Cascade correction-based aerodynamic data fusion method and device
By using a cascaded correction aerodynamic data fusion method, which utilizes a neural network to dynamically fit incremental and proportional correction factors and combines a phased decoupling training strategy, the shortcomings of existing aerodynamic data fusion methods in terms of efficiency and accuracy are solved, and high-precision aerodynamic coefficient prediction is achieved with a small amount of high-fidelity data.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHINA ACAD OF AEROSPACE AERODYNAMICS
- Filing Date
- 2026-03-17
- Publication Date
- 2026-06-12
AI Technical Summary
Existing aerodynamic data fusion methods have shortcomings in balancing efficiency and accuracy. Scale correction models are too idealistic, spatial mapping and Co-Kriging methods have limited generalization ability in high-dimensional spaces, and pure neural network methods fail to effectively utilize the physical trends of low-fidelity data, resulting in high data costs and limited prediction accuracy.
A cascaded correction aerodynamic data fusion method is adopted. Normalization is performed using the lowest fidelity data as a benchmark, a multi-level neural network model is established, and the Adam optimizer and a phased decoupling training strategy are combined to dynamically fit the incremental and proportional correction factors, thereby improving the data accuracy.
With limited high-fidelity data, the fusion model achieves higher prediction accuracy than the single-source model, reducing the need for high-fidelity data and providing technical support for small-sample and multi-source aerodynamic data problems. It is applicable to datasets with different input parameters.
Smart Images
Figure CN122196912A_ABST
Abstract
Description
Technical Field
[0001] This document relates to the field of cross-disciplinary integration technology of aerodynamics and deep learning, and in particular to an aerodynamic data fusion method and device based on cascaded correction. Background Technology
[0002] In aircraft design, aerodynamic performance evaluation primarily relies on aerodynamic data. Currently, aerodynamic data is mainly obtained through flight tests, wind tunnel tests, CFD numerical simulations, and engineering estimations. Flight test data offers the highest fidelity and is generally used as the final verification step, but it has a long cycle and high cost. During the engineering development phase, wind tunnel tests are generally used, offering moderate data fidelity, but due to the long cycle and high cost, only a limited number of wind tunnel tests are conducted. High-fidelity numerical simulations offer moderate data fidelity, but their long cycle makes it difficult to cover the entire parameter space. Low-fidelity numerical simulations and engineering algorithms have lower fidelity, are quick to obtain, and have low cost, but their prediction accuracy is limited.
[0003] To balance efficiency and accuracy, aerodynamic data fusion methods have become essential. These methods combine a small amount of high-fidelity experimental data with low-fidelity experimental data to improve data accuracy while reducing the need for high-fidelity data. Current fusion methods mainly include scaling correction models, spatial mapping models, Co-Kriging-like models, and neural network models. However, scaling correction methods are too idealistic and cannot capture complex nonlinear deviations. Spatial mapping and Co-Kriging methods are sensitive to assumptions about data distribution and covariance models, and their generalization ability is limited in high-dimensional spaces where data is scarce. Pure neural network methods, while capable of learning complex mappings, are like "black boxes," failing to explicitly utilize the physical trends revealed by low-fidelity data and still requiring a large number of high-fidelity samples, thus failing to fundamentally reduce data costs. Summary of the Invention
[0004] The purpose of this invention is to provide a method and apparatus for aerodynamic data fusion based on cascaded correction, in order to solve the above-mentioned problems in the prior art.
[0005] This invention provides a cascaded correction-based aerodynamic data fusion method, comprising: All aerodynamic coefficients from all sources are subjected to maximum and minimum normalization based on the lowest fidelity data to obtain the baseline dataset. Establish j neural network models, including j-1 correction networks and a first-level network. Use the Adam optimizer and use the sum of the loss functions of the j neural networks as the final loss function to establish a multi-level fusion model, where j is a natural number. Based on the baseline dataset, the network structure parameters of each neural network are set, and the multi-level fusion model is trained using a phased decoupling training strategy to obtain the aerodynamic coefficient prediction model. The relative error is defined, and the accuracy of the aerodynamic coefficient prediction model is evaluated using the normalized relative error and the coefficient of determination. Based on the aforementioned aerodynamic coefficient prediction model, the aerodynamic coefficients are obtained by inputting operating condition parameters.
