Railway space line shape considering intelligent rail wear prediction method and system

Abstract

The application discloses a kind of steel rail wear intelligent prediction method and system considering railway space line shape, and the method comprises the following steps: S1, based on vehicle structure characteristic parameters and track structure characteristic parameters, establish vehicle-track coupling dynamics model;S2, based on vehicle-track coupling dynamics model, establish steel rail wear calculation model, calculate the inside and outside steel rail wear value under different track space line shape parameters to construct steel rail wear sample data set;S3, construct steel rail wear prediction artificial neural network model, and train steel rail wear prediction artificial neural network model using steel rail wear sample data set;S4, optimize the trained steel rail wear prediction artificial neural network model, obtain final prediction model;S5, using final prediction model, realize the prediction of railway steel rail wear.The application establishes railway space line shape parameter-steel rail wear prediction model, and efficiently and accurately obtains steel rail wear under different horizontal and vertical section line shape parameters and combination.

Description

Technical Field

[0001] This invention relates to the field of rail wear prediction technology, specifically to an intelligent prediction method and system for rail wear that takes into account the spatial alignment of the railway. Background Technology

[0002] With increasing pressure on urban transportation operations in my country, the wear and tear on subway rails is becoming increasingly severe. Rail wear leads to changes in wheel-rail contact geometry, which in turn affects the stability of train dynamic performance, reduces passenger safety and comfort, and increases maintenance costs. Wheel-rail contact is the fundamental factor influencing rail wear, and the railway's spatial alignment has a significant impact on this relationship. A reasonable combination of horizontal and vertical alignment parameters can significantly reduce rail wear. Therefore, if the impact of railway spatial alignment on rail wear is considered during the route selection and design phase, and the horizontal and vertical alignment parameters are optimized, rail wear can be reduced at its source, ensuring passenger safety and comfort while lowering maintenance costs.

[0003] Current methods for calculating rail wear primarily rely on vehicle-track coupled dynamics models, which are complex and computationally intensive. However, during route selection, multiple route options are typically designed and compared, especially with intelligent route selection methods. The iterative optimization process generates tens of thousands of route options, and calculating rail wear for each option using a vehicle-track coupled dynamics model results in unacceptably long computation times. Some researchers have addressed the issue of long computation times associated with relying on vehicle-track coupled dynamics models by establishing surrogate models, thus neglecting the influence of railway alignment on rail wear. Railway horizontal and vertical alignment parameters include horizontal alignment parameters such as curve radius, transition curve length, and superelevation, as well as vertical alignment parameters such as gradient and gradient algebraic difference. Significant differences in rail wear exist under different horizontal and vertical alignment parameters and their combinations. Therefore, it is necessary to comprehensively consider the impact of track horizontal and vertical profile parameters on rail wear, establish a mapping relationship between railway spatial alignment and rail wear, and efficiently and accurately obtain rail wear under different horizontal and vertical profile parameters and combinations.

[0004] In response, this invention discloses an intelligent prediction method for rail wear, which establishes an artificial neural network model for predicting rail wear based on railway spatial alignment, explores the mapping relationship between railway spatial alignment and rail wear, and achieves efficient and accurate calculation of railway rail wear. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting rail wear that takes into account the spatial alignment of railways. A neural network model is constructed with railway spatial alignment parameters as input and inner and outer rail wear as output. Through training with a large amount of sample data, a mapping relationship between the model input and output is established, so as to achieve efficient and accurate acquisition of inner and outer rail wear under different railway spatial alignment parameters, and solve the problem of limited calculation time in calculating inner and outer rail wear by relying on vehicle-track coupled dynamics models.

[0006] To achieve the above objectives, the present invention provides the following solution:

[0007] A method for intelligent prediction of rail wear considering railway spatial alignment, comprising the following steps:

[0008] S1. Based on the vehicle structural characteristic parameters and the track structural characteristic parameters, establish a vehicle-track coupled dynamic model;

[0009] S2. Based on the vehicle-track coupled dynamics model, establish a rail wear calculation model, calculate the inner and outer rail wear values ​​under different track spatial alignment parameters, and construct a rail wear sample dataset;

[0010] S3. Construct an artificial neural network model for predicting rail wear, and train the artificial neural network model for predicting rail wear using the rail wear sample dataset;

[0011] S4. Optimize the trained artificial neural network model for predicting rail wear to obtain the final prediction model;

[0012] S5. Using the final prediction model, the prediction of railway rail wear is realized.

[0013] Preferably, the vehicle structural characteristic parameters include: frame mass, frame position, frame rotational inertia, vehicle primary suspension stiffness, vehicle secondary suspension stiffness, bogie primary damping parameter, bogie secondary damping parameter, traction rod longitudinal stiffness, and anti-hunting damper damping; the track structural characteristic parameters include: fastener stiffness, concrete support layer thickness, CA mortar elastic modulus, and track spatial alignment parameters, wherein the track spatial alignment parameters include: circular curve radius, circular curve length, transition curve length, superelevation, gradient, gradient algebraic difference, and other horizontal and vertical profile alignment parameters.

[0014] Preferably, the steps for calculating the wear values ​​of the inner and outer rails include:

[0015] S201, Input track spatial alignment parameters, rail profile parameters, vehicle profile parameters, and total weight;

[0016] S202. Calculate wheel-rail contact conditions based on vehicle-track coupled dynamics model;

[0017] S203. Calculate the depth of rail wear within the wheel-rail contact patch based on wheel-rail contact conditions and rail wear calculation model;

[0018] S204. Update rail profile based on rail wear depth;

[0019] S205, Repeat S202-S204 until the maximum number of iterations is reached and then terminate;

[0020] S206. Obtain the wear values ​​of the inner and outer rails.

