Steel rail abrasion intelligent prediction method and system considering railway space line shape

Abstract

The invention discloses a steel rail abrasion intelligent prediction method and system considering railway space line shape, and the method comprises the steps: S1, building a vehicle-track coupling dynamic model based on vehicle structure characteristic parameters and track structure characteristic parameters; s2, based on the vehicle-track coupling dynamic model, establishing a steel rail abrasion calculation model, and calculating inner and outer side steel rail abrasion values under different track space linear parameters to construct a steel rail abrasion sample data set; s3, constructing a steel rail abrasion prediction artificial neural network model, and training the steel rail abrasion prediction artificial neural network model by using the steel rail abrasion sample data set; s4, optimizing the trained steel rail abrasion prediction artificial neural network model to obtain a final prediction model; and S5, predicting the abrasion of the railway steel rail by using the final prediction model. According to the method, the railway space linear parameter-steel rail abrasion prediction model is established, so that the steel rail abrasion under different plane and vertical section linear parameters and combinations is efficiently and accurately obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of rail wear prediction, and particularly relates to an intelligent rail wear prediction method and system considering railway spatial alignment. Background Art

[0002] With the increasing urban traffic operation pressure in China, the wear degree of subway rails is becoming increasingly serious. Rail wear will cause changes in the wheel-rail contact geometry, which in turn affects the stability of the train operation dynamic performance, reduces the safety and comfort of passengers, and increases the maintenance cost. The wheel-rail contact relationship is the fundamental factor affecting rail wear, and the railway spatial alignment has an important impact on the wheel-rail contact relationship. A reasonable combination of railway horizontal and vertical alignment can significantly reduce rail wear. Therefore, if the influence of railway spatial alignment on rail wear is considered in the route selection and design stage, and the horizontal and vertical alignment parameters of the railway are optimized and combined, the rail wear can be reduced from the source, ensuring the safety and comfort of passengers and reducing the maintenance cost.

[0003] The existing rail wear is mainly calculated by establishing a vehicle-track coupling dynamics model. The modeling process is complex and the calculation time is long. However, in the route selection stage, it is usually necessary to design multiple line schemes for comparison. Especially when using intelligent route selection methods, tens of thousands of line schemes will be generated in the iterative optimization process. Calculating the rail wear for each line scheme by establishing a vehicle-track coupling dynamics model, the calculation time is unacceptable. Some scholars have solved the problem of long calculation time for obtaining rail wear by relying on the vehicle-track coupling dynamics model by establishing a surrogate model, but ignored the influence of railway spatial alignment on rail wear. The horizontal and vertical alignment parameters of the railway include: plane alignment parameters such as circular curve radius, transition curve length, circular curve length, superelevation, etc., and vertical alignment parameters such as line gradient, algebraic difference of gradients, etc. There are significant differences in rail wear under different horizontal and vertical alignment parameters and combinations. Therefore, it is necessary to comprehensively consider the influence of track horizontal and vertical alignment parameters on rail wear, establish a mapping relationship between railway spatial alignment and rail wear, and efficiently and accurately obtain the rail wear under different horizontal and vertical alignment parameters and combinations.

[0004] In response to this, the present invention discloses an intelligent rail wear prediction method, establishes a railway spatial alignment-rail wear prediction artificial neural network model, explores the mapping relationship between railway spatial alignment and rail wear, and realizes the efficient and accurate calculation of railway rail wear. Summary of the Invention

[0005] The object of the present invention is to provide a method for predicting rail wear considering the spatial alignment of railways, construct a neural network model with railway spatial alignment parameters as inputs and inner and outer rail wear as outputs, establish the mapping relationship from the model input to the output through training with a large amount of sample data, and achieve efficient and accurate acquisition of inner and outer rail wear under different railway spatial alignment parameters, so as to solve the problem of limited calculation time in calculating inner and outer rail wear relying on the vehicle-track coupling dynamics model.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] An intelligent prediction method for rail wear considering the spatial alignment of railways, the steps include:

[0008] S1. Based on vehicle structure characteristic parameters and track structure characteristic parameters, establish a vehicle-track coupling dynamics model;

[0009] S2. Based on the vehicle-track coupling 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 data set;

[0010] S3. Construct a rail wear prediction artificial neural network model, and train the rail wear prediction artificial neural network model with the rail wear sample data set;

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

[0012] S5. Use the final prediction model to realize the prediction of railway rail wear.

