Unsteady aerodynamic characteristic prediction method based on machine learning

Abstract

The invention provides an unsteady aerodynamic characteristic prediction method based on machine learning. The method comprises the following steps: step 1, determining a wind tunnel test / numerical simulation original data group number N based on variable dimensions and a variable test level number; 2, performing N groups of wind tunnel tests or numerical simulation to obtain an original pneumatic data set; step 3, performing point compensation difference on the N groups of data in the step 2, and expanding the data to Q groups of data; step 4, performing encryption processing on the comprehensive test points obtained in the step 3 through a multivariate interpolation mode; 5, establishing a machine learning framework based on a back propagation neural network (BPNN) model; step 6, based on the pneumatic data encrypted in the step 4, performing network parameter optimization on the BPNN in the step 5 by taking the designed loss function as an evaluation index, and outputting a neural network obtained by training; step 7, obtaining a BPNN network after boundary continuation enhancement; and 8, predicting the unsteady aerodynamic characteristics at non-original data points based on the neural network obtained in the step 7.

Description

Technical Field

[0001] The present invention belongs to the technical field of aerodynamics, and in particular relates to a method for predicting unsteady aerodynamic characteristics based on machine learning. Background Art

[0002] In the field of variable wing sweep, studies have found that variable sweep based on the flight Mach number can not only meet the aircraft's needs for lift and drag during low-speed flight, but also delay the formation of shock waves during high-speed flight, weaken the intensity of shock waves, and effectively reduce flight resistance. It is an effective way to solve the conflicting requirements of aerodynamic performance at high and low speeds for aircraft under a wide flight envelope.

[0003] However, compared with fixed-wing aircraft, the aerodynamic data of variable-sweep wing aircraft will show high unsteadiness, strong nonlinearity, hysteresis effect and other characteristics during the change of sweep angle, which brings great challenges to the control of the aircraft. Building an unsteady aerodynamic database is the key prerequisite for achieving precise attitude control of variable-sweep wing aircraft. The existing methods for obtaining unsteady aerodynamic databases mainly include wind tunnel tests and numerical simulations. Among them, wind tunnel tests are costly, long, and inefficient; unsteady numerical simulation technology has a long computational convergence time, low efficiency, and high resource requirements. At the same time, it is difficult to construct a complete unsteady aerodynamic database with a small number of wind tunnel test and numerical simulation results, so a method for generating variable-sweep wing unsteady aerodynamic data quickly and efficiently is needed.

[0004] At present, machine learning represented by neural networks performs particularly well in high-dimensional data processing and nonlinear function fitting, and is gradually introduced into the field of aerodynamics, and is applied in aerodynamic data fusion, parameter prediction, model correction, etc. However, neural networks are black box models that make it difficult to directly describe the influence of various dependent variables on unsteady aerodynamic characteristics. On the one hand, this restricts the exploration of the laws of unsteady aerodynamic characteristics, and on the other hand, it affects the control of aircraft performance by control professionals. Therefore, a method that can achieve parameterized expression of neural network models is needed. Summary of the invention

[0005] The present invention aims to solve at least one of the technical problems existing in the prior art or related art.

[0006] To this end, the present invention provides a method for predicting unsteady aerodynamic characteristics based on machine learning. This method reduces the demand for original aerodynamic data while ensuring the prediction accuracy of the neural network for a single variable. This method gives an explicit expression of the unsteady aerodynamic characteristics of the neural network, providing a general and convenient tool for relevant professionals to carry out their work.

