Simulation analysis method of heavy-haul railway ballast compaction disease based on ping-pong model

Abstract

The present invention proposes a simulation analysis method for the compaction disease of heavy-duty railway track bed based on the ping-pong model, which belongs to the field of nondestructive testing of ground penetrating radar for railway engineering, including: calculating the overall equivalent dielectric constant and the equivalent dielectric constant of the compaction area based on the ping-pong model; using gprMax to simulate the ping-pong model, and calculating the simulated overall equivalent dielectric constant and the equivalent dielectric constant of the compaction area based on the simulation results; calculating the gprMax compaction area equivalent dielectric constant prediction formula according to the overall equivalent dielectric constant, the compaction area equivalent dielectric constant, the simulated overall equivalent dielectric constant and the compaction area equivalent dielectric constant, so as to realize the simulation and analysis of the compaction disease of heavy-duty railway track bed based on the ping-pong model. The present invention proposes a "model-simulation" compaction area equivalent dielectric constant prediction formula, which is based on the "ping-pong model" modeling, and only relies on the parameters of the model itself, without running the simulation, to obtain the predicted value of the compaction degree.

Description

Technical Field

[0001] The invention relates to the technical field of nondestructive detection of railway engineering ground penetrating radar, and in particular to a simulation analysis method of heavy-load railway ballast compaction disease based on a ping-pong model. Background Art

[0002] As an important part of railway tracks, the performance of heavy-duty railway ballast directly affects the safety and stable operation of trains. With the increasing busyness of railway transportation, the ballast material gradually wears and pulverizes under the long-term dynamic load of trains. At the same time, the invasion of external environmental factors such as wind, sand and dust causes the internal void state of the ballast to change, causing the ballast to compact. This compaction not only changes the physical properties of the ballast, but also causes the elasticity and drainage performance of the ballast to decrease, thereby affecting the smoothness of the track and increasing safety hazards in train operation.

[0003] At present, there is a gap in the industry in the construction of effective simulation models for the compaction of heavy-duty railway ballast. It is very important to effectively analyze, judge and predict the actual situation from the perspective of simulation for the compaction disease on the heavy-duty railway ballast. The lack of simulation models to guide various engineering situations will require additional resources to be spent on the project. Summary of the invention

[0004] In order to solve the problem that there is a lack of effective simulation model and effective analysis method for ballast bed compaction disease in the prior art, the present invention provides a simulation analysis method for heavy-duty railway ballast bed compaction disease based on a ping-pong model, the method comprising:

[0005] Step S1, constructing a "ping-pong model" based on compaction disease based on the compaction disease of the heavy-duty railway ballast bed, wherein the compaction disease of the heavy-duty railway ballast bed includes: severe compaction with soil, moderate compaction with soil, severe compaction without soil, and moderate compaction without soil; calculating the overall equivalent dielectric constant based on the "ping-pong model" based on the constructed "ping-pong model" ;

[0006] Step S2: Use gprMax to simulate the "ping-pong model", and calculate the equivalent dielectric constant of the slab area based on the gprMax simulation based on the simulation results. ;

[0007] Step S3: Based on the overall equivalent dielectric constant of the “ping-pong model” Calculate the prediction formula of the equivalent dielectric constant of the slab-bonded area simulated by gprMax, and compare the prediction results with the equivalent dielectric constant of the slab-bonded area simulated by gprMax A comparison is made to obtain the comparison results, and based on the comparison results, a simulation analysis of the compaction disease of the heavy-duty railway ballast is completed.

[0008] Optionally, the simulation analysis method also includes step S4, based on the comparison result of step S3, using a generalized function to fit the prediction result of the equivalent dielectric constant of the gprMax simulation compaction area to obtain the simulation fitting result of the heavy-duty railway roadbed compaction disease.

[0009] Optionally, in step S1, the modeling process of the "ping-pong model" specifically includes:

[0010] Three balls with different diameters were used to form ballast models with different degrees of wear in a size of 1.0 m × 0.9 m. The generated ballast models were used as "ping-pong models". Large balls with a diameter of 6 cm were used to simulate the ballast with less wear on the top layer, and medium balls with a diameter of 4 cm were used to simulate the ballast with slight wear in the middle layer. Small balls with a diameter of 2 cm were used to simulate the severely worn part of the roadbed at the bottom.

[0011] Optionally, in step S1, the overall equivalent dielectric constant based on the constructed “ping-pong model” is calculated based on the “ping-pong model”. The process specifically includes:

[0012] ;

[0013] Among them, N1 is the normalized component coefficient of the large sphere, N2 is the normalized component coefficient of the medium sphere, N3 is the normalized component coefficient of the small sphere, N4 is the normalized component coefficient of the soil, and N5 is the proportion of air. is the relative dielectric constant of air, is the relative dielectric constant of the large sphere, is the relative dielectric constant of the sphere, is the relative dielectric constant of the small sphere, is the relative dielectric constant of the soil.

[0014] Optionally, in step S2, the gprMax simulation parameters are set as follows: the forward model size is set to 1.0×0.9, in m; the spatial grid step position is 0.0025, in m; the time window is set to 15, in ns; the initial transmitting antenna coordinates are set to (0.03, 0.785), in m; the initial receiving antenna coordinates are set to (0.05, 0.785), in m; the antenna step distance is set to 0.006, in m; the excitation source type is set to ricker; the test number is set to 160; the antenna frequency is set to 1.5, in GHz; and the distance from the upper surface of the roadbed to the antenna is set to 0.3, in m.

