A method for predicting the separation trajectory of external stores based on small sample size

Abstract

This invention relates to the field of aircraft external stores release and separation trajectory prediction technology, specifically a method for predicting external stores release and separation trajectories based on a small sample size. By establishing an external stores aerodynamic prediction model and a trajectory prediction model, and employing an iterative prediction method, the dependence on external stores release and separation datasets is effectively reduced, improving prediction accuracy and efficiency.

Description

[0001] Technical Field This invention relates to the field of aircraft external stores deployment and separation trajectory prediction technology, specifically a method for predicting external stores deployment and separation trajectories based on a small sample size. Background Technology

[0002] Accurate calculation of the trajectory of external stores during the deployment and separation process is crucial for flight safety and mission completion. Traditional methods for obtaining external store separation trajectories rely on numerical simulations based on computational fluid dynamics (CFD) or wind tunnel tests. With the development of machine learning algorithms and technologies, machine learning methods, represented by neural networks, have begun to be applied to external store deployment and separation prediction. For example, reference 1 (External Store Deployment and Separation Prediction Based on Feedforward Neural Network, *Journal of Ballistics*, 2023.09) uses a feedforward neural network to accurately model and predict the trajectory and attitude of external stores during deployment and separation. Conventional external store deployment and separation trajectory prediction methods typically rely on training neural networks with large datasets to improve the network's prediction accuracy. However, in practical applications, obtaining a large amount of high-quality external store deployment and separation datasets is often costly and time-consuming. Specifically, the following aspects limit the application of traditional methods: First, data acquisition is difficult. The deployment and separation process of aircraft involves complex aerodynamic environments and variable flight conditions, making the acquisition of large amounts of high-quality experimental or simulation data costly. Second, experimental data measurement is complex. Testing the external stores deployment and separation trajectory requires high-precision measurement equipment and specialized technicians; the data measurement process is complex and time-consuming. Thirdly, there is the issue of data sparsity. Under certain specific flight conditions, the acquired external stores deployment and separation data may be very sparse, making it difficult to meet the needs of traditional neural network training.

[0003] Therefore, achieving accurate prediction of the deployment and separation trajectory of external attachments under limited data conditions has become a pressing technical challenge. Traditional neural network-based methods for external attachment trajectory prediction use only the external attachment's shape characteristics as network input, requiring a large dataset to establish a nonlinear mapping between the external attachment's shape characteristics and the separation trajectory. In reality, during the deployment and separation process, there is a relationship between the external attachment's aerodynamic history (i.e., the aerodynamic components experienced by the external attachment at each separation time step) and its trajectory history (i.e., the center-of-gravity position component of the external attachment at each separation time step). The external attachment's position determines its flow field distribution, thus affecting the aerodynamic forces experienced by the external attachment. Conversely, the external attachment's aerodynamic forces determine its motion, thus affecting its position; the two are coupled. Based on this coupling phenomenon, the external attachment's aerodynamic history can be used as supplementary input to the neural network, increasing the dimensionality of the neural network's input features and achieving high-precision separation trajectory prediction with limited data. Summary of the Invention

[0004] The purpose of this invention is to propose a method for predicting the separation trajectory of deployed external objects based on a small sample size. This method can accurately predict the separation trajectory of deployed external objects even with limited data, thus solving the problems of high difficulty and high cost in obtaining the separation trajectory of external objects using traditional methods.

[0005] Technical solution of the present invention: In order to achieve the above-mentioned objective, according to the first aspect of the present invention, the present invention adopts the following technical solution:

[0006] A method for predicting the separation trajectory of deployed external objects based on a small sample size is proposed. The specific steps include:

[0007] Step 1: Select N attachments and obtain the external coordinates of each attachment through experimental testing or numerical simulation, as well as the separation trajectory and aerodynamic history of the attachment during the Nt separation time steps during the deployment and separation process; the separation trajectory is the coordinates of the center of gravity of the attachment corresponding to the Nt separation time steps; the aerodynamic history is the collection of aerodynamic forces of the attachment at each time step.

[0008] In one possible implementation, N does not exceed 100. When N does not exceed 100, the method can achieve trajectory prediction with a small sample size.

[0009] In one possible embodiment, the specific process of obtaining the external shape coordinates through numerical simulation includes:

[0010] Import the geometric model of the external attachment into the mesh generation software, perform mesh generation on the surface and flow field of the external attachment, and then extract the coordinates of the mesh points on the surface of the external attachment as the external attachment's shape coordinates.

