Cross validation training method, device and equipment for large-scale flow field agent model

Abstract

The invention relates to a cross validation training method, device and equipment for a large-scale flow field agent model. The method comprises the steps of determining a design variable range and performing normalization processing; recursive permutation evolution experiment design is carried out on the design variables, sample points are generated, numerical simulation is carried out, and flow field data are obtained to serve as response values of all nodes in a flow field; constructing an agent model of each node in the large-scale flow field, and calculating a primary function matrix corresponding to the agent model based on the same shape parameters; by constructing a second intermediate matrix only related to shape parameters and design variables and a global matrix only related to node response values, the sum of squares of errors of full flow field cross validation is calculated, and shape parameter optimization is carried out by taking minimization of the sum of squares of errors as an optimization target. And the flow field prediction task is executed until convergence and output of the optimal proxy model based on the optimal shape parameter. According to the method, rapid and reliable verification and efficient and accurate flow field prediction of the large-scale flow field agent model can be realized.

Description

Technical Field

[0001] This application relates to the technical field of flow field prediction in aircraft design, and particularly to a cross-validation training method, device, and equipment for a large-scale flow field surrogate model. Background Art

[0002] In the field of fluid mechanics, accurate prediction of complex flow field behaviors is crucial for engineering design and performance improvement. Although traditional computational fluid dynamics (CFD) techniques can generate high-precision simulation results, they usually require a large amount of computational resources and time, especially when solving large-scale and complex flow field problems, and this difference is very obvious. Therefore, seeking efficient and accurate flow field prediction methods is of great significance for accelerating the solution of engineering problems.

[0003] The large-scale flow field prediction technology based on surrogate models deeply integrates the numerical simulation method of computational fluid dynamics and data-driven models, and can significantly reduce the consumption of computational resources while ensuring prediction accuracy. However, as the core link for evaluating the reliability of surrogate models, model verification needs to achieve physical field reconstruction through global matrix operations in a multi-dimensional parameter space, and this process faces the bottleneck problem of exponential growth in computational complexity. How to break through the contradiction between verification efficiency and scale under limited resource constraints has become the key challenge restricting the engineering application of this technology. Summary of the Invention

[0004] Based on this, it is necessary to provide a cross-validation training method, device, and equipment for a large-scale flow field surrogate model to achieve fast and reliable verification of the large-scale flow field surrogate model, and further achieve efficient and accurate flow field prediction for the above technical problems.

[0005] A cross-validation training method for a large-scale flow field surrogate model, the method includes: Step 1, determining the range of design variables for aircraft optimization and performing normalization processing; Step 2, performing recursive permutation evolution experimental design on the design variables to generate sample points of the design variables; Step 3, performing flow field numerical simulation on the sample points to obtain large-scale flow field data of the aircraft as the response values of each node in the flow field; Step 4, constructing a surrogate model for each node in the large-scale flow field using the radial basis function algorithm, and calculating the basis function matrix corresponding to the surrogate model based on the same shape parameter in each surrogate model; Step 5: Take the samples of each subspace in the recursive permutation evolution experimental design process as the test set. Extract the overlapping elements corresponding to the current test set from the inverse matrix of the basis function matrix and form them into a submatrix. Combine the submatrices corresponding to all test sets to construct the first intermediate matrix. After constructing the second intermediate matrix that is only related to the shape parameters and design variables based on the first intermediate matrix, construct the sum of squared cross-validation errors of each surrogate model according to the second intermediate matrix and the global matrix that is only related to the nodal response values. Combine the sum of squared cross-validation errors corresponding to each node in the large-scale flow field to construct the sum of squared cross-validation errors of the entire flow field. Step 6: Take the minimization of the sum of squared cross-validation errors of the entire flow field as the optimization objective, and use the particle swarm optimization algorithm to optimize the shape parameters. During the optimization process, the global matrix remains unchanged. Update the surrogate model based on the optimized shape parameters and recalculate the sum of squared cross-validation errors of the entire flow field until the error converges, and output the optimal surrogate model based on the optimal shape parameters to perform the flow field prediction task.

[0006] In one embodiment, step 2 includes: Step 2.1: Define the number of samples required for the aircraft optimization as , and recursively split the space containing samples until each subspace contains or samples; where the splitting number is and obtain subspaces. Step 2.2: Use the optimized Latin hypercube experimental design algorithm to generate an initial sample set with the number of samples being ; where represents the th sample. Step 2.3: Perform a cyclic deletion operation on the samples in the initial sample set, and select the samples with the best uniformity after the deletion operation as the evolutionary sample set . Step 2.4: Fill the samples in the evolutionary sample set into each subspace, and perform PIO optimization on the filled samples to obtain the optimized sample points.

[0007] In one embodiment, step 3 includes: Step 3.1: Geometric modeling, including: defining the flow field calculation domain based on the physical characteristics of the aircraft, simplifying the complex structure of the aircraft and repairing geometric defects, and applying periodic or mirror boundary conditions to the symmetric flow field, and outputting in a general geometric format. Step 3.2, structured network generation, including: optimizing the topological structure after importing the geometric model, arranging high-precision boundary layer grids near the wall surface, using the O-grid technology to process the curved surface area to reduce grid distortion, and performing grid quality verification, and outputting in a general grid format; Step 3.3, flow field solution and post-processing, including: first selecting a pressure-velocity coupling algorithm to activate the energy equation and the turbulence model, and setting the material properties and boundary conditions; then using a second-order discretization format to solve the energy equation and the turbulence model, and setting a residual convergence criterion of 1e-6, and monitoring through force coefficients and heat fluxes during the solution process to ensure the stability of the solution results; finally, using an adaptive time step to accelerate convergence, and extracting the flow field cloud map, streamline and quantitative data as the response values of each node in the flow field.