[0015] Optionally, in step S2, the equivalent dielectric constant of the slab region based on the gprMax simulation is calculated based on the simulation results. The process specifically includes:

[0016] The time information of the simulation results is divided into interfaces: the interface F3 between the middle sphere and the small sphere and the bottom surface F4 of the ejection model. The corresponding time information based on F3 and F4 is: and ,based on and The equivalent dielectric constant of the entire simulation calculated from the gprMax simulation :

[0017] ;

[0018] in, is the speed of light in vacuum, is the depth of the hardened area.

[0019] Optionally, in step S3, according to the overall equivalent dielectric constant of the "ping-pong model" The contents of the prediction formula for the equivalent dielectric constant of the gprMax simulation slab region specifically include:

[0020] ;

[0021] in, is the predicted value of the equivalent dielectric constant of the junction area, is the relative dielectric constant of soil, , is the relative permittivity of the large sphere, is the relative dielectric constant of the sphere, is the relative dielectric constant of the small sphere.

[0022] Compared with the prior art, the present invention has the following beneficial effects:

[0023] The present invention constructs a new electromagnetic simulation model, the "ping-pong model". Compared with the traditional modeling method, the "ping-pong model" uses regular small balls to build the model. This new modeling method is not only more in line with the characteristics of heavy-duty railway trackbed ballast in engineering practice, but also has low modeling difficulty, is easy to modify and study, and the conclusions obtained are more generalizable. In addition, the present invention also provides a corresponding complete research method, from model building to electromagnetic forward simulation, and then to subsequent tolerance analysis and generalization solution, which fully describes the heavy-duty railway trackbed compaction disease analysis method based on the "ping-pong model", which is used to more accurately simulate and analyze the compaction disease of the heavy-duty railway trackbed, thereby providing a scientific basis for the maintenance and optimization of the railway trackbed. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0025] Figure 1 This is a preview image of the gprMax2D "ping pong model" of the embodiment of the present invention;

[0026] Figure 2 This is a single-channel waveform comparison of the "compacted area - non-compacted area" area of ​​heavily compacted soil in an example of an embodiment of the present invention;

[0027] Figure 3 This is an analysis diagram of "model - time domain waveform - radar spectrum" of a soil with severe compaction in an example of an embodiment of the present invention;

[0028] Figure 4 A method step diagram of a simulation analysis method for heavy-haul railway ballast compaction disease according to an embodiment of the present invention;

[0029] Figure 5 It is a schematic diagram of calculation results of the formula shown in the example of the embodiment of the present invention;

[0030] Figure 6 The bar graph corresponding to the test result of case 1 of the embodiment of the present invention;

[0031] Figure 7 This is a bar chart of the test results of test case 2 of the embodiment of the present invention;

[0032] Figure 8 This is a bar chart of the results of test case 3 of the embodiment of the present invention;

[0033] Fig. 9 This is a bar chart of the results of test case 4 of the embodiment of the present invention;

[0034] Fig.10 A generalized function image for an embodiment of the present invention;

[0035] Fig.11 This is a diagram showing the degree of fit between the generalization function and the test data set according to an embodiment of the present invention. DETAILED DESCRIPTION

[0036] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0037] Example

[0038] Simulation analysis method of heavy-duty railway ballast compaction disease based on ping-pong model, such as Figure 4 As shown, the method includes:

[0039] Step S1, constructing a "ping-pong model" based on compaction disease based on the compaction disease of the heavy-duty railway ballast bed, wherein the compaction disease of the heavy-duty railway ballast bed includes: severe compaction with soil, moderate compaction with soil, severe compaction without soil, and moderate compaction without soil; calculating the overall equivalent dielectric constant based on the "ping-pong model" based on the constructed "ping-pong model" .

[0040] S11. This embodiment relates to the technical field of railway track bed simulation. Specifically, it provides a new simulation model, called "ping-pong model", which is used to simulate the physical and dielectric properties of railway track bed.

[0041] The design of the "ping-pong model" is inspired by the structure and material properties of the actual railway track bed. The model has a size of 1.0m x 0.9m x 0.0025m and is composed of three balls with different diameters, representing ballast with different degrees of wear. Among them, the 6-cm diameter ball simulates the top layer of ballast with less wear; the 4-cm diameter ball represents the slightly worn ballast; and the 2-cm diameter ball is used to simulate the part with severe wear that may cause the track bed to harden.

[0042] The equivalent dielectric constant is a key parameter to characterize the dielectric properties of the model. The present invention obtains the travel time t inside the ballast and the height d inside the model ballast through simulation results, and then calculates the propagation speed v=d / t in the medium, and finally obtains the equivalent dielectric constant according to ε=c / v, where c0 is the speed of light in a vacuum.

[0043] During the modeling process, different relative dielectric constants were set for each sphere to simulate the dielectric properties of different materials. The relative dielectric constant of the larger diameter sphere, which simulates normal ballast, is set to 5, a conservative value based on the relative dielectric constant of granite, which ranges from 5 to 8. For the smallest size sphere simulating the area where the railway track bed is damaged, the relative dielectric constant is set to 15 or 30, depending on the severity of the damage, to distinguish different degrees of compaction.

[0044] The "ping-pong model" of the present invention not only simulates the structure of the actual roadbed in terms of geometric dimensions, but also accurately simulates the physical and dielectric properties, providing an effective tool for the detection, maintenance and research of heavy-duty railway roadbeds. Through this model, the physical state and dielectric properties of the hardening disease of the heavy-duty railway roadbed can be better understood, providing a new perspective and method for the health management and fault diagnosis of the heavy-duty railway roadbed.

[0045] S12. Calculation of equivalent dielectric constant based on the model itself

[0046] Calculation method of relative dielectric constant of the model: First, calculate various necessary parameters, including: the overall volume of the model; the diameter, relative dielectric constant, quantity, and arrangement of the three types of small balls, large, medium, and small, which are set by yourself during modeling; if the influence of soil is considered, the relative dielectric constant and placement of the soil in the soil-containing part also need to be calculated.

