A method for predicting aerodynamic loads of high-speed trains based on compressed sensing

Abstract

The present invention provides a method for predicting aerodynamic loads of high-speed trains based on compressed sensing, which transforms irregular three-dimensional control points of the surface grid of the high-speed train into normalized and geometrically regular two-dimensional control points. For known working condition data, the main modes of the flow field are obtained by intrinsic orthogonal decomposition as a sparse matrix for compressed sensing reconstruction, and the positions of the optimal characteristic sections and the optimal observation points at each group of characteristic sections are obtained by particle swarm optimization as a measurement matrix for compressed sensing reconstruction. Finally, based on a small number of observations, the pressure distribution matrix of the two-dimensional full field can be predicted, and then mapped back to the three-dimensional control point coordinates before the transformation, so as to realize the prediction of the aerodynamic loads of the high-speed train. The present invention can accurately predict the aerodynamic loads of high-speed trains under multiple working conditions based on the aerodynamic load data of high-speed trains under limited working conditions.

Description

Technical Field

[0001] The present invention belongs to the technical field of high-speed train numerical simulation, and in particular relates to a method for predicting aerodynamic loads of high-speed trains based on compressed sensing. Background Art

[0002] Compressed sensing (CS) technology can sample at a frequency much lower than that required by Shannon's sampling theorem, and thus can reconstruct the complete signal with high precision based on sparse data. This method has been widely used in the fields of communications, medicine, aerospace, remote sensing, etc., and various mature algorithms have gradually been developed, mainly divided into greedy iterative algorithms, convex optimization or optimization approximation algorithms, and reconstruction algorithms based on the Bayesian framework.

[0003] Zhao Xuan proposed a sparse reconstruction method for aircraft aerodynamic loads based on compressed sensing in his published dissertation "Reconstruction Method Based on Sparse Distributed Data and Research on Consistency of Force and Pressure Measurement Data" (CNKI, Northwestern Polytechnical University, 2023, Master's Thesis, Classification Number V19). This method can extract the characteristics of CFD calculation data, incorporate sparse pressure measurement information, and complete the reconstruction of distributed loads on two-dimensional and three-dimensional scales. However, the shortcoming of this method is that its reconstruction of three-dimensional distributed loads is actually performed on flat airfoils, and it is actually only a reconstruction of the upper and lower surfaces.

[0004] The Shenyang Aerodynamics Research Institute of Aviation Industry Corporation of China proposed a method for reconstructing wing surface pressure by constructing a deep neural network model in its patent application "A method for reconstructing wing surface pressure, electronic equipment and storage medium" (application number CN202310432279.X). This method uses a two-dimensional U-shaped convolutional neural network structure to obtain a deep neural network model for reconstructing the wing surface pressure for the holographic grid node coordinate information data of the unfolded three-dimensional wing model. However, the shortcomings of this method are: due to the use of a deep neural network model to reconstruct the surface pressure, the algorithm itself is highly complex, and at the same time cost, the scale of information data that can be processed is limited, and the interpretability of the deep learning method is poor, while compressed sensing reconstruction is about finding the minimum norm solution to underdetermined equations, and has rigorous mathematical logic. Summary of the invention

[0005] In view of the technical problems existing in the above-mentioned background technology, the present invention proposes a method for predicting the aerodynamic load of a high-speed train based on compressed sensing, which can accurately predict the aerodynamic load of a high-speed train under multiple working conditions based on the aerodynamic load data of the high-speed train under limited working conditions, thereby solving the problem that it is difficult to arrange enough sensors to obtain complete surface pressure distribution information in the current high-speed train model test, and the torque obtained by direct integration is insufficient in accuracy.

[0006] In order to solve the above technical problems, the present invention provides a method for predicting the aerodynamic load of a high-speed train based on compressed sensing. The method transforms the irregular three-dimensional control points of the surface grid of the high-speed train into normalized and geometrically regular two-dimensional control points. For known working condition data, the main modes of the flow field are obtained by intrinsic orthogonal decomposition as a sparse matrix for compressed sensing reconstruction. The positions of the optimal characteristic sections and the optimal observation points at each group of characteristic sections are obtained by particle swarm optimization as a measurement matrix for compressed sensing reconstruction. Finally, based on a small number of observation values, the pressure distribution matrix of the two-dimensional entire field can be predicted, and then mapped back to the three-dimensional control point coordinates before the transformation, so as to realize the prediction of the aerodynamic load of the high-speed train.

[0007] The method for predicting aerodynamic load of a high-speed train based on compressed sensing specifically comprises the following steps:

[0008] (1) Regularization of 3D control points on the surface of high-speed trains

[0009] (1.1) Extracting 3D control point data of high-speed train surface mesh

[0010] That is, extract the three-dimensional control point coordinate data of the high-speed train surface grid in CFD simulation, take the real body size as the standard, retain all x, y, z coordinates to the required accuracy, reduce the size of the data, delete the repeated control points, take the average pressure value as the value of the control point, and then use the three-dimensional Cartesian coordinate system to sort all the control points in multiple levels;

[0011] (1.2) Expand the 3D control point data into 2D control points and perform normalization and interpolation processing

[0012] That is, the x value of the three-dimensional coordinate is used as the x' value in the two-dimensional expansion, and the sorting number when the x value is the same is used as the y' value in the two-dimensional expansion. The x' and y' are normalized, and the accuracy of x' is retained to 0.001m, and the accuracy of y' is retained to 0.005m, that is, the data points in the y' direction are no more than 200, and the normalized two-dimensional control point coordinate data is obtained. For each two-dimensional control point, the association with its three-dimensional coordinate data before sorting is retained; then the normalized two-dimensional control point coordinate data is used to interpolate x' and y' at intervals of 0.001m;

