High-speed train surface flow field rapid prediction method based on extremely sparse measurement data

Abstract

The application provides a high-speed train surface flow field rapid prediction method based on extremely sparse measurement data, which comprises the following steps: (1) constructing a high-precision surface pressure distribution database; (2) extracting a dominant space mode of a training set pressure distribution matrix; (3) compressive sensing reconstruction; (4) adopting an improved particle swarm optimization algorithm to obtain an optimal sensor layout scheme; and (5) establishing a rapid prediction model. The application has reasonable conception, can accurately reconstruct the surface pressure field of the high-speed train under multiple working conditions, and can rapidly and effectively predict the surface pressure distribution of the high-speed train under different working conditions through the construction of the high-precision surface pressure distribution database.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of object surface flow field prediction, and particularly relates to a high-speed train surface flow field rapid prediction method based on extremely sparse measurement data. BACKGROUND

[0002] Traditional experimental methods for obtaining the aerodynamic force of a high-speed train, such as wind tunnel tests and real vehicle tests, need to arrange a large number of sensors on the surface of the high-speed train. Precise sensors are often expensive and easy to damage, and it is difficult to economically and effectively obtain the accurate surface pressure distribution of the high-speed train. Taking the joint debugging and testing of a new vehicle model before it is officially put into operation as an example, 70-80 pressure sensors need to be arranged on the surface of the head vehicle. These sensors are usually arranged in large quantities depending on engineering experience, and even so, the pressure distribution data obtained is still highly sparse. Therefore, interpolation processing of the experimental measurement data is often required, but the fitting accuracy is often not ideal, and the reliability of the results is not high enough.

[0003] Compressed sensing (CS) is a signal reconstruction method proposed in the field of signal processing in 2006, which can reconstruct and recover sparse or compressible signals at a sampling frequency much lower than the requirement of the Shannon-Nyquist sampling theorem through random subsampling. With the rapid development of compressed sensing methods, it has been widely applied in signal reconstruction, remote sensing, infrared spectral imaging, medical imaging, and nonlinear complex network system reconstruction fields, and several mature algorithms based on different implementation ideas have been developed, including greedy iterative algorithm, convex optimization algorithm, and Bayesian framework-based algorithm. Since the storage method of flow field information is consistent with the storage method of image pixels, it is feasible to apply compressed sensing method to the field of sparse flow field reconstruction.

[0004] Bright et al. proposed a sparse flow field reconstruction method combining reduced order model, compressed sensing and machine learning, which realized the reconstruction of the flow field around a cylinder in the low Reynolds number range. However, this method only proves that the compressed sensing method can reconstruct a two-dimensional flow field from fewer measurements, and does not optimize the sensor layout scheme. In his published dissertation "Reconstruction method based on sparse distributed data and consistency study of force and pressure measurement data" (CNKI, Northwestern Polytechnical University, 2023, Master's thesis, category V19), Zhao Xuan proposed a sparse reconstruction method for aircraft aerodynamic load based on compressed sensing, which reconstructed the pressure distribution curve that matched the real test most completely based on fewer test data. However, the wing type processed by this method has a flat structure from top to bottom in terms of geometric shape, which can be approximated as a two-dimensional flow field for analysis, but the geometric shape of a high-speed train is more complex and slender. The application range of compressed sensing method in flow field reconstruction is still relatively narrow, and there is no work on the reconstruction of surface pressure field of objects with three-dimensional complex geometric shape. . SUMMARY

[0005] In order to solve the engineering problem of difficult and economical acquisition of aerodynamic force of three-dimensional complex shape object in experimental measurement, reduce the large number of redundant sensors on the surface, and make the flow field reconstruction technology truly applied in practical application, the present application provides a kind of fast prediction method for surface flow field of high-speed train based on extremely sparse measurement data, which is reasonable in concept, and accurately reconstructs the surface pressure field of high-speed train under multiple working conditions by constructing a high-precision surface pressure distribution database.

[0006] To solve the above technical problems, the present application provides a kind of fast prediction method for surface flow field of high-speed train based on extremely sparse measurement data, which includes the following steps:

[0007] (1) Construct a high-precision surface pressure distribution database

[0008] Accurately calculate the pressure distribution data of the surface of high-speed train under a limited set of working conditions; reorganize the three-dimensional data under each working condition into a column vector and merge it into a pressure distribution matrix; divide the pressure distribution matrix into training set, validation set and test set data;

[0009] (2) Extract the dominant space mode of the training set pressure distribution matrix

[0010] Perform generalized eigenvalue orthogonal decomposition on the training set data, extract the dominant space mode according to the energy of each mode from large to small, and generate a sparse matrix for compressed sensing reconstruction;

[0011] (3) Compressed sensing reconstruction

[0012] Based on the sparse matrix obtained by the generalized eigenvalue orthogonal decomposition process, the measurement matrix constructed according to the position information of the sensor and the measurement value of the sensor, the sparse coefficient vector is reconstructed by the basis pursuit algorithm, the predicted surface pressure field is obtained by inverse transformation, and the relative error size of the predicted surface pressure field and the surface pressure field obtained by CFD is calculated.

[0013] (4) The improved particle swarm optimization algorithm is used to obtain the optimal sensor layout scheme

[0014] According to the relative error size calculated in the above step (3), the optimal sensor layout scheme is searched by the improved particle swarm optimization algorithm, the number of measurement points required for compressed sensing reconstruction is reduced, and the optimal measurement matrix is obtained.

