Method and system for fast prediction of aerodynamic loads on aircraft surfaces

Abstract

The application belongs to the field of aircraft aerodynamic load calculation, and discloses a method and system for rapidly predicting the aerodynamic load of an aircraft surface. The method obtains pressure data of discrete points on the aircraft surface under multiple sets of flight parameter combinations; constructs a radial basis matrix and a polynomial basis matrix based on the flight parameter combinations and combines them to generate a global matrix G; uses the physical characteristics of all discrete points sharing the same set of flight parameters to solve a matrix equation set to obtain coefficient matrices A and B shared by all discrete points at one time, thereby forming a prediction model; and when predicting, the prediction model outputs the predicted pressure values of all discrete points at one time through matrix multiplication based on a target flight parameter combination. The application reduces the complexity of the traditional method of constructing hundreds of thousands of independent models to only constructing one global model, and the prediction speed is improved by more than 3 times compared with the two-dimensional linear interpolation method, and the application has small storage capacity, high prediction accuracy, and is suitable for large-scale aerodynamic load rapid calculation in aircraft preliminary design and multidisciplinary optimization.

Description

Technical Field

[0001] This invention relates to the field of aircraft aerodynamic load calculation technology, and particularly to a rapid prediction method and system for aircraft surface aerodynamic loads. This invention is especially applicable to the rapid construction of surface pressure fields at tens of thousands to hundreds of thousands of discrete points on an aircraft surface under multi-dimensional flight parameter combinations, belonging to the interdisciplinary technical field of computational fluid dynamics and aircraft strength load analysis. Background Technology

[0002] Aerodynamic loads are important input data for aircraft structural design, strength verification, flight performance evaluation, and flight control system design. Their calculation accuracy and efficiency are directly related to flight safety, structural weight optimization, and design iteration cycle.

[0003] I. Existing Calculation Process and Scale of Aerodynamic Loads Completing a full flight load analysis requires covering tens of thousands of flight state combinations within the flight envelope (including different weights, centers of gravity, speeds, altitudes, angles of attack, sideslip angles, flap deflections, and control surface deflections). In practical engineering, aerodynamic loads under hundreds of typical operating conditions are typically calculated first using computational fluid dynamics (CFD) methods. Each operating condition includes pressure values ​​at hundreds of thousands of discrete points on the aircraft surface. Then, based on these calculations, interpolation or surrogate modeling methods are used to extend the analysis to all flight states.

[0004] Specifically, raw aerodynamic data has the following scale characteristics: High parameter dimensions: Flight parameters include at least angle of attack (α), sideslip angle (β), flap deflection, deflection of each control surface, Mach number, altitude, etc., and are usually 4 to 8 dimensions.

[0005] Large number of operating conditions: Even after optimization by Design of Experiment (DOE), the number of typical operating conditions is still in the hundreds (approximately 500 to 2000).

[0006] Large data set: Each CFD calculation result contains pressure values ​​of tens of thousands to hundreds of thousands of discrete points on the aircraft surface (approximately 100,000 to 650,000 points on the entire aircraft surface).

[0007] The volume of data is enormous: the total data volume can reach tens of GB or even hundreds of GB.

[0008] II. Existing aerodynamic load proxy model methods and their shortcomings To reduce the reliance on CFD in aerodynamic load calculations and accelerate design iteration, surrogate model methods are commonly used in engineering to construct rapid prediction models of aerodynamic loads. Existing methods mainly include the following categories: (I) Sparsification Reconstruction Methods This type of method first performs sparsification reconstruction on the surface points, reducing the number of points from hundreds of thousands to thousands or tens of thousands (e.g., by selecting key points using the Kriging method), and then constructs a surrogate model from the sparsified reconstructed points. Its drawback is: 1. The pressure gradient is extremely large in areas such as the leading edge, wingtip, and shock wave location of aircraft. The number of surface points that are sparsified will cause the loss of pressure information in these key areas, and the prediction accuracy cannot meet the strength verification requirements.

[0009] 2. Even with sparsification and reconstruction to tens of thousands of points, the number of surrogate models remains enormous, and the computational cost of training and prediction remains high.

[0010] (II) Single-point independent modeling method (taking classic RPIM as an example) The classic radial point interpolation method (RPIM) is a meshless interpolation method with the advantages of high interpolation accuracy, good numerical stability, and the ability to accurately pass through all sample points. It has been applied to the modeling and prediction of single scalar fields.

[0011] However, when directly applying it to predict aircraft aerodynamic loads, a separate RPIM model needs to be built for each discrete surface point. When dealing with hundreds of thousands of surface points across the entire aircraft, hundreds of thousands of independent RPIM models need to be established. During the prediction phase, each model needs to be solved independently. Specifically: Modeling efficiency is extremely low: it usually takes several hours to build hundreds of thousands of models, which cannot meet the needs of rapid engineering iteration.

[0012] Slow prediction speed: When predicting a flight condition, hundreds of thousands of models need to be called in turn for calculation. Even if the calculation time of each model is only in milliseconds, the total time is still in minutes or even hours.

[0013] High storage overhead: Each model needs to store its parameters independently, and the total storage space required for hundreds of thousands of models is enormous, making deployment and integration inconvenient.

[0014] (III) Multidimensional linear interpolation method Multidimensional linear interpolation methods (such as bilinear interpolation and trilinear interpolation) are commonly used fast interpolation methods in engineering. Their shortcomings include: Aerodynamic loads have strong nonlinear characteristics (e.g., abrupt changes in lift coefficient near stall angle of attack, shock wave position shifts with Mach number), and linear interpolation is not accurate enough.

[0015] When the training data points are sparse, the error of the linear interpolation results increases significantly.

[0016] As the dimensionality of parameters increases, the computational cost of linear interpolation grows exponentially, leading to the "curse of dimensionality" problem.