[0007] The technical solution of the present invention is as follows:

[0008] According to one aspect, a method for predicting unsteady aerodynamic characteristics based on machine learning is provided, the prediction method comprising:

[0009] Step 1: Determine the number of wind tunnel test / numerical simulation raw data sets N based on the variable dimension and the number of test levels of the variable;

[0010] Step 2: Perform N groups of wind tunnel tests or numerical simulations to obtain an original aerodynamic data set;

[0011] Step 3: Add the difference of the N groups of data obtained in step 2 to expand them to Q groups of data;

[0012] Step 4: Encrypt the comprehensive test points obtained in step 3 by multivariate interpolation;

[0013] Step 5: Establish a machine learning framework based on the back propagation neural network (BPNN) model;

[0014] Step 6: Based on the aerodynamic data obtained after encryption in step 4, the network parameters of the BPNN in step 5 are optimized with the designed loss function as the evaluation index, and the trained neural network is output;

[0015] Step 7: Based on the BPNN model obtained in step 6, the aerodynamic characteristics outside the test space boundary are predicted in turn, and an extended data set is formed with the data obtained in step 4. The BPNN model is retrained until the set prediction range is traversed, and the BPNN network with boundary extension enhancement is output;

[0016] Step 8: Based on the neural network obtained in step 7, predict the unsteady aerodynamic characteristics at non-original data points.

[0017] Furthermore, in step one, based on the single variable method, extending from the selected center point to the boundary of each axis, and considering the boundary effect at the corner point, a center-corner extension sampling method is designed, and the number of original data sets N of the wind tunnel test / numerical simulation is obtained according to this method.

[0018] Furthermore, the number of wind tunnel test / numerical simulation groups N is obtained by formula (1):

[0019]

[0020] Among them, D i is the number of experimental levels of the i-th dimension variable; n represents the n-dimensional variable.

[0021] Furthermore, the method further comprises:

[0022] Step 9. Based on the optimal Latin hypercube sampling method, L sample points are extracted in the entire test space. The neural network obtained in step 6 is Taylor expanded at the L sample points respectively, and a total of L Taylor expansions are obtained. The coefficients are average-weighted to obtain the explicit expression of the neural network for the unsteady aerodynamic characteristics.

[0023] Furthermore, before implementing step three, the method further includes:

[0024] Preprocess the original wind tunnel test / numerical simulation data, including:

[0025] The obvious bad pixel data obtained by wind tunnel test / numerical simulation are eliminated, and the eliminated bad pixels are replaced by linear interpolation method.

[0026] Furthermore, the step three specifically includes:

[0027] According to the comprehensiveness requirement of the test, the data processed in step 2 are interpolated using the Lagrange interpolation method, expanding from N groups of test data to Q groups of data. The expression of Q is as follows:

[0028]

[0029] Furthermore, in step 4, the number of levels in each dimension after interpolation should be no less than 10.

[0030] Furthermore, the step five specifically includes:

[0031] 5.1 Regularize the input data of each dimension;

[0032] 5.2 Building a Neural Network Model

[0033] The BP neural network (BPNN) architecture is adopted, which consists of three parts: input layer-hidden layer-output layer. The number of neurons in the input layer is equal to the dimension n of the aerodynamic characteristics to be fitted. The number of neurons in the output layer m is 1 by default. The hidden layer consists of three layers, and the number of neurons in each layer l is determined by the following formula:

[0034]

[0035] Here, k can take any value between 0 and 10.

[0036] 5.3 Setting the neuron activation function

[0037] 5.4 Constructing the loss function

[0038] 5.5 Setting the optimization algorithm

[0039] 5.6 Setting the loop termination condition

[0040] Set the square error sum accuracy index and simulation step size. When the loss function is less than the accuracy index or meets the number of simulation steps, the simulation terminates.

[0041] Furthermore, the number of hidden layer neuron nodes is set to 8, the neuron activation function selects the “Gaussian” function, the loss function selects the sum of squared errors, and the optimization algorithm adopts the BFGS algorithm.

[0042] According to another aspect, a computer device is provided, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned prediction method when executing the computer program.