[0013] (2) After normalizing x' and y' to the range of [0,1], select all data points where y' = 0.5, obtain the multi-condition pressure distribution matrix, and divide it into a training set and a validation set;

[0014] (3) Extract the main modes of the flow field of the training set;

[0015] (4) Obtaining the optimal characteristic cross-section position of the high-speed train perpendicular to the x' axis;

[0016] (5) Obtain the multi-condition pressure distribution matrix at all characteristic sections of the high-speed train perpendicular to the x' axis;

[0017] (6) Extract the main modes of the flow field of all characteristic sections of the high-speed train perpendicular to the x' axis;

[0018] (7) Obtaining the optimal observation point position at each set of characteristic sections;

[0019] (8) Obtain the multi-condition pressure distribution matrix of all cross sections of the high-speed train perpendicular to the y' axis;

[0020] (9) Extract the main modes of all sections of the high-speed train perpendicular to the y' axis;

[0021] (10) reconstructing the two-dimensional pressure distribution of the entire vehicle based on the data observed by the pressure sensors installed on the vehicle body;

[0022] (11) The predicted three-dimensional pressure distribution is integrated to obtain the prediction result of the aerodynamic load of the high-speed train.

[0023] The method for predicting aerodynamic loads of high-speed trains based on compressed sensing, wherein the specific process of step (2) is as follows: randomly generate an arrangement from the regularized two-dimensional control point coordinate data, reorder all known working conditions according to the arrangement, and divide the training set and the verification set into a ratio of 8:2; then merge the data at y'=0.5 under all working conditions to obtain a multi-working condition pressure distribution matrix.

[0024] The method for predicting aerodynamic loads of high-speed trains based on compressed sensing, wherein the step (3) is to use intrinsic orthogonal decomposition to extract the first 10 basis functions of the flow field of the training set as the sparse matrix reconstructed by compressed sensing.

[0025] The method for predicting aerodynamic loads of high-speed trains based on compressed sensing, wherein the step (4) is iteratively optimized by a particle swarm optimization algorithm, specifically comprising the following steps:

[0026] (4.1) Initialize the particle swarm dimension d, scale n, particle velocity state matrix v, particle position state matrix x, and individual extreme values and global extremum

[0027] (4.2) Establish a mapping between temporary random mutation particles and negative ideal points, and determine the random mutation particles; the specific process is:

[0028] exist Randomly search for a point in the neighborhood of As the position of the temporary random mutation particle, the formula is as follows:

[0029]

[0030] in, is the position state vector of the ith particle at the kth iteration, r is a random number in the range [-0.5, 0.5], x max is the maximum feasible variation interval, set to 1;

[0031] (4.3) According to individual extreme values Global extreme value With random mutation particles To update the speed and position status of each particle; the specific process is:

[0032] By temporarily randomly mutating particles The location and individual extreme value of The location and global extremum of The position of constitutes the mutation parent, select the negative ideal point x F , the formula is as follows:

[0033]

[0034] Assumption Selection As a negative ideal point, find the midpoint x of the other two points C , the formula is as follows:

[0035]

[0036] Perform negative ideal point mapping and obtain the mapping point x R is the random mutation point p k if The position of is as follows:

[0037]

[0038] Among them, α is the negative ideal point mapping coefficient, which is generally taken as α = 1.3 ~ 0.5 decreasing;

[0039] (4.4) The position state of the particle is used as the observation matrix reconstructed by compressed sensing to update the fitness of each particle; the specific process is:

[0040] According to individual extreme value Global extreme value With random mutation particles To update the speed and position status of each particle, the formula is as follows:

[0041]

[0042]

[0043] Among them, v is the particle velocity state matrix, x is the particle position state matrix, k is the number of iterations, i is the particle number, d is the velocity dimension, ω1, ω2 are inertia factors, c1, c2 are learning factors, r1, r2, r3 are random numbers in the range [0, 1], p k i is the optimal position experienced by the i-th particle up to the kth generation, p k g is the optimal position experienced by the entire particle swarm up to generation k, p k if are random mutation particles;

[0044] (4.5) Update the individual extreme value of the particle swarm Global extreme value Specifically:

[0045] When updating the speed and position status of each particle, check whether it exceeds the limit range. The speed limit range is [-0.5, 0.5], and the position limit range is [0, 1];

[0046] (4.6) Randomly select the validation set working condition at the same interval of iteration number, record the result matrix of compressed sensing reconstruction using the position state of the current global extreme value as the observation matrix, and the root mean square error with the validation set experimental data; the specific process is:

[0047] The particle position state is used as the observation matrix reconstructed by compressed sensing to update the fitness of each particle. The observation matrix is ​​initialized to d rows, the column coordinate range is between [0,1], and it is an all-zero matrix with an interval of 0.001. Then the dth row, the vth id The position of the column element is assigned 1, indicating that a sensor is placed here, where v id Represents the value of the dth dimension of the ith particle in the velocity state matrix;

[0048] For the section at position y'=0.5, for all training set conditions, the corresponding observation values ​​are extracted respectively, and the sensor matrix and the observation values ​​are used as input for compressed sensing reconstruction. The root mean square error is calculated from the reconstructed values ​​of all training set conditions and the numerical values ​​obtained by CFD simulation as the new fitness of the particle. The numerical expressions of the sensor matrix and the root mean square error are as follows:

[0049]

[0050] Among them, Θ is the sensor matrix, Φ is the measurement matrix, Ψ is the sparse matrix, RMSE is the root mean square error, β rec is the reconstructed signal vector, β ori is the original signal vector, n β is the signal length;