[0017] III. Key Differences Between Existing Technical Solutions and This Invention In existing technologies, there are several schemes that use radial basis functions (RBF) for aerodynamic data interpolation or surrogate modeling. For example: Some solutions utilize RBF for data transfer at the fluid-structure interaction interface (interpolating the pressure on the fluid mesh onto the structural mesh), but this is for data mapping between two fields, rather than batch modeling and prediction of hundreds of thousands of fields.

[0018] Some solutions incorporate RBF as part of a global proxy model, but in essence, they still fall under the category of "independent modeling of each response".

[0019] None of these solutions have solved the technical problem of efficient unified modeling and batch prediction of hundreds of thousands of fields (surface points) sharing the same set of input parameters. The core of this invention lies in: utilizing the physical characteristic that all surface points share the same set of flight parameters, matrixing the data of all points, constructing a globally unified model, and achieving the effect of "one-time training, batch prediction". Summary of the Invention

[0020] The present invention aims to overcome the shortcomings of the prior art and provide a rapid prediction method and system for aerodynamic loads on aircraft surfaces.

[0021] The specific technical problem this invention aims to solve is that, during the preliminary design or multidisciplinary optimization of aircraft, when faced with aerodynamic load data involving tens of thousands to hundreds of thousands of surface points, hundreds of training conditions, and multi-dimensional flight parameter combinations, existing surrogate modeling methods (including single-point independent RPIM, multi-dimensional linear interpolation, and dimensionality reduction modeling) suffer from extremely low modeling and prediction computation efficiency, insufficient accuracy, or excessive storage overhead. This results in slow aerodynamic load calculation speed, an inability to quickly respond to design change requirements, and consequently, extended design cycles and difficulties in real-time comparison and optimization iteration of multiple schemes. This invention significantly improves the computational efficiency of aerodynamic loads by performing matrix-based unified modeling and batch prediction of the pressure fields of all surface points, supporting rapid iteration in aircraft design.

[0022] The present invention adopts the following technical solution: On one hand, the present invention provides a rapid prediction method for aerodynamic loads on aircraft surfaces, comprising the following steps: S1: Acquire training data, which includes pressure data of N discrete points on the surface of an aircraft under n combinations of flight parameters. The pressure data of each discrete point under the n combinations of flight parameters constitutes a response column vector. The response column vectors of all discrete points form a result matrix U. The dimension of the result matrix U is n×N, and each column represents the pressure response sequence of a discrete point under the n combinations of flight parameters. S2: Based on the n sets of flight parameter combinations, construct the radial basis matrix R and the polynomial basis matrix P, and combine them to generate the global matrix G=[R,P;P T [0], the global matrix G depends only on the combination of flight parameters and is independent of the pressure data; S3: Construct the augmented result matrix [U;0], and obtain the coefficient matrix A and coefficient matrix B shared by all discrete points by solving the linear equation system G·[A;B]=[U;0] in one go. Each column of the coefficient matrix A corresponds to the radial basis coefficient of a discrete point, and each column of the coefficient matrix B corresponds to the polynomial coefficient of a discrete point. S4: Store the coefficient matrix A, coefficient matrix B, and the combination of flight parameters to form a prediction model; S5: For the target flight parameter combination, the predicted pressure values ​​of all discrete points under the target flight parameter combination are output at once by matrix multiplication based on the prediction model.

[0023] In addition to any of the possible implementations described above, another implementation is provided in which the elements of the radial basis matrix R are: ,in and These represent the i-th and j-th flight parameter combinations, where i and j both take values ​​[1, n]; R(·) is the radial basis function; the elements of the polynomial basis matrix P are P ij =p j (x i ), where p j (·) are polynomial basis functions.

[0024] In addition to any of the possible implementations described above, another implementation is provided in which the radial basis function R(r) is selected from any of the following forms: (1) Multiple quadratic functions: R(r) = (r^2 + (a_c·d_c)^2)^q; (2) Exponential function: R(r) = exp(-a_c·(r / d_c)^2); (3) Thin plate spline: R(r) = r^η; (4) Logarithmic function: R(r) = r^η·log10(r); Where r is the Euclidean distance between the two sets of flight parameter combinations, and a_c, d_c, q, and η are preset parameters.

[0025] In addition to any of the possible implementations described above, another implementation is provided where the polynomial basis functions are d-order complete polynomial bases in the k-dimensional flight parameter space, and their form is: ,in ,and The integer is a non-negative integer; the number of the polynomial basis functions. .

[0026] In addition to any of the possible implementations described above, another implementation is provided in which, in step S3, the linear equation system is solved by Gaussian elimination or LU decomposition to obtain the coefficient matrix A and coefficient matrix B of all discrete points at once.

[0027] In addition to any of the possible implementations described above, another implementation is provided in which, in step S5, for the target flight parameter combination set { 1, 2,…, M}, where M is the number of target flight conditions, and a new radial basis matrix R is constructed. new and the new polynomial basis matrix P new The R new The element is R new (i,j)=R(|| i -x j ||), the P new The element is P new (i,j)=p j ( i The predicted pressure value is obtained through the following matrix multiplication: U pred =[1]·([R new ,P new ] T ⊙[A;B]) Where ⊙ represents element-wise multiplication, [1] is a row vector of all 1s, which outputs the predicted pressure values ​​of all discrete points under all target flight parameter combinations at once.

[0028] In addition to any of the possible implementations described above, a further implementation is provided in which, when the number of discrete points N exceeds the available memory capacity of the computer, the N discrete points are divided into multiple data blocks, and the coefficient matrix solution in step S3 and the prediction value calculation in step S5 are performed on each data block respectively, and the results of each data block are merged to generate a complete predicted pressure value; the prediction model stored in step S4 is a global model shared by all data blocks.