[0006] This invention provides a pneumatic data fusion device based on cascaded correction, comprising: The data preprocessing module is used to perform max-min normalization on all aerodynamic coefficients from all sources based on the lowest fidelity data to obtain the baseline dataset. The model building module is used to build j neural network models, including j-1 correction networks and a first-level network. It uses the Adam optimizer and uses the sum of the loss functions of the j neural networks as the final loss function to build a multi-level fusion model, where j is a natural number. The training and evaluation module is used to set the network structure parameters of each neural network based on the baseline dataset, train the multi-level fusion model using a phased decoupling training strategy to obtain the aerodynamic coefficient prediction model, define the relative error, and use the normalized relative error and the coefficient of determination to evaluate the accuracy of the aerodynamic coefficient prediction model. The prediction module is used to obtain aerodynamic coefficients by inputting operating condition parameters based on the aerodynamic coefficient prediction model.
[0007] This invention also provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, implements the steps of the above-described aerodynamic data fusion method based on cascaded correction.
[0008] This invention also provides a computer-readable storage medium storing an information transmission implementation program, which, when executed by a processor, implements the steps of the above-described aerodynamic data fusion method based on cascaded correction.
[0009] By employing embodiments of the present invention, scaling function correction is combined with neural network methods. Deep neural networks are used to fit incremental scaling functions and proportional scaling functions, combining the physical intuitiveness of scaling correction methods with the powerful nonlinear fitting capabilities of neural networks. Using low-fidelity prediction as a "baseline," intelligent learning performs refined nonlinear correction on it, thereby achieving a leap in accuracy with minimal high-fidelity data. Attached Figure Description
[0010] To more clearly illustrate the technical solutions in one or more embodiments of this specification or in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0011] Figure 1 This is a flowchart of the aerodynamic data fusion method based on cascaded correction according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the aerodynamic data fusion model according to an embodiment of the present invention; Figure 3 This is a schematic diagram comparing the predicted results of the fusion model on the baseline dataset of this invention. Figure 4 This is a schematic diagram comparing the predicted results of the fusion model on the full rudder deflection dataset according to an embodiment of the present invention; Figure 5 This is a schematic diagram of a pneumatic data fusion device based on cascaded correction according to an embodiment of the present invention; Figure 6 This is a schematic diagram of an electronic device according to an embodiment of the present invention. Detailed Implementation
[0012] To enable those skilled in the art to better understand the technical solutions in one or more embodiments of this specification, the technical solutions in one or more embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this specification, and not all of the embodiments. Based on one or more embodiments of this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of this document.
[0013] Method Implementation Examples According to embodiments of the present invention, a method for fusing low- and high-fidelity aerodynamic data based on cascaded correction networks is provided, which provides technical support for aerodynamic modeling of small sample problems and multi-source data aerodynamic prediction. Figure 1 This is a flowchart of the aerodynamic data fusion method based on cascaded correction according to an embodiment of the present invention, as shown below. Figure 1 As shown, the aerodynamic data fusion method based on cascaded correction according to an embodiment of the present invention specifically includes: Step S101 involves performing max-min normalization on all aerodynamic coefficients from all sources, using the lowest fidelity data as a benchmark, to obtain the baseline dataset; specifically including: The aerodynamic coefficients from j sources are sorted according to data fidelity. Using the aerodynamic coefficient with the lowest fidelity as the benchmark, the aerodynamic coefficients from j sources are subjected to max-min normalization to obtain the benchmark dataset.