[0043] Compared with the prior art, the benefits of the present invention are:

[0044] (1) The present invention designs an experimental design method for center-angle extension sampling, which reduces the requirement for the number of experimental groups while focusing on the influence of a single variable on unsteady aerodynamic characteristics, ensuring the effectiveness of the neural network model finally learned in fitting the aerodynamic characteristics;

[0045] (2) The present invention designs a learning process of "basic model training + boundary extension enhancement", which increases the prediction accuracy of unsteady aerodynamic characteristics at a long distance in the test space;

[0046] (3 The present invention designs a method for obtaining the display expression of unsteady aerodynamic characteristics based on neural network training, which provides a general and convenient tool for relevant professionals to carry out their work. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] The included drawings are used to provide a further understanding of the embodiments of the present invention, which constitute a part of the specification, are used to illustrate the embodiments of the present invention, and together with the text description, explain the principles of the present invention. Obviously, the drawings in the following description are only some embodiments of the present invention, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0048] Figure 1 It is a flow chart of “basic model training + boundary extension and enhancement”. DETAILED DESCRIPTION

[0049] It should be noted that, in the absence of conflict, the embodiments in this application and the features in the embodiments can be combined with each other. The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is by no means intended to limit the present invention and its application or use. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0050] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0051] Unless otherwise specifically stated, the relative arrangement of the parts and steps set forth in these embodiments, numerical expressions and numerical values ​​do not limit the scope of the present invention. The technology, method and equipment known to those of ordinary skill in the relevant art may not be discussed in detail, but in appropriate cases, the technology, method and equipment should be considered as a part of the authorization specification. In all examples shown and discussed here, any specific value should be interpreted as being merely exemplary, rather than as a limitation. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters represent similar items in the following drawings, so that once an item is defined in an accompanying drawing, it does not need to be further discussed in subsequent drawings.

[0052] like Figure 1 As shown, in one embodiment of the present invention, a method for predicting unsteady aerodynamic characteristics based on machine learning is provided, and the prediction method includes:

[0053] Step 1: determine the number of wind tunnel test / numerical simulation raw data sets N based on the variable dimension and the number of test levels of the variable;

[0054] Step 2: Perform N groups of wind tunnel tests or numerical simulations to obtain an original aerodynamic data set;

[0055] Step 3: Add the difference of the N groups of data obtained in step 2 to expand them to Q groups of data;

[0056] Step 4: Encrypt the comprehensive test points obtained in step 3 by multivariate interpolation;

[0057] Step 5: Establish a machine learning framework based on the back propagation neural network (BPNN) model;

[0058] Step 6: Based on the aerodynamic data obtained after encryption in step 4, the network parameters of the BPNN in step 5 are optimized with the designed loss function as the evaluation index, and the trained neural network is output;

[0059] Step 7: Based on the BPNN model obtained in step 6, the aerodynamic characteristics outside the test space boundary are predicted in turn, and an extended data set is formed with the data obtained in step 4. The BPNN model is retrained until the set prediction range is traversed, and the BPNN network with boundary extension enhancement is output;

[0060] Step 8: Based on the neural network obtained in step 7, predict the unsteady aerodynamic characteristics at non-original data points.

[0061] Among them, in the step one, based on the single variable method, extending from the selected center point to the boundary of each axis, and then considering the boundary effect at the corner point, a center-corner extension sampling method is designed, and the number of original data groups N of the wind tunnel test / numerical simulation is obtained according to this method.

[0062] Specifically, the number of wind tunnel test / numerical simulation groups N is obtained by the following formula:

[0063]

[0064] Among them, D i is the number of experimental levels of the i-th dimension variable; n represents the n-dimensional variable.

[0065] Furthermore, the method further comprises:

[0066] Step 9. Based on the optimal Latin hypercube sampling method, L sample points are extracted in the entire test space. The neural network obtained in step 6 is Taylor expanded at the L sample points respectively, and a total of L Taylor expansions are obtained. The coefficients are average-weighted to obtain the explicit expression of the neural network for the unsteady aerodynamic characteristics.

