Abstract

In this paper, the least square support vector machine (LSSVM) is used to study the safety of a high-speed railway. According to the principle of LSSVM regression prediction, the parameters of the LSSVM are optimized to model the natural disaster early warning of safe operation of a high-speed railway, and the management measures and methods of high-speed railway safety operation under natural disasters are given. The relevant statistical data of China's high-speed railway are used for training and verification. The experimental results show that the LSSVM can well reflect the nonlinear relationship between the accident rate and the influencing factors, with high simulation accuracy and strong generalization ability, and can effectively predict the natural disasters in the safe operation of a high-speed railway. Moreover, the early warning system can improve the ability of safety operation evaluation and early warning of high-speed railway under natural disasters, realize the development goals of high-speed railway (safety, speed, economic, low-carbon and environmental protection) and provide a theoretical basis and technical support for improving the safety of a high-speed railway.

1. Introduction

As a safe, reliable, fast, comfortable, large carrying capacity, low-carbon and environmentally friendly transportation mode, high-speed railway (HSR) has become the main mode of transportation for the development of the world's transportation industry, leading humankind to a new era [1–3]. In the safe operation of HSR, natural disasters, such as gales, rainstorms, heavy snow, earthquake, geology disaster, thunder and lightning, have low probability but cause great harm [4–6]. It is of great social and economic significance to study the early warning system of natural disasters of HSR to ensure the safe operation [7]. Therefore, there have been a lot of studies on the safe operation of HSR under natural disasters, and a real-time quality control method for rainfall monitoring data of HSR has been proposed. Liu et al. [8] studied the railway disaster monitoring and warning system based on assessment of landslide stability. Li et al. [9] researched the equipment reliability of a monitoring unit for HSR natural disasters, and summarized the earthquake monitoring and early warning system for HSR (Shinkansen) in Japan. Hu et al. [10] studied a data-perception model for the safe operation of HSP in rainstorms. However, the above researches on the natural environment impact analysis of HSR mainly focuses on theoretical analyses.

Disaster prevention and safety monitoring of HSR is an issue that many countries in the world attach great importance to. Some developed countries have carried out research in the field of railway disaster prevention and safety monitoring for many years, and have achieved good results, among which Japan and France are the most prominent. Japan has installed monitoring equipment in the location where foreign matter and natural disasters are prone to occur along the Shinkansen line. The foreign matter is sent back to the control centre through the monitoring system at the first time, so the system has very high security. Shibayama [11] gave an overview of Japan's national-level transport planning schemes, and discussed interplays between them and recoveries from natural disasterd. Because France is located at the juncture of the continental plate, where earthquakes and other natural disasters often occur, French technical staff have installed protective nets at all HSR tunnel entrances and the locations where foreign bodies often invade the limit. The protective nets use double cable sensors to receive signals, which can monitor the safety of railway traffic. Once the train is in danger, it can also stop by switch to ensure the safety of personnel. Even though research on the natural environment's impact on HSR began earlier in foreign countries, China's early warning system for natural disasters on HSR is also under continuous research and development, providing a safety guarantee for HSR train's operation. For example, the Beijing-Tianjin Intercity Transportation has established the corresponding disaster monitoring system, set up the corresponding monitoring subsystem for wind, rain, snow and other disaster monitoring, and reserved other relevant interfaces to facilitate the subsequent earthquake and foreign body intrusion monitoring. Wuhan-Guangzhou HSR is equipped with a disaster prevention and safety monitoring system, which is composed of monitoring equipment and corresponding monitoring units. Monitoring equipment, such as wind, rain and foreign matter intrusion are set along the railway. However, the relevant researches show that most of China's HSR detection systems lack the early warning function for earthquakes and typhoons. Because the rainfall alarm is sensitive to the vibration caused by the train, in some lines with large vibration amplitude, even if filtering measures are taken, the vibration cannot be eliminated, and the phenomenon of rainfall value alarm will appear even if there is no rainfall. Therefore, this paper will study the earthquake warning system of HSR safe operation.