[0051] The representation of compressed sensing reconstruction using the basis pursuit algorithm is:

[0052]

[0053] Among them, γ is the observation value, s is the sparse vector, and β is the target reconstruction matrix;

[0054] Let γ=uw, rewrite the constraint as γ=Θ(uw), and use l1 norm instead of l0 norm to transform the problem into a linear programming problem, as shown below:

[0055]

[0056] Among them, x = [u; w] is the solution to be found; c is a vector of all 1s, that is, [1,1,…,1] 1×2n ; So c T x constitutes a linear equation system to be solved, n is the order of the sparse matrix, which is the same as the length of the sparse vector, A is the artificially constructed matrix [Θ, -Θ], b = γ; solve the linear programming problem, and get x0 = [u0; w0], then s0 = x0 (1: n) - x0 (n + 1: 2n), x is the solution obtained by the linear programming function, subscript 0 indicates the solution to be solved, n is the length of the s sparse vector, n is equal to the length of u0 and w0, and the first n bits of x0 are subtracted from the last n bits, that is, s0 = u0 - w0; then the reconstructed result matrix is ​​obtained through β = Ψs, and finally the spatial average value Mean at the cross section is added;

[0057] According to the new fitness of all particles, the individual extreme value and global extreme value of the particle swarm are updated. The formula is as follows:

[0058]

[0059] A validation set condition is randomly selected every time the same number of iterations is gapped, and the result matrix of compressed sensing reconstruction using the position state of the current global extreme value as the observation matrix is ​​recorded, as well as the relative error with the validation set experimental data;

[0060] (4.7) Determine whether the current iteration number k of the particle swarm optimization reaches the preset maximum iteration number. If so, execute the following step (4.8); otherwise, increase the iteration number by 1 and execute the above step (4.2);

[0061] (4.8) Determine whether the relative error of the compressed sensing reconstruction of the verification set working condition using the current global extreme value position state as the observation matrix scheme is less than the error required by the project. If so, execute the following step (4.9), otherwise, increase the particle swarm size by 1, reset the iteration number to zero, and then execute the above step (4.2);

[0062] (4.9) Determine whether the particle swarm size has reached the upper limit. If so, execute the following step (4.10). Otherwise, increase the particle swarm size by 1, reset the iteration number, and then select random mutation particles.

[0063] (4.10) Obtain the optimal characteristic section position

[0064] That is, the current position state of the global extreme value is taken as the optimal characteristic section position, and N groups of characteristic section positions are obtained.

[0065] The method for predicting aerodynamic load of a high-speed train based on compressed sensing, wherein the step (5) specifically comprises the following steps:

[0066] (5.1) From the normalized pressure distribution matrix, for all known working conditions, select N groups of characteristic sections according to the results of step (4);

[0067] (5.2) Re-dividing the working conditions reordered in step (2) into a training set, a validation set, and a test set in a ratio of 6:2:2;

[0068] (5.3) The data of each group of cross sections under all working conditions are combined to obtain N groups of multi-condition pressure distribution matrices.

[0069] The method for predicting aerodynamic loads of high-speed trains based on compressed sensing, wherein: step (6) is to use intrinsic orthogonal decomposition to extract basis functions of each order for the training set data of each group of cross sections, and retain the first 10 basis functions as the sparse matrix of compressed sensing reconstruction; step (7) is to perform iterative optimization through a particle swarm optimization algorithm, and take the position state of the global extreme value when the iteration terminates as the optimal observation point.

[0070] The method for predicting aerodynamic loads of high-speed trains based on compressed sensing, wherein: step (8) is to merge the data of all cross sections perpendicular to the y' axis under the working conditions of the training set from the regularized pressure distribution matrix to obtain a multi-condition pressure distribution matrix; step (9) is to use intrinsic orthogonal decomposition to extract the first 10 basis functions of all cross sections perpendicular to the y' axis as a sparse matrix for compressed sensing reconstruction.

[0071] The method for predicting aerodynamic load of a high-speed train based on compressed sensing, wherein the step (10) specifically includes the following steps:

[0072] (10.1) Randomly select a working condition from the test set data divided in step (5), and use the optimal observation point to obtain the result matrix of compressed sensing reconstruction at all characteristic sections perpendicular to the x' axis;

[0073] (10.2) Taking the characteristic section position as the observation point, the result matrix of compressed sensing reconstruction perpendicular to the y' axis is obtained, which is the predicted two-dimensional full-field pressure distribution matrix;

[0074] (10.3) Extract the predicted data at the two-dimensional control point corresponding to the original three-dimensional control point as the predicted three-dimensional control point data.

[0075] The high-speed train aerodynamic load prediction method based on compressed sensing, wherein the formula for the high-precision high-speed train aerodynamic load prediction result in step (11) is as follows:

[0076]

[0077]

[0078] Where ρ is the fluid density, which is 1.225 kg / m 3 , V is the velocity of the incoming airflow relative to the train, S x is the reference area, the cross-sectional area of ​​the train in the x direction is selected as the reference area, H is the reference length, the height of the train compartment is selected as the reference length, D is the resistance, L is the lift, S is the lateral force, M x is the overturning moment; M y is the pitching moment, M z is the lateral moment, and the moment points are selected as the centroid positions of each car of the train; C D is the drag coefficient, C L is the lift coefficient, C S is the lateral force coefficient, C mx is the overturning moment coefficient, C my is the pitch moment coefficient, C mz is the cornering moment coefficient.