[0013] Preferably, the vehicle structure characteristic parameters include: frame mass, frame position, frame moment of inertia, primary suspension stiffness of the vehicle, secondary suspension stiffness of the vehicle, damping parameter of the first bogie, damping parameter of the second bogie of the vehicle, longitudinal stiffness of the traction rod, and damping of the anti-hunting damper; the track structure characteristic parameters include: fastener stiffness, thickness of the concrete support layer, elastic modulus of the CA mortar, and track spatial alignment parameters, where the track spatial alignment parameters include: radius of the circular curve, length of the circular curve, length of the transition curve, superelevation, gradient, algebraic difference of gradients, etc., which are horizontal and vertical alignment parameters.

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

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

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

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

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

[0019] S205. Repeat steps 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. Among them, the input layer is the track spatial alignment parameters, including: the radius of the circular curve R, the length of the circular curve L y , the length of the transition curve l0, the superelevation h, the forward slope i1, the backward slope i2, and the algebraic difference in slope Δi; the output layer is the rail wear values, including: the wear value of the inner rail V w1 , the wear value of the outer rail V w2 ; the number of neurons in the hidden layer is determined within a range using an empirical formula, and the optimal number of neurons in the hidden layer is determined by the trial-and-error method. The empirical formula is as follows:

[0022]

[0023] In the formula, H is the number of nodes in the hidden layer; n is the number of nodes in the input layer; m is the number of nodes in the output layer; a takes 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, and use the Sigmoid function as the activation function to calculate and output the calculated value of the current sample;

[0027] S303. Backpropagate the error, and calculate the error gradient terms of the output layer neurons and the hidden layer neurons based on the error between the calculated value of the current sample and the true value;

[0028] S304. Update the weights between the hidden layer and the output layer, the weights between the input layer and the hidden layer, the thresholds of each neuron in the output layer, and the thresholds of each neuron in the hidden layer according to the calculation results of the error gradient terms of each neuron in the hidden layer and the output layer;

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

[0030] S306. Evaluate the final training effect of the model using the root mean square error (RMSE) based on the test set data.

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

[0032] Use the Sobol sensitivity analysis method to analyze the track spatial alignment parameters and their influence on the inner rail wear V w1 and the outer rail wear V w2 ;

[0033] Based on the Sobol analysis results, eliminate the track spatial alignment parameters with less influence on the inner and outer rail wear, and adjust the input layer data of the model to obtain the artificial neural network model for inner rail wear prediction and the artificial neural network model for outer rail wear prediction respectively;

[0034] Train the model based on the rail wear sample data set to obtain the optimized artificial neural network models for inner and outer rail wear prediction, establish the mapping relationship from track spatial alignment parameters to inner and outer rail wear, and realize the acquisition of inner and outer rail wear values.

[0035] The present invention also provides an intelligent prediction system for rail wear considering railway spatial alignment. The system is used to implement the above method and includes: a model construction module, a data set construction module, a training module, an optimization module, and a prediction module;

[0036] The model construction module is used to establish a vehicle-track coupling dynamics model based on vehicle structure characteristic parameters and track structure characteristic parameters;

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

[0038] The training module is used to construct an artificial neural network model for rail wear prediction and train the artificial neural network model for rail wear prediction using the rail wear sample data set;

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

[0040] The prediction module is used to use the final prediction model to realize the prediction of railway rail wear.

[0041] Preferably, the vehicle structure characteristic parameters include: bogie mass, bogie position, bogie moment of inertia, primary suspension stiffness of the vehicle, secondary suspension stiffness of the vehicle, damping parameter of the first bogie, damping parameter of the second bogie of the vehicle, longitudinal stiffness of the traction link, damping of the anti-hunting damper; the track structure characteristic parameters include: fastener stiffness, thickness of the concrete supporting layer, elastic modulus of the CA mortar, and track spatial alignment parameters, where the track spatial alignment parameters include: radius of the circular curve, length of the circular curve, length of the transition curve, superelevation, gradient, algebraic difference of gradients, and other horizontal and vertical alignment parameters.