[0021] Preferably, the rail wear prediction artificial neural network model includes: an input layer, an output layer, and a hidden layer. The input layer consists of track spatial linear parameters, including: the radius R of the circular curve and the length L of the circular curve. y The parameters include: transition curve length l0, superelevation h, front slope i1, rear slope i2, and algebraic difference of slope Δi; the output layer is the rail wear value, including: inner rail wear value V. w1 Outer rail wear value V w2 The number of neurons in the hidden layer is determined using an empirical formula, and the optimal number of neurons in the hidden layer is determined through trial and error. The empirical formula is as follows:

[0022]

[0023] In the formula, H is the number of hidden layer nodes; n is the number of input layer nodes; m is the number of output layer nodes; and a is an integer from 1 to 10.

[0024] Preferably, the method for training the rail wear prediction artificial neural network model includes:

[0025] S301. Normalize the data using the "maximum-minimum" normalization principle;

[0026] S302. Initialize the weights and thresholds of the artificial neural network, input the normalized data into the artificial neural network for forward propagation, use the Sigmoid function as the activation function to calculate and output the calculated value of the current sample.

[0027] S303, Backpropagation of error: Based on the error between the calculated value and the true value of the current sample, calculate the error gradient term of the output layer neuron and the error gradient term of the hidden layer neuron.

[0028] S304. Based on the calculation results of the error gradient terms of each neuron in the hidden layer and the output layer, update the weights between the hidden layer and the output layer, the weights between the input layer and the hidden layer, the threshold of each neuron in the output layer, and the threshold of each neuron in the hidden layer.

[0029] S305. Repeat steps S302-S304 to train the model until the maximum number of training iterations or the error requirement is met, then terminate the training.

[0030] S306. Based on the test set data, the root mean square error (RMSE) is used to evaluate the final training effect of the model.

[0031] Preferably, the method for optimizing the artificial neural network model for predicting rail wear includes:

[0032] The Sobol sensitivity analysis method was used to analyze the spatial alignment parameters of the track and the wear V of the inner rail. w1 and outer rail wear V w2 The impact;

[0033] Based on the Sobol analysis results, track spatial alignment parameters that have little impact on the wear of the inner and outer rails were removed, and the model input layer data was adjusted to obtain the artificial neural network model for predicting the wear of the inner rail and the artificial neural network model for predicting the wear of the outer rail, respectively.

[0034] The model is trained based on the rail wear sample dataset to obtain an optimized artificial neural network model for predicting inner and outer rail wear. The mapping relationship between track spatial linear parameters and inner and outer rail wear is established to obtain the wear values ​​of inner and outer rails.

[0035] The present invention also provides an intelligent prediction system for rail wear that takes into account the spatial alignment of railways. The system is used to implement the above method and includes: a model building module, a dataset building module, a training module, an optimization module, and a prediction module.

[0036] The model building module is used to establish a vehicle-track coupled dynamics model based on vehicle structural characteristic parameters and track structural characteristic parameters.

[0037] The dataset construction module is used to establish a rail wear calculation model based on the vehicle-track coupled dynamics model, and to calculate the inner and outer rail wear values ​​under different track spatial alignment parameters to construct a rail wear sample dataset.

[0038] The training module is used to construct an artificial neural network model for predicting rail wear, and to train the artificial neural network model for predicting rail wear using the rail wear sample dataset.

[0039] The optimization module is used to optimize the trained artificial neural network model for predicting rail wear to obtain the final prediction model.

[0040] The prediction module is used to predict railway rail wear using the final prediction model.

[0041] Preferably, the vehicle structural characteristic parameters include: frame mass, frame position, frame rotational inertia, vehicle primary suspension stiffness, vehicle secondary suspension stiffness, bogie primary damping parameter, bogie secondary damping parameter, traction rod longitudinal stiffness, and anti-hunting damper damping; the track structural characteristic parameters include: fastener stiffness, concrete support layer thickness, CA mortar elastic modulus, and track spatial alignment parameters, wherein the track spatial alignment parameters include: circular curve radius, circular curve length, transition curve length, superelevation, gradient, gradient algebraic difference, and other horizontal and vertical profile alignment parameters.

[0042] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0043] This invention establishes a railway spatial alignment parameter-rail wear prediction model to efficiently and accurately obtain rail wear under different horizontal and vertical profile alignment parameters and combinations, providing guidance for railway alignment design. Attached Figure Description

[0044] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0045] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention;

[0046] Figure 2 The diagram shows the vehicle-track coupling dynamics model according to an embodiment of the present invention; wherein, (a) is a schematic diagram of the dynamics model of the vehicle bogie system; (b) is a schematic diagram of the dynamics model of the track structure; and (c) is a schematic diagram of the overall vehicle-track coupling dynamics model.

[0047] Figure 3 This is a structural diagram of the inner and outer rail wear prediction model according to an embodiment of the present invention;

[0048] Figure 4 The figures show the Sobol sensitivity analysis results of the inner and outer rail wear prediction models in this embodiment of the invention; where (a) is the Sobol analysis result of the inner rail wear prediction model; and (b) is the Sobol analysis result of the outer rail wear prediction model.

[0049] Figure 5 The figures show a comparison of the prediction effects of the inner and outer rail models before and after optimization in an embodiment of the present invention; where (a) is the comparison result of the inner rail wear prediction model before and after optimization; and (b) is the comparison result of the outer rail wear prediction model before and after optimization.

