An intelligent prediction method for embedded track dynamic response

Abstract

The present invention relates to an intelligent prediction method for the dynamic response of an embedded track, comprising: obtaining target embedded track parameters; inputting the target embedded track parameters into a PSO-BP prediction model, and outputting a predicted value of the dynamic performance of the target embedded track, wherein the PSO-BP prediction model is obtained by training a training set, the training set includes embedded track parameters and track dynamic performance simulation values, and the PSO-BP prediction model is constructed using a PSO particle swarm optimization BP neural network. The present invention can achieve real-time acquisition of the dynamic response of a track system under different track structure parameters.

Description

Technical Field

[0001] The invention relates to the technical field of track parameter design, and in particular to an embedded track dynamic response intelligent prediction method. Background Art

[0002] The existing subway vibration reduction tracks are mostly elastic short sleeper tracks, elastic long sleeper tracks, trapezoidal sleeper tracks, and floating plate tracks. Although the above track structures have a certain effect on alleviating the ground vibration caused by the subway, the effect on vehicle and wheel-rail noise is still not significant enough. At the same time, the ordinary fastener track form adopts discrete point support, and the rigidity of the rolling track structure is difficult to ensure its uniformity, which easily leads to unevenness of the rails and increases the vibration response of the track structure. In comparison, the embedded track adopts a continuous support method, and the rails are wrapped with elastic materials. It has significant advantages in vibration reduction and noise reduction. At the same time, it can also enable the train to have a larger axle weight and faster speed, which provides conditions for the increase of subway transportation volume.

[0003] However, the existing embedded track design, manufacturing, construction, maintenance and repair technologies are based on the tram system, and the research on the dynamic analysis of the embedded track structure is also mainly based on the tram. Compared with the tram, the subway has a higher speed, a larger axle weight, and more complex line conditions. Therefore, the existing tram-embedded track dynamics model cannot be directly used to analyze the dynamics of the subway train-embedded track system, and a new dynamics model needs to be established. At the same time, the structure of the subway embedded track is also relatively complex, and its structural parameters are closely related to its dynamic performance. If the parameter values ​​are unreasonable, the performance of the embedded track will be significantly reduced. Therefore, the parameter selection of the embedded track is very important.

[0004] The methods used in China to determine the dynamic performance of tracks mainly rely on field measurements and dynamic simulations, but both methods have major drawbacks. Field measurements cannot meet the experimental requirements because there are currently few subway embedded tracks built in China. Therefore, it is usually necessary to cast track models with different parameters to determine their dynamic performance, which has problems such as high experimental costs and low timeliness. Although dynamic simulation solves the problem of high costs, the time required for simulation is relatively long, and embedded tracks with different parameters require different models to be established, making it impossible to obtain the track dynamic performance in real time.

[0005] If the dynamic performance corresponding to the track parameters can be predicted in the design stage, the appropriate track parameters can be obtained accordingly, thereby obtaining better dynamic performance, while improving the riding comfort of passengers and reducing the impact of subway vibration on the environment. However, most of the current domestic research on the prediction method of the impact of track parameters on track dynamics is aimed at ballasted tracks, plate ballastless tracks and double-block ballastless tracks. The above tracks are mainly used in conventional railways, high-speed railways and early-constructed subways. There are relatively few predictions on the dynamic impact of subway embedded track parameters. Therefore, if a method for quickly predicting the dynamic performance of subway embedded tracks can be proposed, it does not require more stringent experimental conditions and higher experimental costs for on-site measurements, and at the same time solves the problems of complex modeling process and limited calculation time in obtaining the dynamic response of the system by relying on dynamic simulation. In this regard, the present invention discloses an intelligent prediction method for the dynamic response of embedded tracks. Summary of the invention

[0006] The purpose of the present invention is to provide an intelligent prediction method for the dynamic response of an embedded track. By constructing a neural network model with structural parameters such as the geometric dimensions of the embedded track, and material parameters such as the vertical and lateral stiffness and damping of the embedded track and the filling materials in the track groove as inputs, and with the dynamic response of the embedded track as output, a mapping relationship from the model input to the output is established through training with massive sample data, so as to achieve real-time acquisition of the system dynamic response (objective function) under different embedded track parameters (design variables), and solve the problem of limited calculation time in obtaining the system dynamic response by relying on dynamic simulation.