[0008] In one of the embodiments, step 4 includes: Constructing a surrogate model for each node in the large-scale flow field using the radial basis function algorithm, expressed as: ; where, is the model output value of the point to be predicted ; is the number of samples in the training set, which is equal to the number of samples required for aircraft optimization; is the sample serial number in the training set, is the th weight coefficient of the Gaussian basis function, is the th Gaussian basis function, and the specific expression is: ; where, is the Euclidean distance between the sample point to be predicted and the known sample point , is the shape parameter, and the surrogate model for each node in the large-scale flow field selects the same shape parameter. After determining the shape parameter, the surrogate model is inverted, and the corresponding weight coefficient is calculated, and then the basis function matrix corresponding to each surrogate model is deduced, expressed as: ; where, represents the weight coefficient matrix, which is composed of the weight coefficients of the Gaussian basis functions corresponding to all samples in the training set; is the inverse matrix of the basis function matrix , is the physical quantity in the training set.

[0009] In one embodiment, in step 5, the samples of each subspace in the recursive permutation evolution experimental design process are used as the test set, and the overlapping elements corresponding to the current test set are extracted from the inverse matrix of the basis function matrix and assembled into a submatrix. The submatrices corresponding to all test sets are comprehensively constructed into a first intermediate matrix, including: Each time, take the samples in one subspace of the recursive permutation evolution experimental design process or as the test set, and the rest as the training set; From the inverse matrix of the basis function matrix Extract the r rows r and r columns of the elements that overlap to form a order matrix and assemble it into a submatrix ; Comprehensively construct the submatrices corresponding to all test sets into a first intermediate matrix ; Among them, is the splitting number of the subspace.

[0010] In one embodiment, in step 5, after constructing a second intermediate matrix related only to the shape parameters and design variables based on the first intermediate matrix, the sum of squared cross-validation errors of each surrogate model is constructed according to the second intermediate matrix and the global matrix related only to the node response values, including: Define the calculation formula for the sum of squared cross-validation errors of the surrogate model at each node in the large-scale flow field as: ; Among them, represents the second intermediate matrix related only to the shape parameters and design variables constructed based on the first intermediate matrix , is the global matrix related only to the node response values, and the superscript T represents matrix transpose; Furthermore, the sum of squared cross-validation errors at each node is expressed as: ; Among them, represents taking the trace of the matrix.

[0011] In one embodiment, in step 5, the sum of squared cross-validation errors of the entire flow field is constructed by comprehensively combining the sum of squared cross-validation errors corresponding to each node in the large-scale flow field, ; Among them, Nrepresents the number of nodes in the flow field, represents the response value of the th node in the flow field; represents the sum of squared cross-validation errors corresponding to the th node; represents the second intermediate matrix of the th node; Stored in the global matrix The global matrix remains unchanged in each optimization iteration of the shape parameter.

[0012] In one of the embodiments, step 6 includes: Step 6.1, initialize the particle swarm, including the number of particles, position, and velocity; Step 6.2, define the iteration parameter update rules, including the position update formula and the velocity update formula, which are respectively expressed as: ; ; where, represents the velocity of the th particle iterated to the th generation; represents the position of the th particle iterated to the th generation; is the inertia weight; and are the learning factors; rand() is a random number between [0,1]; is the individual historical best position of the th particle; is the global historical best position; Step 6.3, with the minimization of the sum of squared cross-validation errors of the entire flow field as the optimization objective, optimize the shape parameter as the iteration parameter. During the optimization process, the global matrix remains unchanged. Update the surrogate model based on the optimized shape parameter and recalculate the sum of squared cross-validation errors of the entire flow field; Step 6.4, if the relative change rate of the sum of squared cross-validation errors of the entire flow field is lower than the preset threshold in several consecutive iterations, it is considered that the error has converged; otherwise, continue the iteration, continuously approaching the optimal shape parameter until the error converges, and output the optimal surrogate model based on the optimal shape parameter to perform the flow field prediction task.