[0029] In addition to any of the possible implementations described above, another implementation is provided in which the flight parameter combination includes any two or more combinations of angle of attack, sideslip angle, flap deflection, control surface deflection, Mach number, and altitude.

[0030] In addition to any of the possible implementations described above, another implementation is provided in which the number N of discrete points on the aircraft surface is in the range of tens of thousands to hundreds of thousands, and the predicted pressure value of each discrete point is obtained by uniformly calculating by sharing the same set of coefficient matrices A and B.

[0031] On the other hand, the present invention also provides a rapid prediction system for aerodynamic loads on aircraft surfaces, the system being used to implement the above-described method, the system comprising: The data acquisition module is used to acquire training data, which includes pressure data of N discrete points on the surface of an aircraft under n combinations of flight parameters, and the flight parameter combinations include flight state parameters that affect aerodynamic loads. The matrix construction module is used to construct a radial basis matrix R and a polynomial basis matrix P based on the n sets of flight parameter combinations, and combine them to generate a global matrix G=[R,P;P] T ,0]; The model training module is used to construct the augmented result matrix [U;0]. By solving the linear equation system G·[A;B]=[U;0], the coefficient matrix A and coefficient matrix B, which are shared by all discrete points, are obtained in one step. The model storage module is used to store the coefficient matrix A, the coefficient matrix B, and the combination of flight parameters to form a prediction model; The prediction calculation module is used to output the predicted pressure values ​​of all discrete points under the target flight parameter combination in one go by matrix multiplication, based on the target flight parameter combination and the prediction model.

[0032] The beneficial effects of this invention are as follows: 1. Modeling efficiency is greatly improved The complexity of traditional single-point independent RPIM methods, which require building hundreds of thousands of models, is reduced to building only a single globally unified mathematical model. The coefficient matrices A and B are obtained through a single matrix solution, reducing modeling time from hours to minutes. This achievement stems from the matrix-based unified modeling scheme proposed in this invention—all surface points share the same global matrix G, solving for the coefficient matrices A and B of all fields at once, rather than solving them separately for each field.

[0033] 2. Prediction speed is significantly accelerated. This invention belongs to a model-based method, which is significantly more efficient than interpolation methods based on raw data (such as multidimensional linear interpolation) when making a large number of predictions. The prediction stage requires only one matrix multiplication and a small amount of distance calculation, and the computation process is highly vectorized, making it suitable for parallel acceleration using modern GPUs. Experimental results (see Example 2) show that, under the same computational environment, the prediction speed of this invention is approximately 3.3 times faster than the two-dimensional linear interpolation method. This effect is achieved because the prediction stage only requires constructing an R... new Matrix and a P new The matrix can obtain the prediction results for all fields with a single matrix multiplication, avoiding the repetitive overhead caused by calculating each field separately in traditional methods.

[0034] 3. Storage and Deployment Optimization The stored data includes only coefficient matrices A and B, the set of input parameters X for the training samples, the type and parameters of the radial basis functions, and the order d of the polynomial basis functions. This small data volume facilitates system integration and deployment. This effect is achieved by using a globally unified model to merge the model parameters of all fields into two matrices A and B, avoiding the enormous storage overhead of storing hundreds of thousands of independent models.

[0035] 4. High prediction accuracy This invention fully inherits the interpolation accuracy and numerical characteristics of the classical RPIM method, and can accurately pass through all training sample points, ensuring the prediction accuracy of strongly nonlinear aerodynamic data (such as pressure abrupt changes at the leading edge shock wave, nonlinear changes near the stall angle of attack, etc.). This effect is achieved by: the radial basis function's ability to accurately characterize local nonlinearities in the RPIM method, and the polynomial basis function's ability to preserve global trends. The combination of the two ensures the smoothness of the interpolation surface and the accuracy of local fitting.

[0036] 5. Good engineering applicability The data partitioning strategy provided by this invention can be flexibly adjusted according to the size of computer memory, making it suitable for engineering applications under different computing resource conditions. This effect is achieved by dividing a large number of surface points into multiple data blocks for separate computation, avoiding the extreme memory requirements of large-scale matrix operations and improving the algorithm's hardware adaptability.

[0037] In summary, the five benefits of this invention—improved modeling efficiency, faster prediction speed, optimized storage, high accuracy, and engineering applicability—stem from: unified matrix modeling (all fields share the G matrix for one-time solution of A and B), matrix-based batch computation in the prediction stage (one-time matrix multiplication outputs all field results), merged storage of model parameters (only storing matrices A and B), the combined characteristics of RBF and polynomial basis functions in the RPIM method, and the adaptive data partitioning strategy. These technical features work synergistically to achieve efficient modeling and rapid prediction of aircraft aerodynamic loads. Attached Figure Description

[0038] Figure 1 This is a flowchart illustrating a method for rapid prediction of aerodynamic loads on aircraft surfaces according to an embodiment of the present invention.

[0039] Figure 2 This is a flowchart illustrating the modeling process of this invention.

[0040] Figure 3 This is a flowchart illustrating the prediction process of the present invention.

[0041] Figure 4 This is a model prediction effect diagram of a certain surface point on the wing in an embodiment of the present invention, where the dots are training data and the mesh surface is prediction data.

[0042] Figure 5 This is a bar chart comparing the computation time of the present invention with that of existing two-dimensional linear interpolation methods. Detailed Implementation

[0043] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments and the accompanying drawings. It should be understood that these descriptions are merely exemplary and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0044] The accompanying drawings illustrate a layer structure according to an embodiment of the present invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0045] Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0046] In the description of this invention, it should be noted that the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0047] Furthermore, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0048] This invention provides a method for rapid prediction of aerodynamic loads on aircraft surfaces. The core of this method is to utilize the physical characteristic that all discrete points on the aircraft surface share the same set of flight parameters, thereby extending the classical RPIM method from modeling and predicting a single scalar field to unified modeling and batch prediction of multiple related scalar fields (pressure fields of all surface points), achieving "one-time training, high-efficiency service".