[0015] (5) Establish a fast prediction model

[0016] The trained fast prediction model is composed of the sparse matrix Ψ obtained by the generalized eigenvalue orthogonal decomposition, the optimal measurement matrix Φ obtained by the improved particle swarm optimization algorithm and the basis pursuit algorithm; when the fast prediction model is called, the measurement value of the sensor corresponding to the optimal measurement matrix Φ is input, and the predicted high-speed train surface pressure data distribution is output.

[0017] The high-speed train surface flow field fast prediction method based on extremely sparse measurement data, wherein the specific process of obtaining the pressure distribution matrix in step (1) is: according to the actual scene of engineering application, for a certain type of vehicle, the range of design working condition domain is reasonably determined, and the running speed and crosswind speed of high-speed train are designed with the same speed interval increasing; after high-precision numerical simulation and solution of the flow field of each design working condition by CFD software, the pressure distribution data of high-speed train surface under each working condition is exported, saved as pressure distribution column vectors with the same space length m and sequence, and combined into a pressure distribution matrix with space x working condition according to working condition:

[0018]

[0019] Wherein, m is the number of points contained in the pressure distribution data under each working condition, i.e. the space length; n is the total number of design working conditions, and p is the pressure value.

[0020] The high-speed train surface flow field fast prediction method based on extremely sparse measurement data, wherein the specific process of step (2) is:

[0021] For the training set data obtained by dividing in step (1), first calculate the average value under different working conditions as the zero-order mode ψ0, and the calculation formula is as follows:

[0022]

[0023] Wherein, ntrain total number of training set conditions;

[0024] Then, subtract the zero-order mode from the pressure distribution matrix obtained in step (1), specifically:

[0025]

[0026] The matrix U, Σ and V are obtained by singular value decomposition function, and the specific formula is:

[0027] P = UΣV T ,

[0028] Finally, the first t-order dominant space modes with energy greater than 99% are intercepted as a sparse matrix, and the formula of the energy E of the first t-order modes is as follows:

[0029]

[0030] wherein, r is the rank of the matrix P; λ is the eigenvalue of the matrix P; β is the energy threshold required for the approximate original flow field, n train total number of training set conditions;

[0031] The final sparse matrix can be represented as:

[0032]

[0033] The high-speed train surface flow field rapid prediction method based on extremely sparse measurement data, wherein the specific process of step (3) is:

[0034] When performing compressed sensing reconstruction, for the jth condition, input the dominant space mode Ψ obtained by generalized eigenvalue orthogonal decomposition, the position information of the sensor and the measurement value y of the sensor; the initial position of the sensor is a set of randomly generated non-repeating positive integers:

[0035] ξ = (ξ1, ξ2, …, ξ d ), 1≤ξ i ≤m,

[0036] wherein, d is the number of sensors, and m is the number of points contained in the pressure distribution data under each condition, i.e. the length of the space;

[0037] The initial number of sensors d = 2, and the measurement matrix is constructed according to the position information of the sensor. The construction method is to generate a full zero matrix with d rows and m columns, and each row corresponds to a sensor. The value at the position of each sensor in the full zero matrix is set to 1, and the specific formula for constructing the measurement matrix is as follows:

[0038]

[0039] The mathematical description of realizing the compressed sensing reconstruction by using the basis pursuit algorithm is as follows:

[0040] s.t.y=Θs′=ΦΨs′,

[0041] Wherein, y is the measurement value, s is the sparse vector to be reconstructed, Θ is the sensing matrix;

[0042] Let s=u-v s.t.u,v≥0, the constraint condition can be rewritten as:

[0043]

[0044] By solving the l1 norm minimization approximation instead of the l0 norm minimization problem:

[0045] s.t.y=Θs′=ΦΨs′,

[0046] And then converted into solving a linear programming problem:

[0047] s.t.y=Θs′,s′≥0,

[0048] Wherein, c T s′ is the objective function, y=Θs′ is a set of equality constraints, and s′≥0 defines the boundary; the solution s0 is obtained by solving the linear programming equation, and the reconstruction coefficient s is obtained as s=s0(1:m)-s0(m+1:2m), the inverse transformation obtains the predicted surface pressure field p rec =Ψs+ψ0, and the relative error size ε between the predicted surface pressure field and the surface pressure field obtained by CFD under the working condition is calculated j , and the calculation formula is as follows:

[0049]

[0050] Wherein, in the above formula, p k,rec is the pressure value of the kth point in the predicted surface pressure field, p k,cfd is the pressure value of the kth point in the surface pressure field obtained by CFD, and e k is the relative error size of the kth point between the predicted surface pressure field and the surface pressure field obtained by CFD.

[0051] The high-speed train surface flow field rapid prediction method based on extremely sparse measurement data, wherein the specific process of step (4) is:

[0052] (4.1) First, initialize each parameter in the improved particle swarm optimization algorithm:

[0053] <m,n train ,num,dmax h, h max v max,initial v max,final w initial w final c1, c2, p train e h e limit >

[0054] wherein m is the total number of control points on the surface of the vehicle body; n train is the total number of training set conditions; num is the number of particle swarm; d max is the maximum value of the number of measurement points that can be used; h is the current iteration number; h max is the maximum iteration number allowed for a single iteration of particle swarm optimization; v max,initial and v max,final are the initial value and the terminal value of the maximum speed of the particle, respectively; w initial and w final are the initial value and the terminal value of the inertia weight factor, respectively; c1 and c2 are the individual learning factor and the social learning factor, respectively; p train is the proportion of training set conditions extracted for calculating the fitness function, which reduces the possibility of overfitting of the results; e h is the current iteration error; e limit is the required convergence error;