[0047] Secondly, according to the parameter values ​​obtained in the first step, symbols are used to correspond to the parameters for convenience, as shown in Table 1 (unless otherwise specified, the symbols in the content of the present invention shall prevail).

[0048] Table 1

[0049] ;

[0050] The individual volumes of spheres of different sizes are calculated using the sphere volume formula:

[0051] ;

[0052] Based on the individual volumes of the balls of different sizes, multiply them by their respective numbers to get the overall volume of balls of different sizes, and then divide it by the overall volume of the model V m , and obtain the normalized component coefficients N1, N2, and N3 of each model. Similarly, S / V m The normalized component coefficient N4 of the soil is calculated. Obviously, the proportion of air can be calculated by the following formula:

[0053] .

[0054] The relative permittivity of air is ε0, which is set to 1 by default.

[0055] Calculate two important parameters: the overall equivalent dielectric constant of the "ping-pong model" and the equivalent dielectric constant of the plate-bonded area of ​​the "ping-pong model" It is worth noting that when calculating the overall equivalent dielectric constant, it can be directly calculated based on the above normalized component coefficient N m When calculating the equivalent dielectric constant of the hardened area, it is necessary to renormalize the elements in the area. Taking the soil-containing case as an example, a simple method is as follows:

[0056] ;

[0057] This operation can obtain the new normalized component coefficient N3 of the elements in the compacted area (the ball with the smallest diameter, soil, and air) ’ 、N4 ’ 、N5 ’ , and then substitute it into the subsequent formula for calculation.

[0058] The overall equivalent dielectric constant of the "Ping-Pong Model" and the equivalent dielectric constant of the plate-bonded area of ​​the "ping-pong model" The calculation formulas are as follows:

[0059] ;

[0060] ;

[0061] Through the above operations, the overall equivalent dielectric constant of the "ping-pong model" based on the four conditions of "severe soil compaction", "moderate soil compaction", "no severe soil compaction" and "no moderate soil compaction" can be obtained respectively. and the equivalent dielectric constant of the plate-bonded area of ​​the "ping-pong model" Two columns of parameters, which are particularly important in subsequent analysis and processing.

[0062] The exemplary modeling table tennis model provided by the present invention is shown in FIG. Figure 1 As shown in the figure, the basic structure is 2 rows of large balls with a diameter of 0.06m, 12 in each row; 3 rows of medium balls with a diameter of 0.04m, 18 in each row; small balls with a diameter of 0.02m are placed in the lower left corner of the overall model to indicate the diseased area, 6 rows, 14 in each row, and the rest are regularly filled with medium balls with a diameter of 0.04m. Figure 1 In the middle model, the rectangle is used to represent the soil, which surrounds the area where the small ball is located, and is used to study the influence of soil. In the setting of relative dielectric constant, the large and medium balls are set to 5, and the small balls are set to 30 or 15 to distinguish the degree of compaction. The soil is set to 11, and the air is set to 1 by default. The calculation steps are shown in the above operation, and the results can be obtained as shown in Table 2:

[0063] Table 2

[0064] ;

[0065] for For example, the calculation method of this parameter is based on the characteristics of the model itself. The diameters of the three types of balls, large, medium and small, their components, relative dielectric constants, air volume and other factors will be taken into consideration. The calculations are all independent of simulation and can be obtained based on the modeling in the first step. Rather than ,because Taking into account the overall characteristics of the model, The influence of many other parts will be ignored. Therefore, this embodiment uses This parameter is used for subsequent steps.

[0066] Step S2: Use gprMax to simulate the "ping-pong model", and calculate the equivalent dielectric constant of the slab area based on the gprMax simulation based on the simulation results. .

[0067] S21, gprMax simulation parameter setting: First, the basic parameters of the simulation platform gprMax are set. The specific basic parameters of the example given in the present invention are shown in Table 3:

[0068] Table 3

[0069] ;

[0070] After the basic parameters are set, you need to build the .in file model parameters. Next, the corresponding model settings for the model diagram shown above are given, as shown in Table 4:

[0071] Table 4

[0072] ;

[0073] Based on the above model parameter settings and position settings, running 160 gprMax simulations can obtain 160 Ascan single-channel time domain waveforms, and using the "tools.outputfiles_merge" command to obtain the corresponding Bscan images.

[0074] S22, preliminary processing of gprMax simulation data: The radar echo parameters obtained in the above steps are obtained by scanning the entire model from left to right. However, both simulation analysis and actual engineering processing will not be analyzed and processed based on the entire model. Therefore, the present invention performs preliminary processing on the simulation data obtained by gprMax here, that is, obtaining a single-channel time domain average waveform in a specific area. The specific steps are as follows:

[0075] S221. Divide the area. Obviously, in the model diagram described above, it can be clearly found that the area where the small ball is located is the roadbed compaction disease area set by the "ping-pong model", so the center of gravity should be placed here when dividing the area. Considering that the left and right sides are in contact with medium-sized balls, in order to reduce the edge effect, the selected range should be slightly narrower than the overall compaction area width; in order to enhance the contrast, the non-compacted area on the right side of the model also needs to be divided into an area of ​​the same width to form a contrast image of "compacted area-non-compacted area".

[0076] S222, calculate the average. In S221, the hardening area and the sub-hardening area have been divided, and each area contains n Ascan waveforms. Based on MATLAB, the time domain average single waveform of the n waveforms in the corresponding area is obtained, such as Figure 2As shown, as a typical waveform of the area, it has the typical characteristics of the divided area. At the same time, it is more convenient to compare and analyze only a single waveform.