[0007] To achieve the above object, the present invention provides the following solutions:

[0008] An embedded track dynamic response intelligent prediction method, comprising:

[0009] Get the target embedded track parameters;

[0010] The target embedded orbit parameters are input into the PSO-BP prediction model, and the dynamic performance prediction value of the target embedded orbit is output, wherein the PSO-BP prediction model is obtained by training with a training set, the training set includes embedded orbit parameters and orbit dynamic performance simulation values, and the PSO-BP prediction model is constructed using a PSO particle swarm optimization BP neural network.

[0011] Optionally, obtaining the track dynamics performance simulation value includes:

[0012] Construct subway embedded track finite element model and subway vehicle model;

[0013] The wheel-rail force is obtained based on the subway vehicle model, and the wheel-rail force is applied to the subway embedded track finite element model to obtain a track dynamic performance simulation value.

[0014] Optionally, constructing a subway embedded track finite element model includes:

[0015] Using translation and section rotation partial differential equations, the lateral motion, vertical motion and torsional motion of the rail in the subway embedded track finite element model are obtained;

[0016] According to the finite element principle, the motion equation of the track plate in the subway embedded track finite element model is obtained.

[0017] Optionally, the motion equation of the track plate is:

[0018]

[0019] Where, [M] i , [C] i , [K] i represents the mass, damping and stiffness matrix of the embedded track plate; {x} i , represents the displacement, velocity, and acceleration array of the embedded track plate node; i represents the number of the embedded track; {F Γs} i , {Fg} i An array of equivalent nodal loads representing the interaction forces between the rail / foundation and the embedded track slab.

[0020] Optionally, obtaining the wheel-rail force based on the subway vehicle model includes: taking track unevenness as an excitation source for the wheel-rail system, and obtaining the wheel-rail force under track unevenness conditions based on the subway vehicle model through vertical, horizontal, directional and gauge unevenness of the track.

[0021] Optionally, the PSO-BP prediction model includes several BP neural networks, and each BP neural network output corresponds to one of the track dynamics response parameters.

[0022] Optionally, inputting the target embedded track parameters into a PSO-BP prediction model, and outputting the target embedded track dynamic performance prediction value includes:

[0023] S1. Input the target embedded orbit parameters;

[0024] S2, determining the topological structure of the BP neural network, and initializing the weights and thresholds of the BP neural network;

[0025] S3, introduce the particle swarm algorithm to optimize the weights and thresholds of the BP neural network and obtain the speed and position of the initialized particles;

[0026] S4, using the fitness function, calculate the fitness of each particle;

[0027] S5, iteratively update the initial individual and global extreme values, and obtain new particle speed and position;

[0028] S6, determine whether the iteration end condition is met, if not, return to S3 to iterate until the end condition is met, if so, enter S7;

[0029] S7. Assign the obtained global optimal solution to the weights and thresholds of the BP neural network to obtain the BP neural network optimized by the PSO particle swarm, and output the predicted value of the target embedded track dynamics performance through the optimized BP neural network.

[0030] The beneficial effects of the present invention are:

[0031] Aiming at the design problem of subway embedded track, the present invention establishes a PSO-BP neural network to predict the dynamic response of the subway embedded track system, and introduces a particle swarm algorithm to optimize the BP neural network. The dynamic response of the embedded track system can be obtained efficiently and accurately based on the structural parameters and material parameters of the embedded track, eliminating tedious modeling and simulation steps, thereby significantly improving the design efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the implementation cases of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0033] Figure 1 A flow chart of an embedded track dynamic response intelligent prediction method according to an embodiment of the present invention;

[0034] Figure 2 The finite element model of the subway embedded track according to the embodiment of the present invention;

