A neural network model-based experiment design method

Abstract

A test design method based on a neural network model, comprising the following steps: selecting test working condition points in an initial test design, constructing a test data set containing flight working condition parameters and lift-drag coefficients at all initial test sample points; constructing a neural network aerodynamic model and training it using the test data; judging whether the prediction accuracy of the trained neural network aerodynamic model meets the requirements; if the prediction accuracy does not meet the requirements, constructing an information matrix based on the trained neural network aerodynamic model; selecting new test working condition points using an optimal test design method, and adding new test point data to the test data set; repeating the steps until the prediction accuracy meets the requirements, then stopping adding points, and using the current neural network model as a prediction model to predict the lift-drag coefficients under all flight working conditions. The present application gradually increases the sample size based on a neural network model to improve the neural network modeling accuracy. The test efficiency is improved, and the modeling cost is saved.

Description

Technical Field

[0001] This invention relates to the field of experimental design and modeling technology, and specifically to an experimental design method based on a neural network model. Background Technology

[0002] In aircraft design, once the aircraft's shape is determined, its aerodynamic characteristics need to be analyzed through wind tunnel testing. Traditional testing methods require wind tunnel tests under multiple key flight conditions, such as different Mach numbers, angles of attack, and sideslip angles, to obtain the aircraft's lift and drag coefficients under these conditions. Then, linear interpolation methods are used to obtain the lift and drag coefficients for all conditions to analyze the merits of the aircraft's aerodynamic shape. Mathematical model-based testing methods, on the other hand, use experimental data to optimize model parameters to establish a highly accurate aerodynamic mathematical model, which is then used to predict the lift and drag coefficients for all conditions. In comparison, mathematical model-based testing methods can reduce the number of test points and lower testing costs.

[0003] Neural network models, due to their powerful nonlinear fitting capabilities, possess stronger expressive power than traditional mathematical models. Neural networks can automatically extract the underlying correlations between input and output data from training data, thereby establishing a precise mapping model between input and output. However, training neural networks requires a large amount of data, and the acquisition cost of many datasets (such as wind tunnel experiments) is too high, making it impossible to provide large amounts of data for training neural networks. How to train neural networks using limited data has become a hot topic of common interest in both academia and industry.

[0004] Patent CN113901594B discloses an intelligent prediction method for the aerodynamic thermal environment of an aircraft surface, and patent CN115619035A discloses a prediction method for carbon electrical intensity based on a neural network. However, both of these patents directly use a large amount of data to train the neural network model, without addressing the use of experimental design methods to reduce the sample size required for training the neural network. Patent CN106021865B discloses a batch-based experimental design method based on D-optimal design, and patent CN107368649A discloses a sequential optimization experimental design method based on incremental Kriging. The above experimental design methods are applicable to polynomial models or Kriging; currently, no published invention patents propose experimental design methods for neural network models. Summary of the Invention

[0005] To overcome the problems existing in the prior art, the present invention aims to provide an experimental design method based on a neural network model. This method involves sequentially adding experimental points based on the neural network model to gradually improve the accuracy of the neural network aerodynamic model. The selected new experimental operating points are all those most effective in improving model accuracy. Therefore, establishing a neural network aerodynamic model of equivalent accuracy requires only a minimal number of experiments, improving experimental efficiency and saving aerodynamic analysis costs.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] An experimental design method based on a neural network model includes the following steps;

[0008] Step 1: Initial test design. Select test operating points and construct a test dataset containing flight operating parameters and lift and drag coefficients at all initial test sample points.

[0009] Step 2: Construct a neural network aerodynamic model and train it using the experimental data;

[0010] Step 3: Determine whether the prediction accuracy of the trained neural network aerodynamic model meets the requirements;

[0011] Step 4: If the prediction accuracy does not meet the requirements, construct an information matrix based on the trained neural network aerodynamic model;

[0012] Step 5: Use the optimal experimental design method to select new test conditions and incorporate the data from the new test conditions into the experimental dataset;

[0013] Step 6: Repeat steps 2 to 5 until the prediction accuracy in step 3 meets the requirements. Then stop adding points. The current neural network model is used as the prediction model to predict the lift and drag coefficients under all flight conditions.

[0014] Step one specifically involves:

[0015] (1) Determine the number of initial test points based on the number of flight condition parameters. The number of initial test points should be at least ten times the number of flight condition parameters.

[0016] (2) Randomly select initial test sample points within the range of flight operating parameters of the target aircraft, and design initial point selection multiple times. Use the maximization of the distance between sample points as the criterion to select the optimal one among these initial point selection designs.

