A method and related device for early warning of temperature gradient of ballastless track

Abstract

The application discloses a kind of temperature gradient early warning methods of ballastless track and related equipment, the method includes: obtaining ambient temperature, solar radiation, wind speed, humidity, rainfall and track structure internal temperature;Calculate the ballastless track temperature gradient threshold based on axial force and the ballastless track temperature gradient threshold based on displacement;The optimal ballastless track temperature gradient classification early warning model is obtained by joint construction and optimization of PSO algorithm and the SVM classification early warning model of optimal kernel function;According to the two ballastless track temperature gradient thresholds, ambient temperature, solar radiation, wind speed, humidity, rainfall and track structure internal temperature are input into the optimal ballastless track temperature gradient early warning model to output track structure temperature gradient classification early warning result.The application sets the vertical temperature gradient threshold of ballastless track based on axial force and displacement as classification standard, realizes the classification early warning of ballastless track temperature gradient, and improves the accuracy of ballastless track temperature gradient early warning.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of rail transit, in particular to a ballastless track temperature gradient early warning method, system, terminal and computer readable storage medium. BACKGROUND

[0002] CRTS II type slab ballastless track is an important ballastless track structure form of high-speed railway in China, and temperature load is one of important loads. The CRTS II type slab ballastless track structure is exposed to the atmospheric environment for a long time, and is directly affected by various meteorological factors such as environmental temperature, solar radiation, wind speed, humidity and rainfall. During the day, the solar radiation intensity is large, the environmental temperature is high, the structure surface is warmed up quickly, and a positive temperature gradient distribution of cold upper and hot lower is gradually formed. At night, the track structure temperature distribution is mainly affected by environmental temperature, wind speed and humidity, and a negative temperature gradient distribution of hot upper and cold lower is formed. The alternating action of the positive and negative temperature gradients easily causes the interface damage of the vertical multilayer structure of the track, thereby leading to the track slab upwarping and joint separation and other diseases, and seriously affecting the safety and smoothness of the line. Therefore, it is of important guiding significance to establish the correlation between the external environmental factors and the track structure temperature gradient, set a reasonable and effective early warning threshold for the track slab temperature gradient, and realize the temperature early warning of the track structure diseases, so as to guarantee the normal service performance of the CRTS II type slab ballastless track.

[0003] At present, the temperature gradient selected in the design of the ballastless track structure is mainly determined by referring to the positive temperature gradient empirical formula of the relevant railway track structure, highway asphalt pavement and box girder structure at home and abroad. The specification stipulates that the positive temperature gradient design value of the track slab is 90℃ / m, and the negative temperature gradient design value is-45℃ / m. However, the threshold value does not have scientific basis, and cannot truly reflect the actual distribution of the temperature gradient of the ballastless track slab, leading to the interlayer damage of the ballastless track slab under complex temperature.

[0004] For the massive monitoring data, the data-driven model based on machine learning and deep learning can more accurately predict the temperature, but the existing various data-driven models have certain limitations and application scope. The selection of the ballastless track temperature gradient threshold is relatively single, and most of them are classified and warned by taking the threshold value of the design specification as the standard, without fully considering the mechanical characteristics of the CRTS II type slab ballastless track structure.

[0005] Therefore, the prior art still needs to be improved and developed. SUMMARY

[0006] The main purpose of the present application is to provide a ballastless track temperature gradient early warning method, system, terminal and computer readable storage medium, which aims to solve the problem of low accuracy of the longitudinal connected ballastless track slab temperature field prediction in the prior art under complex service environment.

[0007] To achieve the above object, the application provides a ballastless track temperature gradient early warning method, which comprises the following steps:

[0008] Obtaining the environmental temperature, solar radiation, wind speed, humidity, rainfall and internal temperature of the track structure;

[0009] Calculating the ballastless track temperature gradient threshold based on the axle force and the ballastless track temperature gradient threshold based on the displacement;

[0010] Building a ballastless track temperature gradient SVM classification early warning model of four kernel functions, inputting the environmental temperature, solar radiation, wind speed, humidity, rainfall and internal temperature of the track structure into the ballastless track temperature gradient SVM classification early warning model of the four kernel functions, selecting the SVM classification early warning model of the best kernel function according to the output track structure temperature gradient classification early warning result;

[0011] Jointly building and optimizing the PSO algorithm and the SVM classification early warning model of the best kernel function to obtain the optimal ballastless track temperature gradient early warning model;

[0012] According to the ballastless track temperature gradient threshold based on the axle force or the ballastless track temperature gradient threshold based on the displacement, inputting the environmental temperature, solar radiation, wind speed, humidity, rainfall and internal temperature of the track structure into the optimal ballastless track temperature gradient early warning model to output the track structure temperature gradient classification early warning result.

[0013] The ballastless track temperature gradient early warning method, wherein the ballastless track temperature gradient early warning method further comprises:

[0014] Pre-calculating the ballastless track temperature gradient threshold, which is used for comparison when the ballastless track temperature gradient early warning model outputs the track structure temperature gradient classification early warning result.

[0015] The ballastless track temperature gradient early warning method, wherein the ballastless track is a vertical multi-layer concrete structure, comprising a steel rail, a fastener, a sleeper, a track slab, a mortar layer and a base plate, the temperature gradient between the track slab and the base plate is calculated, and the temperature gradient is the ratio of the temperature difference between the track slab and the base plate to the distance;

[0016] Calculating the temperature gradient:

[0017]

[0018] wherein, T g represents the temperature gradient, T s represents the track slab temperature, T bTb represents the temperature of the base plate, and Δx represents the distance between the track plate and the base plate.