[0035] Figure 3 Schematic diagram of the BP neural network structure of an embodiment of the present invention. DETAILED DESCRIPTION

[0036] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0037] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0038] The present invention discloses an embedded track dynamic response intelligent prediction method, comprising:

[0039] Get the target embedded track parameters;

[0040] The target embedded orbit parameters are input into the PSO-BP prediction model, and the dynamic performance prediction value of the target embedded orbit is output. The PSO-BP prediction model is obtained by training a training set, which includes simulation values ​​based on embedded orbit parameters and orbit dynamic performance. The PSO-BP prediction model is constructed using a PSO particle swarm optimization BP neural network.

[0041] Furthermore, obtaining the simulation value of the track dynamic performance includes: constructing a subway embedded track finite element model and a subway vehicle model; obtaining the wheel-rail force based on the subway vehicle model, applying the wheel-rail force to the subway embedded track finite element model, and obtaining the simulation value of the track dynamic performance.

[0042] Furthermore, constructing the subway embedded track finite element model includes:

[0043] The lateral motion, vertical motion and torsional motion of the rail in the finite element model of subway embedded track are obtained by using partial differential equations of translation and section rotation. According to the finite element principle, the motion equation of the track plate in the finite element model of subway embedded track is obtained.

[0044] The following is combined with Figure 1 -Attached Figure 3 Further explanation of an embedded track dynamic response intelligent prediction method, such as Figure 1 The specific steps shown include:

[0045] S1. Establish a finite element model of subway embedded track, such as Figure 2As shown, the track model is based on the parameters of the track plate length, width, elastic modulus, track groove width and the stiffness and damping of the groove filling material, etc., and the track model with different parameters is established within a reasonable range. The selection range of the established embedded track plate parameters is: the track plate length is 4m-6m, the change interval is 1m; the track plate width is 2.2m-2.6m, the change interval is 0.2m; the track plate elastic modulus is 3.1-3.4Mpa, the change interval is 0.1Mpa; the track groove width is 18cm-22cm, the change interval is 2cm; the vertical stiffness of the groove filling material is 6knm -1 -10knm -1 , the variation interval is 1knm -1 ; Transverse stiffness is 5knm -1 -8knm -1 , the variation interval is 1knm -1 ; Vertical damping and lateral damping are both 1knsm -1 -5knsm -1 , the range is 1knsm -1 According to the above parameter range, 270 sets of embedded track models with different parameters are reasonably established.

[0046] S2. Use multi-body dynamics software to establish a commonly used subway type B vehicle dynamics model in China. The vehicle dynamics model runs on the track. During the actual operation, the track structure forms different track unevenness due to the continuous increase of cumulative deformation. Track unevenness can cause changes in the wheel-rail vertical force and lateral force, thereby causing adverse effects on the wheel-rail system and track quality. In order to make the acquired wheel-rail force closer to reality, this embodiment selects the American five-level spectrum as the track disturbance source, sets the vehicle running speed to 80km / h, and obtains the wheel-rail force required for this example under the action of track unevenness. The parameters of the subway type B vehicle are as follows: the body mass is 39540kg; the bogie mass is 3520kg; the wheelset mass is 1539kg; the vehicle length is 19m; and the wheelbase is 2.2m.

[0047] In the dynamics software, the wheel-rail contact adopts the Hertz contact nonlinear theory, and its calculation formula is as follows:

[0048]

[0049] Where F(t) is the wheel-rail force (N); G is the wheel-rail contact force constant (m / N 2 / 3 );σZ(t) is the elastic compression between the wheel and rail (m); When there is a displacement unevenness input at the wheel-rail interface, the wheel-rail force expression is:

[0050]

[0051] Wheel-rail contact stress:

[0052]

[0053] Where Z0(t) is the unevenness; Z w j(t) is the displacement of the jth wheel at time t (m); Z r (x wj ,t) is the displacement of the rail under the jth wheel at time t (m); s is the stress constant determined by Hertz theory (N 2 / 3 / m 2 ), F j (t) is the wheel-rail force when there is displacement irregularity at the wheel-rail interface (N).