The support vector machine (SVM) is a new general machine learning method proposed by Cortes, C. et al. [12] on the basis of statistical theory and structural risk minimization principles [13, 14]. On this basis, the least square support vector machine (LSSVM) uses quadratic loss function to replace the insensitive loss function in traditional SVM [15]. Thus, the quadratic programming problem in the traditional vector machine is transformed into the problem of solving linear equations, which can improve the accuracy of the model [16]. Therefore, this paper uses SVM based on two multiplications to study the early warning of natural disasters in the safe operation of HSR, mainly carrying out real-time monitoring of natural disasters and emergencies endangering the safety of train operation. The paper also summarizes the monitoring information of various monitoring equipment, so as to realize the distributed acquisition, centralized management and comprehensive application of HSR monitoring information, and comprehensively grasp the natural disasters dynamic, provide timely and accurate disaster alarm and early warning function. According to the severity of the disaster, the research results take corresponding emergency measures immediately to prevent or reduce the loss caused by natural disasters, avoid secondary disasters and provide certain theoretical support for the safe operation and protection of the HSR. It also provides a database for adjusting the operation plan of HSR, issuing traffic control, emergency rescue, maintenance and other work, which is an indispensable technology in the HSR transportation system.

The remainder of this paper is organized as follows. In Section 2, the comprehensive natural disaster monitoring system is introduced. Section 3 gives the natural disaster rapid warning system for safe operation of a HSR. The natural disaster early warning system for the safe operation of HSR is in Section 4. In Section 5, the accuracy of the proposed model is verified by a case study. Conclusions are given in Section 6.

2. Comprehensive natural disaster monitoring system for safe operation of HSR

In order to prevent possible natural disasters (such as wind, rain, lightning, temperature, debris flow, earthquake and others) from affecting the normal operation of the HSR, the comprehensive natural disaster monitoring system for safe operation of a HSR should be constructed. This includes early warning systems for wind, rain, lightning, temperature, geology disaster, earthquake and other natural disasters (Fig. 1). The natural disaster early warning system for HSR consists of four parts on-site monitoring points along the line (wind, rain, snow, earthquake, geology disaster and lightning disaster monitoring equipment), an early warning unit, an early warning centre and the relevant system interface. It provides real-time monitoring, alarm and early warning functions for natural disasters and emergencies on the HSR, so as to realize the emergency disposal of natural disasters, and minimize disasters to prevent the occurrence of secondary disasters. The main functions of the early warning system include a real-time monitoring function, an alarm speed limit prompt function, an emergency disposal function and a query and statistics function, etc. This realizes the data exchange and interconnection of each disaster monitoring system, and realizes the data-sharing function with the disaster monitoring and alarm information of adjacent departments and the related systems inside and outside the HSR.

Comprehensive natural disaster early warning monitoring system
Fig. 1.

Comprehensive natural disaster early warning monitoring system

As shown in Fig. 1, the comprehensive monitoring system includes the HSR network layout, emergency response equipment selection, HSR emergency monitoring system configuration, emergency response equipment selection and an emergency response monitoring system. The system can provide the sharing and exchange of relevant basic data and monitoring data. Relevant personnel can master the natural disaster monitoring and alarm, and equipment application status, and supervise and guide the operation of disaster prevention and safety early warning system for HSR lines. Through the analysis of HSR disaster monitoring data, it can provide decision support services for the construction of an early warning system for HSR disaster prevention.

3. Natural disaster rapid warning system for safe operation of HSR

The impact of natural disasters on the safe operation of HSR is an emergency. Therefore, in the early stage of a natural disaster emergency, rapid comprehensive assessment of the emergency is conducive to timely and accurate understanding of the situation, can meet the timeliness requirements of emergency decision-making and ensure the safe operation of the HSR. Under natural disasters, when the amount of emergency data of HSR is large and the data update is fast, it is too complex to meet the timeliness requirements of emergency decision-making. Therefore, this paper constructs a rapid warning system and evaluation index system (See Fig. 2) of natural disasters for safe operation of HSR.

Evaluation index system of natural disaster rapid warning system for safe operation of HSR
Fig. 2.

Evaluation index system of natural disaster rapid warning system for safe operation of HSR

In the early stage of HSR natural disaster events, monitoring personnel have to face the uncertainty of natural disaster information, variability of data, shortage of resources, and the huge risk of secondary and derivative events. Therefore, it is an important means for successful emergency response to grasp the operation situation of HSR accurately through a real-time comprehensive evaluation model of HSR natural disaster early warning. In this paper, the least square support vector machine (LSSVM) is used to establish a fast evaluation model of HSR safety operation under natural disasters. It can solve the problems of data classification, regression processing and pattern recognition.