[0079] By adopting the above technical solution, the present invention has the following beneficial effects:

[0080] The present invention

[0081] (1) The present invention applies compressed sensing technology to the field of high-speed train numerical simulation technology, enriching the application scope of compressed sensing technology, and realizing the prediction of the aerodynamic load distribution of the entire vehicle using only a small number of observation values, effectively reducing the limitation of sensor layout costs on experiments.

[0082] (2) The two-dimensional control point coordinates of the present invention are denser than the three-dimensional control point coordinates, ensuring that after reconstructing the two-dimensional full-field pressure distribution matrix, the original three-dimensional full-field pressure distribution can be restored without causing information loss in this link.

[0083] (3) The method of the present invention of unfolding the high-speed train in two dimensions perpendicular to the incoming flow direction has a good adaptability to different cross sections, so that the unfolded two-dimensional flow field retains the spatial characteristics of the original three-dimensional flow field to the greatest extent.

[0084] (4) The present invention uses the basis functions obtained by intrinsic orthogonal decomposition as a sparse matrix to utilize the characteristics of the flow field itself. The compressed sensing method used has stronger interpretability than the machine learning method, and can flexibly adjust the number of observation points required according to the actual engineering accuracy requirements.

[0085] (5) The present invention is based on adapting to the accurate prediction of the aerodynamic load of high-speed trains under multiple working conditions. It only needs to replace the multiple working conditions with unsteady conditions and use the flow field snapshot as the input parameter of the intrinsic orthogonal decomposition to realize the prediction of the aerodynamic load of the high-speed train under unsteady operation, which has a broad application space. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings in the following description are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0087] Figure 1 This is a flow chart of a method for predicting aerodynamic load of a high-speed train based on compressed sensing according to the present invention;

[0088] Figure 2 This is a particle swarm optimization flow chart of the high-speed train aerodynamic load prediction method based on compressed sensing of the present invention;

[0089] Figure 3 It is a two-dimensional unfolding schematic diagram of the optimal characteristic cross section of the high-speed train aerodynamic load prediction method based on compressed sensing of the present invention;

[0090] Figure 4 This is a schematic diagram of the optimal characteristic cross-section position of the high-speed train aerodynamic load prediction method based on compressed sensing of the present invention. DETAILED DESCRIPTION

[0091] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. 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.

[0092] The present invention is further explained below in conjunction with specific implementation modes.

[0093] like Figure 1 As shown, the method for predicting the aerodynamic load of a high-speed train based on compressed sensing provided in this embodiment specifically includes the following steps:

[0094] 1) Regularize the 3D control points on the surface of high-speed trains

[0095] Extract the three-dimensional control point coordinate data of the surface mesh of the high-speed train in CFD simulation, take the actual body size as the standard, retain all x, y, z coordinates to the required accuracy, reduce the size of the data, delete duplicate control points, and take the average pressure as the value of the control point. In this implementation, x, y, z are retained to 0.1m, and the size of data points is reduced as much as possible while ensuring that the three-dimensional shape characteristics of the body are not destroyed.

[0096] Using a three-dimensional Cartesian coordinate system, all control points are sorted in multiple levels, first sorted in ascending order by x value. When the x values ​​are the same, all points with y < 0 are first extracted, and sorted in ascending order by z value first. When the z values ​​are the same, if z <z max / 2, sort in descending order according to y value, if z>=z max / 2, sort in ascending order according to the y value; then extract all the points with y ≥ 0, and sort them in descending order according to the z value first. If the z values ​​are the same, <z max / 2, sort in descending order according to y value, if z>=z max / 2 sorts in ascending order according to y value, and the sorting results of y>0 are concatenated after the sorting results of y<0.

[0097] The x value of the three-dimensional coordinate is used as the x' value during two-dimensional expansion; the sorting sequence number when the x value is the same is used as the y' value during two-dimensional expansion, and x' and y' are normalized. The accuracy of x' is retained to 0.001m, and the accuracy of y' is retained to 0.005m, that is, the data points in the y' direction are no more than 200, and the regularized two-dimensional control point coordinate data is obtained. For each two-dimensional control point, the association with its three-dimensional coordinate data before sorting is retained.

[0098] The normalized two-dimensional control point coordinate data is interpolated for x' and y' at intervals of 0.001m.

[0099] (2) After normalizing x' and y' to the range of [0,1], all data points where y'=0.5 are selected to obtain the multi-condition pressure distribution matrix and divide it into a training set and a validation set; specifically, a 1-T arrangement is randomly generated from the regularized pressure distribution matrix, all known working conditions are reordered according to this arrangement, and the training set and the validation set are divided into a ratio of 8:2, where T is the number of groups of known working conditions; the data at y'=0.5 under all working conditions are combined to obtain the multi-condition pressure distribution matrix.

[0100] (3) Extract the main modes of the flow field of the training set

[0101] For the training set data, the spatial average Mean is calculated as the zero-order mode; the spatial average is subtracted from all data points, and the SVD method of intrinsic orthogonal decomposition is used to obtain the basis functions of each order, and the first 10 basis functions are retained as the sparse matrix of compressed sensing reconstruction.