[0014] Step S102: Establish j neural network models, use the Adam optimizer, and use the sum of the loss functions of the j neural networks (MSE) as the final loss function to establish a multi-level fusion model, where j is a natural number; specifically including: The first-level neural network is constructed using the array variable `neruons_per_layer_1` to represent the number of grid layers and the number of neurons in each layer. `neruons_per_layer_1` is a one-dimensional array [a 11 ,a 12 ,…,a 1n ], a 11 Let a be the number of input parameters x1 in the first-level neural network. 12 to a 1,n-1 Let a be the number of neurons in the neural network from layer 2 to layer (n-1). 1n To determine the number of output parameters, softplus is used as the activation function to establish the first-level neural network, whose output is y1, y1=nn(x1); Establish the i-th level correction network, where i is greater than 1: use the array variable `neruons_per_layer_i` to represent the number of grid layers and the number of neurons in each layer. `neruons_per_layer_i` is a one-dimensional array [b i1 ,b i2 ,…,b ii ,…,b in ], b i1 Input parameters x for the i-th level network i The number of parameters is a, which is the number of input parameters a of the (i-1)th level network. i-1,1 Add the number of output parameters a of the (i-1)th level network i-1,n , that is, x i =[x i-1 ,y i-1 ], b i2 to b i,n-1 b represents the number of neurons in the neural network from layer 2 to layer (n-1). in To determine the number of output parameters, softplus is used as the activation function, and the incremental correction factor delta is set. i =nn(x i The scaling correction factor ρ(rho) is set as a parameter of the neural network, and the output of the i-th level correction network is y. i =rho*y i-1 +delta i ; Set up a neural network model with j neural networks, i.e., j-1 corrected network number and first-level network. Use the Adam optimizer and use mse as the loss function of the multi-level fusion architecture. The loss function of the multi-level fusion architecture is obtained by summing the loss functions of j neural networks. The damage function of each neural network is the mse of its output and the corresponding ground truth value. Establish a multi-level fusion model.
[0015] Step S103: Based on the baseline dataset, set the parameters of each neural network, train the multi-level fusion model to obtain the aerodynamic coefficient prediction model, define the relative error, and use the normalized relative error and coefficient of determination to evaluate the accuracy of the aerodynamic coefficient prediction model; specifically including: Based on the aforementioned baseline dataset, the network structure parameter `neruons_per_layer_i` for each neural network is set. The first-level neural network is trained using low-fidelity data, and the parameters of other correction networks are frozen. Then, the parameters of neural networks from level 1 to level i-1 are frozen, and the level i correction network is trained using level i fidelity data. This process is repeated until the level j correction network is reached, completing the training of the entire multi-level fusion model. Relative error is defined according to Formula 1, and the relative error and coefficient of determination are used to evaluate the model's accuracy. The model is compared with a neural network model built using low-fidelity data from a single source, a neural network model built using level j fidelity data from a single source, and a neural network model built using level j fidelity data from another source to evaluate the performance of the fusion method. The level j fidelity data used for training is defined as twice the level j fidelity data from a single source.
[0016] Formula 1; Where N represents the total number of samples in the prediction set, i represents the i-th sample point, and y true This represents the true value of the predictor variable, when y true Less than 1 e-3 When this happens, skip the sample point and do not calculate its relative error, y predict This represents the predicted value of the predictor variable by the fusion framework.
[0017] Step S104: Based on the aerodynamic coefficient prediction model, input the operating condition parameters to obtain the aerodynamic coefficients; this multi-level fusion model framework directly sets the network architecture parameters for datasets with different input parameters, performs model training and testing, and thus obtains the corresponding aerodynamic coefficient prediction model.
[0018] It should be noted that the fusion model framework containing j neural networks established in this embodiment of the invention is applicable to datasets with different numbers of inputs. By setting the network architecture parameters and training the model, aerodynamic coefficient prediction models for datasets with different numbers of inputs can be obtained. During prediction, input parameter x1 can obtain aerodynamic coefficient prediction models for different datasets. x1 may be different. After setting the parameters of each neural network, the model is retrained to obtain the aerodynamic coefficient prediction model. This embodiment of the invention is applicable to datasets with different numbers of input parameters.
[0019] In summary, this invention proposes a fusion method for low- and high-fidelity aerodynamic data based on cascaded correction networks for rapid prediction of aircraft aerodynamic coefficients. This method fuses data from two or more sources with varying fidelities. With a limited amount of high-fidelity data, the fused model achieves higher prediction accuracy than models built from single-source data. Under certain accuracy requirements, it reduces the need for high-fidelity data, providing technical support for addressing the issues of small sample sizes and multiple aerodynamic data sources. The data is sorted according to aerodynamic fidelity. A correction network is built step-by-step based on a hybrid scaling correction method. A neural network is used to fit the incremental and proportional correction factors in the hybrid scaling correction method, and the correction factors are dynamically adjusted based on the input parameters and the predicted values of the previous-level network.