[0050] Figure 6These are the prediction results of the test set after the optimization of the inner and outer rail models in this embodiment of the invention; wherein, (a) is the prediction result of the test set of the inner rail wear prediction model; and (b) is the prediction result of the test set of the outer rail wear prediction model. Detailed Implementation

[0051] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0052] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0053] Example 1

[0054] This embodiment provides an intelligent prediction method for rail wear that considers the spatial alignment of railways, and its flowchart is shown below. Figure 1 As shown. The specific steps include:

[0055] S1. Based on the vehicle structural characteristic parameters and the track structural characteristic parameters, establish a vehicle-track coupled dynamic model.

[0056] This embodiment uses a subway Type A train as a prototype to establish a vehicle-track coupled dynamic model (model as follows). Figure 2 As shown in Table 1, a vehicle-track coupled dynamic model is established based on the structural characteristic parameters of the vehicle and track. The vehicle structural characteristic parameters include: frame mass, frame position, frame moment of inertia, primary suspension stiffness, secondary suspension stiffness, bogie primary and secondary damping parameters, traction rod longitudinal stiffness, and anti-hunting damper damping. The track structural characteristic parameters include: fastener stiffness, concrete support layer thickness, CA mortar elastic modulus, and track spatial alignment parameters. The modeling parameters for the Metro Type A car are shown in Table 1.

[0057] Table 1

[0058]

[0059] S2. Based on the vehicle-track coupled dynamics model, a rail wear calculation model is established, and the inner and outer rail wear values ​​under different track spatial alignment parameters are calculated to construct a rail wear sample dataset.

[0060] S201. Input the track spatial alignment parameters, rail profile parameters, vehicle profile parameters, and total weight.

[0061] Based on relevant subway design specifications, 260 different horizontal and vertical alignment parameters were set through random uniform sampling to generate 260 spatial alignment schemes and establish corresponding track models.

[0062] Based on actual subway operation conditions and subway design specifications, the train operating speed is set at 60 km / h, and the axle load (fully loaded) per car is 1.6 × 10⁻⁶. 4 The subway trains consist of 6 cars and run 40 times a day for 10 years, with a total of 3.504 × 10⁻⁶ wheels passing through them. 6 The total weight was 5.6064 × 10⁻⁶. 10 kg. At a rate of 1.4016 × 10⁻⁶ per liter. 8 kg is used as the condition for one iteration, and a total of 400 iterations are performed.

[0063] S202. Calculate wheel-rail contact conditions based on vehicle-track coupled dynamics model.

[0064] The Kik-Piotrowski wheel-rail contact model was used to calculate the wheel-rail contact parameters when the current wheelset passed, and the cumulative tangential creep rate was obtained.

[0065] S203. Calculate the rail wear depth within the wheel-rail contact patch based on wheel-rail contact conditions and a rail wear calculation model.

[0066] The Archard material wear model is used to calculate the rail wear at any point within the wheel-rail contact zone when the wheelset passes. The calculation formula is as follows:

[0067] V ij =k m W sij

[0068]

[0069] W sij =F ij l j =f(F 0ij ξ ij )∫v sj dt

[0070] In the formula, V ij The wear of the rail at any point i within the contact patch is expressed in meters (m) or kilometers (k). m The corrected wear index is obtained experimentally or empirically; H is the Vickers hardness index, in N·m. -2 μ is the coefficient of friction; W sij The work done by the creep force at any point i in the contact patch along the j direction is obtained from the wheel-rail contact, and the unit is N·m; F ijThe tangential creep force along the j direction at point i within the contact patch, in N; F 0ij ξ is the normal force at point i, in N; ij The wheel-rail creep rate; l j V is the sliding distance of the contacting body, in meters (m). s t represents creep velocity, in m / s; t represents time, in s.

[0071] S204. Update rail profile based on rail wear depth.

[0072] Based on the wear at each point within the rail contact patch calculated by S203, the profile of the rail after wear is obtained after the current wheel and rail pass.

[0073] S205. Repeat S202-S204 until the maximum number of iterations is reached and then terminate.

[0074] Input the rail wear profile into the vehicle-track coupled dynamics model and repeat steps S2-4 to S2-6 for iterative calculation until the number of iterations reaches 400 to obtain the final rail wear profile.

[0075] S206. Obtain the wear values ​​of the inner and outer rails.

[0076] According to the rail wear measurement standards in the "Rules for Maintenance of High-Speed ​​Railway Lines" and the "Rules for Repair of Conventional Railway Lines", the total rail wear can be calculated from the rail profile after wear. The calculation formula is as follows:

[0077]

[0078] In the formula, W t W1 represents the total wear of the rail, in mm; W2 represents the vertical wear of the rail, in mm, measured at 1 / 3 of the width of the top surface of the rail (from the standard working edge); W3 represents the side wear of the rail, in mm, measured 16 mm below the rail tread (according to the standard cross-section).

[0079] Steps S202 to S205 were performed on the track models of different railway spatial alignments in S201 to obtain the total wear of inner and outer rails under different railway spatial alignment conditions. The calculation results are shown in Table 2, and a rail wear sample dataset was established based on this.

[0080] Table 2

[0081]

[0082] S3. Construct an artificial neural network model for predicting rail wear, and train the artificial neural network model for predicting rail wear using a rail wear sample dataset.