[0077] Comparison waveforms of the "compacted area - non-compacted area" of the soil-severe compaction model in this example Figure 2 S223, radar spectrum processing, such as Figure 3 As shown in the figure, in the above steps, only a single waveform is processed, and Bscan plays an irreplaceable role in analyzing the overall target characteristics. It is necessary to comprehensively analyze the three aspects of "model - time domain waveform - radar spectrum". According to the obtained Bscan image, considering the time and space coordinates, it is easy to preliminarily locate the position of the compaction area in the spectrum and mark it for subsequent analysis and processing. Taking the "heavy compaction with soil" as an example, it can be obtained Figure 3 The coordinated analysis image of "model - time domain single-channel average waveform - Bscan spectrum" shown plays a very important role in the feature extraction and analysis of electromagnetic forward modeling results.

[0078] S23. Calculation of equivalent dielectric constant based on gprMax simulation results.

[0079] In the above steps, the time domain single-channel average waveforms in different regions have been obtained. By extracting them separately, it is easy to obtain obvious peaks and troughs in the waveform, which correspond to the various interfaces in the model, such as Figure 3 As shown by the straight line in . Extract time information. In fact, each straight line position represents a sampling point position, and the sampling point contains time information. Assuming that the sampling point position corresponding to the interface (straight line) is D, the result of the entire gprMax simulation is divided into N sampling points (affected by the size of the time window opened), and the time window is set to T (ns), then the time t (ns) corresponding to the appearance of the interface can be calculated by the following formula:

[0080] ;

[0081] In this way, the time when each interface appears in the time domain can be obtained, which is very important for the subsequent calculation of the equivalent dielectric constant. Calculate the equivalent dielectric constant under different conditions. Based on the above operations, the time information of different regions under different conditions has been obtained. Here, the time information is based on two dividing lines to get a contained area, and each dividing line represents the time of its appearance, so the appearance time of this area can be obtained. If the expression method is required, it should be (t1, t2). It can basically be divided into 4 interfaces, namely: incident on the upper surface of the model, the interface between the large ball and the middle ball, the interface between the middle ball and the small ball, and the ejection model.

[0082] For the convenience of representation, the four surfaces are marked as F1, F2, F3, and F4 in order, and the corresponding time information is t1, t2, t3, and t4. The time information here is the pointer. For each interface F, it represents the time t when this surface appears, that is, the corresponding relationship between F and t. According to the following formula, the gprMax simulation overall equivalent dielectric constant can be obtained respectively: 、gprMax simulation of equivalent dielectric constant of plate junction area There are two important parameters. Among them, the incident on the upper surface of the model F1, the interface between the large sphere and the middle sphere F2, the interface between the middle sphere and the small sphere F3, and the ejection of the bottom surface of the model F4. For F4, when modeling, there will be air between the bottom surface of the ping-pong model and the boundary in the entire space, and this place is also counted as an interface F4:

[0083] ;

[0084] The parameters are explained as follows: c0 is the speed of light in vacuum, which is 3x10 ^8 (m / s); d1(m) represents the depth of the hardened area, which can be directly calculated based on the constructed model; D(m) represents the depth of the entire model. According to this formula, the equivalent dielectric constant of the entire gprMax simulation can be calculated: 、gprMax simulation of equivalent dielectric constant of plate junction area These two important parameters provide a concrete understanding of the basic characteristics obtained from the simulation.

[0085] The basic information of this example model is as described above. After running the gprMax simulation, 160 Ascan time-domain waveforms are obtained. The four models of "heavy compaction with soil", "moderate compaction with soil", "heavy compaction without soil", and "moderate compaction without soil" are divided into compaction areas and non-compaction areas. Then, the waveforms in different areas are averaged, and the position of the interface is marked according to the single-channel time-domain average waveform. The sampling point information is extracted to obtain the corresponding appearance time, which can be summarized as shown in Table 5:

[0086] Table 5

[0087] ;

[0088] Applying the formula in step 3 of the above calculation method, taking the soil-containing model as an example, the gprMax simulation overall equivalent dielectric constant can be obtained as shown in Table 6 、gprMax simulation of equivalent dielectric constant of plate junction area Two important parameters:

[0089] Table 6

[0090] ;

[0091] Based on this embodiment, In addition to responding to simulation results, the proposal also has the purpose of corresponding to the two parameters of the model. That is, the two parameters of "overall" and "hardened area" are obtained according to the model, and the two parameters of "overall" and "hardened area" are also obtained according to the simulation results. These two parameters are compared with each other, and this set of corresponding relationships is also used in subsequent analysis. It is the equivalent dielectric constant of the hardened area obtained based on the simulation results. Therefore, this data is relatively accurate and reflects whether the hardening disease occurs and the severity of the disease. Therefore, it can basically be considered as the true value of the analysis. In fact, the formula The closer The more accurate.

[0092] Step S3: Based on the overall equivalent dielectric constant of the “ping-pong model” Calculate the prediction formula of the equivalent dielectric constant of the slab-bonded area simulated by gprMax, and compare the prediction results with the equivalent dielectric constant of the slab-bonded area simulated by gprMax A comparison is made to obtain the comparison results, and based on the comparison results, a simulation analysis of the compaction disease of the heavy-duty railway ballast is completed.

[0093] S31. After the above operations, a relatively complete analysis and feature extraction of the feasibility and sensitivity of the "ping-pong model" for heavy-duty railway track bed compaction disease was conducted from the perspective of electromagnetic forward modeling. The four important parameters mentioned above were specifically analyzed and summarized in Table 7:

[0094] Table 7

[0095] ;

[0096] Specifically, the two columns on the left of the four columns of data are the overall equivalent dielectric constants of the "ping-pong model" , "Ping-Pong Model" equivalent dielectric constant of the plate-bonded area The numerical values ​​of these two parameters are based on the industry's conventional calculation method of equivalent dielectric constant, which is also the widely used method for judging the degree of compaction of heavy-duty railway ballast.