[0020] The technical solutions of the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
[0021] I. Data Processing: 1) Assuming there are a total of j sources of data, sort them according to data fidelity, and use the aerodynamic coefficient of the first level of fidelity (lowest fidelity) as the benchmark, perform maximum and minimum normalization on the aerodynamic coefficients of all sources.
[0022] II. Model Establishment: 2) Establish the first-level neural network: Use the array variable `neruons_per_layer_1` to represent the number of grid layers and the number of neurons in each layer. `neruons_per_layer_1` is a one-dimensional array [a 11 ,a 12 ,…,a 1n ], a 11 Let a be the number of input parameters x1 in the first-level neural network. 12 to a 1,n-1 Let a be the number of neurons in the neural network from layer 2 to layer (n-1). 1n The number of output parameters is given. Softplus is used as the activation function to build the first-level neural network, whose output is y1, y1=nn(x1).
[0023] 3) Establish the i-th level correction network, where i is greater than 1: Use the array variable `neruons_per_layer_i` to represent the number of grid layers and the number of neurons in each layer. `neruons_per_layer_i` is a one-dimensional array [b i1 ,b i2 ,…,b ii ,…,b in ], b i1 Input parameters x for the i-th level network i The number of parameters is a, which is the number of input parameters a of the (i-1)th level network. i-1,1 Add the number of output parameters a of the (i-1)th level network i-1,n , that is, x i =[x i-1 ,y i-1 ], b i2 to b i,n-1 b represents the number of neurons in the neural network from layer 2 to layer (n-1). in To determine the number of output parameters, softplus is used as the activation function, and the incremental correction factor delta is set. i =nn(x i The scaling factor ρ(rho) is set as the parameter rho=nn.parameter(torch.tensor(1.0)) of the neural network, and the output of the i-th level scaling network is y. i =rho*y i-1 +delta i .
[0024] 4) If the total number of networks is j, then adjust the number of networks and the first-level network by j-1. Following steps 2) and 3) completes the model network architecture.
[0025] 5) The Adam optimizer is used, with mse as the loss function. The loss function of the entire fusion framework is obtained by summing the loss functions of j neural networks. The damage function of each neural network is the mse of its output and the corresponding ground truth value. This completes the establishment of the entire multi-level fusion architecture.
[0026] III. Model Training: 6) First, train the first-level neural network using low-fidelity data and freeze the parameters of other correction networks. Then, freeze the parameters of the first to (i-1)th level neural networks, train the i-th level correction network using the i-th level fidelity data, and gradually train up to the j-th level correction network, thus completing the training of the entire fusion model.
[0027] IV. Model Validation: 7) Define relative error, use relative error and coefficient of determination to evaluate the accuracy of the model, and compare it with the neural network model built from low-fidelity data from a single source, the neural network model built from the j-th level fidelity data used in step 5) from a single source, and the neural network model built from the j-th level fidelity data used in step 5) to evaluate the performance of the fusion method.
[0028] The relative error is .
[0029] The following example uses the fusion of aerodynamic data from wind tunnel data and simulation data of a certain aircraft. There are two datasets in total. One is the reference state dataset, with the input being the incoming Mach number, angle of attack, and sideslip angle, a total of 3 input parameters, and the output being the normal force coefficient and axial force coefficient. The other is the full rudder deflection dataset, with the input being the incoming Mach number, angle of attack, sideslip angle, and four rudder deflection angles, a total of 7 input parameters, and the output being the normal force coefficient and axial force coefficient.
[0030] Data preprocessing: 1) Using maximum-minimum normalization for the normal force coefficient and axial force coefficient, the wind tunnel test data are divided into training set and prediction set in a 2:8 ratio.
[0031] The fusion model is established, and the network architecture is as follows: Figure 2 As shown.