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

[0043] By establishing a railway spatial alignment parameter - rail wear prediction model, the present invention can efficiently and accurately obtain rail wear under different horizontal and vertical alignment parameters and combinations, providing guidance for railway route selection and design. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solutions of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0045] Figure 1 It is a schematic flowchart of the method according to an embodiment of the present invention;

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

[0047] Figure 3 It is a structure diagram of the inner and outer rail wear prediction models according to an embodiment of the present invention;

[0048] Figure 4 It is a Sobol sensitivity analysis result diagram of the inner and outer rail wear prediction models according to an embodiment of the present invention; among them, (a) is the Sobol analysis result of the inner rail wear prediction model; (b) is the Sobol analysis result of the outer rail wear prediction model;

[0049] Figure 5 It is a comparison diagram of the prediction effects of the inner and outer rail models before and after optimization according to an embodiment of the present invention; among them, (a) is the comparison result of the inner rail wear prediction model before and after optimization; (b) is the comparison result of the outer rail wear prediction model before and after optimization;

[0050] Figure 6Prediction results of the test set after optimizing the inner and outer rail models in the embodiments of the present invention; among them, (a) is the prediction result of the test set of the inner rail wear prediction model; (b) is the prediction result of the test set of the outer rail wear prediction model. Detailed implementation manners

[0051] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

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

[0053] Embodiment 1

[0054] This embodiment provides an intelligent prediction method for rail wear considering the railway spatial alignment, and its process schematic diagram is as Figure 1 shown. The specific steps include:

[0055] S1. Based on the vehicle structure characteristic parameters and the track structure characteristic parameters, establish a vehicle-track coupling dynamics model.

[0056] In this embodiment, taking the subway Type A vehicle as a prototype, a vehicle-track coupling dynamic model (the model is as Figure 2 shown) is established. Based on the vehicle and track structure characteristic parameters, a vehicle-track coupling dynamics model is established, where the vehicle structure characteristic parameters include: frame mass, frame position, frame moment of inertia, primary suspension stiffness of the vehicle, secondary suspension stiffness, primary and secondary damping parameters of the bogie, longitudinal stiffness of the traction rod, damping of the anti-roll damper, etc.; the track structure characteristic parameters include: fastener stiffness, thickness of the concrete support layer, elastic modulus of the CA mortar, and track spatial alignment parameters. Among them, the modeling parameters of the subway Type A vehicle are shown in Table 1.

[0057] Table 1

[0058]

[0059] S2. Based on the vehicle-track coupling 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 data set.

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

[0061] Based on the subway-related design specifications, 260 groups of different horizontal and vertical alignment parameters are set through random uniform sampling, 260 spatial alignment schemes are generated, and corresponding track models are established.

[0062] Referring to the actual operation status of the subway and the subway design specifications, the vehicle running speed is set to 60 km / h, the axle load (fully loaded) of each vehicle is 1.6×10 4 kg, the subway is composed of 6 carriages, the number of subway train operations per day is 40 times, and it operates for 10 years. The total number of wheel passages is 3.504×10 6 times, and the total passing weight is 5.6064×10 10 kg. Taking every 1.4016×10 8 kg as an iteration condition, a total of 400 iterations are performed.

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

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

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

[0066] The Archard material wear model is used to calculate the wear of the rail at any point within the wheel-rail contact patch when the current wheel set 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 is the wear of the rail at any point i within the contact patch, unit: m; k m is the modified wear index, obtained from experiments or experience; H is the Vickers hardness index, unit: N·m -2 ; μ is the friction coefficient; W sij is the work done by the creep force in the j direction at any point i within the contact patch, obtained from wheel-rail contact, unit: N·m; F ijis the tangential creep force in the j direction at point i within the contact patch, unit: N; F 0ij is the normal force at point i, unit: N; ξ ij is the creep rate between the wheel and the rail; l j is the sliding distance of the contact body, unit: m; v s is the creep speed, unit: m / s; t is the time, unit: s.

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

[0072] Based on the wear at each point within the rail contact patch calculated in S203, obtain the rail profile after wear after the current wheel-rail passage.

[0073] S205. Repeat S202 - S204 until termination after reaching the maximum number of iterations.

[0074] Input the rail profile after wear into the vehicle-rail coupling dynamics model and repeat the steps from S2-4 to S2-6 for iterative calculation until the number of iterative calculations reaches 400 times 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 "High-Speed Railway Line Maintenance Rules" and the "General-Speed Railway Line Repair Rules", the total rail wear can be calculated from the rail profile after wear, and the calculation formula is as follows:

[0077]

[0078] In the formula, W t is the total rail wear, unit: mm; W1 is the vertical rail wear, unit: mm, and the vertical wear is measured at 1 / 3 of the top width of the rail (from the standard working edge); W2 is the side rail wear, unit: mm, and the side wear is measured at 16 mm below the rail tread (according to the standard section).

[0079] Perform the steps from S202 to S205 for the track models with different railway spatial alignments in S201 respectively, obtain the total wear amounts of the inner and outer rails under different railway spatial alignment conditions, and the calculation results are shown in Table 2, and thus establish a rail wear sample data set.