[0102] (4) Obtain the optimal characteristic cross-section position of the high-speed train perpendicular to the x' axis; specifically, it is iteratively optimized through the particle swarm optimization algorithm. The process is shown in the attached figure. Figure 2 ,as follows:

[0103] (4.1) Initialize the particle swarm’s dimension d, size n, velocity state matrix v, position state matrix x, and individual extreme values and global extremum

[0104] (4.2) Establish a mapping between temporary random mutation particles and negative ideal points, and determine the random mutation particles; the specific process is:

[0105] exist Randomly search for a point in the neighborhood of As the position of the temporary random mutation particle, the formula is as follows:

[0106]

[0107] in, is the position state vector of the ith particle at the kth iteration, r is a random number in the range [-0.5, 0.5], x max is the maximum feasible variation interval, set to 1;

[0108] (4.3) According to individual extreme values Global extreme value With random mutation particles To update the speed and position status of each particle; the specific process is:

[0109] By temporarily randomly mutating particles The location and individual extreme value of The location and global extremum of The position of constitutes the mutation parent, select the negative ideal point x F , the formula is as follows:

[0110]

[0111] Assumption Selection As a negative ideal point, find the midpoint x of the other two points C , the formula is as follows:

[0112]

[0113] Perform negative ideal point mapping and obtain the mapping point x R is the random mutation point p k if The position of is as follows:

[0114]

[0115] Among them, α is the negative ideal point mapping coefficient, which is generally taken as α=1.3~0.5 decreasingly.

[0116] (4.4) The position state of the particle is used as the observation matrix reconstructed by compressed sensing to update the fitness of each particle; the specific process is:

[0117] According to individual extreme value Global extreme value With random mutation particles To update the speed and position status of each particle, the formula is as follows:

[0118]

[0119]

[0120] Where v is the particle velocity matrix, x is the particle position matrix, k is the number of iterations, i is the particle number, d is the velocity dimension, ω1, ω2 are inertia factors, c1, c2 are learning factors, r1, r2, r3 are random numbers in the range [0, 1], and p k i is the optimal position experienced by the i-th particle up to the kth generation, p k g is the optimal position experienced by the entire particle swarm up to generation k, p k if are random mutation particles;

[0121] (4.5) Update the individual extreme value of the particle swarm Global extreme value Specifically: when updating the speed and position status of each particle, check whether it exceeds the limit range. The speed limit range is [-0.5, 0.5], and the position limit range is [0, 1];

[0122] (4.6) Randomly select the validation set working condition at the same interval of iteration number, record the result matrix of compressed sensing reconstruction using the position state of the current global extreme value as the observation matrix, and the root mean square error with the validation set experimental data; the specific process is:

[0123] The particle position state is used as the observation matrix reconstructed by compressed sensing to update the fitness of each particle. The observation matrix is ​​initialized to d rows, the column coordinate range is between [0,1], and it is an all-zero matrix with an interval of 0.001. Then the dth row, the vth id The position of the column element is assigned 1, indicating that a sensor is placed here, where v id Represents the value of the dth dimension of the ith particle in the velocity state matrix;

[0124] For the section at position y'=0.5, for all training set conditions, the corresponding observation values ​​are extracted respectively, and the sensor matrix and the observation values ​​are used as input for compressed sensing reconstruction. The root mean square error is calculated between the reconstructed values ​​of all training set conditions and the numerical values ​​obtained by CFD simulation as the new fitness of the particle. The mathematical expressions of the sensor matrix and the root mean square error are as follows:

[0125]

[0126] Among them, Θ is the sensor matrix, Φ is the measurement matrix, Ψ is the sparse matrix, RMSE is the root mean square error, β rec is the reconstructed signal vector, β ori is the original signal vector, n β is the signal length;

[0127] The representation of compressed sensing reconstruction using the basis pursuit algorithm is:

[0128]

[0129] Among them, γ is the observation value, s is the sparse vector, and β is the target reconstruction matrix;

[0130] Since the result of the linear programming function linprog() in Matlab is positive, but the sparse vector itself is not positive or negative, let γ = uw, rewrite the constraint condition as γ = Θ(uw), and use l1 norm instead of l0 norm to transform the problem into a linear programming problem. The expression is as follows:

[0131]

[0132] Among them, x = [u; w] is the solution to be found; c is a vector of all 1s, that is, [1,1,…,1] 1×2n ; So c T x constitutes a linear equation system to be solved, n is the order of the sparse matrix, which is the same as the length of the sparse vector, A is an artificially constructed matrix [Θ, -Θ], and b = γ;

[0133] Solve the linear programming problem and get x0 = [u0; w0], then s0 = x0 (1: n) - x0 (n + 1: 2n), x is the solution obtained by the linear programming function, subscript 0 indicates the solution, n is the length of the s sparse vector, n is equal to the length of u0 and w0, subtract the first n bits from the last n bits in x0, and get s0 = u0 - w0; then get the reconstructed result matrix through β = Ψs, and finally add the spatial average value Mean at the section;

[0134] According to the new fitness of all particles, the individual extreme value and global extreme value of the particle swarm are updated. The formula is as follows:

[0135]

[0136] A validation set condition is randomly selected every time the same number of iterations is gapped, and the result matrix of compressed sensing reconstruction using the position state of the current global extreme value as the observation matrix is ​​recorded, as well as the relative error with the validation set experimental data;

[0137] (4.7) Determine whether the current iteration number k of the particle swarm optimization reaches the preset maximum iteration number. If so, execute the following step (4.8); otherwise, increase the iteration number by 1 and execute the above step (4.2);

[0138] (4.8) Determine whether the relative error of the compressed sensing reconstruction of the verification set working condition using the current global extreme value position state as the observation matrix scheme is less than the error required by the project. If so, execute the following step (4.9), otherwise, increase the particle swarm size by 1, reset the iteration number to zero, and then execute the above step (4.2);

[0139] (4.9) Determine whether the particle swarm size has reached the upper limit. If so, execute the following step (4.10). Otherwise, increase the particle swarm size by 1, reset the iteration number, and then select random mutation particles.