[0017] (3) Obtain the lift and drag coefficients of the aircraft at all initial test points through wind tunnel testing;

[0018] (4) Combine the flight condition parameters and lift-drag coefficients at each test point into a single data set, and construct the test dataset from all the initial test points.

[0019] Step two specifically involves:

[0020] (1) Divide the experimental dataset and its data points into training set and test set according to a certain ratio;

[0021] (2) Determine the form and hyperparameters of the neural network model. If the input is one-dimensional data, choose a fully connected neural network; if the input is two-dimensional data, choose a convolutional neural network. The number of hyperparameters in the neural network should be less than the number of experimental data.

[0022] (3) Train the neural network model using the experimental data in the training set by minimizing the loss function until the loss function converges. The training is then complete. The loss function can be selected from various options. or Where n is the number of experimental data points, y i The true value of the lift and drag coefficient obtained from the wind tunnel test at the i-th test point. Let be the predicted lift and drag coefficient of the neural network at the i-th test point.

[0023] Step three specifically involves:

[0024] (1) The flight condition parameter values ​​in each test data in the test set are transmitted to the trained neural network model, and the neural network can predict the lift and drag coefficients corresponding to each test data point.

[0025] (2) Compare the actual values ​​of lift and drag coefficients obtained from wind tunnel tests at the test data points with the predicted values ​​of lift and drag coefficients predicted by the neural network model, and calculate the MAE loss or MSE loss as the prediction accuracy.

[0026] (3) Determine whether the prediction accuracy is less than 5%. If the requirement is met, stop the process. If not, continue with the subsequent steps.

[0027] Step four specifically involves:

[0028] (1) Input the flight condition parameter values ​​of all selected and one unselected test points into the trained neural network model to obtain the output A of the neuron in the previous layer of the output layer. mn Where the subscript m represents the number of neurons, the subscript n represents the number of wind tunnel test points, the selected test data points are n-1, and the unselected test data point is 1; use all A mn The structure matrix of the current model can be constructed as follows:

[0029] (2) Construct the information matrix M = G T G.

[0030] In step four, the structure matrix G can be constructed using the outputs of neurons from the previous layer or by adding outputs from neurons in other layers. The construction method is as follows: a new column is added to the structure matrix, containing the output values ​​of all test points to be selected at the newly added neurons. The structure matrix after adding neurons can be represented as follows: Where k = m + a is the number of neurons in the current structure matrix, m is the number of neurons in the previous layer of the output layer, and a is the number of newly added neurons.

[0031] Step five specifically involves:

[0032] (1) Determine the number of new test points each time, which is generally 1 or 2;

[0033] (2) Select new test points using one of the following optimal criteria: D-optimal, A-optimal, E-optimal, G-optimal, etc. D-optimal design involves selecting test points that maximize the determinant of the information matrix M; A-optimal design involves selecting test points that maximize tr(M)... -1 To achieve maximum and E-optimal design, experimental points are selected to maximize M. -1 The maximum eigenvalue is minimized, and the G-optimal design aims to minimize the maximum variance of the predicted response value when selecting test points. Specifically, this involves constructing an information matrix M using different candidate test points, calculating the optimal criterion value for each information matrix, comparing the magnitudes of the optimal criterion values ​​across all information matrices, and selecting the optimal new test point based on the optimal criterion.

[0034] (3) Use wind tunnel testing to obtain the lift and drag coefficient values ​​at the newly added test points;

[0035] (4) Combine the flight condition parameter values ​​and the lift and drag coefficient values ​​measured in the wind tunnel at each new test point into a data set and add it to the test dataset.

[0036] The beneficial effects of this invention are:

[0037] This invention proposes using an optimal experimental design method to sequentially add experimental data during neural network modeling, thereby gradually improving modeling accuracy. An information matrix is ​​constructed based on the neural network model, and by selecting new experimental points, the information matrix contains more information, resulting in the most effective new experimental points for improving neural network modeling accuracy. Compared to traditional methods, this invention reduces the amount of data required to build a neural network model of equivalent accuracy by more than half, saving significant wind tunnel testing costs and improving aerodynamic analysis efficiency. Attached Figure Description

[0038] Figure 1 This is a schematic diagram of the experimental design method based on a neural network model according to the present invention. Detailed Implementation

[0039] The present invention will now be described in further detail with reference to the accompanying drawings.

[0040] like Figure 1 As shown:

[0041] Step 1: Initial test design. Select test operating points and construct a test dataset containing flight operating parameters and lift and drag coefficients at all initial test sample points.

[0042] (1) Determine the number of initial test points based on the number of flight condition parameters. The number of initial test points should be at least ten times the number of flight condition parameters.

[0043] (2) Randomly select initial test sample points within the range of flight operating parameters of the target aircraft, and design initial point selection multiple times. Use the maximization of the distance between sample points as the criterion to select the optimal one among these initial point selection designs.