[0080] Table 2

[0081]

[0082] S3. Construct a rail wear prediction artificial neural network model and use the rail wear sample data set to train the rail wear prediction artificial neural network model.

[0083] Build a rail wear prediction artificial neural network model structure, which includes: an input layer, an output layer, and a hidden layer. Among them, the input layer is the track spatial alignment parameters, including: the radius of the circular curve R, the length of the circular curve L y , the length of the transition curve l0, the superelevation h, the forward slope i1, the backward slope i2, and the algebraic difference of slopes Δi; the output layer is the rail wear value, including: the inner rail wear value V w1 , the outer rail wear value V w2 . Determine the optimal number of hidden layer neurons by the trial-and-error method. 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; a takes an integer from 1 to 10.

[0086] From the empirical formula, the range of the number of hidden layer neurons is 3 to 15. When the number of hidden layer neurons in the inner rail wear prediction model is 6, the minimum value of the mean square error RMSE of the model is 0.049; when the number of hidden layer neurons in the outer rail wear prediction model is 8, the minimum value of the mean square error RMSE of the model is 0.058. Therefore, set the number of hidden layer neurons in the inner rail wear prediction model to 6, and set the number of hidden layer neurons in the outer rail wear prediction model to 8.

[0087] After that, use the rail wear sample data set to train the rail wear prediction artificial neural network model. The steps are as follows:

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

[0089] Through normalization, eliminate the influence of the order of magnitude difference of the data on model training. The normalization formula is as follows:

[0090]

[0091] In the formula, x′ is the normalized data, and x is the original data; x min and x max are the minimum and maximum values of x 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, and use the Sigmoid function as the activation function to calculate and output the current sample calculation value.

[0093]

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

[0095] S303. Error backpropagation. Calculate the error between the calculated value and the true value of the current sample, and calculate the error gradient term of the output layer neurons and the error gradient term of the hidden layer neurons. The calculation formulas are as follows:

[0096]

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

[0098]

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

[0100]

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

[0102] S304. According to the calculation results of the error gradient terms of each neuron in the hidden layer and the output layer, update the weight ω hj between the hidden layer and the output layer, the weight v ih between the input layer and the hidden layer, the threshold θ j of each neuron in the output layer, and the threshold γ h of each neuron in the hidden layer. The formulas are 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] Wherein, ω′ hj , v′ ih , θ′ j are the weights and thresholds for the next training 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 times (epoch = 1000) or the error requirement is met (e ≤ 1×10 -6 ), and terminate the training.

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

[0110]

[0111] Wherein, N is the number of samples; y i is the true value of the data; is the predicted value of the data.

[0112] By repeating steps S302 to S305, and performing multiple repeated trainings on the prediction model, it can be obtained that 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 rail wear prediction artificial neural network model to obtain the final prediction model.

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

[0115] S401. Determine the value ranges of the circular curve radius R, circular curve length L y , transition curve length l0, superelevation h, forward slope i1, backward slope i2, and algebraic difference in slope Δi, which are successively: 300 - 1200, 160 - 250, 20 - 55, 35 - 120, -30 - 30, -30 - 30, 0 - 30. According to the above parameter value ranges, Sobol sampling is carried out to obtain two Sobol sequence matrices A and B, both with a size of n×m, where n is the number of sampling samples (n = 260), and m is the number of input parameters (m = 7).

[0116]

[0117] S402. The m replacement matrices can be obtained by replacing the i-th column in matrix B with the i-th column in matrix A

[0118]

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

[0120]

[0121]

[0122] In the formula, is the first-order influence variance of parameter X i , where matrix X ～i represents all variables except X i ; represents the expected value of Y when X i is fixed and X ～i is taken over; V Xi represents the variance of the expected value in the parentheses when X i is taken over; j represents the number of rows of the matrix; f(B) jDenote the model output result corresponding to the j-th row parameter of matrix B; S i is the i-th parameter X i The first-order influence index, indicating the influence of the i-th parameter X i acting alone on the output Y; S Ti is the total effect index, indicating the influence of the interaction between the i-th parameter X i and other variables on the output Y.

[0123] The model was trained 50 times, and Sobol analysis was performed on the training results of each time based on the above steps. The average calculation results are shown in the appendix Figure 4 As shown, for the inner and outer rail wear prediction models, the parameters with the least influence are the circular curve length L y and the algebraic difference in gradient Δi.