[0032] 2) Establish the first-level neural network, using the array variable `neruons_per_layer_1` to represent the number of grid layers and the number of neurons in each layer. `neruons_per_layer_1` is a one-dimensional array [a 11 ,a 12 ,…,a 1i ,…,a 1n ], a 11 The number of input parameters x1 for the first-level network, a 12 - a 1,n-1 Let a be the number of neurons in layers 2 through (n-1) of the neural network. 1n The number of output parameters is given. Softplus is used as the activation function to build the first-level network, whose output is y1, where y1 = nn(x1).
[0033] 3) Establish the second-level correction network, using the array variable `neruons_per_layer_2` to represent the number of grid layers and the number of neurons in each layer. `neruons_per_layer_2` is a one-dimensional array [b 21 ,b 22 ,…,b 2i ,…,b 2n ], b 21x2 is the number of input parameters for the second-level network, and a is the number of input parameters for the first-level network. 11 +Number of output parameters for the 11th-level network, a 1n That is, x2=[x1,y1], b 22 - b 2,n-1 b represents the number of neurons in layers 2 through (n-1) of the neural network. 2n The number of output parameters is given. Softplus is used as the activation function, and the incremental correction factor delta2 = nn(x2) is set as the parameter of the neural network, i.e., rho = nn.parameter(torch.tensor(1.0)). The output of the i-th level correction network is y2 = rho * y1 + delta2.
[0034] 4) The Adam optimizer is used, and MSE is used as the loss function. The loss function of the entire fusion framework is obtained by summing the loss function of the first-level neural network and the loss function of the second-level correction network.
[0035] Model training: 5) For the baseline dataset, taking the axial force coefficient as an example, set the initial values of the network architecture parameters neruons_per_layer_1 and neruons_per_layer_2 as follows: neruons_per_layer_1=[3,8,4,1], neruons_per_layer_2=[4,4,1], a 11 The number of input parameters, with a value of 3, a 1n The number of output parameters, with a value of 1, b 21 It is 4, which is the number of input parameters + 1, b 1n This refers to the number of output parameters. First, the first-level neural network is trained using low-fidelity data. Then, the number of neural network layers and the number of neurons per layer in `neruons_per_layer_1` are adjusted based on the training error, i.e., a. 1i The specific values and the value of i are used to freeze the parameters of the second-level correction network. Then, the parameters of the first-level neural network are frozen. The second-level correction network is trained using high-fidelity data. The number of neural network layers and the number of neurons per layer in neruons_per_layer_2 are adjusted according to the training error, i.e., b. 2i The specific numerical values and the value of i are used to obtain the axial force coefficient prediction model after the training is completed and the model is saved.
[0036] Model validation: Relative error was defined, and the normalized relative error and coefficient of determination were used to evaluate the accuracy of the model. The model was compared with a neural network model built from single-source numerical simulation (CFD), a neural network model built from 20% wind tunnel data from a single source (0.2FD), and a neural network model built from 40% wind tunnel data (0.4FD) to evaluate the performance of the fusion method. The above models were used to predict on a prediction set of 80% wind tunnel data. For the axial force coefficient, the relative errors and coefficients of determination for CFD, 0.2FD, 0.4F, and the fusion model (MFNN) were 23.1%, 12.7%, 5.66%, and 4.41%; and 0.862, 0.935, 0.995, and 0.990, respectively. The predicted results are as follows: Figure 3 As shown.
[0037] Model Application: For the normal force coefficients of the reference state, repeat step 5), set the network architecture parameters neruons_per_layer_1 and neruons_per_layer_2, train and adjust the network architecture parameters, and obtain the reference state normal force coefficient prediction model.
[0038] For the full rudder deflection dataset, repeat step 5) for the normal force coefficient and axial force coefficient, setting the network architecture parameters neruons_per_layer_1 and neruons_per_layer_2. At this point, neruons_per_layer_1 is set to [7,32,16,8,1], where a 11 The value is 7, which represents the number of input parameters, a. 1n The value is 1, and neruons_per_layer_2 is set to [8,8,1], where b 11 The value is 7, which represents the number of input parameters, b. 1n The value is 1. By training and adjusting the network architecture parameters, a predictive model for the normal force coefficient under full rudder deflection can be obtained, and the predicted results are as follows. Figure 4 As shown.