[0049] The mathematical model of the multi-field radial reference point interpolation method (MF-RPIM) proposed in this invention is as follows: For the set of input parameters X = {x1, x2, …, x} of n training samples n}, where each sample has a parameter dimension of k (i.e., each sample contains k flight parameters, such as angle of attack α and sideslip angle β), and each sample contains n p Data from n fields (i.e., n) p (Pressure values ​​at individual surface points). All field data from all samples constitute the result matrix U, with dimensions n×n. p Each column of matrix U represents a sequence of values ​​for a field under n training samples.

[0050] like Figure 1 As shown in the figure, an embodiment of the present invention provides a method for rapid prediction of aerodynamic loads on the surface of an aircraft, comprising the following steps: S1: Acquire training data, which includes pressure data of N discrete points on the surface of an aircraft under n combinations of flight parameters. The pressure data of each discrete point under the n combinations of flight parameters constitutes a response column vector. The response column vectors of all discrete points form a result matrix U. The dimension of the result matrix U is n×N, and each column represents the pressure response sequence of a discrete point under the n combinations of flight parameters. S2: Based on the n sets of flight parameter combinations, construct the radial basis matrix R and the polynomial basis matrix P, and combine them to generate the global matrix G = [R, P; P] T[0], the global matrix G depends only on the combination of flight parameters and is independent of the pressure data; S3: Construct the augmented result matrix [U; 0], and obtain the coefficient matrix A and coefficient matrix B shared by all discrete points by solving the linear equation system G·[A; B] = [U; 0] in one go. Each column of the coefficient matrix A corresponds to the radial basis coefficient of a discrete point, and each column of the coefficient matrix B corresponds to the polynomial coefficient of a discrete point. S4: Store the coefficient matrix A, coefficient matrix B, and the combination of flight parameters to form a prediction model; S5: For the target flight parameter combination, the predicted pressure values ​​of all discrete points under the target flight parameter combination are output at once by matrix multiplication based on the prediction model.

[0051] The specific modeling process is as follows: Step 1: Construct the radial basis matrix R and the polynomial basis matrix P The radial basis matrix R has dimensions n×n, and its elements are: , i=1,2,…,n; j=1,2,…,n; Where R(·) is the radial basis function, and ||·|| represents the Euclidean distance.

[0052] The polynomial basis matrix P has dimensions n×m, and its elements are: P ij = p j (x i ), i=1,2,…,n; j=1,2,…,m; Where {p1, p2, …, p m Let} be the basis functions of a d-order complete polynomial in k-dimensional space. .

[0053] Step 2: Combining to generate the global matrix G Combine R and P to generate the global matrix G: G = [R, P; P T , 0]; The dimension of matrix G is (n+m)×(n+m). Since G depends only on the set of input parameters X of the training samples and is independent of the specific values ​​(pressure values) of each field, all fields share the same matrix G.

[0054] Step 3: Construct the augmented result matrix and solve for the coefficient matrix Construct the augmented result matrix [U; 0], with dimensions (n+m)×n. p , where 0 is m×n p The zero matrix.

[0055] Solve the system of linear equations: G·[A; B] = [U; 0]; Here, A and B are the coefficient matrices to be solved, with dimensions n×np and m×np, respectively. Each column of A corresponds to the radial basis coefficients of a field, and each column of B corresponds to the polynomial coefficients of a field.

[0056] The above system of equations can be solved using Gaussian elimination or LU decomposition to obtain the coefficient matrices A and B for all fields in one step. Since G only needs to be decomposed once, the computational efficiency for solving multiple fields is much higher than solving each field separately.

[0057] Step 4: Storage Model The coefficient matrices A and B, the set of input parameters X of the training samples, the type and parameters of the radial basis functions, and the order d of the polynomial basis functions are stored as the prediction model.

[0058] The prediction process is as follows: For a given set of target flight parameter combinations ={ 1, 2, …, M (where M is the number of target flight conditions, and each condition contains k flight parameters), calculate the predicted value based on the stored model: Step 1: Construct a new radial basis matrix R new and polynomial basis matrix P new R new The dimension is M×n, and its elements are: R new (i,j) = R(|| i - x j ||), i=1,2,…,M; j=1,2,…,n; P new The dimension is M×m, and its elements are: P new (i,j) = p j ( i ), i=1,2,…,M; j=1,2,…,m.

[0059] Step 2: Calculate the predicted value The dimension of the prediction result matrix Û is M×n p It is obtained through the following matrix operations: Û = [1]·([R new , P new ]T ⊙ [A; B]); Where ⊙ represents element-wise multiplication (Hadamard product), [1] is a 1×(n+m) all-1 row vector. This operation is highly vectorized and suitable for parallel acceleration using GPU.

[0060] When n p When the number of surface points exceeds the available memory capacity of the computer, n will be... p Each field is divided into multiple data blocks, each data block containing n block Each field (e.g., n) block = 10000), perform the above modeling and prediction calculations on each data block respectively, and finally merge the results of each data block.

[0061] Example 1: Aerodynamic Load Modeling and Prediction for a Certain Type of Unmanned Aerial Vehicle This embodiment uses the modeling and prediction of the aerodynamic loads of a certain type of UAV as an example to illustrate the implementation process of the present invention in detail.

[0062] See Figure 2 The diagram shown is a flowchart illustrating the modeling process of this invention. The specific modeling process is as follows.