[0011] In one possible embodiment, the specific process of obtaining the separation trajectory and the aerodynamic history of the external attachments during the separation process through numerical simulation includes:

[0012] The flow field mesh of the external attachment is read using computational fluid dynamics software. Then, the deployment and separation conditions of the external attachment are set, including Mach number, angle of attack, sideslip angle, and height. The aerodynamic forces acting on the external attachment at the current time step are calculated, and the position of the external attachment at the next time step is updated based on the aerodynamic forces acting on the external attachment. This process is repeated until the separation motion simulation of all Nt time steps is completed. The separation trajectory is obtained by reading the coordinates of the center of gravity of the external attachment at each time step. The aerodynamic forces acting on the external attachment at each time step are read as the aerodynamic history of the external attachment during the separation process.

[0013] Step 2: Create an aerodynamic prediction network model. Use the external object's shape coordinates and trajectory obtained in Step 1 as inputs and the aerodynamic history of the external object as outputs to train the aerodynamic prediction network model.

[0014] In one possible embodiment, the aerodynamic prediction network model specifically includes:

[0015] The shape coordinate input layer, flattening layer, fully connected layer 1, and then the input point 1 of the merge layer is connected. The trajectory input layer is connected to the long short-term memory network layer, and then the input point 2 of the merge layer is connected. The output point of the merge layer is connected to fully connected layer 2, fully connected layer 3, fully connected layer 4, renormalization layer and output layer in sequence.

[0016] The flattening layer reshapes the input data dimensions into a single dimension;

[0017] The mathematical expression for a fully connected layer is:

[0018] (1)

[0019] in, It is the input value of the i-th neuron; These are the weights connecting the i-th input neuron and the j-th output neuron; It is the bias of the j-th output neuron;

[0020] The output gate expression for a Long Short-Term Memory (LSTM) network layer is:

[0021] (2)

[0022] in, It is the output of the output gate at time step t; and These are the weight matrix and bias of the output gate, respectively; It is the output of the hidden state at time step t-1;

[0023] The remodeling layer remodels the data dimensions to be consistent with the output layer dimensions;

[0024] Step 3: Create a trajectory prediction network model. Use the external object's shape coordinates and aerodynamic history obtained in Step 1 as inputs and the external object's trajectory as output to train the trajectory prediction network model.

[0025] In one possible embodiment, the trajectory prediction network model specifically includes:

[0026] The external coordinate input layer is connected to the flattening layer and the fully connected layer 1. Then, the input point 1 of the merged layer is connected. The aerodynamic history input layer is connected to the long short-term memory network layer and then to the input point 2 of the merged layer. The output point of the merged layer is connected to the fully connected layer 2, the fully connected layer 3, the fully connected layer 4, the renormalization layer, and the output layer in sequence.

[0027] The flattening layer reshapes the input data dimensions into a single dimension;

[0028] The mathematical expression for a fully connected layer is:

[0029] (3)

[0030] in, It is the input value of the i-th neuron; These are the weights connecting the i-th input neuron and the j-th output neuron; It is the bias of the j-th output neuron;

[0031] The output gate expression for a Long Short-Term Memory (LSTM) network layer is:

[0032] (4)

[0033] in, It is the output of the output gate at time step t; and These are the weight matrix and bias of the output gate, respectively; It is the output of the hidden state at time step t-1;

[0034] Step 4: Select an external attachment, initialize its trajectory history and aerodynamic history to 0, and use the external attachment's external coordinates and trajectory as input to predict and update the external attachment's aerodynamic history through a trained aerodynamic prediction network model; use the external attachment's external coordinates and aerodynamic history as input to predict and update the external attachment's trajectory through a trained trajectory prediction network model; iterate this process, predicting and updating the aerodynamic history and trajectory sequentially, until the preset number of iterations is reached; after the iteration is completed, the trajectory output by the trajectory prediction network model is the external attachment's deployment and separation trajectory.