[0019] The method for early warning of the temperature gradient of the ballastless track, wherein the temperature gradient threshold of the ballastless track comprises a temperature gradient threshold of the ballastless track based on an axial force;

[0020] The temperature gradient threshold of the ballastless track based on the axial force is calculated as follows:

[0021] F N = EAaDT; (2)

[0022] Wherein, F N represents the axial force acting on the inside of the ballastless track, E represents the elastic modulus of the ballastless track, A represents the cross-sectional area of the ballastless track, a represents the linear expansion coefficient, and DT represents the temperature difference of the ballastless track structure;

[0023] The temperature difference between the top of the track plate and the bottom of the track plate is calculated as follows:

[0024] DT1 = T1 - T2, wherein T1 represents the temperature of the top of the track plate, and T2 represents the temperature of the bottom of the track plate;

[0025] The temperature gradient threshold between the top of the track plate and the bottom of the track plate is calculated as follows:

[0026] T g1 = DT1 / Dx1, wherein Dx1 represents the distance between the top of the track plate and the bottom of the track plate;

[0027] The temperature difference between the bottom of the track plate and the bottom of the mortar layer is calculated as follows:

[0028] DT2 = T2 - T3, wherein T2 represents the temperature of the bottom of the track plate, and T3 represents the temperature of the bottom of the mortar layer;

[0029] The temperature gradient threshold between the bottom of the track plate and the bottom of the mortar layer is calculated as follows:

[0030] T g2 = DT2 / Dx2, wherein Dx2 represents the distance between the bottom of the track plate and the bottom of the mortar layer;

[0031] The temperature difference between the bottom of the mortar layer and the middle of the base plate is calculated as follows:

[0032] DT3 = T3 - T4, wherein T3 represents the temperature of the bottom of the mortar layer, and T4 represents the temperature of the middle of the base plate;

[0033] The temperature gradient threshold between the bottom of the mortar layer and the middle of the base plate is calculated as follows:

[0034] T g3 = DT3 / Dx3, wherein Dx3 represents the distance between the bottom of the mortar layer and the middle of the base plate;

[0035] calculating the temperature difference between the bottom of the mortar layer and the bottom of the base plate:

[0036] △T4 = T3 - T5, wherein T3 represents the temperature of the bottom of the mortar layer, and T5 represents the temperature of the bottom of the base plate;

[0037] calculating the temperature gradient threshold between the bottom of the mortar layer and the bottom of the base plate:

[0038] T g4 =△T4 / △x4, wherein△x4 represents the distance between the bottom of the mortar layer and the bottom of the base plate.

[0039] The temperature gradient early warning method of the ballastless track, wherein the temperature gradient threshold of the ballastless track comprises a displacement-based temperature gradient threshold of the ballastless track;

[0040] calculating the displacement-based temperature gradient threshold of the ballastless track:

[0041] ΔL = LαΔT; (3)

[0042] wherein ΔL represents the deformation, L represents the length of the track slab, α represents the linear expansion coefficient, and ΔT represents the temperature difference of the ballastless track structure;

[0043] calculating the temperature difference between the top of the track slab and the bottom of the track slab:

[0044] △T1 = T1 - T2, wherein T1 represents the temperature of the top of the track slab, and T2 represents the temperature of the bottom of the track slab;

[0045] calculating the temperature gradient threshold between the top of the track slab and the bottom of the track slab:

[0046] T g1 =△T1 / △x1, wherein△x1 represents the distance between the top of the track slab and the bottom of the track slab.

[0047] calculating the temperature difference between the bottom of the track slab and the bottom of the mortar layer:

[0048] △T2 = T2 - T3, wherein T2 represents the temperature of the bottom of the track slab, and T3 represents the temperature of the bottom of the mortar layer;

[0049] calculating the temperature gradient threshold between the bottom of the track slab and the bottom of the mortar layer:

[0050] T g2 =△T2 / △x2, wherein△x2 represents the distance between the bottom of the track slab and the bottom of the mortar layer.

[0051] calculating the temperature difference between the bottom of the mortar layer and the middle of the base plate:

[0052] △T3 = T3 - T4, wherein T3 represents the temperature of the bottom of the mortar layer, and T4 represents the temperature of the middle of the base plate.

[0053] calculating the temperature gradient threshold value between the bottom of the mortar layer and the middle of the base plate:

[0054] T g3 =△T3 / △x3, wherein △x3 represents the distance between the bottom of the mortar layer and the middle of the base plate;

[0055] calculating the temperature difference between the bottom of the mortar layer and the bottom of the base plate:

[0056] △T4=T3-T5, wherein T3 represents the temperature at the bottom of the mortar layer, and T5 represents the temperature at the bottom of the base plate;

[0057] calculating the temperature gradient threshold value between the bottom of the mortar layer and the bottom of the base plate:

[0058] T g4 =△T4 / △x4, wherein △x4 represents the distance between the bottom of the mortar layer and the bottom of the base plate.

[0059] The temperature gradient early warning method for ballastless track, wherein the temperature gradient early warning method for ballastless track further comprises:

[0060] The first temperature sensor, the second temperature sensor, the third temperature sensor, the fourth temperature sensor, the fifth temperature sensor and the sixth temperature sensor are pre-installed at different vertical heights in the longitudinally connected slab-type ballastless track of the high-speed railway.

[0061] The first temperature sensor is used to collect the temperature at the top of the track slab, the second temperature sensor is used to collect the temperature at the bottom of the track slab, the third temperature sensor is used to collect the temperature at the bottom of the mortar layer, the fourth temperature sensor is used to collect the temperature at the middle of the base plate, the fifth temperature sensor is used to collect the temperature at the bottom of the base plate, and the sixth temperature sensor is used to collect the ambient temperature.

[0062] The temperature gradient early warning method for ballastless track, wherein the temperature gradient early warning method for ballastless track further comprises optimizing the temperature gradient early warning model for ballastless track, specifically comprising:

[0063] initializing the particle swarm size, setting the weight factor, termination condition and initial particle coding of the algorithm;

[0064] setting the individual extreme value of each particle as the current position, calculating the fitness value of each particle by using the fitness function, and taking the corresponding individual extreme value of the good particle as the initial global extreme value;

[0065] iteratively calculating according to the position and speed updating formula of the particle to update the position and speed of the particle;

[0066] Calculating the fitness value of each particle after each iteration according to the fitness function of the particle;

[0067] Comparing the fitness value of each particle with the fitness value of the individual extreme value, if better, then updating the individual extreme value, otherwise keeping the original value;

[0068] Comparing the updated individual extreme value of each particle with the global extreme value, if better, then updating the global extreme value, otherwise keeping the original value;

[0069] Judging whether the termination condition is met, if the maximum number of iterations is reached or the obtained solution converges or the obtained solution has reached the expected effect, then terminating the iteration, otherwise continuing the iteration calculation;

[0070] Obtaining the parameter combination that makes the model best, which is used to obtain the optimal ballastless track temperature gradient early warning model.