[0013] A cross-validation training device for a large-scale flow field surrogate model, the device includes: A design variable determination module, used to determine the range of design variables for aircraft optimization and perform normalization processing; An experimental design module, which is used to perform a recursive permutation evolution experimental design on design variables to generate sample points of the design variables; A numerical simulation module, which is used to perform a numerical simulation of the flow field on the sample points to obtain large-scale flow field data of the aircraft as the response values of each node in the flow field; A surrogate model construction module, which is used to construct a surrogate model for each node in the large-scale flow field by using the radial basis function algorithm, and calculate the basis function matrix corresponding to the surrogate model based on the same shape parameter in each surrogate model; A cross-validation error calculation module, which is used to use the samples of each subspace in the recursive permutation evolution experimental design process as the test set, and extract the overlapping elements corresponding to the current test set from the inverse matrix of the basis function matrix and form them into a sub-matrix. The sub-matrices corresponding to all test sets are comprehensively constructed into a first intermediate matrix, and after constructing a second intermediate matrix related only to the shape parameter and the design variable based on the first intermediate matrix, the sum of squared cross-validation errors of each surrogate model is constructed according to the second intermediate matrix and the global matrix related only to the node response values, and the sum of squared cross-validation errors corresponding to each node in the large-scale flow field is comprehensively constructed to obtain the sum of squared cross-validation errors of the entire flow field; An iterative optimization module, which is used to use the minimization of the sum of squared cross-validation errors of the entire flow field as the optimization goal, and use the particle swarm optimization algorithm to optimize the shape parameter. During the optimization process, the global matrix remains unchanged, the surrogate model is updated based on the optimized shape parameter, and the sum of squared cross-validation errors of the entire flow field is recalculated until the error converges, and the optimal surrogate model based on the optimal shape parameter is output to perform the flow field prediction task.

[0014] A computer device, including a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, the following steps are implemented: Step 1, determine the range of the design variables for aircraft optimization and perform normalization processing; Step 2, perform a recursive permutation evolution experimental design on the design variables to generate sample points of the design variables; Step 3, perform a numerical simulation of the flow field on the sample points to obtain large-scale flow field data of the aircraft as the response values of each node in the flow field; Step 4, construct a surrogate model for each node in the large-scale flow field by using the radial basis function algorithm, and calculate the basis function matrix corresponding to the surrogate model based on the same shape parameter in each surrogate model; Step 5: Use the samples of each subspace in the recursive permutation evolution experimental design process as the test set. Extract the overlapping elements corresponding to the current test set from the inverse matrix of the basis function matrix and form them into a sub-matrix. Combine the sub-matrices corresponding to all test sets to construct a first intermediate matrix. After constructing a second intermediate matrix that is only related to the shape parameters and design variables based on the first intermediate matrix, calculate the sum of squared cross-validation errors of each surrogate model according to the second intermediate matrix and the global matrix that is only related to the nodal response values. Combine the sum of squared cross-validation errors corresponding to each node in the large-scale flow field to construct the sum of squared cross-validation errors of the entire flow field; Step 6: Take minimizing the sum of squared cross-validation errors of the entire flow field as the optimization goal, and use the particle swarm optimization algorithm to optimize the shape parameters. During the optimization process, the global matrix remains unchanged. Update the surrogate model based on the optimized shape parameters and recalculate the sum of squared cross-validation errors of the entire flow field until the error converges, and output the optimal surrogate model based on the optimal shape parameters to perform the flow field prediction task.

[0015] Regarding the above cross-validation training method, device, and equipment for large-scale flow field surrogate models, aiming at the problems of repeated calculation and high computational complexity in calculating the cross-validation error for a single node in a large-scale flow field, a matrix pre-computation strategy of "construct once, reuse multiple times" is provided. On the one hand, considering that a large amount of repeated information is contained in the basis function matrix of each surrogate model, by extracting the overlapping elements corresponding to the test set from the inverse matrix of the basis function matrix and constructing a second intermediate matrix that is only related to the shape parameters and design variables, the repeated calculation of the basis function matrix can be reduced; on the other hand, only at the initialization stage of the surrogate model optimization iteration, the global matrix that is only related to the nodal response values is solved once and directly called in subsequent iterations to calculate the sum of squared cross-validation errors. For the verification calculation of a surrogate model with millions of grid numbers in a large-scale flow field, the computational amount can be effectively reduced. Therefore, this application can achieve the fast and reliable verification of large-scale flow field surrogate models and improve the practicality of large-scale flow field surrogate model prediction. Description of the Drawings

[0016] Figure 1 It is a schematic flowchart of the cross-validation training method for a large-scale flow field surrogate model in an embodiment; Figure 2 It is a schematic diagram of the calculation duration of different cross-validation methods in each round of optimization iteration in an embodiment; Figure 3 It is a flow field cloud map of CFD (Computational Fluid Dynamics) simulation in an embodiment; among them, Figure 3 (a) is the CFD simulation cloud map of the horizontal flow velocity field of the flow field, Figure 3(b) is the CFD simulation cloud map of the vertical flow velocity field of the flow field, Figure 3 (c) is the CFD simulation cloud map of the pressure field of the flow field; Figure 4 is the flow field cloud map predicted by the optimized surrogate model of the present application in an embodiment; wherein, Figure 4 (a) is the horizontal flow velocity field cloud map of the flow field predicted by the optimized surrogate model of the present application, Figure 4 (b) is the vertical flow velocity field cloud map of the flow field predicted by the optimized surrogate model of the present application, Figure 4 (c) is the pressure field cloud map of the flow field predicted by the optimized surrogate model of the present application; Figure 5 is the flow field prediction error cloud map of the optimized surrogate model of the present application in an embodiment; wherein, Figure 5 (a) is the horizontal flow velocity field prediction error cloud map of the flow field of the optimized surrogate model of the present application, Figure 5 (b) is the vertical flow velocity field prediction error cloud map of the flow field of the optimized surrogate model of the present application, Figure 5 (c) is the pressure field prediction error cloud map of the flow field of the optimized surrogate model of the present application; Figure 6 is the internal structure diagram of a computer device in an embodiment. Detailed implementation manners

[0017] In order to make the purpose, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0018] In one embodiment, as Figure 1 shown, a cross-validation training method for a large-scale flow field surrogate model is provided, including the following steps: Step 1, determine the range of the design variables optimized for the aircraft and perform normalization processing.