[0140] (4.10) Obtain the optimal characteristic section position

[0141] That is, the current position state of the global extreme value is taken as the optimal characteristic section position, and N groups of characteristic section positions are obtained.

[0142] The two-dimensional development diagram of the optimal characteristic section is shown in the attached Figure 3The optimal characteristic section position is selected according to the attached Figure 4 .

[0143] (5) Obtain the multi-condition pressure distribution matrix at all characteristic sections of the high-speed train perpendicular to the x' axis; the specific process is as follows:

[0144] (5.1) From the normalized pressure distribution matrix, for all known working conditions, all data points with the same x value are extracted with x = 0.1 m as the initial value and 0.5 m as the interval. Assume that a total of N groups of sections are selected, and there are a total of T working conditions;

[0145] (5.2) Re-dividing the working conditions reordered in step (2) into a training set, a validation set, and a test set in a ratio of 6:2:2;

[0146] (5.3) The data of each group of cross sections under all working conditions are combined to obtain N groups of multi-condition pressure distribution matrices.

[0147] (6) Extract the main modes of the flow field of all characteristic sections of the high-speed train perpendicular to the x' axis. The method is the same as step (3), specifically: use intrinsic orthogonal decomposition to extract the basis functions of each order for the training set data of each group of sections, and retain the first 10 basis functions as the sparse matrix of compressed sensing reconstruction.

[0148] (7) Using a particle swarm optimization method to obtain the optimal observation point for each group of cross sections; wherein the particle swarm optimization method is the same as step (4), and the position state of the global extreme value when the iteration terminates is used as the optimal observation point.

[0149] (8) Obtain a multi-condition pressure distribution matrix of all cross sections perpendicular to the y' axis of the high-speed train; specifically, from the normalized pressure distribution matrix, select all cross sections perpendicular to the y' axis at intervals of 0.001 m, merge their data under the training set working conditions, and obtain a multi-condition pressure distribution matrix.

[0150] (9) Extract the main modes of all sections of the high-speed train perpendicular to the y' axis; specifically, for all sections perpendicular to the y' axis, use the intrinsic orthogonal decomposition to extract the first 10 basis functions as the sparse matrix of compressed sensing reconstruction.

[0151] (10) Reconstruct the two-dimensional pressure distribution of the entire vehicle based on the data observed by a limited number of pressure sensors arranged on the vehicle body; the specific process is as follows:

[0152] (10.1) Randomly select a working condition from the test set data divided in step (5), extract the pressure distribution data at the optimal observation point of all characteristic sections perpendicular to the x' axis as the observation value, and use the optimal observation point to obtain the result matrix of compressed sensing reconstruction at all characteristic sections respectively;

[0153] (10.2) Taking the characteristic section position as the observation point and the reconstructed result matrix as the observation value, the result matrix of compressed sensing reconstruction perpendicular to the y' axis is obtained, which is the predicted two-dimensional full-field pressure distribution matrix;

[0154] (10.3) Extract the predicted data at the two-dimensional control points corresponding to all the original three-dimensional control points as the predicted three-dimensional control point data.

[0155] (11) By integrating the predicted three-dimensional pressure distribution, the high-precision prediction result of the aerodynamic load of the high-speed train can be obtained, and the formula is as follows:

[0156]

[0157]

[0158] Where ρ is the fluid density, which is 1.225 kg / m 3 , V is the velocity of the incoming airflow relative to the train, S x is the reference area, the cross-sectional area of ​​the train in the x direction is selected as the reference area, H is the reference length, the height of the train compartment is selected as the reference length, D is the resistance, L is the lift, S is the lateral force, M x is the overturning moment (or rolling moment); M y is the pitching moment, M z is the lateral moment (or yaw moment), and the moment points are selected as the centroid positions of each car of the train; C D is the drag coefficient, C L is the lift coefficient, C S is the lateral force coefficient, C mx is the overturning moment coefficient, C my is the pitch moment coefficient, C mz is the cornering moment coefficient.

[0159] The present invention can accurately predict the aerodynamic load of a high-speed train under multiple working conditions based on the aerodynamic load data of the high-speed train under limited working conditions, solving the problem that it is difficult to arrange enough sensors to obtain complete surface pressure distribution information in the current high-speed train model test, and the torque obtained by direct integration is insufficient in accuracy.

[0160] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting aerodynamic loads of high-speed trains based on compressed sensing, characterized in that: After transforming the irregular three-dimensional control points of the high-speed train surface grid into normalized and geometrically regular two-dimensional control points, for known working condition data, the main modes of the flow field are obtained by intrinsic orthogonal decomposition as the sparse matrix of compressed sensing reconstruction, and the position of the optimal characteristic section and the optimal observation point position at each group of characteristic sections are obtained by particle swarm optimization as the measurement matrix of compressed sensing reconstruction. Finally, based on a small number of observations, the pressure distribution matrix of the two-dimensional full field can be predicted, and then mapped back to the coordinates of the three-dimensional control points before the transformation, so as to realize the prediction of the aerodynamic load of the high-speed train. The prediction method specifically comprises the following steps: (1) Regularization of 3D control points on the surface of high-speed trains (1.1) Extracting 3D control point data of high-speed train surface mesh Extract the three-dimensional control point coordinate data of the surface grid of the high-speed train in CFD simulation, take the real body size as the standard, retain all x, y, z coordinates to the required accuracy, reduce the size of the data, delete the repeated control points, take the average pressure as the value of the control point, and then use the three-dimensional Cartesian coordinate system to sort all the control points in multiple levels; (1.2) Expand the 3D control point data into 2D control points and perform normalization and interpolation processing. The x value of the 3D coordinate is used as the x' value when the 2D expansion is performed, and the sorting sequence number when the x value is the same is used as the y' value when the 2D expansion is performed. The x' value and y' value are normalized and interpolated. (2) After normalizing x' and y' to the range of [0,1], select all data points where y' = 0.5, obtain the multi-condition pressure distribution matrix, and divide it into a training set and a validation set; (3) Extract the main modes of the flow field of the training set; (4) Obtaining the optimal characteristic cross-section position of the high-speed train perpendicular to the x' axis; (5) Obtain the multi-condition pressure distribution matrix at all characteristic sections of the high-speed train perpendicular to the x' axis; (6) Extract the main modes of the flow field of all characteristic sections of the high-speed train perpendicular to the x' axis; (7) Obtaining the optimal observation point position at each set of characteristic sections; (8) Obtain the multi-condition pressure distribution matrix of all cross sections of the high-speed train perpendicular to the y' axis; (9) Extract the main modes of all sections of the high-speed train perpendicular to the y' axis; (10) reconstructing the two-dimensional pressure distribution of the entire vehicle based on the data observed by the pressure sensors installed on the vehicle body; (11) The predicted three-dimensional pressure distribution is integrated to obtain the prediction result of the aerodynamic load of the high-speed train.