[0071] In addition, to achieve the above purpose, the application also provides a ballastless track temperature gradient early warning system, wherein the ballastless track temperature gradient early warning system comprises:

[0072] An information acquisition module is configured to acquire environmental temperature, solar radiation, wind speed, humidity, rainfall and track structure internal temperature;

[0073] A threshold calculation module is configured to calculate a ballastless track temperature gradient threshold based on axial force and a ballastless track temperature gradient threshold based on displacement;

[0074] A model selection module is configured to construct a ballastless track temperature gradient SVM classification early warning model of four kinds of kernel functions, input the environmental temperature, the solar radiation, the wind speed, the humidity, the rainfall and the track structure internal temperature into the ballastless track temperature gradient SVM classification early warning model of the four kinds of kernel functions, and select a SVM classification early warning model of the best kernel function according to an output track structure temperature gradient classification early warning result;

[0075] A joint optimization module is configured to jointly construct and optimize the PSO algorithm and the SVM classification early warning model of the best kernel function to obtain an optimal ballastless track temperature gradient early warning model;

[0076] A classification early warning module is configured to input the environmental temperature, the solar radiation, the wind speed, the humidity, the rainfall and the track structure internal temperature into the optimal ballastless track temperature gradient early warning model according to the ballastless track temperature gradient threshold based on axial force or the ballastless track temperature gradient threshold based on displacement, so as to output a track structure temperature gradient classification early warning result.

[0077] In addition, to achieve the above object, the application further provides a terminal, wherein the terminal comprises a memory, a processor and a ballastless track temperature gradient early warning program stored in the memory and executable on the processor, and the ballastless track temperature gradient early warning program realizes the steps of the ballastless track temperature gradient early warning method when executed by the processor.

[0078] In addition, to achieve the above object, the application further provides a computer readable storage medium, wherein the computer readable storage medium stores a ballastless track temperature gradient early warning program, and the ballastless track temperature gradient early warning program realizes the steps of the ballastless track temperature gradient early warning method when executed by a processor.

[0079] In the application, the environment temperature, solar radiation, wind speed, humidity, rainfall and track structure internal temperature are obtained, the ballastless track temperature gradient threshold based on the axial force and the ballastless track temperature gradient threshold based on displacement are calculated, the ballastless track temperature gradient SVM classification early warning model of four kinds of kernel functions is constructed, the environment temperature, the solar radiation, the wind speed, the humidity, the rainfall and the track structure internal temperature are input into the ballastless track temperature gradient SVM classification early warning model of the four kinds of kernel functions, the optimal kernel function SVM classification early warning model is selected according to the output track structure temperature gradient classification early warning result, the optimal ballastless track temperature gradient early warning model is obtained by combining and optimizing the PSO algorithm and the optimal kernel function SVM classification early warning model, and the environment temperature, the solar radiation, the wind speed, the humidity, the rainfall and the track structure internal temperature are input into the optimal ballastless track temperature gradient early warning model according to the ballastless track temperature gradient threshold based on the axial force or the ballastless track temperature gradient threshold based on displacement to output the track structure temperature gradient classification early warning result. The application sets the vertical temperature gradient threshold of the ballastless track based on the axial force and displacement, takes the vertical temperature gradient threshold as the classification standard, realizes the classification early warning of the ballastless track temperature gradient, and improves the classification accuracy of the ballastless track temperature gradient early warning. BRIEF DESCRIPTION OF DRAWINGS

[0080] Figure 1 is a flow chart of a preferred embodiment of the ballastless track temperature gradient early warning method of the application;

[0081] Figure 2 is a schematic diagram of the calculation of the track structure temperature gradient threshold based on the axial force in the preferred embodiment of the ballastless track temperature gradient early warning method of the application;

[0082] Figure 3 is a schematic diagram of the calculation of the track structure temperature gradient threshold based on displacement in the preferred embodiment of the ballastless track temperature gradient early warning method of the application;

[0083] Figure 4 is a schematic diagram of the installation position of the track temperature sensor in the preferred embodiment of the track temperature gradient early warning method of the present application;

[0084] Figure 5 is a schematic diagram of one and a half years of solar radiation monitoring data in the preferred embodiment of the track temperature gradient early warning method of the present application;

[0085] Figure 6 is a schematic diagram of the process of optimizing the track temperature gradient early warning model in the preferred embodiment of the track temperature gradient early warning method of the present application;

[0086] Figure 7 is a schematic diagram of the principle of track temperature gradient early warning in the preferred embodiment of the track temperature gradient early warning method of the present application;

[0087] Figure 8 is a schematic diagram of the early warning results of the four kernel functions SVM in the preferred embodiment of the track temperature gradient early warning method of the present application;

[0088] Figure 9 is a schematic diagram of the early warning results of the temperature gradient between the bottom of the track slab and the middle of the base plate in the preferred embodiment of the track temperature gradient early warning method of the present application;

[0089] Figure 10 is a schematic diagram of the principle of the preferred embodiment of the track temperature gradient early warning system of the present application;

[0090] Figure 11 is a schematic diagram of the running environment of the preferred embodiment of the terminal of the present application. DETAILED DESCRIPTION

[0091] In order to make the purpose, technical scheme and advantages of the present application clearer and more explicit, the present application will be further described in detail below with reference to the drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application.

[0092] The track temperature gradient early warning method described in the preferred embodiment of the present application, as shown in Figure 1 The track temperature gradient early warning method comprises the following steps:

[0093] Step S10, obtaining the ambient temperature, solar radiation, wind speed, humidity, rainfall and internal temperature of the track structure;

[0094] Step S20, calculating the track temperature gradient threshold based on the axle force and the track temperature gradient threshold based on the displacement;

[0095] Step S30, a ballastless track temperature gradient SVM classification early warning model of four kernel functions is constructed, the environmental temperature, the solar radiation, the wind speed, the humidity, the rainfall and the track structure internal temperature are input into the ballastless track temperature gradient SVM classification early warning model of the four kernel functions, according to the output track structure temperature gradient classification early warning result, the SVM classification early warning model of the best kernel function is selected;

[0096] Step S40, the PSO algorithm and the SVM classification early warning model of the best kernel function are combined to construct and optimize an optimal ballastless track temperature gradient early warning model;

[0097] Step S50, according to the ballastless track temperature gradient threshold value based on the axial force or the ballastless track temperature gradient threshold value based on displacement, the environmental temperature, the solar radiation, the wind speed, the humidity, the rainfall and the track structure internal temperature are input into the optimal ballastless track temperature gradient early warning model to output the track structure temperature gradient classification early warning result.