The natural disaster early warning system of HSR is a nonlinear system. Let |$\{ { {( {{x_i},{y_i}} ),i = 1,2, \cdots ,n} \}} $| be the training sample set of the HSR natural disaster early warning system, where |${x_i}$| is the input set of the sample, |${y_i}$| is the target set of the HSR natural disaster early warning system, n is the sample number of the HSR natural disaster early warning system, then the optimal decision-making function of the natural disaster early warning of safe operation of HSR can be obtained
(1)

where |$y( x )$| is the target set of the HSR natural disaster early warning system, which is determined by the deviation of natural disaster early warning system b, the regression coefficient of natural disaster early warning system |$\omega $| and the mapping function of natural disaster early warning system |$\varphi ( x )$|⁠.

  • Step 1. The original data were normalized. Because the type, dimension and size of the data in the input vector set of the model are very different, if the original data are used directly, the accuracy of the prediction results will be greatly reduced. Normalization helps to improve the convergence speed and shorten the training time. Each sample datum is linearly transformed to the range of |$[0,1]$|⁠. The method of normalization is as follows
    (2)

    where |${A_i}$| is the quantity of data in the sample, |$i = 1,2, \cdots ,n$|⁠, |${\| \cdot \|_2}$| is the 2-norm of the vector.

  • Step 2. Define the optimization function. Based on the principle of structural risk minimization, the minimum formula |$\omega $|⁠, b of the HSR natural disaster early warning system is obtained. Then the optimization function of the HSR natural disaster early warning system is
    (3)
     where |$F( {\omega ,e} )$| is the objective function of the natural disaster, |${e_i} \in R$| is the error variable of the HSR natural disaster early warning system, μ and c are the regularized parameters of the natural disaster early warning for safe operation of the HSR, respectively.
  • Step 3. Construct linear equations. The Lagrange function of natural disaster early warning of safe operation of HSR is as follows
    (4)
  • where |${a_i}$||$(i = 1,2, \cdots ,n)$| is the Lagrange multiplier. Eq. (4) is optimized to obtain the linear equations of natural disaster early warning of safe operation of HSR
    (5)
  • Step 4. Construct LSSVM regression model. The radial basis function of natural disaster early warning of safe operation of HSR is selected in Eq. (5).
    (6)

    The LSSVM regression model of natural disaster early warning of safe operation of HSR is obtained by using the least square method to calculate |$a,b$|⁠.

(7)
  • Step 5. Calculate the relative mean square error. According to the basic principle of LSSVM and experimental experience, the parameter values are selected in the maximum value range, and the |${( {Y,\sigma } )^{ - 2d}}$| grid plane of parameters of HSR natural disaster early warning system is constructed. Input the parameters |$( {Y,\sigma } )$| of each node into LSSVM, and use the validation data to evaluate the performance and output the learning error. The calculation formula of the relative mean square error of the natural disaster early warning of safe operation of HSR is as follows
    (8)

    where |${l_i}$| and |${l_i}^\prime$| are actual and predicted values, respectively, and the node value |${( {Y,\sigma } )_{\min }}$|⁠, corresponding to the minimum error, is the optimal parameter pair.

The rapid natural disaster early warning model of HSR can quickly identify and deeply analyse the relevant information of HSR emergencies in the early stage of natural disasters, in particular, HSR emergency information acquisition and analysis under natural disasters, multifactor risk assessment and emergency decision-making under complex conditions. The comprehensive rapid evaluation model should not be limited by the size of data, but should be simple and easy to operate, so as to meet the requirements of emergency decision-making on the evaluation speed under the situation of dynamic data updating and increasing data scale at the initial stage of natural disasters.

4. Natural disaster early warning system for safe operation of HSR

The natural disaster early warning of safe operation of HSR is one of the important basic tools to ensure the safety and high-speed operation of high-speed trains. The system is based on the communication transmission system and analyses the data that endanger railway transportation safety collected by field monitoring equipment, e.g. wind, rain, lightning, temperature, geology disaster, earthquake and so on. The system can provide disaster warning information, speed limit information or outage information after processing, which can provide basis for decision-making by the dispatching centre and ensure safe, punctual and efficient operation of trains. The natural disaster early warning of safe operation of HSR is mainly composed of on-site monitoring equipment, an early warning unit, early warning data processing equipment, dispatching station equipment and other equipment.