[0067] It can be seen that the embodiment of the present invention designs an experimental design method for center corner extension sampling, which focuses on the influence of a single variable on unsteady aerodynamic characteristics while reducing the requirement for the number of test groups, thereby ensuring the effectiveness of the aerodynamic characteristics fitting of the neural network model finally learned; at the same time, the embodiment of the present invention designs a learning process of "basic model training + boundary extension enhancement", which increases the prediction accuracy of unsteady aerodynamic characteristics at a long distance in the test space; in addition, the embodiment of the present invention also designs a method for obtaining a display expression of unsteady aerodynamic characteristics based on neural network training, which provides a general and convenient tool for relevant professionals to carry out their work.

[0068] In the above embodiment, in order to ensure the accuracy of the data, before implementing step three, the following steps are also included:

[0069] Preprocess the original wind tunnel test / numerical simulation data, including:

[0070] The obvious bad pixel data obtained by wind tunnel test / numerical simulation are eliminated, and the eliminated bad pixels are replaced by linear interpolation method.

[0071] Preferably, the step three specifically includes:

[0072] According to the comprehensiveness requirement of the test, the data processed in step 2 are interpolated using the Lagrange interpolation method, expanding from N groups of test data to Q groups of data. The expression of Q is as follows:

[0073]

[0074] Preferably, in step 4, the number of levels in each dimension after interpolation should be no less than 10.

[0075] In the above embodiment, the step five specifically includes:

[0076] 5.1 Regularize the input data of each dimension;

[0077] 5.2 Building a Neural Network Model

[0078] The BP neural network (BPNN) architecture is adopted, which consists of three parts: input layer-hidden layer-output layer. The number of neurons in the input layer is equal to the dimension n of the aerodynamic characteristics to be fitted. The number of neurons in the output layer m is 1 by default. The hidden layer consists of three layers, and the number of neurons in each layer l is determined by the following formula:

[0079]

[0080] Wherein, k is any value between 0 and 10. Preferably, l is an integer power of 2 in a similar range;

[0081] 5.3 Setting the neuron activation function

[0082] 5.4 Constructing the loss function

[0083] 5.5 Setting the optimization algorithm

[0084] 5.6 Setting the loop termination condition

[0085] Set the square error sum accuracy index and simulation step size. When the loss function is less than the accuracy index or meets the simulation step size, the simulation terminates.

[0086] Preferably, the number of hidden layer neuron nodes is set to 8, the neuron activation function selects the "Gaussian" function, the loss function selects the sum of squared errors, and the optimization algorithm adopts the BFGS algorithm.

[0087] According to another embodiment, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned prediction method when executing the computer program.

[0088] That is, the embodiment of the present invention determines the number of wind tunnel tests / numerical simulations based on the proposed center-angle extension sampling method, then conducts wind tunnel tests / numerical simulations and uses machine learning methods to learn and train the unsteady aerodynamic characteristics of the aircraft based on the original aerodynamic data obtained, thereby achieving aerodynamic characteristics prediction for non-original data points. This method reduces the demand for original aerodynamic data while ensuring the prediction accuracy of the neural network for a single variable. This method gives an explicit expression of the neural network for unsteady aerodynamic characteristics, providing a general and convenient tool for relevant professionals to carry out their work.

[0089] In order to further understand the prediction method provided by the present invention, a specific embodiment is described in detail below:

[0090] like Figure 1 As shown, the specific implementation steps of the present invention are as follows:

[0091] Step 1: Determine the number of wind tunnel test / numerical simulation original data sets.