[0054] The power spectral density function is a statistical function that describes track irregularities, and the U.S. track spectrum function is as follows:

[0055] (1) The track is uneven:

[0056]

[0057] (2) The track direction is not smooth:

[0058]

[0059] (3) Track level is not smooth:

[0060]

[0061] (4) Uneven track gauge:

[0062]

[0063] Where S(φ) is the power spectrum density of track irregularity [m 2 / (1 / m)]; φ is the spatial frequency of track irregularity (1 / m); A is the roughness constant (m); φ1 and φ2 are the cutoff frequencies (1 / m).

[0064] S3, the wheel-rail force obtained in S2 is applied to the embedded track plate established in S3 through finite element software, where the analysis step is set to 0.003S, and the wheel-rail force movement speed is consistent with the vehicle running speed. Six dynamic performance indicators, including vertical displacement and acceleration of the rail, lateral displacement and acceleration of the rail, and vertical displacement and acceleration of the track plate, are obtained respectively. Based on this, 270 sets of sample data sets are established.

[0065] Firstly, an embedded track model is established using finite element software, in which the rail is simulated by a Timoshenko beam to consider the vertical, lateral and torsional vibration characteristics of the rail. The lateral, vertical and torsional motions of the rail are represented by partial differential equations of translation and section rotation.

[0066] (1) Rail lateral vibration equation:

[0067]

[0068] (2) Rail vertical vibration equation:

[0069]

[0070] (3) Rail torsional vibration equation:

[0071]

[0072] Where y, z, φ represent the lateral, vertical and torsional displacements of the rail (m); Ψ y ,Ψ z Indicates the deformation of the rail section around the z / y coordinate axis (rad); sr 、z sr ,φ sr Indicates the lateral, vertical and torsional displacements of the trackbed plate at the rail groove (m); K yr , K zr , K φr Indicates the transverse, vertical and torsional shear stiffness of the rail filling material (N / m); C yr , C zr , C φr Indicates the transverse, vertical and torsional shear damping of the rail filling material (Ns / m); F wryj 、F wrzj 、M Gj It represents the vertical and lateral loads (N) and moments (N·m) acting on the rail by the wheels; I z ,I y Indicates the moment of inertia of the rail section about the y / z coordinate axis (mm 4 ); ρ, G, GK, A represent the density of the rail per unit length (kg / m 3 ), shear modulus (Mpa), torsional stiffness (N·m / rad), cross-sectional area (mm 2 );K y , K z N represents the shear shape factor in the y / z direction of the rail section; w is the total number of wheels; is the wheel coordinate at time t; x is the rail coordinate; t is the wheel movement time; E is the rail elastic modulus (Mpa); I ois the rail polar moment of inertia (mm 4 ).

[0073] A finite element model of embedded ballastless track slab is established using three-dimensional six-sided solid elements.

[0074] According to the finite element principle, the motion equation of the track plate can be expressed as:

[0075]

[0076] Where, [M] i , [C] i , [K] i represents the mass, damping and stiffness matrix of the embedded track plate; {x} i , {x(·)} i , {x(··)} i represents the displacement, velocity, and acceleration array of the embedded track plate node; i represents the number of the embedded track; N slab Indicates the total number of track plates in the model; {F Γs} i 、{F g} i An array of equivalent nodal loads representing the interaction forces between the rail / foundation and the embedded track slab.

[0077] S4. Build the initial BP neural network structure and set the BP neural network to a three-layer structure, such as Figure 3 As shown in the figure, they are the input layer, hidden layer and output layer respectively, where a total of 6 BP neural networks are built to correspond to 6 dynamic performances. Assume that the BP neural network input layer has O nodes, the hidden layer has H nodes, and the output layer has Q nodes.

[0078] Since this embodiment adopts a single-output BP neural network model, a total of 6 BP neural network prediction models corresponding to 6 output quantities are established and integrated into a unified network model. The error function is defined as:

[0079]

[0080] Where: is the output of output node k when sample p acts on it, is the target value of the output node k when sample p acts, m is the dimension of the output variable, and N is the number of training samples.