[0124] Based on the calculation results of Sobol analysis, the structure of the inner and outer rail wear prediction models was optimized. The circular curve length L y and the algebraic difference in gradient Δi were removed from the input parameters, and training was performed again to establish the final prediction model. The model was trained 50 times after optimization, and the comparison of the prediction effects before and after optimization is as Figure 5 shown. For the inner rail wear prediction model, the maximum RMSE after optimization is 0.350, the minimum is 0.050, the range is 0.300, and the standard deviation is 0.062; for the outer rail wear prediction model, the maximum RMSE after optimization is 0.427, the minimum is 0.113, the range is 0.313, and the standard deviation is 0.059.

[0125] Select the model with the smallest error for saving, and its prediction effect on the test set is as Figure 6 shown. The mean absolute percentage error MAPE was used to evaluate its prediction accuracy:

[0126]

[0127] where N is the number of samples; y i is the true value of the data; is the predicted value of the data.

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

[0129] S5. Use the final prediction model to achieve the prediction of railway rail wear.

[0130] Example 2

[0131] This embodiment also provides an intelligent prediction system for rail wear considering the railway spatial alignment, including: a model construction module, a data set construction module, a training module, an optimization module, and a prediction module; the model construction module is used to establish a vehicle-track coupling dynamics model based on vehicle structure characteristic parameters and track structure characteristic parameters; the data set construction module is used to establish a rail wear calculation model based on the vehicle-track coupling dynamics model, calculate the inner and outer rail wear values under different track spatial alignment parameters, and construct a rail wear sample data set; 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 data set; the optimization module is used to optimize the trained rail wear prediction artificial neural network model to obtain a final prediction model; the prediction module is used to use the final prediction model to realize the prediction of railway rail wear.

[0132] Next, in combination with this embodiment, it will be detailed how the present invention solves technical problems in real life.

[0133] The model construction module establishes a vehicle-track coupling dynamics model based on vehicle structure characteristic parameters and track structure characteristic parameters.

[0134] In this embodiment, taking the subway Type A vehicle as a prototype, a vehicle-track coupling dynamic model (the model is as Figure 2 shown) is established. A vehicle-track coupling dynamics model is established based on vehicle and track structure characteristic parameters. The vehicle structure characteristic parameters include: frame mass, frame position, frame moment of inertia, primary suspension stiffness of the vehicle, secondary suspension stiffness, primary and secondary damping parameters of the bogie, longitudinal stiffness of the traction rod, damping of the anti-hunting damper, etc.; the track structure characteristic parameters include: fastener stiffness, thickness of the concrete support layer, elastic modulus of the CA mortar, and track spatial alignment parameters. Among them, the modeling parameters of the subway Type A vehicle are shown in Table 1.

[0135] The data set construction module establishes a rail wear calculation model based on the vehicle-track coupling dynamics model, calculates the inner and outer rail wear values under different track spatial alignment parameters, and constructs a rail wear sample data set.

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

[0137] Based on the relevant subway design specifications, 260 groups of different horizontal and vertical alignment parameters are set by random uniform sampling, 260 spatial alignment schemes are generated, and corresponding track models are established.

[0138] Referring to the actual operation status of the subway and the subway design specifications, the vehicle running speed is set to 60 km / h, and the axle weight (fully loaded) of each vehicle is 1.6×104 kg, the subway is composed of 6 carriages, the daily operation frequency of subway trains is 40 times, and it operates for 10 years in total. The total number of wheel passes is 3.504×10 6 times, and the total passing weight is 5.6064×10 10 kg. Taking every 1.4016×10 8 kg as an iteration condition, a total of 400 iterations are performed.

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

[0140] Use the Kik-Piotrowski wheel-rail contact model to calculate the wheel-rail contact parameters when the current wheel set passes, and obtain the cumulative tangential creep rate.

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

[0142] Use the Archard material wear model to calculate the rail wear at any point within the wheel-rail contact patch when the current wheel set 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 is the rail wear at any point i within the contact patch, unit: m; k m is the modified wear index, obtained from experiments or experience; H is the Vickers hardness index, unit: N·m -2 ; μ is the friction coefficient; W sij is the work done by the creep force in the j direction at any point i within the contact patch, obtained from wheel-rail contact, unit: N·m; F ij is the tangential creep force in the j direction at point i within the contact patch, unit: N; F 0ij is the normal force at point i, unit: N; ξ ij is the creep rate between the wheel and the rail; l j is the sliding distance of the contact body, unit: m; v s is the creep speed, unit: m / s; t is the time, unit: s.

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

[0148] Based on the wear at each point within the rail contact patch calculated in S203, obtain the profile of the rail after wear after the current wheel-rail passage.