[0035] Preferably, in step 2, the aerodynamic prediction network model requires both input and output datasets for training to achieve the prediction effect. The data obtained in step 1 is organized into the input and output datasets needed for training the aerodynamic prediction network model. The input dataset includes an external attachment shape coordinate matrix and a separation trajectory history matrix. The external attachment shape coordinate matrix is ​​an N×Np×n matrix, representing N external attachment samples. Each sample is described by Np point clouds, and the coordinate dimension of each point cloud is n. For two-dimensional cases, n=2; for three-dimensional cases, n=3. The separation trajectory matrix is ​​an N×Nt×m matrix, representing N external attachment samples. The separation time of each sample is described by Nt discrete time steps, and the trajectory data dimension of each time step is m. For two-dimensional cases, m=3; for three-dimensional cases, m=6. The output dataset contains an external attachment aerodynamic history matrix, which is also an N×Nt×m matrix, representing N external attachment samples. The separation time of each sample is described by Nt discrete time steps, and the aerodynamic data dimension of each time step is m. For the two-dimensional case, m=3; for the three-dimensional case, m=6.

[0036] Preferably, in step 2, the aerodynamic prediction network model uses the mean squared error (MSE) as the loss function, where MSE is defined as:

[0037] (5)

[0038] Where n is the number of data samples; It is the true value of the i-th data sample; It is the predicted value of the i-th data sample.

[0039] Preferably, in step 2, the optimization training method for the aerodynamic prediction network model is the Adam algorithm.

[0040] Preferably, in step 3, the trajectory prediction network model requires both an input dataset and an output dataset for training to achieve the prediction effect. The data obtained in step 1 is organized into the input and output datasets needed for training the trajectory prediction network model. The input dataset includes an external attachment shape coordinate matrix and an aerodynamic history matrix. The external attachment shape coordinate matrix is ​​an N×Np×n matrix, representing N external attachment samples. Each sample is described by Np point clouds, and the coordinate dimension of each point cloud is n. For two-dimensional cases, n=2; for three-dimensional cases, n=3. The aerodynamic history matrix is ​​an N×Nt×m matrix, representing N external attachment samples. The separation time of each sample is described by Nt discrete time steps, and the aerodynamic data dimension of each time step is m. For two-dimensional cases, m=3; for three-dimensional cases, m=6. The output dataset contains an external attachment trajectory matrix, which is an N×Nt×m matrix, representing N external attachment samples. The separation time of each sample is described by Nt discrete time steps, and the trajectory data dimension of each time step is m. For the two-dimensional case, m=3; for the three-dimensional case, m=6.

[0041] Preferably, in step 3, the trajectory prediction network model uses the mean squared error (MSE) as the loss function, where MSE is defined as:

[0042] (6)

[0043] Where n is the number of data samples; It is the true value of the i-th data sample; It is the predicted value of the i-th data sample.

[0044] Preferably, in step 3, the optimization training method for the trajectory prediction network model is the Adam algorithm.

[0045] Preferably, in step 4, the preset number of iterations is no less than 10.

[0046] The advantages of this invention are as follows: 1. The method described in this invention can achieve rapid and accurate prediction of the trajectory of external attachment deployment and separation even with a small sample size. By establishing an aerodynamic prediction model and a trajectory prediction model for the external attachment, and employing an iterative prediction method, the dependence on the external attachment deployment and separation dataset is effectively reduced, improving prediction accuracy and efficiency. Specifically, in experimental verification, with a dataset of 80 samples, the prediction results of this invention are almost identical to the CFD calculation results, while the calculation speed is significantly improved compared to CFD calculation, completing trajectory prediction within 1 second.

[0047] 2. Compared to directly predicting the separation trajectory of an external attachment based on its external shape coordinates, the method described in this invention improves the accuracy of the trajectory prediction model in the case of small samples by establishing an aerodynamic prediction model for the external attachment and predicting its aerodynamic history as a feature supplement to the external shape coordinates. Attached Figure Description

[0048] Figure 1 This is a schematic diagram of the iterative prediction process of an external object deployment and separation trajectory prediction method based on a small sample size, as described in this application.

[0049] Figure 2 The shape of all external attachments in the specific embodiments of the method described in this application;

[0050] Figure 3 The two-dimensional trajectory and attitude prediction effect of a specific embodiment of the method described in this application;