[0081] Among them, the number of training samples N is 200, and the dimension m of the output variable is 1.

[0082] Building the initial BP neural network structure includes:

[0083] (1) Initialize network weights wnk 、v kj , thresholds a, b

[0084] (2) Calculate the output value q of the hidden layer neuron k

[0085]

[0086] Where: k = 1, 2…h; f is the hidden layer activation function; x n is the nth input signal.

[0087] (3) Calculate the output value o of the output neuron j .

[0088]

[0089] (4) Weight update

[0090]

[0091] v kj (t+1)=v kj (t)+ηq k (y j -o j )

[0092] In the formula, η is the parameter of the learning rate, where the learning rate η is 0.01.

[0093] (5) Threshold update

[0094]

[0095] b j (t+1)=b j (t)+(y j -o j )

[0096] (6) Determine whether the iteration end condition is met. If not, continue to iterate until the condition is met. The maximum number of iterations is 70.

[0097] The number of nodes in the hidden layer is calculated using the formula: Where: H is the number of hidden layer nodes; i is the number of input layer nodes; m is the number of output layer nodes; a is an integer from 1 to 10, and there are 10 hidden layer nodes in this model.

[0098] S5. In order to improve the prediction ability of BP neural network, the particle swarm optimization (PSO) algorithm is introduced to optimize it. By finding the global optimal solution, the optimal weights and thresholds of BP neural network are obtained. At the same time, the data set obtained in S4 is used to train and test it, and the mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE) are used as evaluation indicators to evaluate the performance of BP neural network.

[0099] The particle speed and position update formula is:

[0100]

[0101] Where: ω is the inertia weight, which controls the inertia of velocity update; v ij t+1 is the new velocity of particle i in dimension j; x t ij is the current position of particle i in dimension j; Pbest ij is the value of the jth dimension of the individual best position of particle i; gbest ij is the value of the jth position of the global optimal position; c1 and c2 are acceleration factors, representing the influence of individual experience and group experience on speed update respectively; r1 and r2 are random numbers between 0 and 1.

[0102] The calculation formulas for MAE, RMSE, and MAPE are:

[0103]

[0104]

[0105] In the formula, y is the true value; M is the number of represented values; is the predicted value;

[0106] S6. Through the above steps from S1 to S5, a PSO-BP neural network prediction model corresponding to six dynamic performance indicators, namely, vertical displacement and acceleration of the rail, lateral displacement and acceleration of the rail, and vertical displacement and acceleration of the track plate, is obtained.

[0107] S7. The obtained PSO-BP neural network prediction model can be used to make real-time predictions on the track dynamics performance when the embedded track material parameters are known.

[0108] The specific process of using the built PSO-BP neural network for prediction is as follows:

[0109] S71. Input the embedded track parameters, where the track plate length is 5m, width is 2.2m, central plate thickness is 25cm, elastic modulus is 34Mpa, and vertical stiffness of the filling material in the track groove is 9kn·m -1 , lateral stiffness is 7kn·m -1 , vertical damping is 5kns·m -1 , lateral damping is 4kns·m -1 , track groove width is 20cm;

[0110] S72, determine the BP neural network topology, initialize the weights and thresholds of the BP neural network; the weights can represent the strength of the connection between two neurons; the threshold can remove weak signals from the input signal to reduce the amount of calculation. By initializing the weights and thresholds of the BP neural network, the network can converge quickly in the early stage of training.

[0111] S73, introducing the particle swarm (PSO) algorithm to optimize the hyperparameters such as weights and thresholds of the BP neural network, firstly obtaining the speed and position of the initialized particles; wherein each particle represents a random solution, the speed represents the moving speed of the particle in the search space, and the position represents the position in the search space, also called the solution vector;

[0112] S74, calculate the fitness of the particles of PSO; all particles have a fitness value determined by the fitness function, which can be used to evaluate the quality of the current solution. The particles with higher fitness values ​​are more likely to become the basis for the next search, thereby finding a better solution. Among them, the fitness function used in this embodiment is:

[0113]

[0114] Where X is the value of the objective function; Yj is the true value; Yj′ is the predicted value; and N is the number of samples.