[0149] S205. Repeat S202 - S204 until termination after reaching the maximum number of iterations.

[0150] Input the profile of the rail after wear into the vehicle-track coupling dynamics model and repeat the steps from S2-4 to S2-6 for iterative calculation until the number of iterative calculations reaches 400 times 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 "High-Speed Railway Line Maintenance Rules" and the "General-Speed Railway Line Repair Rules", the total rail wear can be calculated from the profile of the rail after wear. The calculation formula is as follows:

[0153]

[0154] In the formula, W t is the total rail wear, unit: mm; W1 is the vertical rail wear, unit: mm, and the vertical wear is measured at 1 / 3 of the top width of the rail (from the standard working edge); W2 is the lateral rail wear, unit: mm, and the lateral wear is measured at 16 mm below the rail tread (according to the standard section).

[0155] Perform the steps from S202 to S205 on the track models with different railway spatial alignments in S201 respectively, obtain the total wear amounts of the inner and outer rails under different railway spatial alignment conditions, and the calculation results are shown in Table 2. Then establish a rail wear sample data set from this.

[0156] Use the training module 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 data set.

[0157] Establish the structure of the rail wear prediction artificial neural network model. The structure includes: an input layer, an output layer, and a hidden layer. Among them, the input layer is the track spatial alignment parameters, including: the radius of the circular curve R, the length of the circular curve L y , the length of the transition curve l0, the superelevation h, the forward slope i1, the backward slope i2, and the algebraic difference of slopes Δi; the output layer is the rail wear values, including: the inner rail wear value V w1 , the outer rail wear value V w2 . Determine the optimal number of neurons in the hidden layer through the trial-and-error method. The empirical formula is as follows:

[0158]

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

[0160] According to the empirical formula, 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 minimum value of the mean square error RMSE of the model is 0.049; when the number of hidden layer neurons in the outer rail wear prediction model is 8, the minimum value of the mean square error RMSE of the model is 0.058. Therefore, the number of neurons in the hidden layer of the inner rail wear prediction model is set to 6, and the number of neurons in the hidden layer of the outer rail wear prediction model is set to 8.

[0161] After that, use the rail wear sample data set to train the rail wear prediction artificial neural network model. The steps are as follows:

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

[0163] Through normalization, eliminate the influence of the magnitude difference of the data on model training. The normalization formula is as follows:

[0164]

[0165] Wherein, x' is the normalized data, x is the original data; x min and x max are the minimum and maximum values of x 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, and use the Sigmoid function as the activation function to calculate and output the calculated value of the current sample.

[0167]

[0168] Wherein, f is the activation function; β j is the input of the j - th neuron in the output layer; θ j is the threshold of the j - th neuron in the output layer.

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

[0170]

[0171] Wherein, g j is the error gradient term of the j - th neuron in the output layer; f is the activation function; β jis the input to the j-th neuron in the output layer; θ j is the threshold of the j-th neuron in the output layer; E k is the mean squared error of the neural network on the training set, and the calculation formula is as follows:

[0172]

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

[0174]

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

[0176] S304. According to the calculation results of the error gradient terms of each neuron in the hidden layer and the output layer, update the weights ω hj between the hidden layer and the output layer, the weights v ih between the input layer and the hidden layer, the thresholds θ j of each neuron in the output layer, and the thresholds γ h of each neuron in the hidden layer. The formulas are 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] where ω′ hj , v′ ih , θ′ j are the weights and thresholds for the next training 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 times (epoch = 1000) or the error requirement (e ≤ 1×10 -6 ) is met, and then terminate the training.

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

[0184]

[0185] where N is the number of samples; y i is the true value of the data; is the predicted value of the data.

[0186] Repeating steps S302 to S305, and performing multiple repeated trainings on the prediction model, we can obtain: 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] Use the optimization module to optimize the trained rail wear prediction artificial neural network model to obtain the final prediction model.

[0188] First, use the Sobol sensitivity analysis method to analyze the influence of track spatial alignment parameters on the wear of inner and outer rails, and optimize the inner and outer rail wear prediction artificial neural network models (hereinafter referred to as the inner and outer rail wear prediction models) based on the Sobol analysis results to achieve efficient and accurate prediction of railway rail wear. The inner and outer rail wear prediction artificial neural network models are as Figure 3 shown.