[0092] Wind tunnel tests / numerical simulations are conducted within the flight envelope of the variable-sweep wing aircraft to obtain the initial aerodynamic data of the variable-sweep wing under different working conditions. Based on the single variable method, an experimental design method called the center-edge-corner extension sampling method is given by extending from the selected center point to the boundary of each axis and considering the boundary effect at the corner point. Assuming that the nonlinear aerodynamic characteristics of the n-dimensional variable-sweep wing need to be fitted, let the number of test levels required in the i-dimensional dimension be D i (where 1 dimension defaults to the sweep angle δ), then at least N sets of wind tunnel tests / numerical simulations are required, and the expression of N is shown in formula (1);

[0093] The following is an example to illustrate the meaning of formula (1):

[0094] Taking the five-dimensional aerodynamic characteristics fitting as an example, the first dimension is the sweep angle δ, the second dimension is the sweep angular velocity δ', the third dimension is the flight Mach number Ma, the fourth dimension is the angle of attack α, and the fifth dimension is the flight altitude H. In view of the fact that this patent studies the unsteady aerodynamic data generation method of the variable sweep wing, each set of wind tunnel tests / numerical simulations uses the sweep angle as the independent variable δ, and the corresponding aerodynamic force / moment coefficient as the dependent variable.

[0095] Assume that (δ'*, Ma*, α*, H*) is the central test group of wind tunnel test / numerical simulation.

[0096] Among them, δ'* is δ'1, δ'2, δ'3,..., δ' D2 Any value, Ma* is Ma1,Ma2,Ma3,…,Ma D3 , α* is α1,α2,α3,…,α D4 Any value, H* is H1,H2,H3,…,H D5 Any value. Preferably,

[0097] In order to verify the influence of the swept angular velocity δ' on the unsteady aerodynamic data, the D2 group of tests were carried out for different swept angular velocities δ' with fixed Mach number Ma*, angle of attack α*, and altitude H*.

[0098] Similarly, in order to verify the influence of Mach number Ma, angle of attack α and altitude H on unsteady aerodynamic data, D3, D4 and D5 groups of tests are required respectively.

[0099] In addition, to ensure the influence of each influencing factor boundary on the unsteady aerodynamic data, two n-1 = 16 groups of experiments, that is

[0100] Among them, (δ'*,Ma*,α*,H*) conducted n-1 groups of experiments in total, and n-2 groups need to be subtracted.

[0101] Therefore, a total of N sets of wind tunnel tests / numerical simulations are required, and the expression of N is as follows:

[0102]

[0103] In particular, when the central test group (δ'*, Ma*, α*, H*) is selected as a corner point (such as (δ'1, Ma1, α1, H1)), the expression of N is as follows:

[0104]

[0105] Preferably, in order to ensure the accuracy of the data,

[0106] Step 2: Based on step 1, N groups of wind tunnel tests or numerical simulations are performed to obtain the original aerodynamic data set;

[0107] Step 3: Preprocess the original wind tunnel test / numerical simulation data

[0108] That is, the data of obvious bad pixels obtained by wind tunnel test / numerical simulation are eliminated, and the eliminated bad pixels are replaced by linear interpolation method;

[0109] Step 4: According to the requirements of the comprehensive test, the data processed in step 3 are interpolated using the Lagrange interpolation method;

[0110] Take the five-dimensional aerodynamic characteristics interpolation as an example:

[0111] 4.1 First, orthogonal encryption interpolation is performed on the three-dimensional aerodynamic characteristics: the first dimension is the sweep angle δ, the second dimension is the sweep angular velocity δ', and the third dimension is the flight Mach number Ma. The angle of attack and altitude are fixed. The D2 group of aerodynamic data with the sweep angular velocity δ' as the dependent variable and the D3 group of aerodynamic data with the flight Mach number Ma as the dependent variable are required;

[0112] 4.2 The Lagrangian method is used to interpolate the aerodynamic data in step 4.1, and a total of D2×D3 groups of aerodynamic data are interpolated. o ,Ma p ,α*,H*) point interpolation as an example;

[0113] 4.2.1 Obtaining 4D boundary data from 5D boundary data

[0114]

[0115] 4.2.2 Obtaining 3D boundary data from 4D boundary data

[0116]

[0117] Similarly, we obtain (δ' D2 ,Ma1,α*,H*)、(δ'1,Ma D3 ,α*,H*)、(δ' D2 ,Ma D3 ,α*,H*) boundary data.