[0039] The advantages of this invention compared to the prior art are: The hybrid scaling correction architecture based on neural network dynamic fitting transforms the static, constant correction factors in the traditional hybrid scaling correction method into intelligent factors that are dynamically generated by the neural network and change nonlinearly with the input parameters.
[0040] A phased decoupling training strategy for data scarcity can be adopted. For example, when there are two sources of data, the first-level network can be fully trained with a large amount of low-fidelity data, the parameters of the first-level network can be frozen, and the second-level correction network can be trained with only a small amount of high-fidelity data, so as to achieve the core goal of "reducing the demand for high-fidelity data".
[0041] A fusion framework suitable for various input parameters, including those including rudder deflection, expands application scenarios.
[0042] A scalable, multi-level progressive correction framework can extend the core idea of "benchmark prediction + dynamic neural network correction" to multiple levels. For example, when there are three types of multi-fidelity data, a three-level network can be constructed: the intermediate network performs a first-level correction on the low-level baseline, and the advanced network performs a second-level correction on the intermediate output.
[0043] Device Example 1 According to embodiments of the present invention, a pneumatic data fusion device based on cascaded correction is provided. Figure 5 This is a schematic diagram of a pneumatic data fusion device based on cascaded correction according to an embodiment of the present invention, as shown below. Figure 5 As shown, the aerodynamic data fusion device based on cascaded correction according to an embodiment of the present invention specifically includes: The data preprocessing module 50 is used to perform maximum and minimum normalization on all aerodynamic coefficients from all sources based on the lowest fidelity data to obtain the baseline dataset. Model building module 52 is used to build j neural network models, including j-1 correction networks and a first-level network. It uses the Adam optimizer and takes the sum of the loss functions of the j neural networks as the final loss function to build a multi-level fusion model, where j is a natural number. The training evaluation module 54 is used to set the network structure parameters of each neural network based on the baseline dataset, train the multi-level fusion model using a phased decoupling training strategy to obtain the aerodynamic coefficient prediction model, define the relative error, and use the normalized relative error and the coefficient of determination to evaluate the accuracy of the aerodynamic coefficient prediction model. The prediction module 56 is used to obtain the aerodynamic coefficients by inputting operating condition parameters based on the aerodynamic coefficient prediction model.
[0044] The embodiments of the present invention are device embodiments corresponding to the above method embodiments. The specific operation of each module can be understood with reference to the description of the method embodiments, and will not be repeated here.
[0045] Device Example 2 This invention provides an electronic device, such as... Figure 6 As shown, it includes: a memory 60, a processor 62, and a computer program stored in the memory 60 and executable on the processor 62, wherein the computer program, when executed by the processor 62, performs the steps as described in the method embodiment.
[0046] Device Example 3 This invention provides a computer-readable storage medium storing an information transmission implementation program, which, when executed by a processor 62, performs the steps described in the method embodiment.
[0047] The computer-readable storage media described in this embodiment include, but are not limited to, ROM, RAM, disk, or optical disk.
[0048] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.
Claims
1. A method for aerodynamic data fusion based on cascaded correction, characterized in that, include: All aerodynamic coefficients from all sources are subjected to maximum and minimum normalization based on the lowest fidelity data to obtain the baseline dataset. Establish j neural network models, including j-1 correction networks and a first-level network. Use the Adam optimizer and use the sum of the loss functions of the j neural networks as the final loss function to establish a multi-level fusion model, where j is a natural number. Based on the baseline dataset, the network structure parameters of each neural network are set, and the multi-level fusion model is trained using a phased decoupling training strategy to obtain the aerodynamic coefficient prediction model. The relative error is defined, and the accuracy of the aerodynamic coefficient prediction model is evaluated using the normalized relative error and the coefficient of determination. Based on the aforementioned aerodynamic coefficient prediction model, the aerodynamic coefficients are obtained by inputting operating condition parameters.