[0063] 1. Training Data Preparation Flight parameter settings: In this embodiment, the flight parameters are two-dimensional, including: Angle of attack (α): range -8° to 18°; Sideslip angle (β): range -21° to 21°.

[0064] 126 training sample points were selected in the above parameter space using experimental design methods (full factorial design or Latin hypercube design), i.e., n = 126.

[0065] CFD calculation: CFD calculations (using the Reynolds-averaged Navier-Stokes equations and the SA turbulence model) were performed on the 126 training sample points to obtain the overall surface pressure distribution of the entire aircraft at each sample point. There are 650,000 discrete points on the entire aircraft surface, i.e., n p = 650,000.

[0066] Data organization: All CFD calculation results are organized into a result matrix U with dimensions of 126 × 650,000. Each row of matrix U corresponds to a training sample point (a specific combination of α and β), and each column corresponds to a sequence of pressure values ​​for a surface point under those 126 training sample points.

[0067] 2. Model Building Step 1: Construct the radial basis matrix R The radial basis function of the thin plate spline (TPS) is as follows: R(r) = r η ; In this embodiment, η = 1.

[0068] For any two sets of training flight parameters x i = (α i , β i ) and x j = (α j , β j ), and its Euclidean distance is: r = ||x i - x j || = sqrt((α i - α j )² + (β i - β j )²); The radial basis matrix R has dimensions of 126×126, and its element in the i-th row and j-th column is R. ij = R(||x i - x j ||); Step 2: Construct the polynomial basis matrix P Choose basis functions for a 3rd-order complete polynomial. For a 3rd-order complete polynomial (d = 3) in two-dimensional space (k = 2), the number of polynomial basis functions is: m = C(2+3, 3) = C(5, 3) = 10; The specific basis functions are: {1, α, β, α 2 , β², α·β, α 2 ·β, α·β², α³, β³}; The polynomial basis matrix P has a dimension of 126×10, and its element in the i-th row and j-th column is P. ij = p j (α i , β i ).

[0069] Step 3: Combine to generate the global matrix G Combine R and P to generate the global matrix G: G = [R, P; P T , 0]; The dimension of G is (126+10)×(126+10) = 136×136.

[0070] Step 4: Construct the augmented result matrix Construct the augmented result matrix [U; 0] with dimensions 136×650,000, where 0 is a zero matrix of 10×650,000.

[0071] Step 5: Solve for the coefficient matrix Solve the linear equation system using Gaussian elimination: G·[A; B] = [U; 0]; Obtain coefficient matrix A (dimension 126×650,000) and coefficient matrix B (dimension 10×650,000).

[0072] Since the G matrix depends only on 126 sets of training flight parameters and is independent of the pressure values ​​of 650,000 surface points, the LU decomposition of G only needs to be performed once to solve for the coefficients of all 650,000 fields, which demonstrates the efficiency advantage of this invention.

[0073] Step 6: Storage Model Store the following data as a prediction model file: Coefficient matrix A (126×650,000); Coefficient matrix B (10×650,000); The input parameters X of the training samples (126 sets of α and β values); Radial Basis Function Type Identifier (TPS); Radial basis function parameters (η = 1); The order of the polynomial basis functions (d = 3); The total size of the model files is approximately (126×650,000 + 10×650,000)×8 bytes ≈ 707 MB, which is much smaller than the solution of independently storing 650,000 single-point models.

[0074] 3. Model Prediction See Figure 3 The diagram shown is a flowchart illustrating the prediction process of this invention. The prediction process is as follows.

[0075] Target operating conditions: Suppose we need to make rapid predictions for 100 new flight conditions (e.g., for calculating the load envelope within the flight envelope), with each condition containing a set of (α, β) values.

[0076] Step 1: Load the model Read the model file from the storage medium and load the coefficient matrices A and B, training parameters X, radial basis function type and parameters, and polynomial basis function order d.

[0077] Step 2: Predicting each working condition individually For the t-th target working condition t = (α t , β t Perform the following calculations: (a) Calculate the Euclidean distance between this working condition and all 126 training sample points, and construct the radial basis matrix R. new Line t: R new (t, j) = R(|| t - x j ||), j = 1,2,…,126; (b) Construct the polynomial basis matrix P new Line t: P new (t, :) = [1, α t , β t , α t² , β t² , α t ·β t , α t² ·β t , α t ·β t² , α t³ , β t³ ]; (c) Calculate the predicted pressure vector Û t (Dimension 1 × 650,000): Û t = [R new (t, :), P new (t, :)] · [A; B]; Where [R] new (t, :), P new [t, :)] is a 1×(126+10) row vector, and [A; B] is a (126+10)×650,000 matrix. The product is a 1×650,000 row vector, which is the predicted pressure value of all 650,000 surface points under the target working condition.

[0078] (d) Repeat the above calculations until all 100 target operating conditions have been predicted.

[0079] Step 3: Output Results The prediction results for all target load conditions are organized into a 100×650,000 matrix, and the output is used for subsequent structural strength analysis and load envelope calculation.

[0080] Block processing instructions: In this embodiment, the prediction of 650,000 surface points involves the independent calculation of 650,000 column vectors. When computer memory is sufficient, the calculation of all 650,000 points can be completed at once. If memory is insufficient, the 650,000 points can be divided into multiple data blocks. For example, the 650,000 points can be divided into 65 data blocks, each containing 10,000 points. The results of each block are calculated separately and then merged into a complete prediction result for all 650,000 points. Block division only affects the batch division of the calculation and does not affect the accuracy of the prediction results or the consistency of the model.

[0081] Table 1 compares the results of different block partitioning tests. Test conditions: 120 training points, 2D parameters, 650,000 fields, using the MQ core, computer environment (Intel Core i7-10750H @ 2.60 GHz, 16GB RAM). The results show that block partitioning significantly reduces peak memory usage for modeling and prediction without significantly increasing modeling and prediction time. This indicates that the block partitioning function of this method is effective and suitable for large-scale projects. In engineering applications, it can be applied to the natural partitioning of components such as wings, fuselage, horizontal tail, and vertical tail.