4.1 System architecture of natural disaster early warning of safe operation of HSR

The natural disaster early warning process of HSR is that the alarm data and monitoring data of the integrated system and the off-system flow into the data processing centre. After analysis by the front-end computer, the monitoring data and alarm data flow to the database server, and the alarm data flow into the application server for alarm processing. The alarm data and the monitoring data in the database finally flow into each user terminal, and the alarm information after alarm disposal is encapsulated, and then flows into the relevant systems in each channel. In the safe operation of HSR, the early warning system of natural disasters can be divided into four levels, as shown in Fig. 3.

  • First level: the field information collection layer of HSR comprehensive early warning system. The field information collection layer of high-speed railway directly faces the trackside facilities. The trackside facilities of HSR are not only scattered, but also diversified, so as to ensure the safe operation of HSR under natural disasters.

  • Second level: monitoring and processing layer of comprehensive early warning system for HSR. The monitoring and processing layer of HSR collects the real-time data of field monitoring equipment, processes and stores the data for a short time, and then uploads the data to the regional processing layer of the HSR through the network, and monitors and manages the status information of the field monitoring equipment to realize fault alarm and fault diagnosis.

  • Thirdlevel: regional processing layer of comprehensive early warning system for HSR. The regional processing layer of HSR is mainly responsible for receiving all kinds of information transmitted from each monitoring and processing layer within the jurisdiction of the HSR in real-time, storing, analysing, displaying and printing the data in real-time, and providing a corresponding level of monitoring alarm and early warning according to the information content. According to the operation control rules of high-speed trains, the information of speed limit and shutdown plan is provided, and the alarm information is uploaded to the user layer of HSR.

  • Fourthlevel: user layer of comprehensive early warning system for HSR. This layer is used by dispatchers, and the equipment of this layer is set in the HSR monitoring centre. In this way, the monitoring centre can not only serve the high-speed lines within the jurisdiction of the whole monitoring centre, but also provide alarm information.

Integrated monitoring system of natural disaster early warning
Fig. 3.

Integrated monitoring system of natural disaster early warning

4.2 Subsystem of natural disaster early warning

The natural disaster early warning system of HSR on-site monitoring equipment is mainly used to collect wind speed and direction, rainfall, temperature, geology disaster, lightning, earthquake and other data. Therefore, the corresponding systems are wind early warning system, rainfall early warning system, temperature early warning system, earthquake warning system, geological disaster early warning system and lightning warning system.

(1) Wind monitoring system for HSR natural disaster early warning. The main component of the wind monitoring system is an ultrasonic anemometer, which is used to collect wind speed and direction data. The equipment is installed on the windward side of the line. It is installed on the overhead contact line pole 4±0.1 m away from the rail surface. It has strong anti-electromagnetic interference ability, waterproof and dust-proof functions, and can be applied to complex and harsh environments. For HSR, the wind speed and direction indicator should be set in the area where the maximum instantaneous wind speed on the line is not less than 15 m/s, as shown in Table 1.

Table 1.

Wind speed definition criteria in early warning system

LevelWind speed (m/s)Speed limit (km/h)
Wind speed rangeWind speed warning thresholdOperating speed rangeSpeed warning threshold
First levelWind speed<15300<speed<350350
Second level15<Wind speed<2015250<speed<300300
Third level20<Wind speed<2320200<speed<250250
Fourth level23<Wind speed<2623150<speed<200200
Fifth level26<Wind speed<2726100<speed<150150
Sixth level27<Wind speed<302750<speed<100100
Seventh level30<Wind speed30Stop50
LevelWind speed (m/s)Speed limit (km/h)
Wind speed rangeWind speed warning thresholdOperating speed rangeSpeed warning threshold
First levelWind speed<15300<speed<350350
Second level15<Wind speed<2015250<speed<300300
Third level20<Wind speed<2320200<speed<250250
Fourth level23<Wind speed<2623150<speed<200200
Fifth level26<Wind speed<2726100<speed<150150
Sixth level27<Wind speed<302750<speed<100100
Seventh level30<Wind speed30Stop50
Table 1.