[0097] However, according to the results obtained after gprMax simulation, it can be seen that the equivalent dielectric constant obtained based on the calculation method of this model itself is often inaccurate. From the results, it can also be found that there are relatively large differences from the simulation results.

[0098] S32. Optimizing the prediction formula for the calculation method of equivalent dielectric constant: In order to solve this problem, the present invention proposes a "model-simulation" prediction formula for relative dielectric constant of the slab region based on the "ping-pong model". The specific form of the formula is as follows:

[0099] ;

[0100] First, explain the parameters of the formula: is the relative dielectric constant of soil, , is the relative permittivity of the large sphere, is the relative dielectric constant of the sphere, is the relative dielectric constant of the small sphere. This is the overall equivalent dielectric constant of the "ping-pong model".

[0101] As shown in the formula, the input parameters are: the relative dielectric constant values ​​of the large, medium and small balls set by the user when building the "ping-pong model", according to The calculation formula is not difficult to find. The volume or arrangement of the three balls, such as the large, medium and small balls, will eventually affect The size of , so this formula can fully take into account the various characteristics of the ping-pong model itself.

[0102] The output parameters are The meaning of this parameter is that when the user builds a custom model, the above-mentioned So we can substitute it into the formula to get , It represents the numerical prediction of the equivalent dielectric constant of the slab region of the model. The prediction results are as follows: Figure 5 shown.

[0103] S33. Calculation results based on the prediction formula of the example: Taking the example provided by the present invention as an example, substituting it into the above formula, the results shown in Table 8 can be obtained:

[0104] Table 8

[0105] ;

[0106] The error rate is calculated as follows:

[0107] ;

[0108] Plotting the table data, we can get Figure 5 result.

[0109] S34. Analysis of the role of prediction formula based on the "ping-pong model"

[0110] First, the role of the prediction formula. In short, when the user builds a heavy-duty railway track bed compaction disease model based on the "ping-pong model", the formula can be used to quickly calculate the equivalent dielectric constant of the most important compaction area in the model. From the results in Table 8, the error rate is around 3% or less, and the prediction accuracy is very high.

[0111] The value and significance of the formula are summarized as follows: 1. From the calculation results of the formula, the severity of the hardened area can be evaluated directly based on the results obtained by the formula calculation, that is, the connection between the model and the simulation / actual measurement results is complete, so that the construction of the model is not just for simulation, but also has a good effect and a large space for guiding the problems in actual engineering. 2. Simplify the process and improve efficiency. After applying the formula, the user does not need to perform a complex simulation process, and can directly obtain the results through the formula calculation. This process greatly saves computing resources and time. 3. More flexible and easy to verify. Compared with running complex simulation models, formulas are easier to derive and verify mathematically, which also helps to improve the accuracy and credibility of predictions. In addition, the formula can be continuously adjusted according to the new heavy-duty railway roadbed environment to adapt to the ever-changing environment, and is very flexible in use. 4. Potential application scenarios, application in engineering can reduce the hardware and software resources required for simulation and reduce engineering costs. For scenarios with timeliness requirements, the formula calculation method has more advantages than gprMax or other platform simulations.

[0112] Step S4, performing tolerance analysis on the gprMax simulation compaction area equivalent dielectric constant prediction formula, characterizing the "ping-pong model" based on the tolerance analysis results, obtaining characterization results, and realizing simulation and analysis of heavy-duty railway ballast compaction diseases based on the ping-pong model.

[0113] Tolerance testing is a technique to evaluate the performance and reliability of a system or product under parameter changes. It is used to determine the allowable range of variation of components or parameters and evaluate the impact of these changes on the overall system performance. The purpose of tolerance testing is to ensure that the product meets performance and safety requirements under specified operating conditions, while optimizing the design, improving product reliability, and reducing the risk of failure.

[0114] S41. (1) The steps of tolerance capability test are as follows: 1. Define the analysis target. For the components of the "ping-pong model", it is possible to formulate changes in the compacted area alone (the relative dielectric constant increases proportionally due to precipitation or decreases proportionally due to dryness), changes in the non-compacted area alone, and changes in the compacted area and the non-compacted area together. Taking into account the actual project, different heavy-duty railway ballast conditions and ground problems are different, and the arrangement of large and medium balls can be changed, such as adjusting the number of rows, columns, density, etc.; the latter takes into account the different laying materials and daily use of ballast, and the relative dielectric constants of large, medium and small balls can be changed to adapt to different problems. 2. Establish a tolerance capability test model. For the above-mentioned test conditions, the "ping-pong model" is rebuilt respectively, and the arrangement of the balls and the relative dielectric constant in the non-compacted area are changed, and this is used as a new model for calculation. 3. Collect and analyze relevant data. Based on the above research methods and the calculation methods of each important parameter, they are applied to the four new models for generalization ability testing, and new data in the format shown in Table 8 are obtained for subsequent analysis and processing. 4. Based on the results, the tolerance capacity of the entire process and model formula is analyzed.

[0115] S42, tolerance capability test model construction: Test case 1: change the composition of the non-hardened area. The changes in test case 1 compared with the initial situation are: one row of large balls is added while the number of columns, diameter and relative dielectric constant remain unchanged; one row of medium-sized balls is also added on the original basis. This is used as a generalized test case 1 to evaluate and test different heavy-load railway trackbed conditions.