[0083] A neural network model for predicting rail wear was established, comprising an input layer, an output layer, and hidden layers. The input layer consists of track spatial linear parameters, including the radius R and length L of the circular curve. y The parameters include: transition curve length l0, superelevation h, front slope i1, rear slope i2, and algebraic difference of slope Δi; the output layer is the rail wear value, including: inner rail wear value V. w1 Outer rail wear value V w2 The optimal number of neurons in the hidden layer is determined through trial and error; the empirical formula is as follows:

[0084]

[0085] In the formula, H is the number of hidden layer nodes; n is the number of input layer nodes; m is the number of output layer nodes; and a is an integer from 1 to 10.

[0086] Empirical formulas show that the number of hidden layer neurons ranges from 3 to 15. When the number of hidden layer neurons in the inner rail wear prediction model is 6, the model's mean squared error (RMSE) is minimized to 0.049; when the number of hidden layer neurons in the outer rail wear prediction model is 8, the model's RMSE is minimized to 0.058. Therefore, the number of hidden layer neurons in the inner rail wear prediction model is set to 6, and the number of hidden layer neurons in the outer rail wear prediction model is set to 8.

[0087] Next, an artificial neural network model for predicting rail wear was trained using a rail wear sample dataset. The steps are as follows:

[0088] S301. Normalize the data using the "maximum-minimum" normalization principle.

[0089] Normalization eliminates the impact of magnitude differences in data on model training. The normalization formula is as follows:

[0090]

[0091] In the formula, x′ represents the normalized data, and x represents the original data; x min and x max Let x be the minimum and maximum values, respectively.

[0092] S302. Initialize the weights and thresholds of the artificial neural network, input the normalized data into the artificial neural network for forward propagation, use the Sigmoid function as the activation function to calculate and output the calculated value of the current sample.

[0093]

[0094] In the formula, f is the activation function; β j θ is the input to the j-th neuron in the output layer;j The threshold value is the value of the j-th neuron in the output layer.

[0095] S303. Error backpropagation: Based on the error between the calculated value and the true value of the current sample, calculate the error gradient terms of the output layer neurons and the hidden layer neurons. The calculation formula is as follows:

[0096]

[0097] In the formula, g j β is the error gradient term of the j-th neuron in the output layer; f is the activation function; β j θ is the input to the j-th neuron in the output layer; j E is the threshold of the j-th neuron in the output layer. k The mean squared error of the neural network on the training set is calculated using the following formula:

[0098]

[0099] In the formula, Let j be the j-th output of the neural network.

[0100]

[0101] In the formula, e h The error gradient term of the h-th neuron in the hidden layer; E k b is the mean squared error of the neural network on the training set; h The output of the h-th neuron in the hidden layer; α h β is the input to the h-th neuron in the hidden layer; j γ is the input to the j-th neuron in the output layer; h ω is the threshold of the h-th neuron in the hidden layer; hj The weights are the values ​​between the h-th neuron in the hidden layer and the j-th neuron in the output layer.

[0102] S304. Update the weights ω between the hidden layer and the output layer based on the calculation results of the error gradient terms of each neuron in the hidden layer and the output layer. hj Weights v between the input layer and the hidden layer ih Threshold θ of each neuron in the output layer j and the threshold γ of each neuron in the hidden layer h The formula is as follows:

[0103] ω′ hj =ω hj +Δω hj =ω hj +ηg j b h

[0104] v′ ih =vih +Δv ih =v ih +ηe h x i

[0105] θ′ j =θ j +Δθ j =θ j -ηg j

[0106] γ′ h =γ h +Δγ h =γ h -ηe h

[0107] In the formula, ω′ hj v′ ih , θ′ j η represents the weights and thresholds for the next training iteration of the model; η is the learning rate, η = 0.001.

[0108] S305. Repeat steps S302-S304 to train the model until the maximum number of training iterations (epoch = 1000) or the error requirement (e ≤ 1 × 10⁻⁶) is met. -6 Training was terminated.

[0109] S306. Based on the test set data, the root mean square error (RMSE) is used to evaluate the final training effect of the model. The calculation formula is as follows:

[0110]

[0111] In the formula, N is the number of samples; y i The actual data value; These are the predicted values ​​for the data.

[0112] Repeating steps S302 to S305 to repeatedly train the prediction model yields the following results: For the inner rail wear prediction model, the maximum RMSE before optimization is 0.403, the minimum is 0.056, the range is 0.347, and the standard deviation is 0.067; For the outer rail wear prediction model, the maximum RMSE before optimization is 0.501, the minimum is 0.170, the range is 0.331, and the standard deviation is 0.064.

[0113] S4. Optimize the trained artificial neural network model for predicting rail wear to obtain the final prediction model.

[0114] First, the Sobol sensitivity analysis method was used to analyze the impact of track spatial alignment parameters on the wear of the inner and outer rails. Based on the Sobol analysis results, the artificial neural network models for predicting the wear of the inner and outer rails (hereinafter referred to as the inner and outer rail wear prediction models) were optimized to achieve efficient and accurate prediction of railway rail wear. The artificial neural network models for predicting the wear of the inner and outer rails are as follows: Figure 3 As shown.

[0115] S401. Determine the radius R and length L of the circular curve. y The ranges of values ​​for the transition curve length l0, superelevation h, front slope i1, back slope i2, and algebraic difference of slope Δi are, respectively: 300~1200, 160~250, 20~55, 35~120, -30~30, -30~30, and 0~30. Sobol sampling is performed according to these parameter ranges to obtain two Sobol sequence matrices A and B, each with a size of n×m, where n is the number of samples (n=260) and m is the number of input parameters (m=7).

[0116]

[0117] S402. Replacing the i-th column of matrix A with the i-th column of matrix B yields m replacement matrices.