[0055] (4.2) The speed state of each particle is initialized to a random number between [-v max,initial , v max,initial ], and the position state is initialized to a random integer between [0, m]; the fitness of each particle is calculated according to the current position state of each particle, and the calculation formula of the fitness function is as follows:

[0056]

[0057] wherein c j represents whether the reconstruction error of the jth group of training conditions meets the allowed convergence error; c is a scaling factor, representing the proportion of training set conditions that meet the training requirements in the total number of extracted training set conditions, and the value of c tends to 1, which means that the sensor layout scheme performs well in all extracted training set conditions, and c cannot be equal to zero when it is the dividend; when the fitness function f i tends to zero, it means that the proportion of control points with a relative reconstruction error greater than 5% using the sensor layout scheme in almost all training set conditions tends to zero; e limit is the required convergence error; p train is the proportion of training set conditions extracted for calculating the fitness function; n train is the total number of training set conditions;

[0058] (4.3) Update the inertia weight factor and the maximum velocity of the particle swarm at present, the formula is as follows:

[0059]

[0060] Wherein, h is the current iteration number; h max is the maximum iteration number allowed for a single iteration of particle swarm optimization; w h is the inertia weight factor at the hthiteration; w initial and w final are the initial value and the terminal value of the inertia weight factor respectively; v max,initial and v max,final are the initial value and the terminal value of the maximum particle velocity respectively;

[0061] Then, a single iteration calculation is performed on the particle swarm, and the velocity state, position state and fitness of each particle are updated; the update formula of the velocity state of each particle is as follows:

[0062]

[0063] Wherein, r1 and r2 are random numbers between 0 and 1 respectively; xbest_local is the local optimal position; xbest_global is the global optimal position;

[0064] Check whether the velocity state of each particle is within the allowed range, and reverse and decelerate the particles that exceed the velocity range:

[0065]

[0066] Update the position state of each particle:

[0067]

[0068] Check whether the position state of each particle is within the allowed range, and reset the particles that exceed the position range at the boundary:

[0069]

[0070] Update the fitness f i h of each particle, h is the current iteration number;

[0071] Update the local optimal fitness of each particle, and take the position state of the particle that obtains the local optimal fitness as the local optimal position

[0072]

[0073] updating the global optimal fitness of the particle swarm, and taking the position state of the particle swarm obtaining the global optimal fitness as the global optimal position xbest_global h :

[0074]

[0075] updating the error of the current iteration:

[0076] ε h = min(fbest_global h , ε h-1 );

[0077] (4.4) judging whether the current error ε h is less than the allowed convergence error ε limit , if yes, returning the current global optimal fitness and position and exiting the optimization process, i.e., exiting the whole step (4), otherwise, continuing to execute;

[0078] judging whether the current iteration number h is equal to the maximum iteration number h max , if yes, continuing to execute, otherwise, adding 1 to the iteration number and updating the velocity and position state of the particle swarm again;

[0079] every interval of a certain iteration number, a group of working condition data is randomly extracted from the verification set, and compressed sensing reconstruction is performed by using the sparse matrix obtained based on the generalized eigenvalue orthogonal decomposition process and the current global optimal position to construct a measurement matrix, and the size of the relative error is recorded to feed back the search and convergence performance of the particle swarm optimization under the current hyperparameter setting;

[0080] judging whether the current sensor number d is equal to the maximum value d max of the measurable measurement points, if yes, returning the current global optimal fitness and position and exiting the optimization process, i.e., exiting the whole step (4), otherwise, adding 1 to the sensor number and starting a new round of initialization and iteration optimization process.

[0081] The high-speed train surface flow field rapid prediction method based on extremely sparse measurement data, wherein the specific process of the step (5) is: setting the dominant space mode obtained through the generalized eigenvalue orthogonal decomposition as a sparse matrix of compressed sensing, constructing a measurement matrix of compressed sensing according to the optimal sensor layout position obtained by the improved particle swarm optimization algorithm, and combining the constructed high-precision surface pressure distribution database to form a trained high-speed train surface pressure field rapid prediction model.

[0082] By adopting the technical scheme, the present application has the following beneficial effects:

[0083] The present application concept is reasonable, and through constructing a high-precision surface pressure distribution database, the surface pressure field of the high-speed train under multiple working conditions is accurately reconstructed, so that the surface pressure distribution of the high-speed train under different working conditions can be quickly and effectively predicted.

[0084] The features and advantages of the present application mainly lie in the following aspects:

[0085] (1) The present application combines the compressed sensing method with the numerical simulation technology of the high-speed train, realizes the pressure distribution of the whole train surface from a small amount of observation values, effectively reduces the difficulty of the large number of measurement instruments, enriches the application range of the compressed sensing method, and makes the flow field reconstruction method truly applicable to practical engineering applications.

[0086] (2) Compared with the flow field reconstruction algorithm using the neural network, as the complexity of the high-speed train running scene and the scale of the solved space are enlarged, the number of neurons, the number of layers of the network, and the number of weights and biases required for constructing the model will also be enlarged, which greatly improves the cost required for training the neural network model, and the training of the super parameters of the neural network needs to rely on the adjustment of human experience and the method has poor interpretability. The flow field reconstruction method using the neural network has not been applied to the flow field reconstruction problem under the high Reynolds number complex scene. The present application realizes the flow field reconstruction by using the compressed sensing method, based on the mathematical problem of solving the minimum l1 norm, avoids the iterative training of a large number of parameters on the basis of ensuring the reconstruction accuracy, and greatly reduces the training cost of the model.

