A method for fast prediction of aerodynamic characteristics of soft tail attached behind high-speed projectile

Abstract

The application discloses a kind of for high-speed projectile rear soft tail's aerodynamic characteristic fast prediction method.Establish the parameterization characterization system of soft tail stability augmentation characteristic, determine the key input parameter of influence soft tail response and the output parameter to be predicted;High-fidelity sample data is obtained using CFD / CSD two-way fluid-structure coupling method, and the output data is subjected to frequency domain feature extraction and statistical quantity calculation, and training set and verification set are divided;Multi-channel deep neural network including feature encoding layer, intermediate hidden layer and prediction output layer is constructed;Two-stage training strategy is used to complete model training by designing composite loss function;The model trained is deployed for fast prediction, and incremental updating is carried out on the model using elastic weight consolidation method.The application realizes end-to-end fast prediction of soft tail aerodynamic characteristics through deep neural network, greatly improves the calculation efficiency while ensuring the prediction accuracy, and can effectively support the rapid design and optimization iteration of soft tail parameters.

Description

Technical Field

[0001] This invention relates to the fields of aircraft aerodynamics and rapid prediction technology, specifically a method for rapidly calculating the aerodynamic characteristics of a flexible tail attached to the tail of a high-speed projectile. Background Technology

[0002] To improve flight stability during high-speed missile flight, an effective technical solution is to attach a flexible tail made of a flexible material to the missile's rear. Under aerodynamic forces, the flexible tail undergoes adaptive bending deformation, generating additional stabilizing torque, thereby suppressing pitch oscillations and significantly improving flight stability. Therefore, accurately obtaining the aerodynamic characteristics of the flexible tail during flight is a prerequisite for evaluating its stabilization effect and optimizing its geometry and material parameters.

[0003] Currently, the main method for obtaining the aerodynamic characteristics of soft tails is the coupled computational fluid dynamics and structural dynamics (CFD / CSD) approach. This method calculates the flow field around the soft tail numerically, achieving high computational accuracy, but it is computationally time-consuming, requiring several days for a single operating condition. Furthermore, mesh generation, solver settings, and convergence judgment all rely on experience, making rapid iteration difficult and resulting in high overall costs. Therefore, there is an urgent need for a method for predicting the aerodynamic characteristics of soft tails that balances computational speed and accuracy, providing predictions with engineering-level precision in a shorter time to support the rapid design and optimization of soft tail parameters.

[0004] Currently, no relevant technical content has been proposed for a rapid calculation method that uses soft tails to provide stabilization for high-speed projectiles. Summary of the Invention

[0005] The purpose of this invention is to provide a rapid prediction method for the aerodynamic characteristics of a soft tail attached to a high-speed projectile. By constructing a deep neural network model, a mapping relationship between soft tail parameters and aerodynamic characteristics is established, thereby achieving rapid prediction of the aerodynamic characteristics of the soft tail.

[0006] The technical solution for achieving the objective of this invention is as follows:

[0007] A method for rapid prediction of aerodynamic characteristics for a high-speed projectile with a soft tail includes:

[0008] Step 1: Determine the input parameters affecting the soft-tail response and the output parameters to be predicted; the input parameters include angle of attack α, Mach number Ma, soft-tail length l, soft-tail diameter d, soft-tail density ρ, and soft-tail elastic modulus E; the output parameters include the soft-tail drag coefficient. Pitching moment coefficient of the soft-tailed projectile The growth rate of the pitching moment coefficient of the soft-tailed projectile relative to the bare projectile Location of the pressure center of the bare projectile Position of pressure center of the soft-tailed projectile , rearward displacement of the pressure center of the attached soft-tailed projectile ;

[0009] Step 2: Perform numerical simulations on different combinations of input parameters to obtain sample data, and divide the data into training and validation sets;

[0010] Step 3: Construct a multi-channel deep neural network, including a feature encoding layer, intermediate hidden layers, and a prediction output layer; the feature encoding layer input parameter vector X=[α,Ma,l,d,ρ,E], consists of 3 fully connected layers, with ReLU activation function, and pre-... , , ;

[0011] Step 4: Design a composite loss function and adopt a two-stage training strategy to complete the training of the multi-channel deep neural network. In the first stage, pre-training is performed using a simulation dataset. In the second stage, experimental data is introduced to fine-tune the multi-channel deep neural network model. The parameters inside the neural network corresponding to the output parameters that meet the prediction accuracy are frozen, and additional training is performed only for the output parameters that do not meet the accuracy.