[0044] (3) Obtain the lift and drag coefficients of the aircraft at all initial test points through wind tunnel testing;

[0045] (4) Combine the flight condition parameters and lift-drag coefficients at each test point into a single data set, and construct the test dataset from all the initial test points.

[0046] Step 2: Construct a neural network aerodynamic model and train it using the experimental data;

[0047] (1) Divide the experimental dataset and its data points into training set and test set according to a certain ratio;

[0048] (2) Determine the form and hyperparameters of the neural network model. If the input is one-dimensional data, choose a fully connected neural network; if the input is two-dimensional data, choose a convolutional neural network. The number of hyperparameters in the neural network should be less than the number of experimental data.

[0049] (3) Train the neural network model using the experimental data in the training set by minimizing the loss function until the loss function converges. The training is then complete. The loss function can be selected from various options. or Where n is the number of experimental data points, y i The true value of the lift and drag coefficient obtained from the wind tunnel test at the i-th test point. Let be the predicted lift and drag coefficient of the neural network at the i-th test point.

[0050] Step 3: Determine whether the prediction accuracy of the trained neural network aerodynamic model meets the requirements;

[0051] (1) The flight condition parameter values ​​in each test data in the test set are transmitted to the trained neural network model, and the neural network can predict the lift and drag coefficients corresponding to each test data point.

[0052] (2) Compare the actual values ​​of lift and drag coefficients obtained from wind tunnel tests at the test data points with the predicted values ​​of lift and drag coefficients predicted by the neural network model, and calculate the MAE loss or MSE loss as the prediction accuracy.

[0053] (3) Determine whether the prediction accuracy is less than 5%. If the requirement is met, stop the process. If not, continue with the subsequent steps.

[0054] Step 4: If the prediction accuracy does not meet the requirements, construct an information matrix based on the trained neural network aerodynamic model; (1) Construct a structure matrix using the output of the neurons in the previous layer of the trained neural network model, which can be expressed as: Where A is the output of the neurons in the previous layer of the output layer, the subscript m represents the number of neurons, and the subscript n represents the number of sample points to be selected; (2) Construct the information matrix M = G T G;

[0055] Step 5: Use the optimal experimental design method to select new test conditions and incorporate the data from the new test conditions into the experimental dataset;

[0056] (1) Determine the number of new test points each time, which is generally 1 or 2;

[0057] (2) Select new test points using one of the following optimal criteria: D-optimal, A-optimal, E-optimal, G-optimal, etc. D-optimal design involves selecting test points that maximize the determinant of the information matrix M; A-optimal design involves selecting test points that maximize tr(M)... -1 To achieve maximum and E-optimal design, experimental points are selected to maximize M. -1 The maximum eigenvalue is minimized, and the G-optimal design aims to minimize the maximum variance of the predicted response value when selecting test points. Specifically, this involves constructing an information matrix M using different candidate test points, calculating the optimal criterion value for each information matrix, comparing the magnitudes of the optimal criterion values ​​across all information matrices, and selecting the optimal new test point based on the optimal criterion.

[0058] (3) Use wind tunnel testing to obtain the lift and drag coefficient values ​​at the newly added test points;

[0059] (4) Combine the flight condition parameter values ​​and the lift and drag coefficient values ​​measured in the wind tunnel at each new test point into a data set and add it to the test dataset.

[0060] Step Six: Repeat steps two through five.

[0061] In step one, the initial sampling method can not only be the Latin hypercube experimental design method, but also other experimental design methods based on the space filling idea, such as uniform experimental design method, orthogonal experimental design method, etc.

[0062] In step four, the structure matrix G can be constructed not only using the outputs of neurons in the previous layer of the output layer, but also by adding the outputs of neurons in other layers;

[0063] In step five, the optimal experimental design method for selecting new sample points can be based on various criteria, such as D-optimal, A-optimal, E-optimal, G-optimal, etc. The above embodiments are only used to illustrate the technical solution of the present invention and are not intended to limit it; the present invention can also be used in fields such as power, transportation, chemical industry, and agriculture; any modifications to the application field of this technical solution, or equivalent substitutions of some technical features, will not cause the essence of the corresponding technical solution to deviate from the spirit and scope of the implementation technical solution of the present invention.