[0118] 4.2.3 Find (δ'1,Ma p ,α*,H*)

[0119] Assume (δ' o ,Ma p ,α*,H*) is closer to the point (δ'1,Ma1,α*,H*)

[0120]

[0121] 4.2.4 Find (δ' o ,Ma p ,α*,H*)

[0122]

[0123] The variable sweep angular velocity and Mach number are interpolated to obtain D2×D3 groups of aerodynamic data

[0124] 4.3 Similarly, according to step 4.2, the aerodynamic data groups D2×D4, D2×D5, D3×D4, D3×D5, and D4×D5 can be interpolated;

[0125] 4.4 Similarly, for the interpolation of three-dimensional aerodynamic characteristics, for the interpolation of four-dimensional aerodynamic characteristics, first determine the four-dimensional boundary data according to the five-dimensional boundary data, and then interpolate the data after interpolation in step 4.3 to obtain D2×D3×D4, D2×D3×D5, D2×D4×D5, D3×D4×D5 groups of aerodynamic data;

[0126] 4.5 Similarly, for the five-dimensional aerodynamic characteristics interpolation, interpolation is performed based on the five-dimensional boundary data and the aerodynamic data of step 4.4, and finally a set of aerodynamic data D2×D3×D4×D5 is obtained;

[0127] Similarly, for n-dimensional aerodynamic characteristic interpolation: Q groups of data can be interpolated in the end, and the expression of Q is shown in the above embodiment;

[0128] Step 5: Data encryption

[0129] Through multivariate interpolation, the comprehensive test points in step 4 are encrypted, and the number of levels in each dimension after interpolation should be no less than 10;

[0130] Step 6: Build a machine learning framework

[0131] 6.1 Preprocess (regularize) the input data of each dimension. This step mainly deals with the situation where the data size of different dimensions is too different, and the output results of different parameters are the same.

[0132] 6.2 Building a Neural Network Model

[0133] The BP neural network (Back Propagation Neural Network, BPNN) architecture is adopted, which consists of three parts: input layer-hidden layer-output layer. The number of neurons in the input layer is equal to the dimension n of the aerodynamic characteristics that need to be fitted. To reduce the difficulty of fitting, the number of neurons in the output layer m is 1 by default, that is, each neural network model only fits one aerodynamic force / torque coefficient; the hidden layer consists of three layers, and the number of neurons in each layer l is determined by the following formula

[0134]

[0135] Where k is any value between 0 and 10. Preferably, l is an integer power of 2 in a similar range. In this method, l=8.

[0136] 6.3 Setting the neuron activation function

[0137] The activation function mainly introduces nonlinear characteristics into the neural network to help the neural network learn the complex effects of unsteady aerodynamic characteristics. In this embodiment, the "Gaussian" activation function is selected;

[0138] 6.4 Constructing the loss function

[0139] The loss function is used to evaluate the difference between the predicted aerodynamic characteristics and the wind tunnel test / numerical simulation. The sum of squared error (SSE) is used as the loss function, which is defined as follows:

[0140]

[0141] Among them, m is the number of samples, is the sample prediction value, Y i is the true value of the sample;

[0142] 6.5 Setting the Optimization Algorithm

[0143] The optimization algorithm is mainly to find the parameters of the neural network to best fit the unsteady aerodynamic characteristics. In view of the small number of parameters to be optimized in the proposed BPNN model, this embodiment adopts the BFGS optimization algorithm to accelerate the optimization process;

[0144] 6.6 Setting the loop termination condition

[0145] Set the square error sum accuracy index and simulation step size. When the loss function is less than the accuracy index or meets the number of simulation steps, the simulation terminates.