[0082] Table 1 Comparison of different block tests Using the classic single-field RPIM method, it requires 650,000 loop calls and a large number of I / O operations, and tests show that the modeling time and prediction time are about 10 times higher.

[0083] Example 2: Validation of Prediction Accuracy and Speed 1. Accuracy Verification Twenty flight conditions that were not included in the training were selected as the validation set, and the surface pressure distribution of the entire aircraft under each condition was obtained by the method of this invention and CFD direct calculation.

[0084] See Figure 4 The image shows the model prediction result for a typical surface point on the wing in an embodiment of the present invention. The dots in the image represent data from 126 training sample points, and the mesh surface represents the prediction result of the method of the present invention. This surface point is located near the leading edge of the wing, a region with a large pressure gradient, best demonstrating the method's ability to capture nonlinear aerodynamic data.

[0085] from Figure 4As can be seen, the predicted surface passes precisely through all training sample points (the dots in the figure are all located on the grid surface), indicating that the method of this invention fully inherits the interpolation accuracy of RPIM and can reproduce the training data without error. In the region between training sample points, the predicted surface is smooth and conforms to physical laws (pressure increases with the angle of attack and exhibits a nonlinear trend near the stall angle of attack), without overfitting or non-physical oscillations, indicating that this invention maintains high prediction accuracy even in strongly nonlinear regions.

[0086] As shown in Table 2, a comparison is given between the results of the whole aircraft resultant force (forces Fx, Fy, Fz in three directions and moments Mx, My, Mz in three directions) predicted by the method of this invention and the results of direct CFD calculation under a typical flight condition (α = 6°, β = 3°).

[0087] Table 2 Comparison of the overall resultant force predicted by the method of the present invention and the CFD calculation value

[0088] As shown in Table 2, the relative errors between the total force predicted by the method of the present invention and the CFD calculation results are all within 3%, and the errors of the main components (Fy, Fz, My) are within 0.4%, indicating that the prediction accuracy of the method of the present invention at the level of total load meets the engineering design requirements.

[0089] Explanation of the relationship between accuracy and efficiency: The accuracy of this invention stems from the combination of the radial basis function's precise characterization of local nonlinearities (e.g., the TPS basis function in the embodiment accurately captures the pressure gradient changes at the wing leading edge) and the polynomial basis function's ability to preserve global trends (the third-order polynomial can effectively describe the overall trend of the lift coefficient with the angle of attack). This mathematical construction ensures that the interpolation surface is neither excessively rigid (without losing nonlinear characteristics) nor overfitting (without generating non-physical oscillations).

[0090] 2. Speed ​​Verification See Figure 5 The figure shows a bar chart comparing the computation time of the method of the present invention and the existing two-dimensional linear interpolation method under different calculation methods.

[0091] Under the same computing environment (Intel Core i7-10750H @ 2.60 GHz, 16GB memory), 100 target operating conditions were predicted using the method of this invention and the existing two-dimensional linear interpolation method, respectively, and the computation time of the two methods was recorded.

[0092] Table 3 Comparison of computation speed between the method of this invention and the two-dimensional linear interpolation method Depend on Figure 5As shown in Table 3, the prediction speed of the method of this invention is approximately 3.3 times faster than the two-dimensional linear interpolation method. This 3.3-fold speed improvement stems from the difference in the computational process between the two methods: the two-dimensional linear interpolation method requires locating and calculating the weighted average in the training data grid for each target working condition, and this process needs to be performed independently for each surface point, i.e., 650,000 surface points × 100 working conditions = 65,000,000 independent grid location and interpolation calculations; while the method of this invention organizes the data of all surface points into a matrix U, solves the coefficient matrix of all points at once during the training phase, and only needs to construct R for each target working condition during the prediction phase. new Row vectors and P new The row vectors are then used, and the prediction results for all 650,000 points can be obtained through a single matrix-vector multiplication operation—even when calculated column-by-column, there is no need to repeatedly construct the interpolation skeleton. This comparative result fully demonstrates the computational efficiency advantage of the method of this invention at the algorithm level.

[0093] If GPU parallel acceleration is used, the prediction time of the method of the present invention can be further reduced to less than 1 second, which is much faster than the CPU-based linear interpolation method.

[0094] Example 3: Parameter Selection in Different Scenarios 1. High-precision scenes When high prediction accuracy is required (such as in the structural strength verification stage), the following parameter configuration is recommended: Radial basis function: TPS (thin plate spline), η = 3 (higher-order TPS has better smoothness); The order of the polynomial basis functions: d = 3; Number of training samples: Try to cover the boundaries and key internal regions of the parameter space (such as dense sampling near the stall boundary).

[0095] 2. High-efficiency scenarios When high computational speed is required (such as in the initial stage of multidisciplinary optimization), the following parameter configuration is recommended: Radial basis function: MQ (multiple quadratic function), q = -0.5; Polynomial basis function order: d = 2 (reducing the number of polynomial bases to reduce computational cost); Number of training samples: Use sparse DOE design (such as response surface design) to reduce n.

[0096] 3. High-dimensional parameter scenarios When the number of flight parameters is high (e.g., considering more than 6 parameters including angle of attack, sideslip angle, Mach number, altitude, flap deflection, and deflection of each control surface), the following configuration is recommended: The order of polynomial basis functions: d = 1 or d = 2 (to avoid the number of basis functions m being too large, as m grows rapidly with k and d); Training sample size: Use the optimal Latin hypercube design or uniform design, and the sample size is recommended to be 5 to 10 times the parameter dimension; Radial basis function: TPS (has good numerical stability for high-dimensional data).