[0019] Specifically, determine the design variable set and its lower limit set of values and upper limit set of values . By the th design variable , perform normalization processing on each dimension parameter to obtain the normalized design variable set . Among them, D is the number of design variables, and respectively represent the lower limit and upper limit of the values of the th design variable , is the Design variables.

[0020] Step 2: Conduct a recursive permutation and evolution experimental design on the design variables to generate sample points of the design variables.

[0021] Specifically, Step 2 includes: Step 2.1: Define the number of samples for the aircraft optimization requirements as n , and recursively split the space containing n samples until each subspace contains or samples; where the number of splits is and obtain subspaces.

[0022] Step 2.2: Use the optimized Latin hypercube experimental design algorithm to generate an initial sample set with the number of samples being ; where represents the st sample.

[0023] Step 2.3: Perform a cyclic deletion operation on the samples in the initial sample set, and select the samples with the best uniformity after the deletion operation as the evolutionary sample set .

[0024] Step 2.4: Fill the samples in the evolutionary sample set into each subspace, and perform PIO (Pigeon-Inspired Optimization) optimization on the filled samples to obtain optimized sample points.

[0025] Step 3: Conduct a numerical simulation of the flow field for the sample points to obtain large-scale flow field data of the aircraft as the response values of each node in the flow field.

[0026] Specifically, Step 3 includes: Step 3.1: Geometric modeling, including: defining the flow field calculation domain based on the physical characteristics of the aircraft (e.g., expanding the external flow field by 5 - 10 times the characteristic length), simplifying the complex structure of the aircraft (e.g., removing non-critical details such as <0.1mm fillets and bolt holes), repairing geometric defects (e.g., eliminating small gaps and overlapping surfaces), ensuring surface smoothness, and applying periodic or mirror boundary conditions for symmetric flow fields (such as flow around a cylinder), and outputting in a common geometric format.

[0027] Step 3.2, structured network generation, including: optimizing the topological structure after importing the geometric model, arranging high-precision boundary layer grids near the wall surface (meeting the requirement of y+ < 1, where y+ is a dimensionless parameter representing the distance from the first grid cell to the surface wall), using the O-type grid technology to process the curved surface area to reduce grid distortion, and performing grid quality verification (i.e., verifying indicators such as orthogonality and aspect ratio), and outputting in a general grid format.

[0028] Step 3.3, flow field solution and post-processing, including: first, selecting a pressure-velocity coupling algorithm to activate the energy equation and turbulence model (specifically selecting the Realizable k-ε turbulence model combined with enhanced wall functions), and setting the material properties and boundary conditions (velocity inlet / pressure outlet); then, using a second-order discretization format to solve the energy equation and turbulence model, setting a residual convergence criterion of 1e-6, and monitoring through force coefficients and heat fluxes during the solution process to ensure the stability of the solution results; finally, using an adaptive time step to accelerate convergence, extracting the flow field cloud map, streamlines, and quantitative data as the response values of each node in the flow field.

[0029] Step 4, constructing a surrogate model for each node in the large-scale flow field using the radial basis function algorithm, and calculating the basis function matrix corresponding to the surrogate model based on the same shape parameter in each surrogate model.

[0030] Specifically, Step 4 includes: Constructing a surrogate model for each node in the large-scale flow field using the radial basis function algorithm. The radial basis function uses simple odd functions for weighted superposition to achieve prediction of new sample points, expressed as: ; Among them, is the model output value of the point to be predicted , is the number of samples in the training set, equal to the number of samples required for aircraft optimization; is the sample serial number in the training set, is the weight coefficient of the th Gaussian basis function, is the th Gaussian basis function, which uses the Euclidean distance from the unknown sample to the known sample as the independent variable, and the specific expression is: Among them, is the Euclidean distance between the sample point to be predicted and the known sample point , is the shape parameter, and the surrogate models of each node in the large-scale flow field all select the same shape parameter. After determining the shape parameter, the surrogate model is inversely deduced, and the corresponding weight coefficients are calculated , and then by calculation, the basis function matrix corresponding to each surrogate model is obtained, which is expressed as: ; Among them, represents the weight coefficient matrix, which is composed of the weight coefficients of the Gaussian basis functions corresponding to all samples in the training set; is the basis function matrix of the inverse matrix, is the physical quantity in the training set.

[0031] Step 5: Take the samples in each subspace during the recursive permutation evolution experimental design process as the test set, and extract the overlapping elements corresponding to the current test set from the inverse matrix of the basis function matrix and form them into a submatrix. The submatrices corresponding to all test sets are comprehensively constructed into a first intermediate matrix. After constructing a second intermediate matrix that is only related to the shape parameters and design variables based on the first intermediate matrix, the sum of the squared cross-validation errors of each surrogate model is constructed according to the second intermediate matrix and the global matrix that is only related to the node response values, and the sum of the squared cross-validation errors corresponding to each node in the large-scale flow field is comprehensively constructed to obtain the sum of the squared cross-validation errors of the entire flow field.

