epochs) is 5000 times, the training accuracy (goal) is 0.001, the learning rate (lr) takes 0.01, learning rate growth ratio (lr_inc) is 1.05, the learning rate reduction ratio (lr_dec) is 0.8, and the maximum performance increment (max_perf_inc) is 1.04. The rest are taken as default values. The training results are shown in Table 10.Table 7
Number 20 countries in Europe.
Number 1 2 3 4 5 6 7 8 9 10 Country Albania Estonia Belarus Bulgaria Bosnia Poland Russia Montenegro Czech Croatia  Number 11 12 13 14 15 16 17 18 19 20  Country Latvia Lithuania Romania Macedonia Moldova Serbia Slovakia Slovenia Ukraine HungaryTable 8
Risk scores for railway construction projects in 20 countries in Europe.
NO. R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12 R13 R14 R15 R16 R17 score 1 0.33 0.27 0.35 0.66 0.32 0.40 0.36 0.68 0.73 0.47 0.34 0.50 0.91 0.38 0.45 0.41 0.47 0.525 2 0.51 0.87 0.23 0.52 0.96 0.98 0.56 0.35 0.24 0.43 0.89 0.66 0.95 0.18 0.45 0.85 0.71 0.563 3 0.46 0.48 0.79 0.36 0.16 0.36 0.63 0.78 0.33 0.66 0.43 0.33 0.63 0.90 0.72 0.55 0.44 0.532 4 0.53 0.56 0.15 0.26 0.75 0.72 0.62 0.32 0.44 0.25 0.97 0.90 0.32 0.58 0.28 0.57 0.54 0.623 5 0.11 0.40 0.76 0.63 0.34 0.33 0.36 0.74 0.67 0.51 0.31 0.79 0.37 0.33 0.57 0.42 0.25 0.543 6 0.88 0.72 0.44 0.62 0.79 0.80 0.76 0.43 0.87 0.61 0.73 0.47 0.23 0.90 0.52 0.72 0.88 0.811 7 0.85 0.73 0.77 0.39 0.42 0.27 0.82 0.76 0.19 0.92 0.26 0.42 0.04 0.90 0.15 0.38 0.33 0.802 8 0.16 0.49 0.78 0.66 0.56 0.54 0.42 0.56 0.33 0.58 0.53 0.90 0.45 0.38 0.40 0.55 0.60 0.621 9 0.84 0.90 0.42 0.63 0.94 0.93 0.75 0.29 0.93 0.82 0.85 0.62 0.49 0.72 0.38 0.69 0.93 0.767 10 0.42 0.68 0.73 0.72 0.66 0.64 0.62 0.50 0.52 0.34 0.63 0.73 0.70 0.43 0.68 0.62 0.69 0.621 11 0.42 0.75 0.13 0.58 0.85 0.83 0.65 0.39 0.26 0.16 0.80 0.55 0.83 0.18 0.67 0.66 0.63 0.602 12 0.48 0.77 0.11 0.62 0.89 0.86 0.56 0.34 0.35 0.10 0.81 0.41 0.62 0.18 0.36 0.74 0.79 0.654 13 0.66 0.60 0.58 0.51 0.60 0.57 0.81 0.54 0.63 0.31 0.59 0.70 0.51 0.58 0.87 0.61 0.50 0.625 14 0.23 0.37 0.57 0.58 0.55 0.52 0.31 0.58 0.63 0.86 0.51 0.96 0.58 0.38 0.76 0.46 0.31 0.571 15 0.09 0.12 0.09 0.44 0.37 0.35 0.42 0.71 0.85 0.56 0.39 0.43 0.76 0.38 0.08 0.34 0.36 0.455 16 0.35 0.40 0.62 0.46 0.49 0.47 0.45 0.64 0.61 0.27 0.44 0.97 0.16 0.90 0.35 0.46 0.41 0.620 17 0.73 0.83 0.20 0.69 0.73 0.71 0.68 0.45 0.79 0.77 0.68 0.52 0.66 0.38 0.58 0.65 0.93 0.725 18 0.59 0.99 0.04 0.66 0.85 0.82 0.62 0.38 0.71 0.84 0.77 0.30 0.77 0.18 0.80 0.81 0.84 0.651 19 0.83 0.20 0.68 0.35 0.21 0.21 0.82 0.79 0.54 0.39 0.20 0.36 0.45 0.72 0.83 0.39 0.17 0.589 20 0.79 0.70 0.33 0.55 0.71 0.70 0.52 0.44 0.77 0.36 0.70 0.83 0.42 0.38 0.92 0.59 0.75 0.713Table 9