[0098] Specifically, the ballastless track is a vertical multi-layer concrete structure, and the ballastless track structure mainly comprises a rail, a fastener, a sleeper, a track slab, a mortar layer and a base plate and the like vertical multi-layer concrete structures, wherein the temperature difference and distance ratio between the track slab, the mortar layer and the base plate is a temperature gradient, the temperature gradient between the track slab and the base plate is calculated, and the temperature gradient is the ratio of the temperature difference and the distance between the track slab and the base plate; the temperature gradient is calculated as follows:

[0099]

[0100] wherein, T g represents the temperature gradient, T s represents the track slab temperature, T b represents the base plate temperature, and Δx represents the distance between the track slab and the base plate.

[0101] The ballastless track temperature gradient threshold value is calculated in advance, and is used for comparison when the ballastless track temperature gradient early warning model outputs the track structure temperature gradient classification early warning result, that is, the ballastless track temperature gradient early warning model needs to be compared with the ballastless track temperature gradient threshold value when outputting the track structure temperature gradient classification early warning result, so as to realize the ballastless track temperature gradient classification early warning.

[0102] The ballastless track temperature gradient threshold value of the application comprises a ballastless track temperature gradient threshold value based on an axial force and a ballastless track temperature gradient threshold value based on displacement, the application proposes a threshold setting method of the ballastless track temperature gradient early warning model based on the axial force and displacement formula, and takes the threshold as a classification standard to realize the ballastless track temperature gradient classification early warning.

[0103] (1) Calculate the temperature gradient threshold of the ballastless track based on axial force:

[0104] The track slab is approximated as a slender axial compression bar fixed at both ends. The temperature difference is calculated using the formula for the maximum axial force of the track slab structure and the deformation. Under the influence of the temperature difference between the environment and the structure, tensile and compressive internal forces are generated in the cross section of the track slab. The axial force generated in the track slab due to temperature rise is calculated according to formula (2). The temperature gradient threshold in the ballastless track structure is:

[0105] F N =EAαΔT; (2)

[0106] Among them, F N E represents the axial force acting inside the ballastless track, in N; E represents the elastic modulus of the ballastless track, in MPa; A represents the cross-sectional area of ​​the ballastless track, in m³. 2 α represents the coefficient of linear expansion, / ℃; ΔT represents the temperature difference of the ballastless track structure, ℃;

[0107] Taking a track slab cracking axial force of 2080kN as an example, calculate the temperature difference between the top and bottom of the track slab:

[0108] △T1=T1-T2, where T1 represents the temperature at the top of the track slab and T2 represents the temperature at the bottom of the track slab; △T1=T1-T2=11℃;

[0109] Calculate the temperature gradient threshold between the top and bottom of the track slab:

[0110] T g1 = △T1 / △x1, where △x1 represents the distance between the top and bottom of the track slab; T g1 =△T1 / △x1=11 / 0.2=55℃ / m, as Figure 2 As shown, △x1=0.2m;

[0111] Calculate the temperature difference between the bottom of the track slab and the bottom of the mortar layer:

[0112] △T2=T2–T3, where T2 represents the temperature at the bottom of the track slab and T3 represents the temperature at the bottom of the mortar layer;

[0113] Calculate the temperature gradient threshold between the bottom of the track slab and the bottom of the mortar layer:

[0114] T g2 = △T2 / △x2, where △x2 represents the distance between the bottom of the track slab and the bottom of the mortar layer; T g2 =△T2 / △x2=8.25℃ / m, such as Figure 2 As shown, Δx2 = 0.03m;

[0115] Calculate the temperature difference between the bottom of the mortar layer and the middle of the base plate:

[0116] △T3 = T3 - T4, where T3 represents the temperature at the bottom of the mortar layer, and T4 represents the temperature at the middle of the base plate;

[0117] Calculate the temperature gradient threshold between the bottom of the mortar layer and the middle of the base plate:

[0118] T g3 =△T3 / △x3, where△x3 represents the distance between the bottom of the mortar layer and the middle of the base plate; T g3 =△T3 / △x3 = 41.25 ℃ / m, as shown in Figure 2 △x3 = 0.15 m;

[0119] Calculate the temperature difference between the bottom of the mortar layer and the bottom of the base plate:

[0120] △T4 = T3 - T5, where T3 represents the temperature at the bottom of the mortar layer, and T5 represents the temperature at the bottom of the base plate;

[0121] Calculate the temperature gradient threshold between the bottom of the mortar layer and the bottom of the base plate:

[0122] T g4 =△T4 / △x4, where△x4 represents the distance between the bottom of the mortar layer and the bottom of the base plate; T g4 =△T4 / △x4 = 82.5 ℃ / m, as shown in Figure 2 △x3 = 0.3 m.

[0123] (2) Calculate the temperature gradient threshold of the displacement-based ballastless track:

[0124] The temperature difference of the track structure is calculated according to the tension displacement formula (3):

[0125] ΔL = LαΔT; (3)

[0126] Where ΔL represents the deformation, m; L represents the length of the track plate, m, α represents the linear expansion coefficient, / ℃; ΔT represents the temperature difference of the ballastless track structure, ℃;

[0127] Taking the gap ΔL = 0.5 mm as the displacement allowance standard, calculate the temperature difference between the top of the track plate and the bottom of the track plate:

[0128] △T1 = T1 - T2, where T1 represents the temperature at the top of the track plate, and T2 represents the temperature at the bottom of the track plate; △T1 = T1 - T2 = 7.8 ℃;

[0129] Calculate the temperature gradient threshold between the top of the track plate and the bottom of the track plate:

[0130] T g1= AT1 / Ax1, where Ax1represents the distance between the top of the track slab and the bottom of the track slab; T g1 = AT1 / Ax1= 7.8 / 0.2 = 39 °C / m, as shown in FIG. 1, where Ax1= 0.2 m; Figure 3

[0131] The temperature difference between the bottom of the track slab and the bottom of the mortar layer was calculated as follows:

[0132] AT2= T2- T3, where T2represents the temperature at the bottom of the track slab and T3represents the temperature at the bottom of the mortar layer;

[0133] The temperature gradient threshold between the bottom of the track slab and the bottom of the mortar layer was calculated as follows:

[0134] T g2 = AT2 / Ax2, where Ax2represents the distance between the bottom of the track slab and the bottom of the mortar layer; T g2 = AT2 / Ax2= 5.85 °C / m, as shown in FIG. 2, where Ax2= 0.03 m; Figure 3

[0135] The temperature difference between the bottom of the mortar layer and the middle of the base slab was calculated as follows:

[0136] AT3= T3- T4, where T3represents the temperature at the bottom of the mortar layer and T4represents the temperature at the middle of the base slab;

[0137] The temperature gradient threshold between the bottom of the mortar layer and the middle of the base slab was calculated as follows:

[0138] T g3 = AT3 / Ax3, where Ax3represents the distance between the bottom of the mortar layer and the middle of the base slab; T g3 = AT3 / Ax3= 29.25 °C / m, as shown in FIG. 3, where Ax3= 0.15 m; Figure 3

[0139] The temperature difference between the bottom of the mortar layer and the bottom of the base slab was calculated as follows:

[0140] AT4= T3- T5, where T3represents the temperature at the bottom of the mortar layer and T5represents the temperature at the bottom of the base slab;

[0141] The temperature gradient threshold between the bottom of the mortar layer and the bottom of the base slab was calculated as follows:

[0142] T g4 = AT4 / Ax4, where Ax4represents the distance between the bottom of the mortar layer and the bottom of the base slab; T g4 = AT4 / Ax4= 58.5 °C / m, as shown in FIG. 4, where Ax4= 0.3 m. Figure 3

[0143] ​​​​Specifically, the application can be used in the longitudinal slab-type ballastless track of high-speed railway, which is pre-installed with first, second, third, fourth, fifth and sixth temperature sensors at different vertical heights; the first temperature sensor is used to collect the temperature at the top of the track slab, the second temperature sensor is used to collect the temperature at the bottom of the track slab, the third temperature sensor is used to collect the temperature at the bottom of the mortar layer, the fourth temperature sensor is used to collect the temperature at the middle of the base plate, the fifth temperature sensor is used to collect the temperature at the bottom of the base plate, and the sixth temperature sensor is used to collect the ambient temperature. For example, as shown in Figure 4 , five temperature sensors are installed to collect the temperature at different positions.

[0144] The ambient temperature can be collected by a temperature sensor or an automatic small weather station. For example, an automatic small weather station is installed beside the ballastless track line, which can monitor meteorological data such as ambient temperature, solar radiation, wind speed, humidity, rainfall, etc. For example, as shown in Figure 5 , the monitoring data of solar radiation in a year, as shown in Figure 5 , the radiation value of solar radiation changes between 0W / m^2 and 1185W / m^2 in a monitoring period of one and a half years, the maximum value appears at about 14:00 on July 7, 2021, and the highest radiation is about 1185W / m^2, and the minimum value of daytime radiation appears at 11 o'clock on January 17, 2022, and the minimum solar radiation is 577w / m^2.

[0145] In the application, the relationship between environmental factors and track temperature is: the correlation between ambient temperature and temperature at different heights in the track is established, for example, the relationship between track temperature and ambient temperature in a day, and a highest temperature day is selected. With the increase of vertical distance, the temperature change trend of track structure gradually slows down, the temperature change in the track slab is faster than that in the base plate, the temperature change in the middle of the base plate is faster than that at the bottom of the base plate, and the peak value of the temperature in the track lags behind the peak value of the ambient temperature by about 2h.

[0146] Specifically, the present application combines the PSO (Particle Swarm Optimization) algorithm and the SVM (Support Vector Machine) method, among the four kernel functions selected by the SVM classification early warning model (i.e. the ballastless track temperature gradient early warning model), are the linear kernel function, the polynomial kernel function, the Gaussian kernel function (rbf) and the Sigmoid kernel function. The SVM classification model with the rbf Gaussian kernel function as the kernel function can be well applied to the classification and early warning of the ballastless track structure temperature gradient. The particle swarm optimization algorithm is used to further determine the values of the penalty factor c and the kernel parameter g. Starting from a random solution, the optimal solution is found through iteration, and the quality of the solution is evaluated by the fitness. The PSO is initialized as a group of random particles (random solutions), and then the optimal solution is found through iteration. All particles have two attributes of position and speed. In each iteration, the particles are updated by the optimal solution found by the particle itself and the global extreme value of the optimal solution found by the whole population.

[0147] The kernel function is one of the important technologies of the support vector machine, which enables the support vector machine to process infinite or nonlinear features in a high-dimensional feature space. Since the kernel function parameters will affect the mapping function, and then determine the complexity of the sub-sample data space distribution. Currently, the following four kernel functions are widely used in SVM classification problems:

[0148] (1) The linear kernel function is mainly used for linearly separable cases, the dimension of the feature space to the input space is the same, and the optimal linear classifier is found in the original space, which has the advantages of fewer parameters and faster speed.

[0149] (2) The polynomial kernel function can map the low-dimensional input space to the high-dimensional feature space, which is suitable for orthogonal normalized data. The larger the parameter d is, the higher the dimension of the mapping is. When the order of the polynomial is relatively high, the element value of the kernel matrix will tend to infinity or infinitesimal, and the computational complexity will be too large to calculate.

[0150] (3) The Gaussian radial basis function can also map the sample into a higher dimensional space, which mainly measures the similarity of two feature vectors. The higher the similarity is, the closer the value of this term is to 0, and the value of the kernel function is also closer to 1.

[0151] (4) The Sigmoid kernel function comes from neural networks, and the support vector machine is a kind of multi-layer perception neural network.

[0152] Although different kernel functions are small factors affecting the performance of the support vector machine, their parameters and error penalty factors have a key influence on the performance of the support vector machine. Selecting appropriate kernel parameters and error penalty factors is an important step for applying the support vector machine to temperature prediction.