[0012] Step 5: Deploy the trained multi-channel deep neural network for prediction and output soft-tail dynamic response feature parameters;

[0013] Step 6: Use the elastic weight consolidation method to incrementally update the multi-channel deep neural network: After the multi-channel deep neural network is trained, calculate and save the Fisher information of each parameter and the original internal parameter values ​​of the multi-channel deep neural network. When new simulation data is obtained, construct the EWC loss function to update the multi-channel deep neural network. After the update, recalculate the prediction accuracy of the new multi-channel deep neural network on the old validation set. If the accuracy drops beyond the preset threshold, increase the tradeoff coefficient and perform incremental updates again.

[0014] The significant advantages of this invention compared to existing technologies are:

[0015] (1) This invention adopts a deep neural network end-to-end prediction method, which significantly shortens the traditional CFD / CSD bidirectional fluid-structure interaction calculation time through offline training and online prediction, providing a solution to the problem that traditional methods have too long calculation time and are difficult to support rapid parameter scanning and design iteration.

[0016] (2) This invention integrates static feature encoding (geometric and material parameters) with dynamic temporal encoding (fluid-structure interaction evolution process) by constructing a multi-channel deep neural network. Compared with a single fully connected network, it can simultaneously capture the static properties and dynamic response features of the soft tail, which significantly improves the prediction accuracy. Attached Figure Description

[0017] Figure 1 A simplified schematic diagram of a soft tail model attached to the rear of the projectile.

[0018] Figure 2 This is a schematic diagram of the overall process.

[0019] Figure 3 A schematic diagram showing the setup of the computing domain.

[0020] Figure 4 This is a partial simulation result cloud map.

[0021] Figure 5 Neural network construction framework diagram. Detailed Implementation

[0022] The present invention will now be described in further detail with reference to specific implementation examples and accompanying drawings.

[0023] In this example, the projectile has a maximum diameter D = 28 mm and a length L = 130 mm, with a cross-shaped tail fin. The projectile flies in the air at different Mach numbers (Ma) and angles of attack (α), and is equipped with cylindrical soft tails of varying diameters (d), lengths (l), densities (ρ), and elastic moduli (E), such as... Figure 1 As shown. The implementation process of this invention is as follows. Figure 2 As shown.

[0024] Step 1: Establish a parameterized characterization system for the stabilization characteristics of soft tails.

[0025] Define the input and output parameters. In this example, the input parameters include: angle of attack α, Mach number Ma, soft-tail length l, soft-tail diameter d, soft-tail density ρ, and soft-tail elastic modulus E. The output parameter includes: soft-tail drag coefficient. Pitching moment coefficient of the soft-tailed projectile The growth rate of the pitching moment coefficient of the soft-tailed projectile relative to the bare projectile Location of the pressure center of the bare projectile Position of pressure center of the soft-tailed projectile , The rearward displacement of the pressure center of the soft-tailed projectile .

[0026] Step 2: Construct a high-fidelity sample dataset and divide it into training and validation sets.

[0027] Numerical simulations of different input parameter combinations were performed using a two-way fluid-structure interaction (CFD / CSD) method. The fluid domain employed the finite volume method based on the Reynolds-averaged Navier-Stokes equations, with the SST k-ω model selected for turbulence. The solid domain utilized the finite element method, setting material properties for the solid structure, establishing the fluid-structure interface, and calculating mesh deformation using the radial basis function method. A loosely coupled approach was employed to complete the two-way coupled calculations. In this example, the specific operating conditions are set as follows: (1) Keep the parameters of flexible tail diameter d=5mm, length l=2L, density ρ=1140kg / m³, and elastic modulus E=2GPa unchanged, and only change the incoming Mach number (Ma=1.5, 1.8, 2.0) or angle of attack (α=10°, 20°, 30°), for a total of 9 operating conditions; (2) Keep the flexible tail density ρ=1140kg / m³, elastic modulus E=2GPa, and the incoming Mach number Ma=2.0 and angle of attack α=30° unchanged, and only change the flexible tail diameter (d=5mm, 5.5mm, 6mm) or flexible tail length (l=L, 1.5L, 2L), for a total of 9 operating conditions; (3) Keeping the soft-tail diameter d=5mm, length l=2L, incoming Mach number Ma=2.0, and angle of attack α=30° constant, only changing the soft-tail elasticity model (E=2GPa, 3GPa, 4GPa) or soft-tail density (ρ=1140kg / m³, 1240kg / m³, 1340kg / m³), a total of 9 operating conditions were implemented. A total of 27 operating conditions are set as shown in Table 1 below. Specific computational domain settings are as follows... Figure 3 As shown, some of the simulation results are represented by cloud plots. Figure 4 As shown in the figure, the vorticity near the soft tail is displayed. and the pressure coefficient near the projectile body This allows for a clearer display of the aerodynamic characteristics near the soft tail. The aforementioned core parameter values ​​are then transformed into a core input parameter vector. .