2. The method according to claim 1, characterized in that, All aerodynamic coefficients from all sources are subjected to max-min normalization based on the lowest fidelity data to obtain the baseline dataset, which specifically includes: The aerodynamic coefficients from j sources are sorted according to data fidelity. Using the aerodynamic coefficient with the lowest fidelity as the benchmark, the aerodynamic coefficients from j sources are subjected to max-min normalization to obtain the benchmark dataset.
3. The method according to claim 1, characterized in that, Establish j neural network models, including j-1 correction networks and a first-level network. Use the Adam optimizer and take the sum of the loss functions of the j neural networks as the final loss function. The multi-level fusion model specifically includes: The first-level neural network is constructed using the array variable `neruons_per_layer_1` to represent the number of grid layers and the number of neurons in each layer. `neruons_per_layer_1` is a one-dimensional array [a 11 ,a 12 ,…,a 1n ], a 11 Let a be the number of input parameters x1 in the first-level neural network. 12 to a 1,n-1 Let a be the number of neurons in the neural network from layer 2 to layer (n-1). 1n To determine the number of output parameters, softplus is used as the activation function to establish the first-level neural network, whose output is y1, y1=nn(x1); Establish the i-th level correction network, where i is greater than 1: use the array variable `neruons_per_layer_i` to represent the number of grid layers and the number of neurons in each layer. `neruons_per_layer_i` is a one-dimensional array [b i1 ,b i2 ,…,b ii ,…,b in ], b i1 Input parameters x for the i-th level network i The number of parameters is a, which is the number of input parameters a of the (i-1)th level network. i-1,1 Add the number of output parameters a of the (i-1)th level network i-1,n , that is, x i =[x i-1 ,y i-1 ], b i2 to b i,n-1 b represents the number of neurons in the neural network from layer 2 to layer (n-1). in To determine the number of output parameters, softplus is used as the activation function, and the incremental correction factor delta is set. i =nn(x i The scaling correction factor ρ(rho) is set as a parameter of the neural network, and the output of the i-th level correction network is y. i =rho*y i-1 +delta i ; Set up a neural network model with j neural networks, i.e., j-1 corrected network number and first-level network. Use the Adam optimizer and use mse as the loss function of the multi-level fusion architecture. The loss function of the multi-level fusion architecture is obtained by summing the loss functions of j neural networks. The damage function of each neural network is the mse of its output and the corresponding ground truth value. Establish a multi-level fusion model.
4. The method according to claim 1, characterized in that, Based on the baseline dataset, the network structure parameters of each neural network are set, and a phased decoupling training strategy is used to train the multi-level fusion model to obtain the aerodynamic coefficient prediction model, which specifically includes: Based on the baseline dataset, the network structure parameter neruons_per_layer_i of each neural network is set. The first-level neural network is trained using low-fidelity data, and the parameters of other correction networks are frozen. Then, the parameters of the first to (i-1)th level neural networks are frozen, and the i-th level correction network is trained using the i-th level fidelity data. The training is gradually carried out up to the j-th level correction network to complete the training of the entire multi-level fusion model.
5. The method according to claim 1, characterized in that, The relative error is defined, and the accuracy of the aerodynamic coefficient prediction model is evaluated using the normalized relative error and the coefficient of determination. Specifically, this includes: According to the definition of relative error in Formula 1, the accuracy of the model is evaluated using relative error and coefficient of determination. The model is compared with a neural network model built from low-fidelity data from a single source, a neural network model built from j-th level fidelity data from a single source, and a neural network model built from j-th level fidelity data from a single source to evaluate the performance of the fusion method. The j-th level fidelity data used for training is twice the j-th level fidelity data used for training from a single source. Official 1; Where N represents the total number of samples in the prediction set, i represents the i-th sample point, and y true This represents the true value of the predictor variable, when y true Less than 1 e-3 When this happens, skip the sample point and do not calculate its relative error, y predict This represents the predicted value of the predictor variable by the fusion framework.