[0153] As Figure 6 shown. The optimization of the ballastless track temperature gradient early warning model specifically includes:

[0154] Step 1: initialize the particle swarm size m, set the weight factor of the algorithm, the termination condition and the initial particle coding;

[0155] Step 2: set the individual extreme value of each particle as the current position, calculate the fitness value of each particle by using the fitness function, and take the corresponding individual extreme value of the good particle as the initial global extreme value;

[0156] Step 3: iterative calculation according to the position and speed update formula of the particle, update the position and speed of the particle;

[0157] Step 4: calculate the fitness value of each particle after each iteration according to the fitness function of the particle;

[0158] Step 5: compare the fitness value of each particle with the fitness value of the individual extreme value, if it is better, update the individual extreme value, otherwise keep the original value;

[0159] Step 6: compare the updated individual extreme value of each particle with the global extreme value, if it is better, update the global extreme value, otherwise keep the original value;

[0160] Step 7: judge whether the termination condition is met, if the maximum iteration number is reached or the solution converges or the solution has reached the expected effect, terminate the iteration, otherwise return to Step 3;

[0161] Step 8: get the best parameter combination of the model, which is used to get the optimal ballastless track temperature gradient early warning model.

[0162] For example, as Figure 7 shown, the environmental temperature X1, solar radiation X2, wind speed X3 and track structure internal temperature X4 are taken as the input values of the ballastless track temperature gradient early warning model, and the output value is the track structure temperature gradient classification warning result X4(T n+1 ).

[0163] The ballastless track temperature gradient early warning model: the temperature gradient of the bottom of the track slab and the middle of the base plate calculated by the axle force is 41.25℃ / m, and the temperature gradient of the bottom of the track slab and the bottom of the base plate is 82.5℃ / m as the early warning threshold (ballastless track structure internal temperature gradient threshold). When using four kernel functions to detect and classify the temperature monitoring database, for each test, the track structure temperature gradient dataset is randomly divided into two subsets, training set and test set, which account for 75% and 25% of the original sample respectively.

[0164] The temperature gradient prediction accuracy of the ballastless track: in the SVM classification early warning model of the temperature gradient of the track slab bottom and the base slab bottom, the calculation accuracy of the rbf kernel function is more obvious, and the highest accuracy is as high as 99.2%, and among the three positions of the bridge ballastless track, as shown in the figure, the accuracy of the gradient of the treated separation gap 31 is slightly higher than that of the temperature gradient of the non-separation gap 76, and the classification accuracy of the temperature gradient of the non-treated separation gap 109 is the lowest. As shown in the figure, the early warning analysis accuracy of the temperature gradient of the track slab bottom and the middle part of the base slab optimized by the PSO-SVM algorithm is higher than 97%, and the highest accuracy is 99.4% of the temperature gradient of the treated separation gap 31. Figure 8 Figure 9

[0165] The present application considers the influence of longitudinal plate type ballastless track structure stress and deformation, and derives the vertical temperature gradient threshold of the ballastless track based on the axial force and displacement; according to the correlation between different meteorological factors and the temperature field distribution of the multi-layer track structure, the SVM temperature gradient classification early warning model of different kernel functions is established, and the early warning effect of the input of different meteorological factors is considered; the ballastless track temperature gradient early warning method based on PSO-SVM algorithm is established, and the classification accuracy of the ballastless track temperature gradient early warning model is improved.

[0166] Further, the present application can be aimed at different ballastless track track structure forms, and temperature sensors can be installed in different track positions to study the temperature gradient between different positions in the track; different meteorological factors and service environment influences are considered, such as different soil subgrades and rainfall; nonlinear formula calculation is used to derive the temperature gradient threshold setting based on the set axial force and displacement, other classification early warning methods are used, and more early warning effect evaluation indexes are used; the monitoring data of different regions and periods are used, and the proportion of the training set and the test set is not limited to 75% and 25%.

[0167] Further, as shown in the figure, based on the above ballastless track temperature gradient early warning method, the present application also correspondingly provides a ballastless track temperature gradient early warning system, wherein the ballastless track temperature gradient early warning system comprises: Figure 10 An information acquisition module 51 is used to acquire environmental temperature, solar radiation, wind speed, humidity, rainfall and track structure internal temperature;

[0168] A threshold calculation module 52 is used to calculate the ballastless track temperature gradient threshold based on the axial force and the ballastless track temperature gradient threshold based on the displacement;

[0169]

[0170] ​​​The model selection module 53 is configured to construct four kernel function-based ballastless track temperature gradient SVM classification warning models, input the environmental temperature, the solar radiation, the wind speed, the humidity, the rainfall and the track structure internal temperature into the four kernel function-based ballastless track temperature gradient SVM classification warning models, and select the best kernel function-based SVM classification warning model according to the output track structure temperature gradient classification warning result.

[0171] The joint optimization module 54 is configured to jointly construct and optimize the PSO algorithm and the best kernel function-based SVM classification warning model to obtain an optimal ballastless track temperature gradient warning model.

[0172] The classification warning module 55 is configured to input the environmental temperature, the solar radiation, the wind speed, the humidity, the rainfall and the track structure internal temperature into the optimal ballastless track temperature gradient warning model to output a track structure temperature gradient classification warning result according to the ballastless track temperature gradient threshold value based on the axle force or the ballastless track temperature gradient threshold value based on the displacement.

[0173] Further, as shown in Figure 11 Based on the above ballastless track temperature gradient warning method and system, the application further provides a terminal, which comprises a processor 10, a memory 20 and a display 30. Figure 11 Only some components of the terminal are shown, but it should be understood that all the shown components are not required, and more or less components can be alternatively implemented.

[0174] The memory 20 can be an internal storage unit of the terminal in some embodiments, for example, a hard disk or a memory of the terminal. The memory 20 can also be an external storage device of the terminal in other embodiments, for example, a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card and the like equipped on the terminal. Further, the memory 20 can include both the internal storage unit and the external storage device of the terminal. The memory 20 is configured to store application software and various data installed on the terminal, for example, program codes of the terminal. The memory 20 can also be configured to temporarily store data that has been output or will be output. In an embodiment, the memory 20 stores a ballastless track temperature gradient warning program 40, which can be executed by the processor 10 to implement the ballastless track temperature gradient warning method in the application.

[0175] The processor 10 can be a Central Processing Unit (CPU), a microprocessor or other data processing chip in some embodiments, for running program codes stored in the memory 20 or processing data, such as executing the ballastless track temperature gradient early warning method, etc.

[0176] The display 30 can be an LED display, a liquid crystal display, a touch liquid crystal display, an OLED (Organic Light-Emitting Diode) touch, etc. in some embodiments. The display 30 is used to display information of the terminal and to display a visualized user interface. The components 10-30 of the terminal communicate with each other through a system bus.

[0177] In an embodiment, the steps of the above ballastless track temperature gradient early warning method are implemented when the processor 10 executes the ballastless track temperature gradient early warning program 40 in the memory 20.