[0115] S75. Iteratively update the initial individual and global extreme values ​​of PSO, and obtain new PSO particle speeds and positions; the individual extreme value refers to the optimal solution found by a particle itself; the global extreme value refers to the optimal solution found by particles in the entire population.

[0116] S76, determine whether the PSO algorithm meets the iteration end condition. If not, return to S73 to iterate until the end condition is met. If it is met, proceed to the next step; the iteration end condition is the set maximum number of iterations.

[0117] S77, assigning the obtained global optimal solution to the weight and threshold of the BP neural network, so as to obtain the BP neural network optimized by the PSO algorithm;

[0118] S78. The predicted value of the embedded track dynamics performance can be output through the PSO-BP neural network prediction model.

[0119] Finally, the predicted value of the embedded track dynamic performance can be obtained through iterative optimization of the PSO-BP neural network. The comparison between the predicted value of the dynamic performance and the dynamic performance obtained by simulation is shown in Table 1 below.

[0120] Table 1

[0121]

[0122] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. An embedded track dynamic response intelligent prediction method, characterized in that: include: Get the target embedded track parameters; Input the target embedded track parameters into a PSO-BP prediction model, and output a predicted value of the dynamic performance of the target embedded track, wherein the PSO-BP prediction model is obtained by training a training set, the training set includes embedded track parameters and track dynamic performance simulation values, and the PSO-BP prediction model is constructed by using a PSO particle swarm optimization BP neural network; Obtaining the track dynamics performance simulation value includes: Construct subway embedded track finite element model and subway vehicle model; Acquire wheel-rail force based on the subway vehicle model, apply the wheel-rail force to the subway embedded track finite element model, and acquire a track dynamic performance simulation value; Constructing the subway embedded track finite element model includes: Using translation and section rotation partial differential equations, the lateral motion, vertical motion and torsional motion of the rail in the subway embedded track finite element model are obtained; According to the finite element principle, the motion equation of the track plate in the subway embedded track finite element model is obtained; The motion equation of the track plate is: In the formula, [ M ] i 、[ C ] i 、[ K ] i represents the mass, damping and stiffness matrix of the embedded track plate; { x } i , , represents the displacement, velocity, and acceleration arrays of the embedded track plate nodes; i Indicates the number of the embedded track; F Γs } i 、{ F g } i A load array of equivalent nodes representing the interaction force between the rail / foundation and the embedded track plate; obtaining the wheel-rail force based on the subway vehicle model includes: taking track irregularity as an excitation source of the wheel-rail system, and obtaining the wheel-rail force under track irregularity based on the subway vehicle model through vertical, horizontal, directional and gauge irregularities of the track.

2. The embedded track dynamic response intelligent prediction method according to claim 1 is characterized in that: The PSO-BP prediction model includes several BP neural networks, and each BP neural network output corresponds to one track dynamic response parameter.

3. The embedded track dynamic response intelligent prediction method according to claim 1 is characterized in that: Inputting the target embedded track parameters into the PSO-BP prediction model, and outputting the target embedded track dynamic performance prediction value includes: S1. Input the target embedded orbit parameters; S2, determining the topological structure of the BP neural network, and initializing the weights and thresholds of the BP neural network; S3, introduce the particle swarm algorithm to optimize the weights and thresholds of the BP neural network and obtain the speed and position of the initialized particles; S4, using the fitness function, calculate the fitness of each particle; S5, iteratively update the initial individual and global extreme values, and obtain new particle speed and position; S6, determine whether the iteration end condition is met, if not, return to S3 to iterate until the end condition is met, if so, enter S7; S7. Assign the obtained global optimal solution to the weights and thresholds of the BP neural network to obtain the BP neural network optimized by the PSO particle swarm, and output the predicted value of the target embedded track dynamics performance through the optimized BP neural network.

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