[0028] Table 1

[0029]

[0030] All sample data is randomly divided into training and validation sets proportionally. In this example, an 8:2 ratio is used, meaning 80% of the samples are used for training and 20% for validation. Stratified random sampling is employed to ensure consistent distribution of parameter ranges between the training and validation sets, avoiding model bias caused by uneven data distribution. The specific division process is as follows: First, all sample data is randomly shuffled to eliminate any original order bias. Second, the number of samples in the training and validation sets is calculated according to a preset ratio. Then, a corresponding number of samples are sequentially drawn from the shuffled data and assigned to the training and validation sets respectively. Finally, the similarity of the value ranges and distributions of the input parameters in the training and validation sets is checked; if significant differences are found, the random division is repeated.

[0031] Step 3: Construct a multi-channel deep neural network, including a feature encoding layer, intermediate hidden layers, and a prediction output layer.

[0032] Feature coding layer input parameter vector It has a dimension of 6 and consists of 3 fully connected layers with 64, 128, and 64 neurons in each layer, respectively. The activation function is ReLU (Modified Linear Unit), and its derivative is:

[0033]

[0034] in, This is represented as a weighted input matrix for a certain layer. Furthermore, ReLU itself is nonnegative, giving it a natural advantage in handling engineering data, and no activation function is set between the final hidden layer and the output layer; regarding learning parameter settings, the learning rate of the input parameters... The Decay pattern is used in conjunction with the Adam optimizer, meaning that the learning rate of each parameter increases with the number of iterations. The learning rate will gradually decrease, and the Adam optimizer can further adaptively adjust the learning rate for each parameter; predicting separately. , , The specific structure of the neural network is as follows: Figure 5 As shown;

[0035] Step 4: Design a composite loss function and use a two-stage training strategy to complete model training.

[0036] Using a multi-task learning framework, a composite loss function is defined:

[0037]

[0038] in, For mean square error loss, For physical constraint regularization terms, specifically:

[0039]

[0040]

[0041] in, The number of samples in the training set. For the first The first sample The actual values ​​of each output parameter for The corresponding predicted value, For the first The weighting coefficients of each output parameter. These are the weighting coefficients for the physical constraint regularization term. Let j be the predicted value of the additional pitching moment coefficient of the soft tail for the j-th sample. This is the predicted value of the soft tail drag coefficient. For the first The soft-tail length of each sample, For the first The angle of attack of each sample. In this example, to All values ​​are 0.1. The initial learning rate is set to 0.2. The training strategy employs a two-stage approach: the first stage uses a simulation dataset for pre-training with an initial learning rate of 0.001 and a cosine annealing decay strategy; after pre-training, a small amount of high-precision experimental data (i.e., data obtained through experiments under a set of six input parameter conditions) is introduced. Fine-tuning the network using data from the three output parameters (i.e., using...) This function freezes the parameters within the neural network corresponding to the output parameters that meet the prediction accuracy target, and only performs additional training on the output parameters with poor accuracy.

[0042] Step 5: Deploy the trained model for fast prediction and output soft-tailed dynamic response feature parameters.

[0043] Once trained, the deep neural network model is deployed as a prediction service, for new input parameter vectors... The model calculates three predicted values ​​within a short time using forward propagation. On the validation set, the prediction results of this invention are compared with the actual CFD / CSD values ​​to calculate the mean relative error and coefficient of determination. The formula for calculating the mean relative error is as follows:

[0044]

[0045] in, For the first The actual values ​​of each output parameter for The corresponding predicted value.

[0046] The formula for calculating the coefficient of determination is as follows:

[0047]

[0048] in, This is the mean of the true values ​​of the validation set samples.