[0032] Specifically, Step 5 includes: Step 5.1: Each time, take or samples in a subspace during the recursive permutation evolution experimental design process as the test set, and the rest as the training set.

[0033] Step 5.2: From the inverse matrix of the basis function matrix, extract the rows and columns of elements that overlap with the current test set and form them into a order submatrix.

[0034] Step 5.3: Comprehensively construct the submatrices corresponding to all test sets into a first intermediate matrix , which is expressed as: ; Among them, is the splitting number of the subspace.

[0035] Step 5.4: Define the calculation formula for the sum of the squared cross-validation errors of the surrogate model for each node in the large-scale flow field as: ; Among them, represents the second intermediate matrix constructed based on the first intermediate matrix that is only related to the shape parameters and design variables, is the global matrix related only to the node response values, with the superscript T indicating matrix transpose; Furthermore, the sum of squared cross-validation errors at each node is expressed as: ; where represents taking the trace of the matrix; Based on this, by synthesizing the sum of squared cross-validation errors corresponding to each node in the large-scale flow field, the sum of squared cross-validation errors for the entire flow field is constructed , which is expressed as: ; where N represents the number of nodes in the flow field, represents the th node response value in the flow field, represents the th sum of squared cross-validation errors corresponding to the node, represents the second intermediate matrix of the th node; is stored in the global matrix , and the global matrix remains unchanged in each optimization iteration of the shape parameter, eliminating the need for repeated calculations and significantly reducing the computational cost of cross-validation for the large-scale flow field surrogate model.

[0036] Step 6: With the goal of minimizing the sum of squared cross-validation errors for the entire flow field, the particle swarm optimization algorithm is used to optimize the shape parameter. During the optimization process, the global matrix remains unchanged. Based on the optimized shape parameter, the surrogate model is updated and the sum of squared cross-validation errors for the entire flow field is recalculated until the error converges, and the optimal surrogate model based on the optimal shape parameter is output to perform the flow field prediction task.

[0037] Specifically, Step 6 includes: Step 6.1: Initialize the particle swarm, including the number of particles, position, and velocity.

[0038] Step 6.2: Define the iteration parameter update rules, including the position update formula and the velocity update formula, which are respectively expressed as: ; ; where represents the velocity of the th particle iterated to the th generation; represents the position of the th particle iterated to the th generation; is the inertia weight; and is the learning factor; rand() is a random number between [0, 1]; is the individual historical optimal position of the -th particle; is the global historical optimal position.

[0039] In step 6.3, with the objective of minimizing the sum of squared cross-validation errors of the entire flow field, the shape parameter is optimized as the iterative parameter. During the optimization process, the global matrix remains unchanged. Based on the optimized shape parameter, the surrogate model is updated and the sum of squared cross-validation errors of the entire flow field is recalculated, and the sum of squared cross-validation errors of the entire flow field is used as the fitness to evaluate the individual and the global optimum.

[0040] In step 6.4, if the relative change rate of the sum of squared cross-validation errors of the entire flow field is lower than the preset threshold for several consecutive iterations, it is considered that the error has converged; otherwise, continue the iteration, continuously approaching the optimal shape parameter until the error converges, and output the optimal surrogate model based on the optimal shape parameter to perform the flow field prediction task.

[0041] In summary, the cross-validation training method for a large-scale flow field surrogate model provided by this application can reduce the repeated calculation of the basis function matrix by considering that a large amount of repeated information is contained in the basis function matrix of each surrogate model, and by extracting the overlapping elements corresponding to the test set from the inverse matrix of the basis function matrix and constructing a second intermediate matrix related only to the shape parameter and the design variable; moreover, the method provided by this application only solves the global matrix related only to the node response values once during the initialization of the surrogate model optimization iteration and directly calls this global matrix to calculate the sum of squared cross-validation errors in subsequent iterations. For the verification calculation of a surrogate model of a large-scale flow field with millions of grid numbers, the calculation amount can be effectively reduced, so as to achieve the efficient and reliable verification of the large-scale flow field surrogate model.

[0042] In one embodiment, the method provided by this application is applied to the two-dimensional NACA0012 airfoil flow field for rapid cross-validation of the surrogate model to verify the reliability and efficiency of the method provided by this application. The specific steps include: First, determine that the design variables are the angle of attack and the Mach number, and clarify that the range of the design variables is , , and normalize these two design variables. Then, use the recursive permutation evolution experimental design algorithm to conduct experimental design on the two design variables, generating a total of 64 sample points. Conduct numerical simulation analysis on the two-dimensional NACA0012 airfoil under these 64 working conditions, and obtain the velocity and pressure data of the flow field as the response values of each node in the flow field. Construct a surrogate model for each node in the flow field of the two-dimensional NACA0012 airfoil, divide the training set and the test set based on K-fold cross-validation, and use the cross-validation training method of the large-scale flow field surrogate model proposed in this application to calculate the sum of squared cross-validation errors of the entire flow field. Taking the minimization of the sum of squared cross-validation errors of the entire flow field as the optimization goal, use the particle swarm optimization algorithm to optimize the shape parameters until the optimization converges, and output the optimal surrogate model based on the optimal shape parameters to perform the flow field prediction task.