[0118]

[0119] S403, Matrix A, B There are n×(m+2) sets of input parameter data. The prediction model established by S3 yields n×(m+2) sets of output parameters Y. Based on the calculation principle of the Sobol algorithm and the theory proposed by Salteli, X can be obtained. i The first-order influence index and the total effect index can be expressed as:

[0120]

[0121]

[0122] In the formula, For parameter X i The first-order influence variance, where matrix X ～i Indicates the difference from X i All other variables; X represents i Under a fixed condition, take all of X ～i The expected value of Y at time V; Xi Indicates taking all of X i The variance of the expected value within the parentheses; j represents the number of rows in the matrix; f(B) jS represents the model output corresponding to the parameters in the j-th row of matrix B; i For the i-th parameter X i The first-order influence index represents the i-th parameter X. i The effect of S on the output Y when acting alone; Ti The total effect index represents the value of the i-th parameter X. i The effect of interactions with other variables on the output Y.

[0123] The model was trained 50 times, and Sobol analysis was performed on the training results for each iteration based on the steps described above. The average results are shown in the attached figure. Figure 4 As shown, for the inner and outer rail wear prediction models, the parameter with the least influence is the circular curve length L. y And the algebraic difference in slope Δi.

[0124] Based on the Sobol analysis results, the structural optimization of the inner and outer rail wear prediction models was carried out, and the length L of the circular curve was adjusted. y The algebraic difference in slope Δi is removed from the input parameters, and the model is retrained to build the final prediction model. The optimized model is trained 50 times, and the prediction performance before and after optimization is compared as follows: Figure 5 As shown. For the inner rail wear prediction model, the optimized RMSE is a maximum of 0.350, a minimum of 0.050, a range of 0.300, and a standard deviation of 0.062; for the outer rail wear prediction model, the optimized RMSE is a maximum of 0.427, a minimum of 0.113, a range of 0.313, and a standard deviation of 0.059.

[0125] The model with the smallest error is selected and saved; its prediction performance on the test set is as follows: Figure 6 As shown. The Mean Absolute Error (MAPE) is used to evaluate its prediction accuracy:

[0126]

[0127] In the formula, N is the number of samples; y i The actual data value; These are the predicted values ​​for the data.

[0128] The MAPE of the outer rail wear prediction model is 1.89%, with a prediction accuracy of 98.11%; the MAPE of the inner rail wear prediction model is 2.98%, with a prediction accuracy of 97.02%.

[0129] S5. Using the final prediction model, the wear of railway rails can be predicted.

[0130] Example 2

[0131] This embodiment also provides an intelligent rail wear prediction system considering railway spatial alignment, including: a model building module, a dataset building module, a training module, an optimization module, and a prediction module; the model building module is used to establish a vehicle-track coupled dynamics model based on vehicle structural characteristic parameters and track structural characteristic parameters; the dataset building module is used to establish a rail wear calculation model based on the vehicle-track coupled dynamics model, calculate the inner and outer rail wear values ​​under different track spatial alignment parameters, and construct a rail wear sample dataset; the training module is used to construct a rail wear prediction artificial neural network model, and train the rail wear prediction artificial neural network model using the rail wear sample dataset; the optimization module is used to optimize the trained rail wear prediction artificial neural network model to obtain the final prediction model; the prediction module is used to use the final prediction model to predict railway rail wear.

[0132] The following will, in conjunction with this embodiment, explain in detail how the present invention solves technical problems in real life.

[0133] The model building module establishes a vehicle-track coupled dynamic model based on vehicle structural characteristic parameters and track structural characteristic parameters.

[0134] This embodiment uses a subway Type A train as a prototype to establish a vehicle-track coupled dynamic model (model as follows). Figure 2 As shown in Table 1, a vehicle-track coupled dynamic model is established based on the structural characteristic parameters of the vehicle and track. The vehicle structural characteristic parameters include: frame mass, frame position, frame moment of inertia, primary suspension stiffness, secondary suspension stiffness, bogie primary and secondary damping parameters, traction rod longitudinal stiffness, and anti-hunting damper damping. The track structural characteristic parameters include: fastener stiffness, concrete support layer thickness, CA mortar elastic modulus, and track spatial alignment parameters. The modeling parameters for the Metro Type A car are shown in Table 1.

[0135] The dataset construction module is based on the vehicle-track coupled dynamics model. It establishes a rail wear calculation model and calculates the inner and outer rail wear values ​​under different track spatial alignment parameters to construct a rail wear sample dataset.

[0136] S201. Input the track spatial alignment parameters, rail profile parameters, vehicle profile parameters, and total weight.

[0137] Based on relevant subway design specifications, 260 different horizontal and vertical alignment parameters were set through random uniform sampling to generate 260 spatial alignment schemes and establish corresponding track models.

[0138] Based on actual subway operation conditions and subway design specifications, the train operating speed is set at 60 km / h, and the axle load (fully loaded) per car is 1.6 × 10⁻⁶.4 The subway trains consist of 6 cars and run 40 times a day for 10 years, with a total of 3.504 × 10⁻⁶ wheels passing through them. 6 The total weight was 5.6064 × 10⁻⁶. 10 kg. At a rate of 1.4016 × 10⁻⁶ per liter. 8 kg is used as the condition for one iteration, and a total of 400 iterations are performed.

[0139] S202. Calculate wheel-rail contact conditions based on vehicle-track coupled dynamics model.

[0140] The Kik-Piotrowski wheel-rail contact model was used to calculate the wheel-rail contact parameters when the current wheelset passed, and the cumulative tangential creep rate was obtained.