[0049] If the mean relative error on the validation set meets the engineering requirements (in this embodiment, MRE < 10%), and If the model deployment is successful, it is usable; if the accuracy does not meet the requirements, the network hyperparameters should be adjusted first, and then the model should be retrained by supplementing simulation data.

[0050] Step 6: Use the elastic weight consolidation method to incrementally update the model.

[0051] When new CFD / CSD simulation or experimental data is obtained, the Elastic Weight Consolidation (EWC) method is used to implement incremental updates. The specific loss function of EWC is as follows:

[0052] .

[0053]

[0054] in, The total loss function during incremental updates. The loss function for the new simulation data, This is a matrix containing the set of internal parameters of each layer within the neural network, such as biases and weights. The subscript indicates the number of steps in the neural network learning process. The trainable parameter index is assigned a number; during model training, it's possible that some output parameters perform very well in training, while the prediction accuracy for others is not ideal. In this case, we need to add more simulation or experimental data for retraining. The index corresponding to the well-trained output parameters... Save these parameters, which are less likely to change in subsequent training, as they become part of the old model. .and For the old model One trainable parameter value, For the first Fisher information of each trainable intrinsic parameter value (e.g., bias and weight matrix for each layer of the network), This is the weighting factor (taken as 1000 in this example). , as well as For the first New simulation or experimental data regarding the soft-tail drag coefficient The growth rate of the pitching moment coefficient of the soft-tailed projectile relative to the bare projectile and the rearward displacement of the pressure center of the soft-tailed projectile. The true value, , and It is the first New simulation or experimental data is added to a neural network model to predict the corresponding three output parameter values. This represents the number of samples in the training set.

[0055] The specific formula for calculating Fisher's information content is as follows:

[0056]

[0057] in, This refers to the number of old data samples. Old data refers to the initial data compared to the data added later in the training process, when the accuracy of some output parameters did not meet the requirements. This is the loss function for the old task, which is formally consistent with the loss function for the new simulation data mentioned above. For the first The output parameter matrix of the old data samples; the old task refers to the learning process inside the neural network when learning from old data. That is, the current model number. A number of trainable parameter values.

[0058] The above results show that the presence of the soft tail significantly enhances the flight stability of the projectile, and the stabilization effect increases with the angle of attack and the length of the soft tail. However, this also increases the additional drag on the projectile. In practical applications, appropriate soft tail parameters must be selected based on the specific application scenario. The specific process of incremental updates is as follows: First, after the old model is trained, the Fisher information of each parameter is calculated and saved. and various parameter values ​​inside the old neural network When new simulation data is obtained, the EWC loss function is constructed, and the Adam optimizer is used to update the model. After the update is completed, the prediction accuracy of the new model on the old validation set is recalculated to ensure that the model has not suffered catastrophic forgetting. If the accuracy drops beyond a preset threshold (set to 5% in this embodiment), it is appropriately increased. The values ​​are then incrementally updated again. Using the EWC method, the model can be rapidly iterated and optimized after receiving new data, without needing to be retrained from scratch.

[0059] Clearly, compared to traditional CFD / CSD bidirectional fluid-structure interaction simulations and the need for re-simulation for each new soft-tail design scenario, this invention's multi-channel deep neural network model offers a highly efficient and accurate solution. This model can autonomously learn from limited simulation data the nonlinear deformation characteristics of the soft-tail in high-speed airflow, the dynamic response of fluid-structure interaction, and the aerodynamic interference between the soft-tail and the projectile. The trained model can also achieve rapid forward prediction, significantly improving the iterative speed of soft-tail parameter design and optimization. Furthermore, to more accurately reflect the impact of each output parameter on the soft-tail stabilization effect, the model designs a composite loss function, introducing a physical constraint regularization term on top of the traditional mean square error loss. This ensures that the training process conforms to fundamental aerodynamic laws such as slender body theory, thereby more reasonably predicting the dynamic response characteristics of the soft-tail and the aerodynamic parameters of the projectile. Simultaneously, the model employs an elastic weight consolidation method to support incremental updates, enabling rapid iterative optimization after obtaining new data without retraining from scratch. In summary, the method of this invention can achieve rapid prediction and analysis of the aerodynamic characteristics of the soft tail attached to a high-speed projectile based on a trained deep neural network model, providing convenience for the design and optimization of soft tail stabilization schemes.

[0060] Obviously, the above embodiments of the present invention are merely examples to clearly illustrate the present invention, and are not intended to limit the implementation of the present invention. For those skilled in the art, other variations or modifications can be made based on the above description. It is impossible to exhaustively list all the implementation methods here. All obvious variations or modifications derived from the technical solutions of the present invention are still within the protection scope of the present invention.