[0097] Example 4: System Implementation 1. System Module Composition This invention also provides a rapid prediction system for aerodynamic loads on aircraft surfaces, comprising the following functional modules: (1) Data acquisition module The data acquisition module is used to acquire training data. The input to this module is the pressure field data at discrete points on the aircraft surface obtained from CFD calculations, along with the corresponding combinations of flight parameters. This module parses the original CFD output file (such as CGNS or Tecplot format) into a result matrix U (n×n). p Where n is the number of training samples, n p This module (representing the number of discrete points on the surface) combines and organizes flight parameters into an input parameter set X. It also performs data standardization preprocessing (such as normalization) to improve the numerical stability of matrix solutions. The output of this module is a matrix U and the parameter set X, which are then used by the matrix construction module.

[0098] (2) Matrix construction module The matrix construction module is used to construct radial basis matrices R and polynomial basis matrices P based on the input parameter set X, and combine them to generate a global matrix G = [R, P; P] T This module first calculates the Euclidean distance matrix between all training sample points based on the user-specified radial basis function type (such as TPS, MQ, EXP, or LOG) and its parameters, and then constructs the R matrix. Simultaneously, based on the specified polynomial order d, this module generates a d-order complete polynomial basis in k-dimensional space and constructs the P matrix. Finally, R and P are combined into a global matrix G. The output of this module is the global matrix G, which is used by the model training module.

[0099] (3) Model training module The model training module solves the linear equation system G·[A; B] = [U; 0], obtaining the coefficient matrices A and B shared by all discrete points in one step. This module uses Gaussian elimination or LU decomposition to decompose the G matrix, and then obtains A and B through back-substitution. Since the G matrix depends only on the flight parameter combination X and is independent of the specific pressure values ​​at each discrete point, the LU decomposition of G only needs to be performed once to solve for the coefficients of all discrete points. This module also supports block processing: when np When the number of discrete points on the surface exceeds the available computer memory, the U matrix is ​​divided into multiple data blocks by column, solved block by block, and then the results are merged. The output of this module is coefficient matrices A and B.

[0100] (4) Model storage module The model storage module is used to persistently store the parameters of the trained model. Stored content includes: coefficient matrix A, coefficient matrix B, training sample input parameters X, radial basis function type identifier and parameters (such as the η value of TPS), and the order d of the polynomial basis functions. The storage format uses HDF5 or NumPy binary format to support fast read / write and cross-platform deployment. The output of this module is a model file.

[0101] (5) Prediction Calculation Module The prediction calculation module is used to output the predicted pressure values ​​for all discrete points at once through matrix multiplication, based on the target flight parameter combination and the stored model. This module first loads the model file, and then, for a given set of target flight parameter combinations... (Dimension is M×k, M is the target number of working cases), calculate the new radial basis matrix R. new (of dimension M×n) and polynomial basis matrix P new (Dimension is M×m), then through matrix multiplication Û = [R new , P new [A; B] yields the prediction result matrix Û (with dimensions M×n). p This module also supports block processing, when n p When the available memory is exceeded, the U matrix is ​​divided by column, the calculations are performed separately, and the results are then combined. The output of this module is predicted pressure field data, which can be used for subsequent structural strength analysis.

[0102] The data flow between the modules is as follows: The model structure is as follows: Data Acquisition Module → Matrix Construction Module → Model Training Module → Model Storage Module (closed loop during training); Model Storage Module → Prediction Calculation Module (prediction phase). The Matrix Construction Module and Model Training Module are called only once during the training phase, while the Prediction Calculation Module can be called repeatedly after model deployment.

[0103] 2. Software Deployment and Workflow The system of this invention can be packaged as an independent software module and integrated into an aerospace design platform. The specific deployment method is as follows: Data interface: Reads CFD calculation results and flight parameter tables in CSV format.

[0104] Core computation: Matrix operations are implemented using Python + NumPy / SciPy, and GPU acceleration is achieved using CUDA (optional).

[0105] Output interface: Outputs predicted pressure field data in VTK or CSV format for subsequent structural analysis.

[0106] Invocation method: Provides an API interface that supports platform invocation and batch submission.

[0107] A typical workflow is as follows: the user submits a batch of flight conditions (such as 100 status points) through the design platform, the system automatically calls the prediction calculation module to make predictions, and quickly returns the pressure field data of all surface points for relevant analysts to perform further calculations.

[0108] Industrial applicability The method and system provided by this invention can be directly applied to the preliminary design and multidisciplinary optimization processes of various fixed-wing aircraft (including UAVs, civil airliners, and military aircraft) to rapidly generate aerodynamic load data required for structural design and strength verification. This invention can be deployed on computing clusters or cloud platforms in aerospace design units, supports large-scale parallel computing, and has clear industrial application prospects and commercial value.

[0109] The above description of the embodiments is only for the purpose of helping to understand the method and core idea of ​​this application; at the same time, for those skilled in the art, there will be changes in the specific implementation and application scope based on the idea of ​​this application. Therefore, the content of this specification should not be construed as a limitation of this application.

[0110] Certain terms are used in the specification and claims to refer to specific components. Those skilled in the art will understand that hardware manufacturers may use different names to refer to the same component. This specification and claims do not distinguish components based on differences in name, but rather on differences in function. The terms "comprising" and "including" used throughout the specification and claims are open-ended and should be interpreted as "comprising / including but not limited to". "Approximately" means that within an acceptable margin of error, those skilled in the art can solve the technical problem and substantially achieve the technical effect within a certain margin of error. The following descriptions in the specification are preferred embodiments for carrying out this application; however, these descriptions are for the purpose of illustrating the general principles of this application and are not intended to limit the scope of this application. The scope of protection of this application shall be determined by the appended claims.