Europe model error corresponding to the number of neurons in different hidden layers.
Country Neurons 5 6 7 8 9 10 11 1 1.44% 4.22% 4.31% 3.58% 6.85% 2.67% 4.94% 2 4.73% 4.14% 3.00% 8.54% 4.49% 14.19% 8.70% 3 6.48% 2.29% 3.78% 7.36% 1.99% 10.95% 10.09% 4 7.05% 4.08% 6.23% 1.94% 6.62% 3.82% 4.45% 5 2.18% 2.94% 2.40% 8.07% 4.55% 5.03% 1.36% 6 2.68% 3.73% 5.04% 4.71% 5.29% 16.39% 9.16% 7 7.91% 4.77% 8.36% 0.22% 4.77% 5.95% 9.87% 8 4.08% 4.11% 2.31% 5.98% 3.27% 7.28% 2.45% 9 1.80% 3.56% 0.55% 6.61% 1.88% 14.33% 2.11% 10 1.74% 0.12% 4.44% 3.07% 8.49% 5.57% 5.64% 11 3.56% 4.15% 4.57% 2.27% 8.56% 4.15% 10.01% 12 4.57% 4.46% 1.52% 7.78% 5.83% 3.82% 5.41% 13 2.22% 4.36% 1.78% 5.51% 7.02% 6.27% 0.27% 14 2.67% 3.92% 2.72% 10.75% 7.89% 0.13% 0.69% 15 3.99% 4.56% 8.37% 6.01% 6.85% 7.86% 15.18%Table 10
BP neural network results of training on railway construction risks in 15 European countries.
NO 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Expert mark 0.525 0.563 0.532 0.623 0.543 0.811 0.802 0.621 0.767 0.621 0.602 0.654 0.625 0.571 0.455 Training results 0.547 0.586 0.544 0.648 0.559 0.781 0.764 0.595 0.794 0.620 0.577 0.625 0.652 0.549 0.476 Error (%) 4.22 4.14 2.29 4.08 2.94 3.73 4.77 4.11 3.56 0.12 4.15 4.46 4.36 3.92 4.56It can be seen from Table10 that the average relative error of the 15 training data in Europe is 3.69%, and the maximum error in the sample set is 4.77% which meets the accuracy requirement of 5%; that is to say, the model training learning result is better. Then the verification sample is replaced by the remaining 5 countries to verify whether the model is valid or not; lastly compare the results with the expert score results. The results are shown in Table 11.Table 11
Validation results of BP neural network on construction risk of railways in 5 European countries.
NO. 16 17 18 19 20 Expert mark 0.620 0.725 0.651 0.589 0.713 Training results 0.590 0.761 0.682 0.569 0.686 Error (%) 4.91 4.97 4.76 3.44 3.76It can be seen from Table11 that the average relative error of the verification data set is 4.37% and the maximum relative error of the prediction set is 4.97%, indicating that the neural network model has been able to achieve the accuracy required by the project and can be used for railway outbuilding projects in European national risk evaluation forecast.