[0087] (3) The present application uses the generalized eigenvalue orthogonal decomposition to extract the dominant space mode of the flow field as a sparse matrix, excavates the potential space characteristics of the flow field itself, sparsifies the complex natural flow field data, meets the prerequisite for the successful application of the compressed sensing method, and has stronger interpretability than the neural network method.

[0088] (4) The present application uses the improved particle swarm optimization algorithm to optimize the layout scheme of the sensor, reduces the dependence on the engineering experience of the point layout, greatly reduces the number of pressure sensors required for the experimental measurement, and can flexibly adjust the number of measuring points according to the actual engineering precision requirements.

[0089] (5) The fast prediction method proposed in the present application has strong flexibility, and through constructing a high-precision surface pressure distribution database of the high-speed train, the surface pressure distribution of the corresponding train model under different working conditions can be accurately and timely predicted. According to the marshalling condition of the train, the method supports the parallel training of the train in sections, and the algorithm is relatively easy to improve. The method also supports the introduction of expert experience to help better improve the local prediction accuracy.

[0090] (6) In the model training stage, this invention makes full use of the high-precision surface pressure distribution data obtained by CFD calculation, retains the spatial position information and topological relationship of all three-dimensional control points on the surface of the high-speed train, greatly improves the spatial accuracy of the predicted pressure distribution results, and the prediction results can be visualized in the post-processing software to generate a pressure cloud map of the surface of the high-speed train, so as to intuitively understand the surface pressure distribution of the high-speed train under specific working conditions.

[0091] (7) This invention predicts the surface pressure distribution of high-speed trains under different operating conditions. However, the proposed method is also applicable to the prediction of pressure field, velocity field and temperature field of objects that interact closely with fluids, such as aircraft and submarines, and has a wide range of applications. Attached Figure Description

[0092] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0093] Figure 1 This is a flowchart of the fast prediction method for the surface flow field of high-speed trains based on extremely sparse measurement data according to the present invention;

[0094] Figure 2 This is a flowchart of the improved particle swarm optimization algorithm in the fast prediction method for the surface flow field of high-speed trains based on extremely sparse measurement data of this invention. Detailed Implementation

[0095] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0096] The present invention will be further explained below with reference to specific embodiments.

[0097] like Figure 1 As shown in the figure, this embodiment provides a fast prediction method for the surface flow field of high-speed trains based on extremely sparse measurement data. The compressed sensing method used is a signal reconstruction method derived from the field of signal processing. It is based on the mathematical idea of ​​minimizing the l1 norm to approximate the sparsest solution of the underdetermined equation system. There are two prerequisites for its successful application:

[0098] 1) The original signal is sparse (i.e. only a small number of large coefficients in the signal, the rest of the most value is zero or close to zero) or compressible (through the appropriate transformation matrix can be expressed as sparse signal);

[0099] 2) The measurement matrix and sparse matrix satisfy the finite equidistance property (RIP), the equivalent condition is that the two are not related, that is, the more irrelevant the row vectors of Φ and the column vectors of Ψ, the higher the accuracy of the reconstruction result.

[0100] The traditional compressed sensing method is used to adopt the Gaussian random measurement matrix with high probability to satisfy the RIP and the Fourier sparse transform base, and good reconstruction results can be obtained for any image with certain characteristics. For the flow field data known to have certain flow characteristics, the generalized proper orthogonal decomposition is used to process the reduced order, and the corresponding measurement matrix is customized combined with the optimization algorithm, which can obtain higher reconstruction accuracy.

[0101] The generalized proper orthogonal decomposition can decompose a series of pressure distribution matrices under different working conditions into a linear combination of orthogonal spatial modes and corresponding coefficients. The average value of the pressure distribution vector of each working condition is taken as the zero-order mode ψ0, the pressure distribution matrix is subtracted from the zero-order mode to obtain the matrix P, and the singular value decomposition is performed on the matrix P to obtain the left singular value matrix U, the singular value matrix Σ and the right singular value matrix V. The matrix U and the matrix V are both orthogonal matrices, the matrix U represents the spatial mode, the matrix V is a diagonal matrix, the values on the diagonal are arranged from large to small, and the matrix Σ and the matrix V together represent the coefficients corresponding to the modes. According to the energy cut-off, the spatial mode accounting for 99% of the total energy is taken as the dominant spatial mode, which is further used as the sparse matrix for compressed sensing reconstruction.

[0102] The particle swarm optimization algorithm is an evolutionary optimization meta-heuristic algorithm, which regards each particle as a bird. The process of searching for a solution is analogous to the process of bird foraging. The global optimal solution of a problem is found by combining information sharing and individual cooperation among groups. The improved particle swarm optimization algorithm defines a new fitness function based on statistical significance compared to the traditional algorithm, and adds a weight inertia factor and a linear decay of the maximum particle speed, as well as a particle collision boundary velocity reversal strategy to accelerate the convergence of the particle swarm and improve the stability of the optimization. The sensor layout scheme obtained by the improved particle swarm optimization can capture the measurement values that contribute most to the reconstruction of the flow field to the greatest extent, reducing the number of redundant sensors laid out based on engineering experience.