2. The method for predicting aerodynamic load of a high-speed train based on compressed sensing according to claim 1, characterized in that: The specific process of normalizing and interpolating the x' and y' values ​​in the step (1.2) is as follows: normalize x' and y', retain the accuracy of x' to 0.001m, and retain the accuracy of y' to 0.005m, that is, the number of data points in the y' direction is no more than 200, obtain the regularized two-dimensional control point coordinate data, and retain the association of each two-dimensional control point with its three-dimensional coordinate data before sorting; then interpolate x' and y' with the regularized two-dimensional control point coordinate data at intervals of 0.001m.

3. The method for predicting aerodynamic load of a high-speed train based on compressed sensing according to claim 1, characterized in that: The specific process of step (2) is as follows: randomly generate an arrangement from the regularized two-dimensional control point coordinate data, reorder all known working conditions according to this arrangement, and divide the training set and the verification set into a ratio of 8:2; then merge the data at y'=0.5 under all working conditions to obtain a multi-working condition pressure distribution matrix.

4. The method for predicting aerodynamic load of a high-speed train based on compressed sensing according to claim 1, characterized in that: The step (3) is to use intrinsic orthogonal decomposition to extract the first 10 basis functions of the flow field of the training set as the sparse matrix of compressed sensing reconstruction.

5. The method for predicting aerodynamic load of a high-speed train based on compressed sensing according to claim 1, characterized in that: The step (4) is to perform iterative optimization using a particle swarm optimization algorithm, which specifically includes the following steps: (4.1) Initialize the particle swarm dimension d, scale n, particle velocity state matrix v, particle position state matrix x, and individual extreme values and global extremum (4.2) Establish a mapping between temporary random mutation particles and negative ideal points, and determine the random mutation particles; the specific process is: exist Randomly search for a point in the neighborhood of As the position of the temporary random mutation particle, the formula is as follows: in, is the position state vector of the ith particle at the kth iteration, r is a random number in the range [-0.5, 0.5], x max is the maximum feasible variation interval, set to 1; (4.3) According to individual extreme values Global extreme value With random mutation particles To update the speed and position status of each particle; the specific process is: By temporarily randomly mutating particles The location and individual extreme value of The location and global extremum of The position of constitutes the mutation parent, select the negative ideal point x F , the formula is as follows: Hypothesis selection As a negative ideal point, find the midpoint x of the other two points C , the formula is as follows: Perform negative ideal point mapping and obtain the mapping point x R is the random mutation point p k if The position of is as follows: Among them, α is the negative ideal point mapping coefficient, which is generally taken as α = 1.3 ~ 0.5 decreasing; (4.4) The position state of the particle is used as the observation matrix reconstructed by compressed sensing to update the fitness of each particle; the specific process is: According to individual extreme value Global extreme value With random mutation particles To update the speed and position status of each particle, the formula is as follows: Among them, v is the particle velocity state matrix, x is the particle position state matrix, k is the number of iterations, i is the particle number, d is the velocity dimension, ω1, ω2 are inertia factors, c1, c2 are learning factors, r1, r2, r3 are random numbers in the range [0, 1], p k i is the optimal position experienced by the i-th particle up to the kth generation, p k g is the optimal position experienced by the entire particle swarm up to generation k, p k if are random mutation particles; (4.5) Update the individual extreme value of the particle swarm Global extreme value Specifically: When updating the speed and position status of each particle, check whether it exceeds the limit range. The speed limit range is [-0.5, 0.5], and the position limit range is [0, 1]; (4.6) Randomly select the validation set working condition at the same interval of iteration number, record the result matrix of compressed sensing reconstruction using the position state of the current global extreme value as the observation matrix, and the root mean square error with the validation set experimental data; the specific process is: The particle position state is used as the observation matrix reconstructed by compressed sensing to update the fitness of each particle. The observation matrix is ​​initialized to d rows, the column coordinate range is between [0,1], and it is an all-zero matrix with an interval of 0.