## 3.5. Model Robustness Test

It can be seen from the above training and testing that the accuracy of the model is good, and for machine learning, robustness is also an important feature, and the artificial neural network itself is robust [27–29]. The following is a robust test using the European model as an example: it is assumed that some data in the first 10 countries are randomly interfered and the data is shown in Table 12. The interference data is substituted into the model for simulation calculation, and the error between the verification result and the score given by the expert is shown in Table 13. The error between the verification result and the model score is shown in Table 14.Table 12
Interfered data in the top 10 countries in Europe.
NO 1 2 3 4 5 6 7 8 9 10 R1 0.35 0.51 0.46 0.53 0.19 0.88 0.85 0.16 0.84 0.42 R2 0.27 0.79 0.48 0.56 0.40 0.72 0.73 0.49 0.86 0.68 R3 0.35 0.23 0.79 0.24 0.76 0.46 0.86 0.78 0.42 0.73 R4 0.66 0.52 0.36 0.26 0.63 0.62 0.39 0.72 0.63 0.72 R5 0.32 0.96 0.25 0.75 0.34 0.79 0.42 0.56 0.94 0.62 R6 0.40 0.98 0.36 0.72 0.33 0.80 0.27 0.54 0.93 0.64 R7 0.36 0.56 0.63 0.62 0.36 0.76 0.82 0.42 0.75 0.62 R8 0.68 0.43 0.78 0.32 0.74 0.48 0.76 0.56 0.29 0.50 R9 0.64 0.24 0.33 0.44 0.67 0.87 0.19 0.46 0.93 0.52 R10 0.47 0.43 0.61 0.25 0.59 0.61 0.82 0.58 0.75 0.34 R11 0.34 0.89 0.43 0.97 0.31 0.73 0.26 0.53 0.85 0.58 R12 0.50 0.66 0.33 0.81 0.79 0.47 0.42 0.90 0.62 0.73 R13 0.91 0.87 0.63 0.32 0.37 0.23 0.13 0.45 0.49 0.70 R14 0.38 0.18 0.90 0.58 0.28 0.85 0.90 0.27 0.68 0.43 R15 0.58 0.45 0.85 0.28 0.57 0.52 0.15 0.40 0.38 0.59 R16 0.41 0.85 0.55 0.64 0.42 0.72 0.38 0.55 0.69 0.62 R17 0.47 0.71 0.44 0.54 0.25 0.88 0.33 0.60 0.93 0.69Table 13
Error test of interference data score and expert score.
NO 1 2 3 4 5 6 7 8 9 10 Expert score 0.525 0.563 0.532 0.623 0.543 0.811 0.802 0.621 0.767 0.621 Interference data score 0.541 0.589 0.549 0.609 0.545 0.773 0.782 0.593 0.762 0.652 Error (%) 3.05 4.64 3.15 2.32 0.43 4.68 2.55 4.46 0.66 4.96Table 14
Error test of interference data score and model score.
NO 1 2 3 4 5 6 7 8 9 10 Model score 0.547 0.586 0.544 0.648 0.559 0.781 0.764 0.595 0.794 0.620 Interference data score 0.541 0.589 0.549 0.609 0.545 0.773 0.782 0.593 0.762 0.652 Error (%) 1.14 0.46 0.88 6.47 2.57 1.01 2.33 0.42 4.24 4.87It can be seen from the data in the table that even if the input sample data is partially interfered with the data, the model can guarantee the result that the accuracy requirement (error < 5%) is met after the network is running; that means the robustness test result is good.


## 4. Conclusion

According to different situations in Asia and Europe, BP neural network model is established by using different functions for risk evaluation. Through the created neural network model, only experts can give the scores of the various risks in the macrorisk evaluation of the target country, and the overall construction risk score of the target country can be obtained without cumbersome manual scoring.Due to the complex relationship between the various influencing factors in this project, it is not intuitive to use a linear expression to carry out risk prediction. BP neural network is selected to nonlinearly process the data to obtain the quantitative value of risk assessment. BP neural network does not need corresponding function equations for a set of nonlinear data; instead it iterates out the corresponding results and obtains an equation model that meets the requirements through its own training, which can meet the requirements of the project. It is more effective and convenient than traditional methods; neural networks have broad application prospects in such nonlinear fields.This model is mainly for the risk evaluation of railway macroconstruction. For specific railway project risks such as construction risks and environmental risks, it is necessary to consider the actual target needs and actual risk indicators.



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*Source: 2946158-2019-06-02.xml*