[0116] The parameter calculated here is still the overall equivalent dielectric constant of the "ping-pong model" Equivalent dielectric constant of the plate-bonded area in the "ping-pong model" , the calculation method is the same as above, and the calculation results are listed here, as shown in Table 9:

[0117] Table 9

[0118] ;

[0119] After running the gprMax simulation based on the above process, the gprMax simulation overall equivalent dielectric constant shown in Table 10 can also be calculated The equivalent dielectric constant of the plate junction area simulated by gprMax These two important parameters are:

[0120] Table 10

[0121] ;

[0122] Formula calculation results and overall data integration analysis: Similarly, based on the obtained model parameters, they can be substituted into the formula to obtain a set of formula calculation results for test case 1 for comparison, as shown in Table 11:

[0123] Table 11

[0124] ;

[0125] Plot Table 11, as shown in Figure 6 As shown. Analyzing the above results, the most obvious thing is that the error rate has increased significantly compared with the example case, but it is below 10%, and there is no significant deviation from the actual simulation results. From the specific numerical values, the relative dielectric constant difference is 3 or less. It can be seen that under the background of test case 1, the modeling analysis method and prediction formula of the "ping-pong model" have good results.

[0126] S43, test case 2: changing the relative dielectric constant of the non-slab area. In test case 2, the relative dielectric constant of the non-slab area is changed.

[0127] Specifically, the relative dielectric constants of the large and medium balls are set to 6, which is a relatively large value of the relative dielectric constant in the ballast composition material. On this basis, the tolerance capability test model 2 is analyzed and studied.

[0128] Parameter calculation based on the model itself: The parameter calculated here is still the overall equivalent dielectric constant of the "ping-pong model" Equivalent dielectric constant of the plate-bonded area in the "ping-pong model" The calculation method is the same as above. The calculation results are listed here, as shown in Table 12.

[0129] Table 12

[0130] ;

[0131] After running the gprMax simulation based on the above process, the gprMax simulation overall equivalent dielectric constant shown in Table 13 can also be calculated The equivalent dielectric constant of the plate junction area simulated by gprMax These two important parameters are:

[0132] Table 13

[0133] ;

[0134] Similarly, based on the parameters of the obtained model itself, they can be substituted into the formula to calculate a set of formula calculation results for test case 2 for comparison, as shown in Table 14.

[0135] Table 14

[0136] ;

[0137] Table 14 is plotted, as shown in Figure 7 As shown in the figure, by analyzing the above results, we can see that the error rate has a large fluctuation in the case of extreme test conditions, but the basic focus is only on the case of "moderate soil compaction", while the errors in other cases are basically at a low level. It can be seen that in the context of test condition 2, the modeling analysis method and prediction formula of the "ping-pong model" still have a good effect.

[0138] S44. In test case 3, the relative dielectric constant at the hardened area is changed. Specifically, the relative dielectric constant of the ball is set to 36 and 18 according to the degree of hardening. On this basis, the tolerance capability test model 3 is analyzed and studied. The parameter calculated here is still the overall equivalent dielectric constant of the "ping-pong model". Equivalent dielectric constant of the plate-bonded area in the "ping-pong model" The calculation method is the same as above. The calculation results are listed here, as shown in Table 15.

[0139] Table 15

[0140] ;

[0141] After running the gprMax simulation based on the above process, the gprMax simulation overall equivalent dielectric constant shown in Table 16 can also be calculated The equivalent dielectric constant of the plate junction area simulated by gprMax These two important parameters are:

[0142] Table 16

[0143] ;

[0144] Similarly, based on the parameters of the obtained model itself, they can be substituted into the formula to obtain a set of formula calculation results for test case 3 for comparison, as shown in Table 17.

[0145] Table 17

[0146] ;

[0147] Plot Table 17, as shown in Figure 8 shown.

[0148] S44. In test case 4, the relative dielectric constants in the compacted area and the non-compacted area are changed at the same time. Specifically, according to the actual project, the entire roadbed will become wet under the influence of rainfall, which will increase the overall relative dielectric constant. Therefore, for this situation: the relative dielectric constants of the small balls are set to 36 and 18 respectively according to the degree of compaction, indicating that the relative dielectric constants of the large and medium balls in the non-compacted area are set to 6 (in terms of the increase ratio, both are increased by 20% on the original basis). On this basis, the analysis and research of tolerance capability test model 4 is carried out.

[0149] The parameter calculated here is still the overall equivalent dielectric constant of the "ping-pong model" Equivalent dielectric constant of the plate-bonded area in the "ping-pong model" The calculation method is the same as above, and the calculation results are listed here, as shown in Table 18.

[0150] Table 18

[0151] ;

[0152] After running the gprMax simulation based on the above process, the gprMax simulation overall equivalent dielectric constant shown in Table 19 can also be calculated Simulate the equivalent dielectric constant of the plate junction area with gprMax These two important parameters are:

[0153] Table 19

[0154] ;

[0155] Similarly, based on the parameters of the obtained model itself, they can be substituted into the formula to obtain a set of formula calculation results for test case 4 for comparison, as shown in Table 20.

[0156] Table 20

[0157] ;

[0158] Table 20 is plotted, as shown in Fig. 9 shown.

[0159] After analyzing and processing test cases 1 to 4, the following conclusions can be drawn:

[0160] 1. It has demonstrated excellent performance on multiple independent data sets. Regardless of the test situation, the error range of the prediction formula is at a low level, reaching about 10% in a few cases, and only in one extreme case there is an error of 20%. In most common cases, the error rate calculated by applying the formula is below 10%, and the results show good accuracy.

[0161] 2. The results show consistency and reliability. In the face of different test directions, the presentation of the final results all followed the basic rules of the "ping-pong model" and showed strong consistency and reliability.