[0146] Step 7: Neural network parameter training

[0147] Based on the aerodynamic data encrypted in step 5, the parameters are optimized with the loss function as the evaluation index until the loop termination condition is reached, and the BPNN neural network is obtained after output training;

[0148] Step 8: Boundary extension and enhancement, including:

[0149] 8.1 Set the prediction range for each dimension;

[0150] 8.2 Based on the basic network model obtained after training in step 7, predict the unsteady aerodynamics at the boundary of the multi-dimensional test space, where the prediction points in each dimension shall not exceed 5% of the original data length of the dimension, and the predicted data and the data obtained in step 5 form an extended data set;

[0151] 8.3 Perform model training according to steps 6 and 7, wherein the neural network model inherits the neural network trained in step 7;

[0152] 8.4 Iterate steps 8.2 and 8.3 until all prediction ranges set in step 8.1 are traversed;

[0153] 8.5 BPNN neural network enhanced by output boundary extension;

[0154] Step 9: Prediction of unsteady aerodynamic characteristics

[0155] Based on the neural network obtained in step eight, the unsteady aerodynamic characteristics at non-original data points are predicted.

[0156] Step 10: Obtain the explicit expression of the neural network for the unsteady aerodynamic characteristics

[0157] Here is an example of a 2nd order expression of a lift coefficient neural network with a 5-dimensional dependent variable, as follows:

[0158] 10.1 Based on the optimal Latin hypercube sampling method, L sample points are extracted from the entire test space;

[0159] 10.2 Perform Taylor expansion on the neural network obtained in step 7 at L sample points respectively;

[0160] Assume that the functional relationship described by the neural network obtained in step 7 is as shown in formula (11)

[0161] C l =f(δ,δ′,Ma,α,H) (11)

[0162] Let x = [δ, δ′, Ma, α, H] T

[0163] Expand the formula at the jth sample point, then

[0164]

[0165] in,

[0166]

[0167]

[0168] Use the interpolation quotient to replace the derivative calculation, and combine the various terms to get

[0169]

[0170] 10.3 Perform average weighted processing on the coefficients of the L Taylor expansions to obtain the explicit expression of the unsteady aerodynamic characteristics of the neural network

[0171]

[0172] in,

[0173] Features described and / or illustrated above for one embodiment may be used in the same or similar manner in one or more other embodiments, and / or combined with or used in place of features in other embodiments.

[0174] It should be emphasized that the term "include / comprises" when used herein refers to the presence of features, integers, steps or components, but does not exclude the presence or addition of one or more other features, integers, steps, components or combinations thereof.

[0175] The above methods of the present invention can be implemented by hardware, or by hardware combined with software. The present invention relates to such a computer readable program, which, when executed by a logic component, enables the logic component to implement the above-mentioned device or component, or enables the logic component to implement the above-mentioned various methods or steps.

[0176] The many features and advantages of these embodiments are apparent from this detailed description, and thus the appended claims are intended to cover all such features and advantages of these embodiments that fall within their true spirit and scope. Furthermore, since numerous modifications and changes will readily occur to those skilled in the art, it is not intended that the embodiments of the invention be limited to the exact construction and operation illustrated and described, but rather all suitable modifications and equivalents falling within the scope thereof are intended to be covered.

[0177] Parts of the present invention that are not described in detail are well known to those skilled in the art.