Wind speed definition criteria in early warning system

LevelWind speed (m/s)Speed limit (km/h)
Wind speed rangeWind speed warning thresholdOperating speed rangeSpeed warning threshold
First levelWind speed<15300<speed<350350
Second level15<Wind speed<2015250<speed<300300
Third level20<Wind speed<2320200<speed<250250
Fourth level23<Wind speed<2623150<speed<200200
Fifth level26<Wind speed<2726100<speed<150150
Sixth level27<Wind speed<302750<speed<100100
Seventh level30<Wind speed30Stop50
LevelWind speed (m/s)Speed limit (km/h)
Wind speed rangeWind speed warning thresholdOperating speed rangeSpeed warning threshold
First levelWind speed<15300<speed<350350
Second level15<Wind speed<2015250<speed<300300
Third level20<Wind speed<2320200<speed<250250
Fourth level23<Wind speed<2623150<speed<200200
Fifth level26<Wind speed<2726100<speed<150150
Sixth level27<Wind speed<302750<speed<100100
Seventh level30<Wind speed30Stop50

Due to the impact of strong wind on high-speed trains, manual measures should be taken to control the operation of trains. Therefore, the wind monitoring system is required to have prediction capability, as shown in Fig. 4. When the high-speed train is running on the high-speed line, especially under the action of side winds, the dynamic parameters of the high-speed train, including derailment coefficient, load shedding rate, overturning coefficient and wheel rail lateral force, increase significantly, which leads to the decrease of the safety and reliability of the high-speed train.

HSR gale warning system
Fig. 4.

HSR gale warning system

(2) Rainfall monitoring system for natural disaster early warning of HSR. The main rainfall monitoring system tool is a rain gauge, which is used to collect local rainfall data. See Table 2.

Table 2.

Rainfall definition criteria in early warning system

LevelEarly warning threshold of rainfall (mm)Speed limit (km/h)
NameEarly warning threshold of rainfallSpeed rangeWarning threshold
First levelHourly rainfall25(300, 350)350
Daily rainfall90
Continuous rainfall110
Second levelHourly rainfall30(250, 300)300
Daily rainfall100
Continuous rainfall120
Third levelHourly rainfall35(200, 250)250
Daily rainfall110
Continuous rainfall130
Fourth levelHourly rainfall40(150, 200)200
Daily rainfall120
Continuous rainfall140
Fifth levelHourly rainfall45(100, 150)160
Daily rainfall135
Continuous rainfall160
Sixth levelHourly rainfall55(50, 100)100
Daily rainfall182
Continuous rainfall180
Seventh levelHourly rainfall60Stop50
Daily rainfall200
Continuous rainfall200
LevelEarly warning threshold of rainfall (mm)Speed limit (km/h)
NameEarly warning threshold of rainfallSpeed rangeWarning threshold
First levelHourly rainfall25(300, 350)350
Daily rainfall90
Continuous rainfall110
Second levelHourly rainfall30(250, 300)300
Daily rainfall100
Continuous rainfall120
Third levelHourly rainfall35(200, 250)250
Daily rainfall110
Continuous rainfall130
Fourth levelHourly rainfall40(150, 200)200
Daily rainfall120
Continuous rainfall140
Fifth levelHourly rainfall45(100, 150)160
Daily rainfall135
Continuous rainfall160
Sixth levelHourly rainfall55(50, 100)100
Daily rainfall182
Continuous rainfall180
Seventh levelHourly rainfall60Stop50
Daily rainfall200
Continuous rainfall200
Table 2.