[0141] S203. Calculate the rail wear depth within the wheel-rail contact patch based on wheel-rail contact conditions and a rail wear calculation model.

[0142] The Archard material wear model is used to calculate the rail wear at any point within the wheel-rail contact zone when the wheelset passes. The calculation formula is as follows:

[0143] V ij =k m W sij

[0144]

[0145] W sij =F ij l j =f(F 0ij ξ ij )∫v sj dt

[0146] In the formula, V ij The wear of the rail at any point i within the contact patch is expressed in meters (m) or kilometers (k). m The corrected wear index is obtained experimentally or empirically; H is the Vickers hardness index, in N·m. -2 μ is the coefficient of friction; W sij The work done by the creep force at any point i in the contact patch along the j direction is obtained from the wheel-rail contact, and the unit is N·m; F ij The tangential creep force along the j direction at point i within the contact patch, in N; F 0ij ξ is the normal force at point i, in N; ij The wheel-rail creep rate; l j V is the sliding distance of the contacting body, in meters (m). s t represents creep velocity, in m / s; t represents time, in s.

[0147] S204. Update rail profile based on rail wear depth.

[0148] Based on the wear at each point within the rail contact patch calculated by S203, the profile of the rail after wear is obtained after the current wheel and rail pass.

[0149] S205. Repeat S202-S204 until the maximum number of iterations is reached and then terminate.

[0150] Input the rail wear profile into the vehicle-track coupled dynamics model and repeat steps S2-4 to S2-6 for iterative calculation until the number of iterations reaches 400 to obtain the final rail wear profile.

[0151] S206. Obtain the wear values ​​of the inner and outer rails.

[0152] According to the rail wear measurement standards in the "Rules for Maintenance of High-Speed ​​Railway Lines" and the "Rules for Repair of Conventional Railway Lines", the total rail wear can be calculated from the rail profile after wear. The calculation formula is as follows:

[0153]

[0154] In the formula, W t W1 represents the total wear of the rail, in mm; W2 represents the vertical wear of the rail, in mm, measured at 1 / 3 of the width of the top surface of the rail (from the standard working edge); W3 represents the side wear of the rail, in mm, measured 16 mm below the rail tread (according to the standard cross-section).

[0155] Steps S202 to S205 were performed on the track models of different railway spatial alignments in S201 to obtain the total wear of inner and outer rails under different railway spatial alignment conditions. The calculation results are shown in Table 2, and a rail wear sample dataset was established based on this.

[0156] A rail wear prediction artificial neural network model was constructed using a training module, and the model was trained using a rail wear sample dataset.

[0157] A neural network model for predicting rail wear was established, comprising an input layer, an output layer, and hidden layers. The input layer consists of track spatial linear parameters, including the radius R and length L of the circular curve. y The parameters include: transition curve length l0, superelevation h, front slope i1, rear slope i2, and algebraic difference of slope Δi; the output layer is the rail wear value, including: inner rail wear value V. w1 Outer rail wear value V w2 The optimal number of neurons in the hidden layer is determined through trial and error; the empirical formula is as follows:

[0158]

[0159] In the formula, H is the number of hidden layer nodes; n is the number of input layer nodes; m is the number of output layer nodes; and a is an integer from 1 to 10.

[0160] Empirical formulas show that the number of hidden layer neurons ranges from 3 to 15. When the number of hidden layer neurons in the inner rail wear prediction model is 6, the model's mean squared error (RMSE) is minimized to 0.049; when the number of hidden layer neurons in the outer rail wear prediction model is 8, the model's RMSE is minimized to 0.058. Therefore, the number of hidden layer neurons in the inner rail wear prediction model is set to 6, and the number of hidden layer neurons in the outer rail wear prediction model is set to 8.

[0161] Next, an artificial neural network model for predicting rail wear was trained using a rail wear sample dataset. The steps are as follows:

[0162] S301. Normalize the data using the "maximum-minimum" normalization principle.

[0163] Normalization eliminates the impact of magnitude differences in data on model training. The normalization formula is as follows:

[0164]

[0165] In the formula, x′ represents the normalized data, and x represents the original data; x min and x max Let x be the minimum and maximum values, respectively.

[0166] S302. Initialize the weights and thresholds of the artificial neural network, input the normalized data into the artificial neural network for forward propagation, use the Sigmoid function as the activation function to calculate and output the calculated value of the current sample.

[0167]

[0168] In the formula, f is the activation function; β j θ is the input to the j-th neuron in the output layer; j The threshold value is the value of the j-th neuron in the output layer.

[0169] S303. Error backpropagation: Based on the error between the calculated value and the true value of the current sample, calculate the error gradient terms of the output layer neurons and the hidden layer neurons. The calculation formula is as follows:

[0170]

[0171] In the formula, g j β is the error gradient term of the j-th neuron in the output layer; f is the activation function; β jθ is the input to the j-th neuron in the output layer; j E is the threshold of the j-th neuron in the output layer. k The mean squared error of the neural network on the training set is calculated using the following formula:

[0172]

[0173] In the formula, Let j be the j-th output of the neural network.

[0174]

[0175] In the formula, e h The error gradient term of the h-th neuron in the hidden layer; E k b is the mean squared error of the neural network on the training set; h The output of the h-th neuron in the hidden layer; α h β is the input to the h-th neuron in the hidden layer; j γ is the input to the j-th neuron in the output layer; h ω is the threshold of the h-th neuron in the hidden layer; hj The weights are the values ​​between the h-th neuron in the hidden layer and the j-th neuron in the output layer.