6. A pneumatic data fusion device based on cascaded correction, characterized in that, include: The data preprocessing module is used to perform max-min normalization on all aerodynamic coefficients from all sources based on the lowest fidelity data to obtain the baseline dataset. The model building module is used to build j neural network models, including j-1 correction networks and a first-level network. It uses the Adam optimizer and uses the sum of the loss functions of the j neural networks as the final loss function to build a multi-level fusion model, where j is a natural number. The training and evaluation module is used to set the network structure parameters of each neural network based on the baseline dataset, train the multi-level fusion model using a phased decoupling training strategy to obtain the aerodynamic coefficient prediction model, define the relative error, and use the normalized relative error and the coefficient of determination to evaluate the accuracy of the aerodynamic coefficient prediction model. The prediction module is used to obtain aerodynamic coefficients by inputting operating condition parameters based on the aerodynamic coefficient prediction model.
7. The apparatus according to claim 6, characterized in that, The data preprocessing module is specifically used for: The aerodynamic coefficients from j sources are sorted according to data fidelity. Using the aerodynamic coefficient with the lowest fidelity as the benchmark, the aerodynamic coefficients from j sources are subjected to maximum-minimum normalization to obtain the benchmark dataset. The model building module is specifically used for: The first-level neural network is constructed using the array variable `neruons_per_layer_1` to represent the number of grid layers and the number of neurons in each layer. `neruons_per_layer_1` is a one-dimensional array [a 11 ,a 12 ,…,a 1n ], a 11 Let a be the number of input parameters x1 in the first-level neural network. 12 to a 1,n-1 Let a be the number of neurons in the neural network from layer 2 to layer (n-1). 1n To determine the number of output parameters, softplus is used as the activation function to establish the first-level neural network, whose output is y1, y1=nn(x1); Establish the i-th level correction network, where i is greater than 1: use the array variable `neruons_per_layer_i` to represent the number of grid layers and the number of neurons in each layer. `neruons_per_layer_i` is a one-dimensional array [b i1 ,b i2 ,…,b ii ,…,b in ], b i1 Input parameters x for the i-th level network i The number of parameters is a, which is the number of input parameters a of the (i-1)th level network. i-1,1 Add the number of output parameters a of the (i-1)th level network i-1,n , that is, x i =[x i-1 ,y i-1 ], b i2 to b i,n-1 b represents the number of neurons in the neural network from layer 2 to layer (n-1). in To determine the number of output parameters, softplus is used as the activation function, and the incremental correction factor delta is set. i =nn(x i The scaling correction factor ρ(rho) is set as a parameter of the neural network, and the output of the i-th level correction network is y. i =rho*y i-1 +delta i ; Set up a neural network model with j neural networks, i.e., j-1 corrected network number and first-level network. Use the Adam optimizer and use mse as the loss function of the multi-level fusion architecture. The loss function of the multi-level fusion architecture is obtained by summing the loss functions of j neural networks. The damage function of each neural network is the mse of its output and the corresponding ground truth value. Establish a multi-level fusion model.
8. The apparatus according to claim 6, characterized in that, The training evaluation module is specifically used for: Based on the baseline dataset, set the network structure parameter neruons_per_layer_i for each neural network, train the first-level neural network using low-fidelity data, freeze the other correction network parameters, then freeze the parameters of the first to (i-1)th level neural networks, train the i-th level correction network using the i-th level fidelity data, and gradually train up to the j-th level correction network to complete the training of the entire multi-level fusion model. According to the definition of relative error in Formula 1, the accuracy of the model is evaluated using relative error and coefficient of determination. The model is compared with a neural network model built from low-fidelity data from a single source, a neural network model built from j-th level fidelity data from a single source, and a neural network model built from j-th level fidelity data from a single source to evaluate the performance of the fusion method. The j-th level fidelity data used for training is twice the j-th level fidelity data used for training from a single source. Official 1; Where N represents the total number of samples in the prediction set, i represents the i-th sample point, and y true This represents the true value of the predictor variable, when y true Less than 1 e-3 When this happens, skip the sample point and do not calculate its relative error, y predict This represents the predicted value of the predictor variable by the fusion framework.
9. An electronic device, characterized in that, include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, implements the steps of the aerodynamic data fusion method based on cascaded correction as described in any one of claims 1 to 5.
10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores an implementation program for information transmission, which, when executed by a processor, implements the steps of the aerodynamic data fusion method based on cascaded correction as described in any one of claims 1 to 5.