[0189] S401. Determine the radius R and length L of the circular curve y, the value ranges of the transition curve length \(l_0\), superelevation \(h\), front slope \(i_1\), rear slope \(i_2\), and algebraic difference of slopes \(\Delta i\) are, in sequence: 300 - 1200, 160 - 250, 20 - 55, 35 - 120, -30 - 30, -30 - 30, 0 - 30. According to the above parameter value ranges, Sobol sampling is performed to obtain two Sobol sequence matrices \(A\) and \(B\), both with a matrix size of \(n\times m\), where \(n\) is the number of sampling samples (\(n = 260\)) and \(m\) is the number of input parameters (\(m = 7\)).

[0190]

[0191] S402. The \(i\)-th column in matrix \(B\) can be replaced with the \(i\)-th column in matrix \(A\) to obtain \(m\) replacement matrices

[0192]

[0193] S403. Matrices \(A\), \(B\), There are a total of \(n\times(m + 2)\) groups of input parameter data. Through the prediction model established in S3, \(n\times(m + 2)\) groups of output parameters \(Y\) can be obtained. According to the calculation principle of the Sobol algorithm and the theory proposed by Saltelli, the i first-order influence index and total effect index of \(X\) can be expressed as:

[0194]

[0195] In the formula, is the first-order influence variance of parameter \(X\) i , where matrix \(X\) ～i represents all variables except \(X\) i ; represents the expected value of \(Y\) when \(X\) i is fixed and \(X\) ～i is taken over all values; \(V\) Xi represents the variance of the expected value within the brackets when \(X\) i is taken over all values; \(j\) represents the number of rows of the matrix; \(f(B)\) j represents the model output result corresponding to the parameters in the \(j\)-th row of matrix \(B\); \(S\) i is the first-order influence index of the \(i\)-th parameter \(X\) i , indicating the influence of the \(i\)-th parameter \(X\) i acting alone on the output \(Y\); \(S\) Ti is the total effect index, indicating the influence of the interaction between the \(i\)-th parameter \(X\) i and other variables on the output \(Y\).

[0196] The model is trained 50 times, and Sobol analysis is performed on the results of each training based on the above steps. The average calculation results are as shown in the appendix Figure 4As shown, for the inner and outer rail wear prediction models, the parameters with the least influence are the circular curve length L y and the algebraic difference in gradient Δi.

[0197] Based on the Sobol analysis calculation results, the structure of the inner and outer rail wear prediction models is optimized. The circular curve length L y and the algebraic difference in gradient Δi are removed from the input parameters and retrained to establish the final prediction model. The optimized model is trained 50 times, and the prediction effects before and after optimization are compared as Figure 5 shown. For the inner rail wear prediction model, the maximum RMSE after optimization is 0.350, the minimum is 0.050, the range is 0.300, and the standard deviation is 0.062; for the outer rail wear prediction model, the maximum RMSE after optimization is 0.427, the minimum is 0.113, the range is 0.313, and the standard deviation is 0.059.

[0198] Select the model with the smallest error for saving, and its prediction effect on the test set is as Figure 6 shown. The mean absolute percentage error MAPE is used to evaluate its prediction accuracy:

[0199]

[0200] In the formula, N is the number of samples; y i is the true value of the data; is the predicted value of the data.

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

[0202] Finally, the prediction module uses the final prediction model to achieve the prediction of railway rail wear.

[0203] The embodiments described above are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. An intelligent prediction method for rail wear considering the spatial linear shape of railways, characterized in that the steps include: S1. Establish a vehicle-track coupling dynamics model based on the vehicle structural characteristic parameters and the track structural characteristic parameters; S2. Based on the vehicle-track coupling dynamics model, a rail wear calculation model is established, and the inner and outer rail wear values ​​under different track spatial linear parameters are calculated to construct a rail wear sample data set; S3. Constructing a rail wear prediction artificial neural network model, and using the rail wear sample data set to train the rail wear prediction artificial neural network model; S4. Optimize the trained rail wear prediction artificial neural network model to obtain a final prediction model; S5. Using the final prediction model, the railway rail wear is predicted.

2. The intelligent prediction method for rail wear considering the railway spatial alignment according to claim 1 is characterized in that: The vehicle structural characteristic parameters include: frame mass, frame position, frame moment of inertia, vehicle primary suspension stiffness, vehicle secondary suspension stiffness, bogie primary damping parameter, bogie secondary damping parameter, traction rod longitudinal stiffness, anti-snaking shock absorber damping; the track structural characteristic parameters include: fastener stiffness, concrete support layer thickness, CA mortar elastic modulus and track spatial linear parameters, wherein the track spatial linear parameters include: circular curve radius, circular curve length, transition curve length, superelevation, slope, slope algebraic difference and other horizontal and longitudinal section linear parameters.