[0176] S304. Update the weights ω between the hidden layer and the output layer based on the calculation results of the error gradient terms of each neuron in the hidden layer and the output layer. hj Weights v between the input layer and the hidden layer ih Threshold θ of each neuron in the output layer j and the threshold γ of each neuron in the hidden layer h The formula is as follows:

[0177] ω′ hj =ω hj +Δω hj =ω hj +ηg j b h

[0178] v′ ih =v ih +Δv ih =v ih +ηe h x i

[0179] θ′ j =θ j +Δθ j =θ j -ηg j

[0180] γ′ h =γ h+Δγ h =γ h -ηe h

[0181] In the formula, ω′ hj v′ ih , θ′ j η represents the weights and thresholds for the next training iteration of the model; η is the learning rate, η = 0.001.

[0182] S305. Repeat steps S302-S304 to train the model until the maximum number of training iterations (epoch = 1000) or the error requirement (e ≤ 1 × 10⁻⁶) is met. -6 Training was terminated.

[0183] S306. Based on the test set data, the root mean square error (RMSE) is used to evaluate the final training effect of the model. The calculation formula is as follows:

[0184]

[0185] In the formula, N is the number of samples; y i The actual data value; These are the predicted values ​​for the data.

[0186] Repeating steps S302 to S305 to repeatedly train the prediction model yields the following results: For the inner rail wear prediction model, the maximum RMSE before optimization is 0.403, the minimum is 0.056, the range is 0.347, and the standard deviation is 0.067; For the outer rail wear prediction model, the maximum RMSE before optimization is 0.501, the minimum is 0.170, the range is 0.331, and the standard deviation is 0.064.

[0187] The trained artificial neural network model for predicting rail wear is optimized using an optimization module to obtain the final prediction model.

[0188] First, the Sobol sensitivity analysis method was used to analyze the impact of track spatial alignment parameters on the wear of the inner and outer rails. Based on the Sobol analysis results, the artificial neural network models for predicting the wear of the inner and outer rails (hereinafter referred to as the inner and outer rail wear prediction models) were optimized to achieve efficient and accurate prediction of railway rail wear. The artificial neural network models for predicting the wear of the inner and outer rails are as follows: Figure 3 As shown.

[0189] S401. Determine the radius R and length L of the circular curve. yThe ranges of values ​​for the transition curve length l0, superelevation h, front slope i1, back slope i2, and algebraic difference of slope Δi are, respectively: 300~1200, 160~250, 20~55, 35~120, -30~30, -30~30, and 0~30. Sobol sampling is performed according to these parameter ranges to obtain two Sobol sequence matrices A and B, each with a size of n×m, where n is the number of samples (n=260) and m is the number of input parameters (m=7).

[0190]

[0191] S402. Replacing the i-th column of matrix A with the i-th column of matrix B yields m replacement matrices.

[0192]

[0193] S403, Matrix A, B There are n×(m+2) sets of input parameter data. The prediction model established by S3 yields n×(m+2) sets of output parameters Y. Based on the calculation principle of the Sobol algorithm and the theory proposed by Salteli, X can be obtained. i The first-order influence index and the total effect index can be expressed as:

[0194]

[0195] In the formula, For parameter X i The first-order influence variance, where matrix X ～i Indicates the difference from X i All other variables; X represents i Under a fixed condition, take all of X ～i The expected value of Y at time V; Xi Indicates taking all of X i The variance of the expected value within the parentheses; j represents the number of rows in the matrix; f(B) j S represents the model output corresponding to the parameters in the j-th row of matrix B; i For the i-th parameter X i The first-order influence index represents the i-th parameter X. i The effect of S on the output Y when acting alone; Ti The total effect index represents the value of the i-th parameter X. i The effect of interactions with other variables on the output Y.

[0196] The model was trained 50 times, and Sobol analysis was performed on the training results for each iteration based on the steps described above. The average results are shown in the attached figure. Figure 4As shown, for the inner and outer rail wear prediction models, the parameter with the least influence is the circular curve length L. y And the algebraic difference in slope Δi.

[0197] Based on the Sobol analysis results, the structural optimization of the inner and outer rail wear prediction models was carried out, and the length L of the circular curve was adjusted. y The algebraic difference in slope Δi is removed from the input parameters, and the model is retrained to build the final prediction model. The optimized model is trained 50 times, and the prediction performance before and after optimization is compared as follows: Figure 5 As shown. For the inner rail wear prediction model, the optimized RMSE is a maximum of 0.350, a minimum of 0.050, a range of 0.300, and a standard deviation of 0.062; for the outer rail wear prediction model, the optimized RMSE is a maximum of 0.427, a minimum of 0.113, a range of 0.313, and a standard deviation of 0.059.

[0198] The model with the smallest error is selected and saved; its prediction performance on the test set is as follows: Figure 6 As shown. The Mean Absolute Error (MAPE) is used to evaluate its prediction accuracy:

[0199]

[0200] In the formula, N is the number of samples; y i The actual data value; These are the predicted values ​​for the data.

[0201] The MAPE of the outer rail wear prediction model is 1.89%, with a prediction accuracy of 98.11%; the MAPE of the inner rail wear prediction model is 2.98%, with a prediction accuracy of 97.02%.

[0202] Finally, the prediction module uses the final prediction model to predict the wear and tear of railway rails.