[0162] It can be seen that the prediction formula is built based on the example case, and the test case also follows the example case in the general structure of the model. In this context, the new models of the four test cases derived from the example model all show good results. By extension, the heavy-duty railway ballast compaction disease analysis and formula prediction based on the "ping-pong model" have a good tolerance range, which is sufficient to deal with various common problems in engineering.

[0163] Step S4: Based on the comparison result of step S3, a generalized function is used to fit the prediction result of the equivalent dielectric constant of the hardened area simulated by gprMax to obtain the simulation fitting result of the hardened disease of the heavy-duty railway ballast bed.

[0164] According to the encyclopedia, the original meaning of generalization ability refers to the adaptability of a machine learning model to fresh samples, that is, the performance of the model on data that has not been seen during the training process. A model with good generalization ability can learn universal rules from training data and apply these rules to new, unseen data to make accurate predictions or classifications.

[0165] In the present invention, a more general definition is adopted, that is, to examine the accuracy of the modeling method and the calculation results of the formula under the condition of changed conditions. In short, it is to change some parameters in the model based on the actual engineering of heavy-duty railway track bed and the actual situation, but still use the method and calculation formula of the present invention to perform calculation and analysis, observe the accuracy of the results, and then derive the generalization ability of the analysis method and model calculation formula.

[0166] Define the analysis objectives and scope. In the generalization ability test of the "ping-pong model", we are more concerned about whether the results obtained based on the modeling method of the "ping-pong model" are accurate and have generalization significance. The initial object set in the generalization ability test is the gprMax simulation result, because this is the most accurate evaluation standard for whether the ping-pong model's results on the degree of hardening are accurate.

[0167] 1. Establish a generalization capability model, such as Fig.10 As shown in Figure 1, this is a mathematical model used to describe the generalized characteristics of the above parameters in the process. Extracting the relative bulk dielectric constant of the gprMax simulation slab region For each value, select a suitable fitting function according to its characteristics and analyze its changing rules or characteristics.

[0168] 2. The test results obtained are: a generalized function that conforms to the "ping-pong model" for the problem of heavy-duty railway track bed compaction.

[0169] Based on the above operation, the relative bulk dielectric constant of the gprMax simulation slab region is obtained. Numerical scatter plots are drawn, and nonlinear functions that conform to the law are selected for fitting. It can be seen that the variation law of the sine function is fitted better. Therefore, the sine function is used as the specific function form of the generalized function, as shown below:

[0170] ;

[0171] For the value of the undetermined parameter, it is necessary to consider the specific value. Now a generalized function that conforms to the "ping-pong model" for the problem of heavy-duty railway ballast hardening is given, and its expression is as follows:

[0172] ;

[0173] Its specific function graph is as follows Fig.10 shown.

[0174] Now let's explain it in detail. First, the independent variable x is abstracted from the specific research object, which is a natural number sequence with a step of 1, used to represent the four specific research situations of "severe soil compaction", "moderate soil compaction", "severe soil compaction without soil", and "moderate soil compaction without soil". It is abstracted as the horizontal axis to facilitate function construction; the y value is the corresponding value of the fitting function, and the difference from the specific numerical value is the difference between the good and bad fitting degree.

[0175] Now, we only take the test data obtained in the present invention as an example to check the generalization ability of the generalization function. The fitting results are as follows: Fig.11 As shown in the figure, first further explain the elements in the figure. Each green box represents a situation, from left to right: initial situation, test situation 1, test situation 2, test situation 3, test situation 4, and each box has 4 numerical points (the legend is a sphere), in order: heavy compaction with soil, moderate compaction with soil, heavy compaction without soil, moderate compaction without soil. The solid line is the generalized function mentioned above.

[0176] Based on the arrangement of data points as shown in the figure, the following rules can be summarized: 1. Fig.11As shown in the dotted line in the middle, an average line is drawn on this sine function to divide the upper and lower areas. Then this dividing line of the generalized function that conforms to the "ping-pong model" for the problem of heavy-duty railway track bed compaction disease can well indicate the degree of compaction. Specifically: above the horizontal line is severe compaction, and below the horizontal line is moderate compaction and below, which points out a fairly fast and accurate way to divide the degree of compaction, providing great convenience for specific engineering applications. 2. At the same time, for the dotted line connecting 2 data points, the two points connected are of the same degree of compaction, but the soil content is different. The data point at the high end represents the soil content, and the other end represents the soil-free condition. This represents a direct law of data: the equivalent dielectric constant of the compaction area with soil content will be greater than that without soil. 3. For the two dotted lines in the same box data, it can also be clearly seen that the severe compaction above the center line is much higher than the moderate compaction below the center line, reflecting the embodiment of the degree of compaction in specific data: the heavier the degree of compaction, the higher the image. 4. Finally, by observing the distribution of data points and generalization functions, we can see the degree of fit of the specific values ​​and generalization functions based on the test conditions. The determination coefficient R2 calculated by MATLAB is 0.904, and the degree of fit is quite good, which also indicates that the fitting function can well describe the simulation result law of this "ping-pong model".

[0177] Through the above research on generalization ability, it can be seen that the generalization function that conforms to the "ping-pong model" for the problem of heavy-duty railway track bed compaction has a very good generalization ability, and has good adaptability in the modeling method and research and analysis method based on the "ping-pong model".

[0178] Based on this generalization function, we can get the approximate variation range curve of the electromagnetic forward simulation value of the "ping-pong model", and the degree of hardening can be intuitively distinguished from the curve, which has considerable value and significance both from the perspective of theoretical research and from the perspective of specific guidance of engineering applications. Regarding the role of the generalization function and the discussion on generalization in step 5, in order to clarify its significance and value, further explanation is needed here.