001. Then the dth row, the vth id The position of the column element is assigned 1, indicating that a sensor is placed here, where v id Represents the value of the dth dimension of the ith particle in the velocity state matrix; For the section at position y'=0.5, for all training set conditions, the corresponding observation values ​​are extracted respectively, and the sensor matrix and the observation values ​​are used as input for compressed sensing reconstruction. The root mean square error is calculated from the reconstructed values ​​of all training set conditions and the numerical values ​​obtained by CFD simulation as the new fitness of the particle. The numerical expressions of the sensor matrix and the root mean square error are as follows: Among them, Θ is the sensor matrix, Φ is the measurement matrix, Ψ is the sparse matrix, RMSE is the root mean square error, β rec is the reconstructed signal vector, β ori is the original signal vector, n β is the signal length; The representation of compressed sensing reconstruction using the basis pursuit algorithm is: Among them, γ is the observation value, s is the sparse vector, and β is the target reconstruction matrix; Let γ=uw, rewrite the constraint as γ=Θ(uw), and use l1 norm instead of l0 norm to transform the problem into a linear programming problem, as shown below: Among them, x = [u; w] is the solution to be found; c is a vector of all 1s, that is, [1,1,…,1] 1×2n ; So c T x constitutes a linear equation system to be solved, n is the order of the sparse matrix, which is the same as the length of the sparse vector, A is the artificially constructed matrix [Θ, -Θ], b = γ; solve the linear programming problem, and get x0 = [u0; w0], then s0 = x0 (1: n) - x0 (n + 1: 2n), x is the solution obtained by the linear programming function, subscript 0 indicates the solution to be sought, n is the length of the s sparse vector, n is equal to the length of u0 and w0, and the first n bits of x0 are subtracted from the last n bits, that is, s0 = u0 - w0; then the reconstructed result matrix is ​​obtained through β = Ψs, and finally the spatial average value Mean at the cross section is added; According to the new fitness of all particles, the individual extreme value and global extreme value of the particle swarm are updated. The formula is as follows: A validation set condition is randomly selected every time the same number of iterations is gapped, and the result matrix of compressed sensing reconstruction using the position state of the current global extreme value as the observation matrix is ​​recorded, as well as the relative error with the validation set experimental data; (4.7) Determine whether the current iteration number k of the particle swarm optimization reaches the preset maximum iteration number. If so, execute the following step (4.8); otherwise, increase the iteration number by 1 and execute the above step (4.2); (4.8) Determine whether the relative error of the compressed sensing reconstruction of the verification set working condition using the current global extreme value position state as the observation matrix scheme is less than the error required by the project. If so, execute the following step (4.9), otherwise, increase the particle swarm size by 1, reset the iteration number to zero, and then execute the above step (4.2); (4.9) Determine whether the particle swarm size has reached the upper limit. If so, execute the following step (4.10). Otherwise, increase the particle swarm size by 1, reset the iteration number, and then select random mutation particles. (4.10) Obtain the optimal characteristic section position That is, the current position state of the global extreme value is taken as the optimal characteristic section position, and N groups of characteristic section positions are obtained.

6. The method for predicting aerodynamic load of a high-speed train based on compressed sensing according to claim 1, characterized in that: The step (5) specifically comprises the following steps: (5.1) From the normalized pressure distribution matrix, for all known working conditions, select N groups of characteristic sections according to the results of step (4); (5.2) Re-dividing the working conditions reordered in step (2) into a training set, a validation set, and a test set in a ratio of 6:2:2; (5.3) The data of each group of cross sections under all working conditions are combined to obtain N groups of multi-condition pressure distribution matrices.

7. The method for predicting aerodynamic load of a high-speed train based on compressed sensing according to claim 1, characterized in that: The step (6) is to use intrinsic orthogonal decomposition to extract basis functions of various orders for each group of cross-section training set data, and retain the first 10 basis functions as the sparse matrix of compressed sensing reconstruction; The step (7) is to perform iterative optimization through a particle swarm optimization algorithm, and take the position state of the global extreme value when the iteration terminates as the optimal observation point.

8. The method for predicting aerodynamic load of a high-speed train based on compressed sensing according to claim 1, characterized in that: The step (8) is to combine the data of all cross sections perpendicular to the y' axis under the training set working condition from the normalized pressure distribution matrix to obtain a multi-working condition pressure distribution matrix; The step (9) is to use intrinsic orthogonal decomposition to extract the first 10-order basis functions as the sparse matrix of compressed sensing reconstruction for all cross sections perpendicular to the y' axis.

9. The method for predicting aerodynamic load of a high-speed train based on compressed sensing according to claim 1, characterized in that: The step (10) specifically comprises the following steps: (10.1) Randomly select a working condition from the test set data divided in step (5), and use the optimal observation point to obtain the result matrix of compressed sensing reconstruction at all characteristic sections perpendicular to the x' axis; (10.2) Taking the characteristic section position as the observation point, the result matrix of compressed sensing reconstruction perpendicular to the y' axis is obtained, which is the predicted two-dimensional full-field pressure distribution matrix; (10.3) Extract the predicted data at the two-dimensional control point corresponding to the original three-dimensional control point as the predicted three-dimensional control point data.

10. The method for predicting aerodynamic load of a high-speed train based on compressed sensing according to claim 1, characterized in that: The formula for the high-precision prediction result of the aerodynamic load of the high-speed train in step (11) is as follows: Where ρ is the fluid density, which is 1.225 kg / m 3 , V is the velocity of the incoming air flow relative to the train, S x is the reference area, the cross-sectional area of ​​the train in the x direction is selected as the reference area, H is the reference length, the height of the train compartment is selected as the reference length, D is the resistance, L is the lift, S is the lateral force; M x is the overturning moment, M y is the pitching moment, M z is the lateral moment, and the moment points are selected as the centroid positions of each car of the train; C D is the drag coefficient, C L is the lift coefficient, C S is the lateral force coefficient, C mx is the overturning moment coefficient, C my is the pitch moment coefficient, C mz is the cornering moment coefficient.

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