[0103] As shown in Figure 1 The high-speed train surface flow field rapid prediction method based on extremely sparse measurement data provided by the embodiment specifically includes the following steps:

[0104] (1) Construct a high-precision surface pressure distribution database

[0105] The range of the design working condition domain should be reasonably set according to the actual scene of engineering application, and the driving speed and crosswind speed of the high-speed train are designed in the same speed interval for a specific vehicle model; after high-precision numerical simulation and solution of the flow field of each design working condition by CFD software (the flow field under each working condition is solved by CFD software based on N-S equation and related turbulence model, and the physical quantity field is obtained, which includes the required pressure field data), the pressure distribution data of the surface of the high-speed train under each working condition is derived, saved as a pressure distribution column vector with the same spatial length m and sequence, and combined into a pressure distribution matrix of space x working condition according to the working condition:

[0106]

[0107] Wherein, m is the number of points contained in the pressure distribution data under each working condition, i.e. the spatial length; n is the total number of design working conditions, and p is the pressure value;

[0108] The pressure distribution matrix is divided into a training set, a validation set and a test set according to the ratio of 8:1:1 (for small-scale data, the common division method is: training set 60%-80%, validation set 10%-20%, test set 10%-20%, when the validation set is not used, the training set and the test set can be divided according to the ratio of 7:3, and for large-scale data, the common selection ratio is 98:1:1). The training set is used to obtain the sparse matrix and the optimized measurement matrix by GPOD and IPSO, the validation set is used to evaluate the generalization ability of the model outside the training set data, and the hyperparameters of the model are adjusted, and the test set is used to test the accuracy and reliability of the prediction method.

[0109] (2) Extracting the dominant space mode of the training set pressure distribution matrix

[0110] The training set data is subjected to generalized eigenvalue orthogonal decomposition, the dominant space mode is extracted according to the energy of each mode from large to small, and the sparse matrix for compressed sensing reconstruction is generated; the specific process is as follows:

[0111] For the training set data obtained after step (1) above, the average value under different working conditions is calculated as the zero-order mode ψ0, and the calculation formula is as follows:

[0112]

[0113] Wherein, n train is the total number of training set working conditions;

[0114] Then, the pressure distribution matrix obtained in step (1) above is subtracted from the zero-order mode, specifically:

[0115]

[0116] The matrix U,∑ and V are obtained by singular value decomposition function, and the specific formula is:

[0117] P = U∑V T ,

[0118] Finally, the first t dominant space modes with energy greater than 99% are intercepted as a sparse matrix, and the formula of the energy E of the first t modes is as follows:

[0119]

[0120] Wherein, r is the rank of matrix P; λ is the eigenvalue of matrix P; β is the energy threshold required for approximating the original flow field, which is set to 99%; n train is the total number of training set working conditions; t is 10;

[0121] The final sparse matrix can be represented as:

[0122]

[0123] (3) compressed sensing reconstruction

[0124] Based on the sparse matrix obtained by generalized eigenvalue orthogonal decomposition process, the measurement matrix constructed according to the position information of the sensor and the measurement value of the sensor, the sparse coefficient vector is reconstructed by basis pursuit algorithm, and the predicted surface pressure field is obtained by inverse transformation, and the relative error between the predicted surface pressure field and the surface pressure field obtained by CFD is calculated. The size of the specific process is:

[0125] When compressed sensing reconstruction is performed, for the jth working condition, the dominant space mode Ψ obtained by generalized eigenvalue orthogonal decomposition, the position information of the sensor and the measurement value y of the sensor are input; the initial position of the sensor is a set of randomly generated non-repeating positive integers:

[0126] ξ = (ξ1, ξ2, …, ξ d ),1≤ξ i ≤m,

[0127] Wherein, d is the number of sensors, and m is the number of points contained in the pressure distribution data under each working condition, that is, the space length;

[0128] The initial number of sensors d = 2, and the measurement matrix is constructed according to the position information of the sensor. The construction method is to generate a zero matrix with d rows and m columns, and each row corresponds to a sensor. The value of the zero matrix at the position of each sensor is set to 1, and the specific formula of constructing the measurement matrix is as follows:

[0129]

[0130] The mathematical description of realizing compressed sensing reconstruction by basis pursuit algorithm is:

[0131] s.t.y=Θs′=ΦΨs′,

[0132] where y is the measurement, s is the sparse vector to be reconstructed, Θ is the sensing matrix;

[0133] Let s=u-v s.t.u,v≥0, the constraint condition can be rewritten as:

[0134]

[0135] By solving the l1 norm minimization approximation instead of the l0 norm minimization problem:

[0136] s.t.y=Θs′=ΦΨs′,

[0137] Further converted into solving a linear programming problem:

[0138] s.t.y=Θs′,s′≥0,

[0139] where c T s′ is the objective function, y=Θs′ is a set of equality constraints, and s′≥0 defines the boundary; solving the linear programming equation obtains the solution s0, and the reconstruction coefficient s=s0(1:m)-s0(m+1:2m) is obtained, the inverse transformation obtains the predicted surface pressure field p rec =Ψs+ψ0, and the relative error size ε j between the predicted surface pressure field and the surface pressure field obtained by CFD under the working condition is calculated, and the calculation formula is as follows:

[0140]

[0141] where p k,rec is the value of the kth point in the predicted surface pressure field, p k,cfd is the value of the kth point in the surface pressure field obtained by CFD, and e k is the relative error size of the kth point between the predicted surface pressure field and the surface pressure field obtained by CFD.

[0142] where the above step (3) of compressed sensing reconstruction is for a certain working condition, so the embodiment is for the jth group of working conditions, and p is the pressure distribution matrix. Whether the predicted p k,rec or the p k,cfd obtained by CFD is the pressure value under the jth group of working conditions, and the value will change if it is replaced by another working condition.