Rainfall definition criteria in early warning system

LevelEarly warning threshold of rainfall (mm)Speed limit (km/h)
NameEarly warning threshold of rainfallSpeed rangeWarning threshold
First levelHourly rainfall25(300, 350)350
Daily rainfall90
Continuous rainfall110
Second levelHourly rainfall30(250, 300)300
Daily rainfall100
Continuous rainfall120
Third levelHourly rainfall35(200, 250)250
Daily rainfall110
Continuous rainfall130
Fourth levelHourly rainfall40(150, 200)200
Daily rainfall120
Continuous rainfall140
Fifth levelHourly rainfall45(100, 150)160
Daily rainfall135
Continuous rainfall160
Sixth levelHourly rainfall55(50, 100)100
Daily rainfall182
Continuous rainfall180
Seventh levelHourly rainfall60Stop50
Daily rainfall200
Continuous rainfall200
LevelEarly warning threshold of rainfall (mm)Speed limit (km/h)
NameEarly warning threshold of rainfallSpeed rangeWarning threshold
First levelHourly rainfall25(300, 350)350
Daily rainfall90
Continuous rainfall110
Second levelHourly rainfall30(250, 300)300
Daily rainfall100
Continuous rainfall120
Third levelHourly rainfall35(200, 250)250
Daily rainfall110
Continuous rainfall130
Fourth levelHourly rainfall40(150, 200)200
Daily rainfall120
Continuous rainfall140
Fifth levelHourly rainfall45(100, 150)160
Daily rainfall135
Continuous rainfall160
Sixth levelHourly rainfall55(50, 100)100
Daily rainfall182
Continuous rainfall180
Seventh levelHourly rainfall60Stop50
Daily rainfall200
Continuous rainfall200

In the safe operation of the HSR, continuous heavy rain or rainstorms may cause HSR subgrade collapse or debris flow hazards. For ballastless track and HSR with a high proportion of bridges and tunnels, it is generally unnecessary to consider passive monitoring and alarm, and construct the HSR rainfall warning system. The HSR rainfall warning system is similar to Fig. 4.

(3) HSR earthquake natural disaster early warning system. The main tool of the earthquake early warning system is a strong seismograph. The equipment can warn of the seismic wave in a timely and accurately manner. When the line encounters an earthquake with intensity greater than 6 degrees (ground motion acceleration > 0.04g, equivalent to magnitude 5 earthquake), the earthquake warning system can automatically send out alarm information, and slow down or stop the high-speed train in the earthquake area through the high-speed train control system.

In the safe operation of the HSR, earthquakes may damage the structure of high-speed lines, bridges and tunnels, and cause serious accidents to high-speed trains. Once the early warning system detects that the earthquake intensity has reached the earthquake alarm threshold, it will send an alarm message to the HSR dispatching centre, and immediately trip the main circuit breaker of the substation, stopping the power supply of the catenary, and forcing the train to stop. At the same time, the earthquake monitoring system continues to monitor the subsequent ground motion acceleration, so as to provide the dispatching centre with the basis of train operation control after stopping. The earthquake warning system is similar to Fig. 3.

(4) HSR temperature natural disaster early warning system. The temperature early warning system of HSR natural disasters mainly includes a high-temperature early warning system and a low-temperature early warning system. The high-temperature early warning system is mainly used in high-temperature areas (e.g. deserts in Xinjiang, China, where the temperature reaches 60°C in summer) and low-temperature areas (e.g. in Northeast China, winter is below −50°C) to ensure the safe operation of the HSR.

High temperatures will cause rail expansion and low temperatures will lead to shrinkage. The track temperature monitoring system should be set up in the section where the curve radius of ballasted track is less than 6 000 m and the continuous bridge end with large temperature span or more bridges. Snow disaster has a great impact on the operation of high-speed trains in particularly cold areas. Continuous snowfall and severe cold weather may cause excessive load to catenary and power supply lines, and switch cannot be switched. Therefore, effective monitoring must be carried out to build a snow disaster early warning system for HSR.

(5) Lightning warning system for natural disaster early warning of HSR. The lightning warning system uses the observation data of lightning location, radar, satellite, ground electric field and radiosonde to identify, track, forecast and provide early warning to areas that may see lightning by means of a multidata fusion application, statistical analysis, proximity extrapolation and numerical prediction. The lightning warning system is composed of a central station and several online time difference detection stations distributed in different places. When the lightning cloud discharges to the ground in the monitored area, the lightning monitoring centre station of the HSR can calculate and determine the location of the lightning point through a special program according to the time difference of lightning discharge electromagnetic signal obtained by each time difference detection station. After a period of accumulation, the number and density of ground lightning in the monitored HSR area can be obtained, as well as the occurrence time, location, amplitude and polarity of each lightning stroke.