3. The intelligent prediction method for rail wear considering the railway spatial alignment according to claim 2 is characterized in that: The steps for calculating the inner and outer rail wear values ​​include: S201, input track space linear parameters, rail profile parameters, vehicle profile parameters, and total passing weight; S202, calculating wheel-rail contact conditions based on a vehicle-track coupling dynamics model; S203, calculating the rail wear depth in the wheel-rail contact patch based on the wheel-rail contact condition and the rail wear calculation model; S204, updating the rail profile based on the rail wear depth; S205, repeat S202-S204 until the maximum number of iterations is reached and then terminate; S206. Obtain inner and outer rail wear values.

4. The intelligent prediction method for rail wear considering the railway spatial alignment according to claim 1 is characterized in that: The rail wear prediction artificial neural network model includes: an input layer, an output layer, and a hidden layer; wherein the input layer is the track space linear parameters, including: the circular curve radius R, the circular curve length L y , transition curve length l0, superelevation h, front slope i1, rear slope i2, slope algebraic difference Δi; the output layer is the rail wear value, including: inner rail wear value V w1 , outer rail wear value V w2 ; The hidden layer uses an empirical formula to determine the range of the number of neurons, and the optimal number of neurons in the hidden layer is determined by trial and error. The empirical formula is as follows: 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; a is an integer from 1 to 10.

5. The intelligent prediction method for rail wear considering the railway spatial alignment according to claim 1 is characterized in that: The method for training the rail wear prediction artificial neural network model includes: S301, normalizing the data using the "maximum-minimum" normalization principle; S302, initializing the weights and thresholds of the artificial neural network, inputting the normalized data into the artificial neural network for forward propagation, using the Sigmoid function as the activation function to calculate and output the current sample calculation value; S303, error back propagation, calculating the output layer neuron error gradient term and the hidden layer neuron error gradient term according to the error between the current sample calculated value and the true value; S304, updating the weights between the hidden layer and the output layer, the weights between the input layer and the hidden layer, the thresholds of the neurons in the output layer, and the thresholds of the neurons in the hidden layer according to the calculation results of the error gradient items of the neurons in the hidden layer and the output layer; S305, repeat steps S302-S304 to train the model until the maximum number of training times is reached or the error requirement is met, and then terminate the training; S306. Based on the test set data, the root mean square error (RMSE) is used to evaluate the final training effect of the model.

6. The intelligent prediction method for rail wear considering the railway spatial alignment according to claim 1 is characterized in that: The method for optimizing the rail wear prediction artificial neural network model includes: The Sobol sensitivity analysis method is used to analyze the track spatial linear parameters and the inner rail wear V w1 and outer rail wear V w2 The impact of Based on the Sobol analysis results, the track spatial linear parameters that have little influence on the wear of the inner and outer rails are eliminated, and the model input layer data is adjusted to obtain the artificial neural network model for predicting the wear of the inner and outer rails respectively. The model is trained based on the rail wear sample data set to obtain an optimized inner and outer rail wear prediction artificial neural network model, and a mapping relationship from track spatial linear parameters to inner and outer rail wear is established to achieve the acquisition of inner and outer rail wear values.

7. An intelligent rail wear prediction system considering the spatial linear shape of railways, the system being used to implement the method according to any one of claims 1 to 6, characterized in that: include: Model building module, dataset building module, training module, optimization module and prediction module; The model building module is used to establish a vehicle-track coupling dynamics model based on vehicle structural characteristic parameters and track structural characteristic parameters; The data set construction module is used to establish a rail wear calculation model based on the vehicle-track coupling dynamics model, calculate the inner and outer rail wear values ​​under different track spatial linear parameters to construct a rail wear sample data set; 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 data set; The optimization module is used to optimize the trained rail wear prediction artificial neural network model to obtain a final prediction model; The prediction module is used to realize the prediction of railway rail wear by using the final prediction model.

8. The intelligent rail wear prediction system considering the railway spatial alignment according to claim 7 is characterized in that: The vehicle structural characteristic parameters include: frame mass, frame position, frame moment of inertia, vehicle primary suspension stiffness, vehicle secondary suspension stiffness, bogie primary damping parameter, bogie secondary damping parameter, traction rod longitudinal stiffness, anti-snaking shock absorber damping; the track structural characteristic parameters include: fastener stiffness, concrete support layer thickness, CA mortar elastic modulus and track spatial linear parameters, wherein the track spatial linear parameters include: circular curve radius, circular curve length, transition curve length, superelevation, slope, slope algebraic difference and other horizontal and longitudinal section linear parameters.

Images