[0043] Table 1 shows the comparison of the mean absolute errors of the flow field predictions of different surrogate models. It can be seen from the results that the prediction accuracy of the surrogate model optimized based on the method proposed in this application is significantly improved compared to the initial surrogate model, verifying the reliability of the method proposed in this application for guiding optimization. Figure 2 is the calculation duration in each round of optimization iteration for different cross-validation methods. It can be seen that the method proposed in this application saves 84% in time compared to the traditional cross-validation method, indicating the high efficiency of this method. In Table 1 u , v and p respectively represent the horizontal flow velocity field, vertical flow velocity field, and pressure field of the flow field.

[0044] Table 1 Comparison of the mean absolute errors of the flow field predictions of different surrogate models

[0045] Figure 3 and Figure 4 are respectively the flow field contour maps of the CFD simulation under randomly generated test working conditions and the predictions of the surrogate model optimized in this application. By comparing Figure 3 and Figure 4 , it can be found that the flow field contour map predicted by the surrogate model optimized in this application cannot be distinguished from the high-fidelity CFD results, indicating that the optimized surrogate models have successfully predicted the main flow characteristics around the airfoil. Through Figure 5 the further quantitative error analysis shows that the prediction errors of the surrogate model optimized in this application for the velocity field are mainly concentrated in two key regions: the wake region and the leading edge region. This local error distribution is consistent with the known flow separation phenomenon in the transonic state, confirming that the surrogate model optimized in this application has the ability to capture the main aerodynamic characteristics and can achieve accurate flow field prediction.

[0046] In one embodiment, a cross-validation training device for a large-scale flow field surrogate model is provided, including: A design variable determination module, configured to determine the range of design variables for aircraft optimization and perform normalization processing; An experimental design module, configured to perform a recursive permutation evolution experimental design on the design variables to generate sample points of the design variables; A numerical simulation module, configured to perform a numerical simulation of the flow field on the sample points to obtain large-scale flow field data of the aircraft as the response values of each node in the flow field; A surrogate model construction module, configured to construct a surrogate model for each node in the large-scale flow field using a radial basis function algorithm, and calculate the basis function matrix corresponding to the surrogate model based on the same shape parameters in each surrogate model; A cross-validation error calculation module, configured to use the samples of each subspace in the recursive permutation evolution experimental design process as a test set, and extract the overlapping elements corresponding to the current test set from the inverse matrix of the basis function matrix and form them into a submatrix. The submatrices corresponding to all test sets are comprehensively constructed into a first intermediate matrix, and after constructing a second intermediate matrix related only to the shape parameters and design variables based on the first intermediate matrix, construct the sum of squared cross-validation errors of each surrogate model according to the second intermediate matrix and the global matrix related only to the node response values, and comprehensively construct the sum of squared cross-validation errors of the entire flow field based on the sum of squared cross-validation errors corresponding to each node in the large-scale flow field; An iterative optimization module, configured to use the particle swarm optimization algorithm to optimize the shape parameters with the goal of minimizing the sum of squared cross-validation errors of the entire flow field. During the optimization process, the global matrix remains unchanged, update the surrogate model based on the optimized shape parameters and recalculate the sum of squared cross-validation errors of the entire flow field until the error converges, and output the optimal surrogate model based on the optimal shape parameters to perform the flow field prediction task.

[0047] For the specific limitations of the cross-validation training device of the large-scale flow field surrogate model, reference can be made to the limitations of the cross-validation training method of the large-scale flow field surrogate model in the above text, which will not be elaborated here. Each module in the above cross-validation training device of the large-scale flow field surrogate model can be implemented in whole or in part through software, hardware, and their combinations. The above modules can be embedded in the processor of the computer device in hardware form or independent of it, or stored in the memory of the computer device in software form, so that the processor can call and execute the operations corresponding to the above modules.

[0048] In one embodiment, a computer device is provided. The computer device can be a terminal, and its internal structure diagram can be as Figure 6As shown. The computer device includes a processor, a memory, a network interface, a display screen, and an input device connected through a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The network interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, it realizes a cross-validation training method for a large-scale flow field proxy model. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen. The input device of the computer device can be a touch layer covering the display screen, or a button, a trackball, or a touchpad provided on the housing of the computer device, or an external keyboard, a touchpad, or a mouse, etc.

[0049] Those skilled in the art can understand that Figure 6 the structure shown in is only a block diagram of some structures related to the solution of this application, and does not constitute a limitation on the computer device to which the solution of this application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine some components, or have different component arrangements.

[0050] In one embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program. When the processor executes the computer program, the following steps are implemented: Step 1, determine the range of the design variables for aircraft optimization and perform normalization processing; Step 2, perform a recursive permutation evolution experimental design on the design variables to generate sample points of the design variables; Step 3, perform a flow field numerical simulation on the sample points to obtain the large-scale flow field data of the aircraft as the response values of each node in the flow field; Step 4, use the radial basis function algorithm to construct a proxy model for each node in the large-scale flow field, and calculate the basis function matrix corresponding to the proxy model based on the same shape parameters in each proxy model; Step 5, use the samples of each subspace in the recursive permutation evolution experimental design process as the test set, and extract the overlapping elements corresponding to the current test set from the inverse matrix of the basis function matrix and form them into a sub-matrix. Combine the sub-matrices corresponding to all test sets to construct a first intermediate matrix, and after constructing a second intermediate matrix related only to the shape parameters and design variables based on the first intermediate matrix, construct the sum of squared cross-validation errors of each proxy model according to the second intermediate matrix and the global matrix related only to the node response values, and combine the sum of squared cross-validation errors corresponding to each node in the large-scale flow field to construct the sum of squared cross-validation errors of the entire flow field; Step 6: With the goal of minimizing the sum of squared cross-validation errors of the entire flow field, the particle swarm optimization algorithm is used to optimize the shape parameters. During the optimization process, the global matrix remains unchanged. Based on the optimized shape parameters, the surrogate model is updated and the sum of squared cross-validation errors of the entire flow field is recalculated until the error converges. Then, the optimal surrogate model based on the optimal shape parameters is output to perform the flow field prediction task.