Claims

1. A method for rapid prediction of aerodynamic characteristics of a soft tail attached to a high-speed projectile, characterized in that, include: Step 1: Determine the input parameters affecting the soft-tail response and the output parameters to be predicted; the input parameters include angle of attack α, Mach number Ma, soft-tail length l, soft-tail diameter d, soft-tail density ρ, and soft-tail elastic modulus E; the output parameters include the soft-tail drag coefficient. Pitching moment coefficient of the soft-tailed projectile The growth rate of the pitching moment coefficient of the soft-tailed projectile relative to the bare projectile Location of the pressure center of the bare projectile Position of pressure center of the soft-tailed projectile , rearward displacement of the pressure center of the attached soft-tailed projectile ; Step 2: Perform numerical simulations on different combinations of input parameters to obtain sample data, and divide the data into training and validation sets; Step 3: Construct a multi-channel deep neural network, including a feature encoding layer, intermediate hidden layers, and a prediction output layer; the feature encoding layer input parameter vector X=[α,Ma,l,d,ρ,E], consists of 3 fully connected layers, with ReLU activation function, and pre-... , , ; Step 4: Design a composite loss function and adopt a two-stage training strategy to complete the training of the multi-channel deep neural network. In the first stage, pre-training is performed using a simulation dataset. In the second stage, experimental data is introduced to fine-tune the multi-channel deep neural network model. The parameters inside the neural network corresponding to the output parameters that meet the prediction accuracy are frozen, and additional training is performed only for the output parameters that do not meet the accuracy. Step 5: Deploy the trained multi-channel deep neural network for prediction and output soft-tail dynamic response feature parameters; Step 6: Use the elastic weight consolidation method to incrementally update the multi-channel deep neural network: After the multi-channel deep neural network is trained, calculate and save the Fisher information of each parameter and the original internal parameter values ​​of the multi-channel deep neural network. When new simulation data is obtained, construct the EWC loss function to update the multi-channel deep neural network. After the update, recalculate the prediction accuracy of the new multi-channel deep neural network on the old validation set. If the accuracy drops beyond the preset threshold, increase the tradeoff coefficient and perform incremental updates again.

2. The rapid aerodynamic characteristic prediction method according to claim 1, characterized in that, The composite loss function is: in, For mean square error loss, For physical constraint regularization terms, specifically: in, This represents the total number of samples in the training set. For the first The first sample The actual values ​​of each output parameter for The corresponding predicted value, For the first The weighting coefficients of each output parameter. These are the weighting coefficients for the physical constraint regularization term. Let j be the predicted value of the additional pitching moment coefficient of the soft tail for the j-th sample. This is the predicted value of the soft tail drag coefficient. For the first The soft-tail length of each sample, For the first Angle of attack of each sample.

3. The rapid aerodynamic characteristic prediction method according to claim 1, characterized in that, The loss function of EWC is: in, The total loss function during incremental updates. The loss function for the new simulation data, It is a set matrix of internal parameters such as biases and weights of each layer within the neural network; For the old neural network A trainable intrinsic parameter value, For the first Fisher information for each trainable intrinsic parameter value This is a weighting factor.

4. The rapid aerodynamic characteristic prediction method according to claim 3, characterized in that, The formula for calculating Fisher's information content is: in, This represents the number of old data samples. The loss function for the old task. For the first The output parameter matrix of the old data sample For the new neural network A number of trainable parameter values.

5. The rapid aerodynamic characteristic prediction method according to claim 1, characterized in that, The training and validation sets are divided using stratified random sampling: First, all sample data are randomly shuffled to eliminate the original order bias; second, the number of samples in the training and validation sets is calculated according to a preset ratio; then, the corresponding number of samples are sequentially drawn from the shuffled data and assigned to the training and validation sets respectively; finally, the range and distribution of the input parameters in the training and validation sets are checked to see if they are similar. If the difference is greater than a set value, the random division is performed again.

6. The rapid aerodynamic characteristic prediction method according to claim 1, characterized in that, The numerical simulation adopted the CFD / CSD two-way fluid-structure interaction method. The fluid domain adopted the finite volume method based on the Reynolds-averaged Navier-Stokes equations, the turbulence model adopted the SST k-ω model, and the solid domain adopted the finite element method.

Images