[0203] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for intelligent prediction of rail wear considering railway spatial alignment, characterized in that the steps include... include: S1. Based on the vehicle structural characteristic parameters and the track structural characteristic parameters, establish a vehicle-track coupled dynamic model; The vehicle structural characteristic parameters include: frame mass, frame position, frame rotational inertia, vehicle primary suspension stiffness, vehicle secondary suspension stiffness, bogie primary damping parameters, bogie secondary damping parameters, traction rod longitudinal stiffness, and anti-hunting damper damping; the track structural characteristic parameters include: fastener stiffness, concrete support layer thickness, CA mortar elastic modulus, and track spatial alignment parameters, wherein the track spatial alignment parameters include: circular curve radius, circular curve length, transition curve length, superelevation, gradient, and gradient algebraic difference. S2. Based on the vehicle-track coupled dynamics model, establish a rail wear calculation model, calculate the inner and outer rail wear values ​​under different track spatial alignment parameters, and construct a rail wear sample dataset; the steps for calculating the inner and outer rail wear values ​​include: S201, Input track spatial alignment parameters, rail profile parameters, vehicle profile parameters, and total weight; S202. Calculate wheel-rail contact conditions based on vehicle-track coupled dynamics model; S203. Calculate the depth of rail wear within the wheel-rail contact patch based on wheel-rail contact conditions and rail wear calculation model; S204. Update rail profile based on rail wear depth; S205, Repeat S202-S204 until the maximum number of iterations is reached and then terminate; S206. Obtain the wear values ​​of the inner and outer rails; S3. Construct an artificial neural network model for predicting rail wear, and train the model using the rail wear sample dataset. The artificial neural network model for predicting rail wear includes: an input layer, an output layer, and a hidden layer; wherein, the input layer consists of track spatial linear parameters, including: the radius of the circular curve. R Length of circular curve Ly Length of transition curve l0 Ultra-high h Front slope i 1. Back slope i 2. Algebraic difference of slope Δi The output layer contains rail wear values, including: inner rail wear values. Vw 1. Wear value of outer rail Vw 2. The number of neurons in the hidden layer is determined using an empirical formula, and the optimal number of neurons in the hidden layer is determined through trial and error. The empirical formula is as follows: In the formula, H This represents the number of hidden layer nodes. n The number of nodes in the input layer; m This represents the number of nodes in the output layer. a Take an integer from 1 to 10; S4. Optimize the trained artificial neural network model for predicting rail wear to obtain the final prediction model; the method for optimizing the artificial neural network model for predicting rail wear includes: The Sobol sensitivity analysis method was used to analyze the effect of track spatial alignment parameters on the wear of the inner rail. V w1 and wear of the outer rail V w2 The impact; Based on the Sobol analysis results, track spatial alignment parameters that have little impact on the wear of the inner and outer rails were removed, and the model input layer data was adjusted to obtain the artificial neural network model for predicting the wear of the inner rail and the artificial neural network model for predicting the wear of the outer rail, respectively. The model is trained based on the rail wear sample dataset to obtain an optimized artificial neural network model for predicting inner and outer rail wear. The mapping relationship between track spatial linear parameters and inner and outer rail wear is established to obtain the wear values ​​of inner and outer rails. S5. Using the final prediction model, the prediction of railway rail wear is realized.

2. The intelligent prediction method for rail wear considering railway spatial alignment according to claim 1, characterized in that, The method for training the artificial neural network model for predicting rail wear includes: S301. Normalize the data using the "maximum-minimum" normalization principle; S302. Initialize the weights and thresholds of the artificial neural network, input the normalized data into the artificial neural network for forward propagation, use the Sigmoid function as the activation function to calculate and output the calculated value of the current sample. S303, Backpropagation of error: Based on the error between the calculated value and the true value of the current sample, calculate the error gradient term of the output layer neuron and the error gradient term of the hidden layer neuron. S304. Based on the calculation results of the error gradient terms of each neuron in the hidden layer and the output layer, update the weights between the hidden layer and the output layer, the weights between the input layer and the hidden layer, the threshold of each neuron in the output layer, and the threshold of each neuron in the hidden layer. S305. Repeat steps S302-S304 to train the model until the maximum number of training iterations or the error requirement is met, then terminate the training. S306. Based on the test set data, the root mean square error is used. RMSE The final training results of the model are evaluated.

3. A smart rail wear prediction system considering railway spatial alignment, the system being used to implement the method described in any one of claims 1-2, characterized in that, include: The module includes a model building module, a dataset building module, a training module, an optimization module, and a prediction module. The model building module is used to establish a vehicle-track coupled dynamics model based on vehicle structural characteristic parameters and track structural characteristic parameters. The dataset construction module is used to establish a rail wear calculation model based on the vehicle-track coupled dynamics model, and to calculate the inner and outer rail wear values ​​under different track spatial alignment parameters to construct a rail wear sample dataset. The training module is used to construct an artificial neural network model for predicting rail wear, and to train the artificial neural network model for predicting rail wear using the rail wear sample dataset. The optimization module is used to optimize the trained artificial neural network model for predicting rail wear to obtain the final prediction model. The prediction module is used to predict railway rail wear using the final prediction model.

4. The intelligent rail wear prediction system considering railway spatial alignment according to claim 3, characterized in that, The vehicle structural characteristic parameters include: frame mass, frame position, frame rotational inertia, vehicle primary suspension stiffness, vehicle secondary suspension stiffness, bogie primary damping parameters, bogie secondary damping parameters, traction rod longitudinal stiffness, and anti-hunting damper damping; the track structural characteristic parameters include: fastener stiffness, concrete support layer thickness, CA mortar elastic modulus, and track spatial alignment parameters, wherein the track spatial alignment parameters include: circular curve radius, circular curve length, transition curve length, superelevation, gradient, and gradient algebraic difference.

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