(6) HSR geological disaster early warning system for natural disaster early warning. The geological disaster early warning system's role is to record the change process of various precursor phenomena before and after the occurrence of geological disasters by direct observation and instrument measurement.

5. Early warning model of natural disasters based on SVM

There are three main problems to be solved in the early warning of natural disasters of HSR using the SVM model: the selection of input and output variables, and the selection of kernel function. Therefore, the Gaussian function of radial basis function (RBF) is selected as the kernel function in the HSR natural disaster early warning model. The values of the three parameters are determined by numerical experiments with different combinations of parameters. This paper mainly normalizes the natural disaster frequency data of Beijing-Shanghai HSR line (see Fig. 5) from 2015 to 2019, and then divides the normalized data into a training set and a test set. According to the training set data, the SVM prediction model is established and the parameters of the SVM model are determined; finally, the test set data are putted into the natural disaster number prediction model, the predicted value is output, and the prediction value is compared with the actual data to verify the fitting and prediction performance of the model.

Beijing-Shanghai HSR line.
Fig. 5.

Beijing-Shanghai HSR line.

Step 1. Original data normalized. The number of natural disasters of Beijing-Shanghai HSR line from 2015 to 2018 is shown in Table 3. Training samples are generated from the population data of 2015-2018 in Table 3. The data of the adjacent four years are normalized as the input of training samples, and the data of the fifth year after normalization are used as the output of training samples, forming six groups of training sample data. In the same way, the number of natural disasters in 2019 is normalized to form a group of test samples to test the correctness of the SVM model. The training sample set, test sample set and evaluation object data are standardized according to the standardized formula (2).

Table 3.

Frequency of natural disasters on Beijing-Shanghai HSR

DataYearI1I2I3I4I5I6Total
Training data2015231215132830121
2016211317102734122
2017191221173029128
2018251529183337157
2019231426183233146
Test data2019221527173135147
DataYearI1I2I3I4I5I6Total
Training data2015231215132830121
2016211317102734122
2017191221173029128
2018251529183337157
2019231426183233146
Test data2019221527173135147
Table 3.

Frequency of natural disasters on Beijing-Shanghai HSR

DataYearI1I2I3I4I5I6Total
Training data2015231215132830121
2016211317102734122
2017191221173029128
2018251529183337157
2019231426183233146
Test data2019221527173135147
DataYearI1I2I3I4I5I6Total
Training data2015231215132830121
2016211317102734122
2017191221173029128
2018251529183337157
2019231426183233146
Test data2019221527173135147

Step 2. Parameter selection of SVM autoregressive prediction model. Based on MATLAB 7.0 software and SVM toolbox, the RBF kernel function is selected. The initial value of the penalty factors are C = 1, |${\sigma ^2}$|= 0.2. The 30 valid samples in step 1 are used to train the support vector. Six groups of test samples are substituted into the SVM model. If the corresponding output categories do not conform to the actual situation, the optimization parameters are verified according to formula (3) until the output and test sample categories are consistent. Six groups of evaluation objects, after the index data standardization, are input into the SVM model, and the category is calculated.

Step 3. SVM regression model prediction results. In this paper, the results of traditional polynomial regression prediction method and SVM model are compared and analysed. Fig. 6 shows the fitting results of the two methods to the sample data, which shows that the fitting curve of SVM is closer to the actual data curve, and the fitting error is smaller.

Comparing polynomial results with SVM fitting results
Fig. 6.

Comparing polynomial results with SVM fitting results

Table 4 uses two methods (polynomial regression prediction and SVM model) to predict the number of natural disasters on the Beijing-Shanghai HSR from 2015 to 2018. The results show that the SVM model is more accurate and stable than polynomial prediction.

Table 4.

Comparison of results

NameActual valuePolynomial prediction valueRelative error %SVM prediction valueRelative error %
I123258.695224.348
I2141614.286157.143
I3263015.384273.846
I4182116.667175.556
I532346.250313.125
I6333815.152356.061
Total14616412.3291476.849
NameActual valuePolynomial prediction valueRelative error %SVM prediction valueRelative error %
I123258.695224.348
I2141614.286157.143
I3263015.384273.846
I4182116.667175.556
I532346.250313.125
I6333815.152356.061
Total14616412.3291476.849
Table 4.