[0143] (4) Obtain the optimal sensor layout scheme by using the improved particle swarm optimization algorithm

[0144] According to the relative error size calculated in the step (3), the optimal sensor layout scheme is searched through the improved particle swarm optimization algorithm, the number of measurement points required for compressed sensing reconstruction is reduced, and the optimal measurement matrix is obtained; the specific process is as follows:

[0145] As shown in Figure 2 , first, the parameters in the improved particle swarm optimization algorithm are initialized:

[0146] <m,n train ,num,d max ,h,h max ,v max,initial ,v max,final ,w initial ,w final ,c1,c2,ρ train ,ε h ,ε limit >,

[0147] The particle swarm optimization algorithm refers to: each solution is regarded as a particle, the position information of each particle is the value of the solution, and many particles are iteratively searched in the same search domain to find the optimal position that minimizes the fitness function, so it is called particle swarm optimization algorithm, and the solution value corresponds to the position information of the sensor;

[0148] Wherein, m is the total number of control points on the vehicle body surface; n train is the total number of training sets; num is the number of particle groups, which is set to 50; d max is the maximum value of the number of measurement points that can be used, which is set to 10; h is the current iteration number, which is initially set to 1; h max is the maximum number of iterations allowed for a single iteration of the particle swarm optimization, which is set to 100; v max,initial and v max,final are the initial value and the termination value of the maximum speed of the particle, which are set to 0.1m and 0.05m respectively; w initial and w final are the initial value and the termination value of the inertia weight factor, which are set to 0.9 and 0.4 respectively; c1 and c2 are the individual learning factor and the social learning factor, which are both set to 2, indicating that the individual experience and the group experience are equally important; ρ train is the proportion of training sets extracted for calculating the fitness function, which is set to 0.7 to reduce the possibility of overfitting of the results; ε h is the current iteration error, which is initially set to 10 4 ; ε limit is the required convergence error, which is set to 0.05.

[0149] Then, the speed state of each particle is initialized to [-vmax,initial ,v max,initial The position state is initialized to a random integer between [0, m]; the fitness of each particle is calculated based on its current position state, and the fitness function is calculated as follows:

[0150]

[0151] Among them, c j The value of c represents whether the reconstruction error of the j-th training case meets the allowable convergence error; c is a scaling factor, representing the proportion of training cases that meet the training requirements to the total number of extracted training cases. The closer c is to 1, the better the sensor deployment scheme performs in all extracted training cases. Furthermore, c will not be equal to zero when used as a divisor. When the fitness function f... i When the value approaches zero, the proportion of control points with a relative reconstruction error greater than 5% using this sensor deployment scheme in almost all training set conditions approaches zero; ε limit The required convergence error; ρ train To calculate the proportion of training set conditions extracted for the fitness function; n train The total number of training set conditions;

[0152] The current inertia weighting factor and maximum velocity of the particle swarm are updated using the following formula:

[0153]

[0154] Where h is the current iteration number; h max For particle swarm optimization, the maximum number of iterations allowed in a single iteration; w h It is the inertia weight factor at the h-th iteration; w initial and w final These are the initial and final values ​​of the inertia weighting factor, respectively; v max,initial and v max,final These are the initial and final values ​​of the particle's maximum velocity, respectively.

[0155] Next, a single iteration is performed on the particle swarm to update the velocity state, position state, and fitness of each particle; the update formula for the velocity state of each particle is as follows:

[0156]

[0157] Where r1 and r2 are random numbers between [0,1]; xbest_local is the local optimal position; xbest_global is the global optimal position;

[0158] Check if the velocity of each particle is within the allowable range; reverse and decelerate particles that are out of range.

[0159]

[0160] Update the position state of each particle:

[0161]

[0162] Check whether the position state of each particle is within the allowed range, and reset the particle out of the position range at the boundary:

[0163]

[0164] Update the fitness f of each particle i h h is the current iteration number;

[0165] Update the local optimal fitness of each particle, and take the position state of the particle with the local optimal fitness as the local optimal position

[0166]

[0167] Update the global optimal fitness of the particle swarm, and take the position state of the particle swarm with the global optimal fitness as the global optimal position xb est global h :

[0168]

[0169] Update the error of the current iteration:

[0170] ε h = min(fbest global h , ε h-1 );

[0171] Determine whether the current error ε h is less than the allowed convergence error ε limit , if yes, return the current global optimal fitness and position and exit the optimization process, i.e., exit the entire step (4), otherwise continue to execute;

[0172] Determine whether the current iteration number h is reached the maximum iteration number h max , if yes, continue to execute, otherwise add 1 to the iteration number and update the velocity and position state of the particle swarm again;

[0173] Randomly extract a group of working condition data from the verification set every certain number of iterations, and use the sparse matrix obtained by GPOD (i.e. generalized eigenvalue orthogonal decomposition) and the current global optimal position to construct a measurement matrix to perform compressed sensing reconstruction, and record the size of the relative error, which is used to feedback the search and convergence performance of the particle swarm optimization under the current hyperparameter setting.

[0174] Determine whether the current sensor number d reaches the maximum value d of the number of measurement points max If yes, return the current global optimal fitness and position and exit the optimization process, i.e. exit the entire step (4), otherwise add 1 to the sensor number and start a new round of initialization and iterative optimization process.