[0051] The technical features of the above embodiments can be combined arbitrarily. For the sake of concise description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0052] The above-described embodiments merely represent several implementation manners of the present application. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the present application. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several modifications and improvements can still be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the appended claims.

Claims

1. A cross-validation training method for a large-scale flow field proxy model, characterized in that The method includes the following steps: Step 1: Determine the range of the design variables for the aircraft optimization and perform normalization processing; Step 2: Conduct a recursive permutation evolution experimental design on the design variables to generate sample points of the design variables; Step 3: Perform a numerical simulation of the flow field for the sample points to obtain large-scale flow field data of the aircraft as the response values of each node in the flow field; Step 4: Use the radial basis function algorithm to construct a surrogate model for each node in the large-scale flow field, and calculate the basis function matrix corresponding to the surrogate model based on the same shape parameters in each surrogate model; Step 5: Use the samples in each subspace during the recursive permutation evolution experimental design process as the test sets, extract the overlapping elements corresponding to the current test sets from the inverse matrix of the basis function matrix and form them into submatrices, comprehensively construct the submatrices corresponding to all test sets into the first intermediate matrix, and after constructing the second intermediate matrix related only to the shape parameters and design variables based on the first intermediate matrix, construct the sum of squared cross-validation errors of each surrogate model according to the second intermediate matrix and the global matrix related only to the node response values, and comprehensively construct the sum of squared cross-validation errors of the entire flow field; Step 6: Use the particle swarm optimization algorithm to optimize the shape parameters with the goal of minimizing the sum of squared cross-validation errors of the entire flow field. During the optimization process, the global matrix remains unchanged, update the surrogate model based on the optimized shape parameters and recalculate the sum of squared cross-validation errors of the entire flow field until the error converges, and output the optimal surrogate model based on the optimal shape parameters to perform the flow field prediction task.

2. The cross-validation training method of a large-scale flow field proxy model according to claim 1, characterized in that The Step 2 includes: Step 2.1, define the number of samples for aircraft optimization requirements as n , and recursively split the space containing n samples until each subspace contains or samples; where the splitting number is and obtain subspaces; Step 2.2, generate an initial sample set with the number of samples being using the optimized Latin hypercube experimental design algorithm ; where represents the th sample Step 2.3, perform a cyclic deletion operation on the samples in the initial sample set, and select the samples with the optimal uniformity after the deletion operation as the evolutionary sample set ;​​​​ Step 2.4, fill the evolutionary sample set with samples into each subspace, and perform PIO optimization on the filled samples to obtain optimized sample points.

3. A cross-validation training method for a large-scale flow field proxy model according to claim 1, characterized in that The Step 3 includes: Step 3.1: Geometric modeling, including: defining the flow field calculation domain based on the physical characteristics of the aircraft, simplifying the complex structure of the aircraft and repairing geometric defects, and applying periodic or mirror boundary conditions to the symmetric flow field, and outputting in a general geometric format; Step 3.2: Structured grid generation, including: optimizing the topological structure after importing the geometric model, arranging high-precision boundary layer grids near the wall surface, using the O-grid technology to process the curved surface area to reduce grid distortion, and performing grid quality verification, and outputting in a general grid format; Step 3.3: Flow field solution and post-processing, including: first select the pressure-velocity coupling algorithm to activate the energy equation and the turbulence model, and set the material properties and boundary conditions; then use the second-order discretization format to solve the energy equation and the turbulence model, and set the residual convergence criterion of 1e-6, and monitor through the force coefficient and heat flux during the solution process to ensure the stability of the solution result; finally, use the adaptive time step to accelerate the convergence, and extract the flow field cloud map, streamline and quantitative data as the response values of each node in the flow field.

4. A cross-validation training method for a large-scale flow field proxy model according to claim 1, characterized in that The Step 4 includes: Use the radial basis function algorithm to construct a surrogate model for each node in the large-scale flow field, expressed as: ； Among them, is the model output value of the point to be predicted ; is the number of samples in the training set, which is equal to the number of samples of the aircraft optimization requirements; is the sample serial number in the training set, is the weight coefficient of the th Gaussian basis function, is the th Gaussian basis function, and the specific expression is: ； Among them, is the sample point to be predicted and the known sample points the Euclidean distance between them, is the shape parameter. The surrogate models of each node in the large-scale flow field select the same shape parameter. After determining the shape parameter, the surrogate model is deduced backward, and the corresponding weight coefficients are calculated , and then the basis function matrix corresponding to each surrogate model is deduced and expressed as: ； Among them, represents the weight coefficient matrix, which is composed of the weight coefficients of the Gaussian basis functions corresponding to all samples in the training set; is the inverse matrix of the basis function matrix , is the physical quantity in the training set.