[0178] The present application also provides a computer readable storage medium, wherein the computer readable storage medium stores a ballastless track temperature gradient early warning program, and the ballastless track temperature gradient early warning program implements the steps of the ballastless track temperature gradient early warning method as described above when executed by a processor.

[0179] In summary, the present application provides a ballastless track temperature gradient early warning method and related equipment, the method comprising: obtaining an environmental temperature, solar radiation, wind speed, humidity, rainfall and track structure internal temperature; calculating a ballastless track temperature gradient threshold based on an axial force and a ballastless track temperature gradient threshold based on displacement; constructing a ballastless track temperature gradient SVM classification early warning model of four kinds of kernel functions, inputting the environmental temperature, the solar radiation, the wind speed, the humidity, the rainfall and the track structure internal temperature into the ballastless track temperature gradient SVM classification early warning model of the four kinds of kernel functions, selecting a SVM classification early warning model of the best kernel function according to an output track structure temperature gradient classification early warning result; jointly constructing and optimizing the PSO algorithm and the SVM classification early warning model of the best kernel function to obtain an optimal ballastless track temperature gradient early warning model; inputting the environmental temperature, the solar radiation, the wind speed, the humidity, the rainfall and the track structure internal temperature into the optimal ballastless track temperature gradient early warning model according to the ballastless track temperature gradient threshold based on the axial force or the ballastless track temperature gradient threshold based on the displacement, to output a track structure temperature gradient classification early warning result. The present application sets a vertical temperature gradient threshold of the ballastless track based on the axial force and the displacement, and takes the vertical temperature gradient threshold as a classification standard, realizes classification early warning of the ballastless track temperature gradient, and improves the classification accuracy of the ballastless track temperature gradient early warning.

[0180] It should be noted that, in the present document, the terms "comprising", "including", or any other variant thereof are intended to cover a non-exclusive inclusion, such that processes, methods, articles, or terminals that comprise a list of elements are not limited to those elements, but can also include other elements not expressly listed, or inherent to such processes, methods, articles, or terminals. Without further limitation, an element defined by the statement "comprising a" does not exclude the presence of additional identical elements in the process, method, article, or terminal that includes the element.

[0181] Of course, those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing relevant hardware (such as a processor, a controller, etc.) through a computer program, and the program can be stored in a computer-readable computer-readable storage medium, and the program can include the processes of the above-mentioned method embodiments when executed. The computer-readable storage medium can be a memory, a magnetic disc, an optical disc, etc.

[0182] It should be understood that the application is not limited to the above examples, and those skilled in the art can make improvements or changes according to the above description, and all these improvements and changes should be within the protection scope of the appended claims of the present application.

Claims

1. A method for early warning of temperature gradient of ballastless track, characterized in that, The ballastless track temperature gradient early warning method comprises: obtaining an environmental temperature, solar radiation, wind speed, humidity, rainfall and internal track structure temperature; calculating an axle force-based ballastless track temperature gradient threshold value and a displacement-based ballastless track temperature gradient threshold value; constructing a ballastless track temperature gradient SVM classification early warning model of four kernel functions, inputting the environmental temperature, the solar radiation, the wind speed, the humidity, the rainfall and the internal track structure temperature into the ballastless track temperature gradient SVM classification early warning model of the four kernel functions, selecting a best kernel function SVM classification early warning model according to an output track structure temperature gradient classification early warning result; obtaining an optimal ballastless track temperature gradient early warning model by combining and optimizing the PSO algorithm and the best kernel function SVM classification early warning model; inputting the environmental temperature, the solar radiation, the wind speed, the humidity, the rainfall and the internal track structure temperature into the optimal ballastless track temperature gradient early warning model according to the axle force-based ballastless track temperature gradient threshold value or the displacement-based ballastless track temperature gradient threshold value to output a track structure temperature gradient classification early warning result; The ballastless track temperature gradient threshold value comprises an axle force-based ballastless track temperature gradient threshold value. The axle force-based ballastless track temperature gradient threshold value is calculated as follows: ；（2） wherein, represents the axle force acting inside the ballastless track, represents the elastic modulus of the ballastless track, represents the cross-sectional area of the ballastless track, represents the linear expansion coefficient, represents the temperature difference of the ballastless track structure; The temperature difference between the top of the track slab and the bottom of the track slab is calculated. △T 1= T 1- T 2, wherein, T 1 represents the top track plate temperature, T 2 represents the bottom track plate temperature; The temperature gradient threshold value between the top of the track slab and the bottom of the track slab is calculated. T g1 = △T 1 / △x1, where △x1represents the distance from the top of the track plate to the bottom of the track plate; The temperature difference between the bottom of the track slab and the bottom of the mortar layer is calculated. △T 2= T 2– T 3, wherein, T 2 represents the track plate bottom temperature, T 3 represents the mortar layer bottom temperature; The temperature gradient threshold value between the bottom of the track slab and the bottom of the mortar layer is calculated. T g2 = △T 2 / △x2, where △x2represents the distance between the bottom of the track slab and the bottom of the mortar layer; The temperature difference between the bottom of the mortar layer and the middle of the base plate is calculated. △T 3= T 3– T 4, wherein, T 3 represents the temperature at the bottom of the mortar layer, T 4 represents the temperature at the middle of the base plate; The temperature gradient threshold value between the bottom of the mortar layer and the middle of the base plate is calculated. T g3 = △T 3 / △x3, where △x3 represents the distance between the bottom of the mortar layer and the middle of the base plate; The temperature difference between the bottom of the mortar layer and the bottom of the base plate is calculated. △T 4= T 3– T 5, wherein, T 3 represents the temperature at the bottom of the mortar layer, T 5 represents the temperature at the bottom of the base plate; The temperature gradient threshold value between the bottom of the mortar layer and the bottom of the base plate is calculated. T g4 = △T 4 / △x4, where △x4represents the distance between the bottom of the mortar layer and the bottom of the footing slab. The ballastless track temperature gradient threshold value comprises a displacement-based ballastless track temperature gradient threshold value. The displacement-based ballastless track temperature gradient threshold value is calculated as follows: ；（3） wherein, denotes the deformation, denotes the length of the track slab, denotes the linear expansion coefficient, denotes the temperature difference of the ballastless track structure; The temperature difference between the top of the track slab and the bottom of the track slab is calculated. △T 1 T 1 T 2, wherein, T 1 represents the top track plate temperature, T 2 represents the bottom track plate temperature; The temperature gradient threshold value between the top of the track slab and the bottom of the track slab is calculated. T g1 = △T 1 / △x1, where △x1represents the distance from the top of the track plate to the bottom of the track plate; The temperature difference between the bottom of the track slab and the bottom of the mortar layer is calculated. △T 2= T 2– T 3, wherein, T 2 represents the track plate bottom temperature, T 3 represents the mortar layer bottom temperature; The temperature gradient threshold value between the bottom of the track slab and the bottom of the mortar layer is calculated. T g2 = △T 2 / △x2, where △x2represents the distance between the bottom of the track slab and the bottom of the mortar layer; The temperature difference between the bottom of the mortar layer and the middle of the base plate is calculated. △T 3= T 3– T 4, wherein, T 3 represents the temperature at the bottom of the mortar layer, T 4 represents the temperature at the middle of the base plate; The temperature gradient threshold value between the bottom of the mortar layer and the middle of the base plate is calculated. T g3 = △T 3 / △x3, where △x3 represents the distance between the bottom of the mortar layer and the middle of the base plate; The temperature difference between the bottom of the mortar layer and the bottom of the base plate is calculated. △T 4= T 3– T 5, wherein, T 3 represents the temperature at the bottom of the mortar layer, T 5 represents the temperature at the bottom of the base plate; The temperature gradient threshold value between the bottom of the mortar layer and the bottom of the base plate is calculated. T g4 = △T 4 / △x4, where △x4represents the distance between the bottom of the mortar layer and the bottom of the footing slab.