Claims

1. A method for predicting unsteady aerodynamic characteristics based on machine learning, characterized in that: The prediction method comprises: Step 1: determine the number of wind tunnel test / numerical simulation raw data sets N based on the variable dimension and the number of test levels of the variable; Step 2: Perform N groups of wind tunnel tests or numerical simulations to obtain an original aerodynamic data set; Step 3: Add the difference of the N groups of data obtained in step 2 to expand them to Q groups of data; Step 4: Encrypt the comprehensive test points obtained in step 3 by multivariate interpolation; Step 5: Establish a machine learning framework based on the back propagation neural network (BPNN) model; Step 6: Based on the aerodynamic data obtained after encryption in step 4, the network parameters of the BPNN in step 5 are optimized with the designed loss function as the evaluation index, and the trained neural network is output; Step 7: Based on the BPNN model obtained in step 6, the aerodynamic characteristics outside the test space boundary are predicted in turn, and an extended data set is formed with the data obtained in step 4. The BPNN model is retrained until the set prediction range is traversed, and the BPNN network with boundary extension enhancement is output; Step 8: Based on the neural network obtained in step 7, predict the unsteady aerodynamic characteristics at non-original data points.

2. The unsteady aerodynamic characteristics prediction method based on machine learning according to claim 1 is characterized in that: In the step 1, based on the single variable method, extending from the selected center point to the boundary of each axis, and then considering the boundary effect at the corner point, a center corner extension sampling method is designed, and the number of original data sets N of the wind tunnel test / numerical simulation is obtained according to this method.

3. The unsteady aerodynamic characteristics prediction method based on machine learning according to claim 2 is characterized in that: The number of wind tunnel test / numerical simulation groups N is obtained by the following formula: Among them, D i is the number of experimental levels of the i-th dimension variable; n represents the n-dimensional variable.

4. The unsteady aerodynamic characteristics prediction method based on machine learning according to any one of claims 1 to 3, characterized in that: The method further comprises: Step 9. Based on the optimal Latin hypercube sampling method, L sample points are extracted in the entire test space. The neural network obtained in step 6 is Taylor expanded at the L sample points respectively, and a total of L Taylor expansions are obtained. The coefficients are average-weighted to obtain the explicit expression of the neural network for the unsteady aerodynamic characteristics.

5. The unsteady aerodynamic characteristics prediction method based on machine learning according to claim 4 is characterized in that: Before implementing step three, it also includes: Preprocess the original wind tunnel test / numerical simulation data, including: The obvious bad pixel data obtained by wind tunnel test / numerical simulation are eliminated, and the eliminated bad pixels are replaced by linear interpolation method.

6. The unsteady aerodynamic characteristics prediction method based on machine learning according to claim 4 or 5, characterized in that: The step three specifically includes: According to the comprehensiveness requirement of the test, the data processed in step 2 are interpolated using the Lagrange interpolation method, expanding from N groups of test data to Q groups of data. The expression of Q is as follows:

7. The unsteady aerodynamic characteristics prediction method based on machine learning according to claim 1 is characterized in that: In step 4, the number of levels in each dimension after interpolation should be no less than 10.

8. The unsteady aerodynamic characteristics prediction method based on machine learning according to claim 1 is characterized in that: The step five specifically includes: 5.1 Regularize the input data of each dimension; 5.2 Building a Neural Network Model The BP neural network (BPNN) architecture is adopted, which consists of three parts: input layer-hidden layer-output layer. The number of neurons in the input layer is equal to the dimension n of the aerodynamic characteristics to be fitted. The number of neurons in the output layer m is 1 by default. The hidden layer consists of three layers, and the number of neurons in each layer l is determined by the following formula: Among them, k takes any value between 0 and 10; 5.3 Setting the neuron activation function 5.4 Constructing the loss function 5.5 Setting the optimization algorithm 5.6 Setting the loop termination condition Set the square error sum accuracy index and simulation step size. When the loss function is less than the accuracy index or meets the number of simulation steps, the simulation terminates.

9. The unsteady aerodynamic characteristics prediction method based on machine learning according to claim 8, characterized in that: The number of hidden layer neuron nodes is set to 8, the neuron activation function is selected as the "Gaussian" function, the loss function is selected as the sum of squared errors, and the optimization algorithm is the BFGS algorithm.

10. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the prediction method according to any one of claims 1 to 9 is implemented.

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