Claims

1. An experimental design method based on a neural network model, characterized in that, Includes the following steps; Step 1: Initial test design. Select test operating points and construct a test dataset containing flight operating parameters and lift and drag coefficients at all initial test sample points. Step 2: Construct a neural network aerodynamic model and train it using the experimental data; Step 3: Determine whether the prediction accuracy of the trained neural network aerodynamic model meets the requirements; Step 4: If the prediction accuracy does not meet the requirements, construct an information matrix based on the trained neural network aerodynamic model; Step 5: Use the optimal experimental design method to select new test conditions and incorporate the data from the new test conditions into the experimental dataset; Step 6: Repeat steps 2 to 5 until the prediction accuracy in step 3 meets the requirements, then stop adding points. The current neural network model is used as the prediction model to predict the lift and drag coefficients under all flight conditions. Step four specifically involves: (1) Input the flight condition parameter values ​​of all selected and one unselected test points into the trained neural network model to obtain the output A of the neuron in the previous layer of the output layer. mn Where the subscript m represents the number of neurons, the subscript n represents the number of wind tunnel test points, the selected test data points are n-1, and the unselected test data point is 1; use all A mn The structure matrix of the current model can be constructed as follows: (2) Construct the information matrix M = G T G.

2. The experimental design method based on a neural network model according to claim 1, characterized in that, Step one specifically involves: (1) Determine the number of initial test points based on the number of flight condition parameters. The number of initial test points should be at least ten times the number of flight condition parameters. (2) Randomly select initial test sample points within the range of flight operating parameters of the target aircraft, and design initial point selection multiple times. Use the maximization of the distance between sample points as the criterion to select the optimal one among these initial point selection designs. (3) Obtain the lift and drag coefficients of the aircraft at all initial test points through wind tunnel testing; (4) Combine the flight condition parameters and lift-drag coefficients at each test point into a single data set, and construct the test dataset from all the initial test points.

3. The experimental design method based on a neural network model according to claim 1, characterized in that, Step two specifically involves: (1) Divide the data points in the experimental dataset into a training set and a test set according to a certain ratio; (2) Determine the form and hyperparameters of the neural network model. If the input is one-dimensional data, choose a fully connected neural network; if the input is two-dimensional data, choose a convolutional neural network. The number of hyperparameters in the neural network should be less than the number of experimental data. (3) Train the neural network model using the experimental data in the training set by minimizing the loss function until the loss function converges. The training is then complete. The loss function can be selected from various options. or Where n is the number of experimental data points, y i The true value of the lift and drag coefficient obtained from the wind tunnel test at the i-th test point. Let be the predicted lift and drag coefficient of the neural network at the i-th test point.

4. The experimental design method based on a neural network model according to claim 1, characterized in that, Step three specifically involves: (1) The flight condition parameter values ​​in each test data in the test set are transmitted to the trained neural network model, and the neural network can predict the lift and drag coefficients corresponding to each test data point. (2) Compare the actual values ​​of lift and drag coefficients obtained from wind tunnel tests at the test data points with the predicted values ​​of lift and drag coefficients predicted by the neural network model, and calculate the MAE loss or MSE loss as the prediction accuracy. (3) Determine whether the prediction accuracy is less than 5%. If the requirement is met, stop the process. If not, continue with the subsequent steps.

5. The experimental design method based on a neural network model according to claim 1, characterized in that, In step four, the structure matrix G can be constructed using the output of neurons from the previous layer or by adding the output of neurons from other layers. The construction method is as follows: a new column is added to the structure matrix, containing the output values ​​of all test points to be selected at the newly added neurons. The structure matrix after adding neurons can be represented as follows: Where k = m + a is the number of neurons in the current structure matrix, m is the number of neurons in the previous layer of the output layer, and a is the number of newly added neurons.

6. The experimental design method based on a neural network model according to claim 1, characterized in that, Step five specifically involves: (1) Determine the number of new test points each time, which is generally 1 or 2; (2) Select new test points using one of the following optimal criteria: D-optimal, A-optimal, E-optimal, G-optimal, etc. D-optimal design involves selecting test points that maximize the determinant of the information matrix M; A-optimal design involves selecting test points that maximize tr(M)... -1 To achieve maximum and E-optimal design, experimental points are selected to maximize M. -1 The maximum eigenvalue is minimized, and the G-optimal design is to select test points that minimize the maximum variance of the response prediction value. The specific method is as follows: construct information matrix M by selecting different candidate test points, calculate the optimal criterion value of each information matrix, compare the size of the optimal criterion values ​​of all information matrices, and select the optimal new test point according to the optimal criterion. (3) Use wind tunnel testing to obtain the lift and drag coefficient values ​​at the newly added test points; (4) Combine the flight condition parameter values ​​and the lift and drag coefficient values ​​measured in the wind tunnel at each new test point into a data set and add it to the test dataset.

7. A method for designing experiments based on a neural network model according to any one of claims 1-6, characterized in that, The method is applicable to power, transportation, chemical, and agricultural industries.

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