2. The method according to claim 1, wherein, The ballastless track temperature gradient early warning method further comprises: The ballastless track temperature gradient threshold value is calculated in advance and is used for comparison when the ballastless track temperature gradient early warning model outputs a track structure temperature gradient classification early warning result.

3. The method according to claim 1, wherein the temperature gradient of the ballastless track is calculated by using a temperature gradient calculation formula. The ballastless track is a vertical multi-layer concrete structure comprising a steel rail, a fastener, a sleeper, a track slab, a mortar layer and a base plate, and the temperature gradient between the track slab and the base plate is calculated, wherein the temperature gradient is the ratio of the temperature difference between the track slab and the base plate to the distance; The temperature gradient is calculated. ；（1） wherein T g represents a temperature gradient, T s represents a track plate temperature, T b represents a base plate temperature, and Δx represents a distance between the track plate and the base plate.

4. The method according to claim 1, wherein the temperature gradient of the ballastless track is calculated by using a temperature gradient calculation formula. The ballastless track temperature gradient early warning method further comprises: The first temperature sensor, the second temperature sensor, the third temperature sensor, the fourth temperature sensor, the fifth temperature sensor and the sixth temperature sensor are pre-installed at different vertical heights in a longitudinal slab-type ballastless track of a high-speed railway; The first temperature sensor is used for collecting the temperature at the top of the track slab, the second temperature sensor is used for collecting the temperature at the bottom of the track slab, the third temperature sensor is used for collecting the temperature at the bottom of the mortar layer, the fourth temperature sensor is used for collecting the temperature at the middle of the base plate, the fifth temperature sensor is used for collecting the temperature at the bottom of the base plate, and the sixth temperature sensor is used for collecting the ambient temperature.

5. The method of claim 1, wherein the method further comprises: The ballastless track temperature gradient early warning method further comprises optimizing the ballastless track temperature gradient early warning model, specifically comprising: initializing the particle swarm size, setting the weight factor, termination condition and initial particle coding of the algorithm; setting the individual extreme value of each particle as the current position, calculating the fitness value of each particle by using the fitness function, and taking the corresponding individual extreme value of the particle with good fitness as the initial global extreme value; iteratively calculating according to the position and speed updating formula of the particle to update the position and speed of the particle; calculating the fitness value of each particle after each iteration according to the fitness function of the particle; comparing the fitness value of each particle with the fitness value of the individual extreme value, if it is better, then updating the individual extreme value, otherwise keeping the original value; comparing the updated individual extreme value of each particle with the global extreme value, if it is better, then updating the global extreme value, otherwise keeping the original value; judging whether the termination condition is met, if the maximum number of iterations is reached or the obtained solution converges or the obtained solution has reached the expected effect, then terminating the iteration, otherwise continuing the iteration calculation; obtaining the optimal parameter combination of the model for obtaining the optimal ballastless track temperature gradient early warning model.

6. A temperature gradient early warning system for ballastless track, characterized in that, The ballastless track temperature gradient early warning system is used to implement the ballastless track temperature gradient early warning method of any one of claims 1-5, and comprises: an information acquisition module, configured to acquire the ambient temperature, solar radiation, wind speed, humidity, rainfall and internal temperature of the track structure; a threshold calculation module, configured to calculate the ballastless track temperature gradient threshold based on the axle load and the ballastless track temperature gradient threshold based on the displacement; a model selection module, configured to construct four kinds of kernel function ballastless track temperature gradient SVM classification early warning models, input the ambient temperature, the solar radiation, the wind speed, the humidity, the rainfall and the internal temperature of the track structure into the four kinds of kernel function ballastless track temperature gradient SVM classification early warning models, select the SVM classification early warning model of the best kernel function according to the output track structure temperature gradient classification early warning result; a joint optimization module, configured to jointly construct and optimize the PSO algorithm and the SVM classification early warning model of the best kernel function to obtain the optimal ballastless track temperature gradient early warning model. The classification early warning module is configured to input the ambient temperature, the solar radiation, the wind speed, the humidity, the rainfall and the internal temperature of the track structure into the optimal track temperature gradient early warning model according to the track temperature gradient threshold based on the axle force or the track temperature gradient threshold based on the displacement, so as to output a track structure temperature gradient classification early warning result.

7. A terminal, characterized by comprising: The terminal comprises a memory, a processor and a track temperature gradient early warning program stored on the memory and executable on the processor, and the track temperature gradient early warning program, when executed by the processor, implements the steps of the track temperature gradient early warning method according to any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, The computer readable storage medium stores a track temperature gradient early warning program, and the track temperature gradient early warning program, when executed by the processor, implements the steps of the track temperature gradient early warning method according to any one of claims 1-5.

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