Comparison of results

NameActual valuePolynomial prediction valueRelative error %SVM prediction valueRelative error %
I123258.695224.348
I2141614.286157.143
I3263015.384273.846
I4182116.667175.556
I532346.250313.125
I6333815.152356.061
Total14616412.3291476.849
NameActual valuePolynomial prediction valueRelative error %SVM prediction valueRelative error %
I123258.695224.348
I2141614.286157.143
I3263015.384273.846
I4182116.667175.556
I532346.250313.125
I6333815.152356.061
Total14616412.3291476.849

It can be seen from the prediction results that the prediction accuracy of SVM model is controlled within 8%, while the relative error of polynomial prediction is 2 to 3 times of that of the SVM model. Therefore, the establishment of the prediction model of natural disaster frequency based on SVM can greatly improve prediction accuracy. Fig. 6 shows the comparison between the predicted value and the monitoring value of the LSSVM. The prediction accuracy is high, and the maximum relative error is only 7.143%. The model is used to predict the data of the test set, and the model test curve is shown in Fig. 7.

Error rate of polynomial regression prediction and SVM model prediction
Fig. 7.

Error rate of polynomial regression prediction and SVM model prediction

It can be seen from Fig. 6 that the test output of the model is in good agreement with the actual value. The predicted relative error is shown in Table 4, and the average relative error of the test is 0.0501

Step 4. Result analysis. The results of numerical experiments show that the prediction accuracy of the HSR natural disaster early warning model based on SVM is high, and it has certain practical value for traffic management department.

  1. The LSSVM prediction model constructs the nonlinear related sample data in the HSR accident prediction into a linear function. By solving a set of linear equations, the complexity of the model is independent of the dimension of the sample, and the operation efficiency is very high. It can solve the nonlinear relationship problem in the HSR natural disaster early warning model. Therefore, combined with the historical statistical data, early warning of natural disasters of HSR can achieve satisfactory results.

  2. Considering that the HSR natural disaster early warning is such a complex nonlinear problem with small sample, poor information and multidimensional number, the LSSVM is suitable for prediction. The LSSVM can not only effectively weaken the randomness of the original data and enhance the regularity, but also make full use of the strong nonlinear mapping ability of SVM, and avoid the theoretical defects of other prediction methods and models. Its prediction accuracy is high, which provides a simple, practical and efficient new method for the study of HSR natural disaster early warning.

6. Conclusions

The natural disaster early warning system of HSR can realize data sharing, interconnection and other functions. This paper set up an early warning system for natural disasters on HSR to improve the safety of high-speed train operation. The reliability design of the HSR natural disaster early warning system is not only reflected in the redundant configuration of system hardware, but also strongly related to the setting of alarm thresholds. In this paper, the provided warning threshold value is the recommended value. In fact, the alarm threshold value of HSR needs to be adjusted dynamically according to the actual operating situation of the HSR, so as to achieve the purpose of system early warning.

In the safe operation of the HSR, various advanced technologies and effective methods are used to measure and monitor the geological disaster activities and the dynamic changes of various induced factors. This paper adopted the parameter optimization of the LSSVM to model the natural disaster early warning of safe operation of HSR, and gave the management measures and methods of HSR safety operation under natural disasters. The comprehensive and rapid evaluation model of HSR natural disaster early warning can solve the problem of HSR emergency decision-making.

The HSR natural disaster early warning system is of great significance for the development of China's railway. The design of the natural disaster system needs to consider the natural disaster and the geographical location of the railway. Some of the monitoring systems proposed in this paper do not consider the layout of the placement points and the maintenance of the later personnel. This will be further improved in follow-up research. At the same time, the authors think that the research on the early warning system of HSR under natural disasters, such as gales, heavy rain, thunder, earthquakes and so on, to eliminate the influence of these natural weather on equipment alarm errors, has high requirements for monitoring system materials, installation technology and power optimization.

ACKNOWLEDGEMENTS

The work described in this paper was supported by grants from the National Natural Science Foundation of China 51178157, High-level Project of the Top Six Talents in Jiangsu Province JXQC-021, the Key Science and Technology Program in Henan Province 182102310004 and the Postgraduate Research and Practice Innovation Program of Jiangsu Province KYCX20-0290.

Conflict of interest statement

None declared.

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