[0175] (5) Establish a fast prediction model

[0176] Set the dominant space mode obtained by GPOD (i.e. generalized eigenvalue orthogonal decomposition) as the sparse matrix of compressed sensing, construct the measurement matrix of compressed sensing according to the optimal sensor layout position obtained by IPSO (i.e. improved particle swarm optimization algorithm), and combine the constructed high-precision surface pressure distribution database to form the trained fast prediction model of the surface pressure field of the high-speed train (the process of the aforementioned generalized eigenvalue orthogonal decomposition and improved particle swarm optimization is the training process of the fast prediction model, and once the values of the sparse matrix and the measurement matrix are determined, the training is completed). The compressed sensing method avoids the interpolation operation on sparse data, but based on the main feature information extracted from the training set data, the flow field is expressed in a sparse manner, and the most suitable measurement matrix is customized, which can effectively capture the measurement point data with the highest contribution to flow field reconstruction, and the prediction result can reflect the surface pressure distribution in the real situation to the greatest extent. In practical application, the optimal sensor layout position should be used to arrange the train surface pressure sensors, and the pressure data measured by the sensors under the test working condition is input into the fast prediction model, so that the high-precision surface pressure field prediction data can be obtained. Compared with the CFD method which needs to solve the physical quantities of all control points in the calculation domain, the fast prediction model directly predicts the physical quantities of the control points on the surface, which can greatly reduce the calculation amount and improve the calculation efficiency.

[0177] The present application has reasonable concept, by constructing a high-precision surface pressure distribution database, the surface pressure field of the high-speed train under multiple working conditions is accurately reconstructed, and the surface pressure distribution of the high-speed train under different working conditions can be quickly and effectively predicted.

[0178] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, and are not intended to limit the present application; although the present application has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions recorded in the above embodiments can be modified, or some or all of the technical features can be replaced by equivalents; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A high-speed train surface flow field rapid prediction method based on extremely sparse measurement data, characterized in that, The method comprises the following steps: (1) constructing a high-precision surface pressure distribution database Precisely calculate the pressure distribution data of the surface of the high-speed train under a limited set of working conditions; reorganize the three-dimensional data under each working condition into a column vector and combine them into a pressure distribution matrix; divide the pressure distribution matrix into training set, validation set and test set data; (2) extracting the dominant space mode of the training set pressure distribution matrix Perform generalized eigenvalue orthogonal decomposition on the training set data, extract the dominant space mode according to the energy of each mode from large to small, and generate a sparse matrix for compressed sensing reconstruction; (3) compressed sensing reconstruction Based on the sparse matrix obtained from the generalized eigenvalue orthogonal decomposition process, the measurement matrix constructed according to the position information of the sensors and the measurement values of the sensors, the sparse coefficient vector is reconstructed by the basis pursuit algorithm, and the predicted surface pressure field is obtained by inverse transformation, and the relative error size of the predicted surface pressure field and the surface pressure field obtained by CFD is calculated; (4) obtaining the optimal sensor layout scheme by using the improved particle swarm optimization algorithm According to the relative error size calculated in the above step (3), the optimal sensor layout scheme is searched by the improved particle swarm optimization algorithm, the number of measurement points required for compressed sensing reconstruction is reduced, and the optimal measurement matrix is obtained; (5) establishing a fast prediction model The trained fast prediction model is composed of the sparse matrix Ψ obtained by generalized eigenvalue orthogonal decomposition, the optimal measurement matrix Φ obtained by the improved particle swarm optimization algorithm and the basis pursuit algorithm; when calling the fast prediction model, the measurement values of the sensors corresponding to the optimal measurement matrix Φ are input, and the predicted high-speed train surface pressure data distribution is output.

2. The method of claim 1, wherein the method is characterized by, The specific process of obtaining the pressure distribution matrix in step (1) is as follows: according to the actual scene of engineering application, for a specific vehicle type, reasonably determine the range of design working condition domain, and increase the design speed and crosswind speed of the high-speed train according to the same speed interval; After high-precision numerical simulation and solution of the flow field of each design working condition by CFD software, the pressure distribution data of the surface of the high-speed train under each working condition is exported, saved as a pressure distribution column vector with the same space length m and sequence, and combined into a pressure distribution matrix with space x working condition according to the working condition: Wherein, m is the number of points contained in the pressure distribution data under each working condition, i.e. the space length; n is the total number of design working conditions, and p is the pressure value.

3. The method of claim 1, wherein the method further comprises: The specific process of step (2) is as follows: For the training set data obtained after step (1) is divided, first calculate the average value under different working conditions as the zero-order mode ψ0, and the calculation formula is as follows: wherein n train is the total number of training set conditions; Then subtract the zero-order mode from the pressure distribution matrix obtained in step (1), which is specifically: Get matrix U, Σ and V through singular value decomposition function, and the specific formula is as follows: P train = U∑V T , Finally, the first t dominant space modes with energy greater than 99% are extracted as the sparse matrix, and the energy E of the first t modes is as follows: where λ is the eigenvalue of the matrix P train ; β is the energy threshold required for the approximation of the original flow field, n train is the total number of training set working conditions; The final sparse matrix can be represented as:

4. The method of claim 1, wherein the method further comprises: The specific process of step (3) is as follows: When performing the compressed sensing reconstruction, for the jth group of working conditions, the leading space mode Ψ obtained through the generalized eigenvalue orthogonal decomposition, the position information of the sensor, and the measurement value y of the sensor are input; the initial position of the sensor is a set of randomly generated non-repeating positive integers: Wherein, d is the number of sensors, m is the number of points contained in the pressure distribution data under each working condition, that is, the space length; The initial number of sensors d=2, and the measurement matrix is constructed according to the position information of the sensor. The construction method is to generate a d-row m-column all-zero matrix, each row corresponding to a sensor. The value at the position of each sensor in the all-zero matrix is set to 1. The specific formula for constructing the measurement matrix is as follows: The mathematical description of using basis pursuit algorithm to realize compressed sensing reconstruction is: Wherein, y is the measurement value, s is the sparse vector to be reconstructed, and Θ is the measurement matrix; Let s=u-v s.t.u,v≥0, and the constraint condition can be rewritten as: By solving the l1 norm minimization approximation instead of the l0 norm minimization problem: Further converted into solving a linear programming problem: where c T s' is the objective function, y = Θs' is a set of equality constraints, s' ≥ 0 defines the boundary; solving the linear programming equation gives the solution s0, then the reconstruction coefficient s = s0(1:m) - s0(m+1:2m) is obtained, and the inverse transformation gives the predicted surface pressure field p rec = Ψs + ψ0, and the relative error size ε between the predicted surface pressure field under this working condition and the surface pressure field obtained by CFD is calculated j , and the calculation formula is as follows: wherein p k,rec is the predicted pressure value at the kth point in the surface pressure field, p k,cfd is the CFD-derived pressure value at the kth point in the surface pressure field, e k is the relative error size between the predicted surface pressure field and the CFD-derived surface pressure field at the kth point.

5. The method of claim 1, wherein the method further comprises: The specific process of the step (4) is: (4.1) First, initialize the parameters in the improved particle swarm optimization algorithm: <m, n train , num, d max , h, h max , v max,initial , v max,final , w initial , w final , c1, c2, p train , epsilon h , epsilon limit >, where m is the total number of the control points on the surface of the vehicle body; n train is the total number of the training sets; num is the number of the particle swarm; d max is the maximum value of the number of the measuring points; h is the current iteration number; h max is the maximum iteration number allowed in a single iteration of the particle swarm optimization; v max,initial and v max,final are the initial value and the terminal value of the maximum velocity of the particle, respectively; w initial and w final are the initial value and the terminal value of the inertia weight factor, respectively; c1 and c2 are the individual learning factor and the social learning factor, respectively; p train is the proportion of the training sets extracted for calculating the fitness function, which reduces the possibility of overfitting of the results; e h is the error of the current iteration; e limit is the required convergence error; (4.2) The velocity state of each particle is initialized as a random number between [-v max,initial ,v max,initial ], and the position state is initialized as a random integer between [0, m]; the fitness of each particle is calculated according to the current position state of each particle, and the calculation formula of the fitness function is as follows: wherein c j whether the reconstruction error of the jth group of training working conditions meets the allowed convergence error; c is a scaling factor, representing the proportion of training set working conditions meeting the training requirements in the total number of extracted training set working conditions, the value of c tends to 1, representing that the sensor arrangement scheme performs well in all extracted training set working conditions, and c as the dividend cannot be equal to zero, when the fitness function f i tends to zero, representing that the proportion of control points with a relative reconstruction error greater than 5% in almost all training set working conditions using the sensor arrangement scheme tends to zero; ε limit is the required convergence error; p train is the proportion of training set working conditions extracted for calculating the fitness function; n train is the total number of training set working conditions; (4.3) Update the current inertia weight factor and maximum speed of the particle swarm, and the formula is as follows: where h is the current iteration number; h max is the maximum iteration number allowed for a single iteration of the particle swarm optimization; w h is the inertia weight factor at the hth iteration; w initial and w final are the initial and terminal values, respectively, of the inertia weight factor; v max,initial and v max,final are the initial and terminal values, respectively, of the maximum particle velocity; Then perform single iteration calculation on the particle swarm, update the speed state, position state and fitness of each particle; the update formula of the speed state of each particle is as follows: Wherein, r1 and r2 are random numbers between 0 and 1; xbest_local is the local optimal position; xbest_global is the global optimal position; Check whether the speed state of each particle is within the allowed range. Reverse and slow down the particles that exceed the speed range: Update the position state of each particle: Check whether the position state of each particle is within the allowed range. Reset the particles that exceed the position range at the boundary: updating the fitness f of each particle i h h is the current iteration number; updating the local optimum fitness of each particle and taking the position state of the particle obtaining the local optimum fitness as the local optimum position updating the global optimal fitness of the particle swarm, and taking the position state of the particle swarm obtaining the global optimal fitness as the global optimal position xbest global h : Update the error of the current iteration: ε h = min(fbest_global h , ε h-1 ); (4.4) judging whether the current error ε h is less than the allowed convergence error ε limit , and if so, returning the current global optimum fitness and position and exiting the optimization process, i.e. the entire step (4), otherwise continuing with the following; determining whether the current iteration number h reaches the maximum iteration number h max , if yes, then continue to execute, otherwise, add 1 to the iteration number, and then update the speed and position state of the particle swarm again Every certain number of iterations, a group of working condition data is randomly extracted from the verification set, and the sparse matrix obtained based on the generalized eigenvalue orthogonal decomposition process and the current global optimal position are used to construct the measurement matrix for compressed sensing reconstruction, and the size of the relative error is recorded to feedback the search and convergence performance of the particle swarm optimization under the current hyperparameter setting; determine whether the current sensor number d reaches the maximum number of measurement points d max If yes, return the current global optimal fitness and position and exit the optimization process, i.e. exit the whole step (4). Otherwise, increase the sensor number by 1 and start a new round of initialization and iterative optimization process.

6. The method of claim 1, wherein the method further comprises: The specific process of the step (5) is: set the leading space mode obtained through the generalized eigenvalue orthogonal decomposition as the sparse matrix of compressed sensing, construct the measurement matrix of compressed sensing according to the optimal sensor layout position obtained through the improved particle swarm optimization algorithm, and combine the constructed high-precision surface pressure distribution database to form the rapid prediction model of the surface pressure field of the high-speed train after training.

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