[0111] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a product or system comprising a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a product or system. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the product or system that includes said element.

[0112] It should be understood that the term "and / or" used in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0113] The foregoing description illustrates and describes several preferred embodiments of this application. However, as previously stated, it should be understood that this application is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the application concept described herein through the foregoing teachings or techniques or knowledge in related fields. Any modifications and variations made by those skilled in the art that do not depart from the spirit and scope of this application should be within the protection scope of the appended claims.

Claims

1. A method for rapid prediction of aerodynamic loads on aircraft surfaces, characterized in that, Includes the following steps: S1: Acquire training data, which includes pressure data of N discrete points on the surface of an aircraft under n combinations of flight parameters. The pressure data of each discrete point under the n combinations of flight parameters constitutes a response column vector. The response column vectors of all discrete points form a result matrix U. The dimension of the result matrix U is n×N, and each column represents the pressure response sequence of a discrete point under the n combinations of flight parameters. S2: Based on the n sets of flight parameter combinations, construct the radial basis matrix R and the polynomial basis matrix P, and combine them to generate the global matrix G = [R, P; P] T [0], the global matrix G depends only on the combination of flight parameters and is independent of the pressure data; S3: Construct the augmented result matrix [U; 0], and obtain the coefficient matrix A and coefficient matrix B shared by all discrete points by solving the linear equation system G·[A; B] = [U; 0] in one go. Each column of the coefficient matrix A corresponds to the radial basis coefficient of a discrete point, and each column of the coefficient matrix B corresponds to the polynomial coefficient of a discrete point. S4: Store the coefficient matrix A, coefficient matrix B, and the combination of flight parameters to form a prediction model; S5: For the target flight parameter combination, the predicted pressure values ​​of all discrete points under the target flight parameter combination are output at once by matrix multiplication based on the prediction model.

2. The rapid prediction method for aerodynamic loads on aircraft surfaces as described in claim 1, characterized in that, The elements of the radial basis matrix R are ,in and These represent the i-th and j-th flight parameter combinations, where i and j both take values ​​[1, n]; R(·) is the radial basis function; the elements of the polynomial basis matrix P are P ij = p j (x i ), where p j (·) are polynomial basis functions.

3. The rapid prediction method for aerodynamic loads on aircraft surfaces as described in claim 2, characterized in that, The radial basis function R(r) is selected from any of the following forms: multiple quadratic function, exponential function, thin plate spline function or logarithmic function.

4. The rapid prediction method for aerodynamic loads on aircraft surfaces as described in claim 2, characterized in that, The polynomial basis functions are d-order complete polynomial bases in the k-dimensional flight parameter space, and their form is: ,in ,and The integer is a non-negative integer; the number of the polynomial basis functions. .

5. The rapid prediction method for aerodynamic loads on aircraft surfaces as described in claim 1, characterized in that, In step S3, the linear equation system is solved by Gaussian elimination or LU decomposition to obtain the coefficient matrix A and coefficient matrix B of all discrete points at once.

6. The rapid prediction method for aerodynamic loads on aircraft surfaces as described in claim 1, characterized in that, In step S5, for the target flight parameter combination set { 1, 2, …, M }, where M is the number of target flight conditions, and a new radial basis matrix R is constructed. new and the new polynomial basis matrix P new The R new The element is R new (i,j) = R(|| i - x j ||), the P new The element is P new (i,j) = p j ( i The predicted pressure value is obtained through the following matrix multiplication: U pred = [1]·([R new , P new ] T ⊙ [A; B]) ; Where ⊙ represents element-wise multiplication, [1] is a row vector of all 1s, which outputs the predicted pressure values ​​of all discrete points under all target flight parameter combinations at once.

7. The rapid prediction method for aerodynamic loads on aircraft surfaces as described in claim 1, characterized in that, When the number of discrete points N exceeds the available memory capacity of the computer, the N discrete points are divided into multiple data blocks. The coefficient matrix solution in step S3 and the prediction value calculation in step S5 are performed on each data block respectively. The results of each data block are merged to generate a complete predicted pressure value. The prediction model stored in step S4 is a global model shared by all data blocks.

8. The rapid prediction method for aerodynamic loads on aircraft surfaces as described in claim 1, characterized in that, The flight parameter combination includes any two or more of the following: angle of attack, sideslip angle, flap deflection, control surface deflection, Mach number, and altitude.

9. The rapid prediction method for aerodynamic loads on aircraft surfaces as described in claim 1, characterized in that, The number of discrete points N on the aircraft surface is in the range of tens of thousands to hundreds of thousands, and the predicted pressure value of each discrete point is obtained by uniformly calculating by sharing the same set of coefficient matrices A and B.

10. A rapid prediction system for aerodynamic loads on aircraft surfaces, characterized in that, The system is used to implement the method as described in any one of claims 1-9, the system comprising: The data acquisition module is used to acquire training data, which includes pressure data of N discrete points on the surface of an aircraft under n combinations of flight parameters, and the flight parameter combinations include flight state parameters that affect aerodynamic loads. The matrix construction module is used to construct a radial basis matrix R and a polynomial basis matrix P based on the n sets of flight parameter combinations, and combine them to generate a global matrix G = [R, P; P] T , 0]; The model training module is used to construct the augmented result matrix [U; 0]. By solving the linear equation system G·[A; B] = [U; 0], the coefficient matrix A and coefficient matrix B, which are shared by all discrete points, are obtained in one step. The model storage module is used to store the coefficient matrix A, the coefficient matrix B, and the combination of flight parameters to form a prediction model; The prediction calculation module is used to output the predicted pressure values ​​of all discrete points under the target flight parameter combination in one go by matrix multiplication, based on the target flight parameter combination and the prediction model.

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