5. The cross-validation training method of a large-scale flow field proxy model according to claim 1, characterized in that In step 5, the samples of each subspace in the recursive permutation evolution experimental design process are used as the test set, and the overlapping elements corresponding to the current test set are extracted from the inverse matrix of the basis function matrix and assembled into a submatrix. The submatrices corresponding to all test sets are comprehensively constructed into a first intermediate matrix, including: Each time, take the or samples within a subspace in the recursive permutation evolution experimental design process as the test set, and the rest as the training set; From the inverse matrix of the basis function matrix extract the r rows r that overlap with the elements in the r columns and form them into a submatrix of order; Combine the submatrices corresponding to all test sets Construct it into the first intermediate matrix , which is expressed as: ； Among them, is the splitting number of the subspace.

6. A cross-validation training method for a large-scale flow field proxy model according to claim 5, characterized in that In the said step 5, after constructing a second intermediate matrix related only to the shape parameter and the design variable based on the first intermediate matrix, the sum of squared cross-validation errors of each surrogate model is constructed according to the second intermediate matrix and the global matrix related only to the nodal response values, including: Define the calculation method of the sum of squared cross-validation errors of the surrogate model for each node in the large-scale flow field as: ； Among them, represents a second intermediate matrix constructed based on the first intermediate matrix and is only related to the shape parameters and design variables, is the global matrix only related to the node response values, and the superscript T represents the matrix transpose; Furthermore, the sum of squared cross-validation errors at each node is expressed as: ; where denotes taking the trace of the matrix.

7. A cross-validation training method for a large-scale flow field proxy model according to claim 6, characterized in that In step 5, the sum of squared cross-validation errors corresponding to each node in the large-scale flow field is integrated to construct the sum of squared cross-validation errors for the entire flow field , which is expressed as: ； Among them, N represents the number of nodes in the flow field, represents the response value of the th node in the flow field, represents the sum of squared cross-validation errors corresponding to the th node, represents the second intermediate matrix of the th node; is stored in the global matrix which remains unchanged in each optimization iteration of the shape parameter.

8. A cross-validation training method for a large-scale flow field proxy model according to claim 1, characterized in that The said step 6 includes: Step 6.1, initialize the particle swarm, including the number of particles, positions, and velocities; Step 6.2, define the iteration parameter update rules, including the position update formula and the velocity update formula, which are respectively expressed as: ； ； Among them, represents the velocity of the -th particle iterated to the -th generation; represents the position of the -th particle iterated to the -th generation; is the inertia weight; and are the learning factors; is a random number between ; is the individual historical optimal position of the -th particle; is the global historical optimal position; Step 6.3, with the goal of minimizing the sum of squared cross-validation errors of the entire flow field, optimize the shape parameter as the iteration parameter. During the optimization process, the global matrix remains unchanged. Update the surrogate model based on the optimized shape parameter and recalculate the sum of squared cross-validation errors of the entire flow field; Step 6.4, if the relative change rate of the sum of squared cross-validation errors of the entire flow field is lower than the preset threshold in several consecutive iterations, it is considered that the error has converged; otherwise, continue the iteration, continuously approaching the optimal shape parameter until the error converges, and output the optimal surrogate model based on the optimal shape parameter to perform the flow field prediction task.

9. A cross-validation training device for a large-scale flow field proxy model, characterized in that The said device includes: A design variable determination module, used to determine the range of the design variables for aircraft optimization and perform normalization processing; An experimental design module, used to perform a recursive permutation evolution experimental design on the design variables to generate sample points of the design variables; A numerical simulation module, used to perform a flow field numerical simulation on the said sample points to obtain the large-scale flow field data of the aircraft as the response values of each node in the flow field; A surrogate model construction module, used to construct a surrogate model for each node in the large-scale flow field using the radial basis function algorithm, and calculate the basis function matrix corresponding to the surrogate model based on the same shape parameter in each surrogate model; A cross-validation error calculation module, used to use the samples of each subspace in the recursive permutation evolution experimental design process as the test set, and extract the overlapping elements corresponding to the current test set from the inverse matrix of the basis function matrix and assemble them into a submatrix. The submatrices corresponding to all test sets are comprehensively constructed into a first intermediate matrix, and after constructing a second intermediate matrix related only to the shape parameter and the design variable based on the first intermediate matrix, the sum of squared cross-validation errors of each surrogate model is constructed according to the second intermediate matrix and the global matrix related only to the nodal response values, and the sum of squared cross-validation errors corresponding to each node in the large-scale flow field is comprehensively constructed to obtain the sum of squared cross-validation errors of the entire flow field; The iterative optimization module is used to optimize the shape parameters by using the particle swarm optimization algorithm with the goal of minimizing the sum of the squares of the cross-validation errors of the entire flow field. During the optimization process, the global matrix remains unchanged. The surrogate model is updated based on the optimized shape parameters and the sum of the squares of the cross-validation errors of the entire flow field is recalculated until the error converges, and the optimal surrogate model based on the optimal shape parameters is output to perform the flow field prediction task.

10. A computer device, comprising a memory and a processor, the memory storing a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 8.

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