[0179] In the process of building the electromagnetic forward model, the generalization ability test is a key step. It is based on a pre-defined forward model for simulating the hardening of heavy-duty railway trackbeds: the "ping-pong model". Users can create different test cases by setting a series of typical values, such as the "initial case" and "test case" mentioned above. These test cases can generate corresponding data sets, from which users select key parameters: the equivalent dielectric constant of the gprMax simulation hardening area values ​​and arrange them in a coordinate system according to the group and test order.

[0180] By fitting these data with a sine function, a best fit curve, the generalization function, can be obtained. This function is a direct reflection of the model's characteristics, and it can describe the approximate distribution of the possible results of all simulation operations based on this model. In other words, operations and changes on the model will basically be reflected in the generalization function in the end. From the perspective of reverse application, the generalization function can not only characterize the characteristics of the model, but also has practical application value. Specifically, for example, when the degree of compaction of the heavy-duty railway track bed is difficult to directly judge, new test conditions can be simulated by adjusting the model parameters, and the degree of compaction can be judged according to the position of these new results on the generalization function. In addition, the generalization function can also be used for model verification and optimization. This method provides a quantitative means for evaluating and predicting compaction conditions, thereby providing decision support for maintenance and repair work.

[0181] In conclusion, the generalization function is a powerful tool that can not only describe the characteristics of electromagnetic forward modeling, but also provide guidance in practical applications, helping users to better understand and predict complex physical phenomena such as heavy-duty railway ballast compaction.

[0182] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A simulation analysis method for heavy-duty railway ballast compaction disease based on a ping-pong model, characterized in that: Methods include: Step S1, constructing a "ping-pong model" based on compaction disease based on the compaction disease of the heavy-duty railway ballast bed, wherein the compaction disease of the heavy-duty railway ballast bed includes: severe compaction with soil, moderate compaction with soil, severe compaction without soil, and moderate compaction without soil; calculating the overall equivalent dielectric constant based on the "ping-pong model" based on the constructed "ping-pong model" ; Step S2: Use gprMax to simulate the "ping-pong model", and calculate the equivalent dielectric constant of the slab region based on the gprMax simulation based on the simulation results. , specifically including: The time information of the simulation results is divided into interfaces: the interface F3 between the middle sphere and the small sphere and the bottom surface F4 of the ejection model. The corresponding time information based on F3 and F4 is: and ,based on and The equivalent dielectric constant of the entire simulation calculated from the gprMax simulation : ； in, is the speed of light in vacuum, is the depth of the hardened area; Step S3: Based on the overall equivalent dielectric constant of the "ping-pong model" Calculate the prediction formula of the equivalent dielectric constant of the slab-bonded area simulated by gprMax, and compare the prediction results with the equivalent dielectric constant of the slab-bonded area simulated by gprMax A comparison is made to obtain the comparison results, and based on the comparison results, a simulation analysis of the compaction disease of the heavy-duty railway ballast is completed.

2. The simulation analysis method for heavy-duty railway track bed compaction disease based on the ping-pong model according to claim 1 is characterized in that: The simulation analysis method also includes step S4, based on the comparison result of step S3, using a generalized function to fit the prediction result of the equivalent dielectric constant of the gprMax simulation hardening area to obtain the simulation fitting result of the hardening disease of the heavy-duty railway track bed.

3. The simulation analysis method for heavy-duty railway track bed compaction disease based on the ping-pong model according to claim 1 is characterized in that: In step S1, the modeling process of the "ping-pong model" specifically includes: Three balls with different diameters were used to form ballast models with different degrees of wear in a size of 1.0 m × 0.9 m, and the generated ballast models were used as "ping-pong models". A large ball with a diameter of 6 cm was used to simulate the ballast with less wear on the top layer, a medium ball with a diameter of 4 cm was used to simulate the ballast with slight wear in the middle layer, and a small ball with a diameter of 2 cm was used to simulate the severely worn part of the roadbed at the bottom.

4. The simulation analysis method for heavy-duty railway track bed compaction disease based on the ping-pong model according to claim 2 is characterized in that: In step S1, the overall equivalent dielectric constant based on the constructed "ping-pong model" is calculated based on the "ping-pong model". The process specifically includes: ； Among them, N1 is the normalized component coefficient of the large sphere, N2 is the normalized component coefficient of the medium sphere, N3 is the normalized component coefficient of the small sphere, N4 is the normalized component coefficient of the soil, and N5 is the proportion of air. is the relative dielectric constant of air, is the relative dielectric constant of the large sphere, is the relative dielectric constant of the sphere, is the relative dielectric constant of the small sphere, is the relative dielectric constant of the soil.

5. The simulation analysis method for heavy-duty railway track bed compaction disease based on the ping-pong model according to claim 1 is characterized in that: In step S2, the gprMax simulation parameters are set as follows: the forward model size is set to 1.0×0.9, in m; the spatial grid step position is 0.0025, in m; the time window is set to 15, in ns; the initial transmitting antenna coordinates are set to (0.03, 0.785), in m; the initial receiving antenna coordinates are set to (0.05, 0.785), in m; The antenna step distance is set to 0.006, in meters; the excitation source type is set to ricker; the number of test channels is set to 160; the antenna frequency is set to 1.5, in GHz; the distance from the upper surface of the roadbed to the antenna is set to 0.3, in meters.

6. The simulation analysis method for heavy-duty railway track bed compaction disease based on the ping-pong model according to claim 1 is characterized in that: In step S3, according to the overall equivalent dielectric constant of the "ping-pong model", The contents of the prediction formula for the equivalent dielectric constant of the gprMax simulation slab region specifically include: ； in, is the predicted value of the equivalent dielectric constant of the junction area, is the relative dielectric constant of soil, , is the relative permittivity of the large sphere, is the relative dielectric constant of the sphere, is the relative dielectric constant of the small sphere.

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