[0051] The figure shows trajectory predictions for four external attachment samples. The horizontal and vertical coordinates of the center of gravity and the attitude angle of the external attachments are denoted as x, y, and Theta, respectively. The CFD calculation results are represented by straight lines, and the predicted values ​​are represented by dots. Figure 4 To demonstrate the comparative effects of two-dimensional trajectory and attitude prediction, trajectory prediction was performed on four external attachment samples in the figure. The horizontal and vertical coordinates of the center of gravity of the external attachment and the attitude angle are denoted as x, y, and Theta, respectively. The CFD calculation results are represented by straight lines, and the predicted values ​​are represented by dots. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0053] The features and illustrative embodiments of various aspects of the present invention will now be described in detail. Numerous specific details are set forth in the following detailed description to provide a thorough understanding of the invention. However, it will be apparent to those skilled in the art that the invention may be practiced without requiring some of these specific details. The following description of embodiments is merely intended to provide a better understanding of the invention by illustrating examples of the invention. The invention is by no means limited to any specific setups and methods set forth below, but covers any improvements, substitutions, and modifications to structures, methods, and devices without departing from the spirit of the invention. Well-known structures and techniques are not shown in the drawings and the following description to avoid unnecessarily obscuring the invention.

[0054] It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other, and the various embodiments can be referenced and cited in each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0055] Example

[0056] A method for predicting the optimal center of gravity position of an aircraft based on a deep neural network is illustrated in the following diagram: Figure 1 As shown. Includes the following steps:

[0057] Step 1: Select 80 external items. The shapes of all external items are as follows: Figure 2 As shown. The geometric model of the external attachment is imported into the mesh generation software, and the surface and flow field of the external attachment are meshed. Then, the coordinates of a total of 256 mesh points on the surface of the external attachment are extracted as the external attachment's shape coordinates. The flow field mesh of the external attachment is read using computational fluid dynamics software. Then, the deployment and separation conditions of the external attachment are set, including Mach number, angle of attack, sideslip angle, height, etc., and the aerodynamic forces on the external attachment at the current time step are calculated. The position of the external attachment at the next time step is updated based on the aerodynamic forces on the external attachment. This process is repeated until the separation motion simulation of all 26 time steps is completed. The separation trajectory is obtained by reading the horizontal and vertical coordinates of the center of gravity and the attitude angle of the external attachment at each time step. The aerodynamic forces on the external attachment at each time step are read as the aerodynamic history of the external attachment during the separation process.

[0058] Step 2: Create an aerodynamic prediction network model, which specifically includes:

[0059] The shape coordinate input layer, flattening layer, fully connected layer 1, and then the input point 1 of the merge layer is connected. The trajectory input layer is connected to the long short-term memory network layer, and then the input point 2 of the merge layer is connected. The output point of the merge layer is connected to fully connected layer 2, fully connected layer 3, fully connected layer 4, renormalization layer and output layer in sequence.

[0060] The flattening layer reshapes the input data dimensions into a single dimension;

[0061] The mathematical expression for a fully connected layer is:

[0062] (1)

[0063] in, It is the input value of the i-th neuron; These are the weights connecting the i-th input neuron and the j-th output neuron; It is the bias of the j-th output neuron;

[0064] The output gate expression for a Long Short-Term Memory (LSTM) network layer is:

[0065] (2)

[0066] in, It is the output of the output gate at time step t; and These are the weight matrix and bias of the output gate, respectively; It is the output of the hidden state at time step t-1;

[0067] The remodeling layer remodels the data dimensions to be consistent with the output layer dimensions;

[0068] The data obtained in step 1 is organized into the input and output datasets required for training the aerodynamic prediction network model. The input dataset contains an external attachment shape coordinate matrix and a separation trajectory history matrix. The external attachment shape coordinate matrix is ​​an 80×256×2 matrix, representing 80 external attachment samples. Each sample is described by 256 point clouds, and the coordinate dimension of each point cloud is 2. The separation trajectory matrix is ​​an 80×26×3 matrix, representing 80 external attachment samples. The separation time of each sample is described by 26 discrete time steps, and the trajectory data dimension of each time step is 3. The output dataset contains an external attachment aerodynamic history matrix, which is also an 80×26×3 matrix, representing 80 external attachment samples. The separation time of each sample is described by 26 discrete time steps, and the aerodynamic data dimension of each time step is 3.

[0069] The aerodynamic prediction network model uses the mean squared error (MSE) as the loss function. MSE is defined as:

[0070] (3)

[0071] Where n is the number of data samples; It is the true value of the i-th data sample; It is the predicted value of the i-th data sample.

[0072] The optimization training method for the aerodynamic prediction network model is the Adam algorithm.

[0073] Step 3: Create a trajectory prediction network model, which specifically includes:

[0074] The external coordinate input layer is connected to the flattening layer and the fully connected layer 1. Then, the input point 1 of the merged layer is connected. The aerodynamic history input layer is connected to the long short-term memory network layer and then to the input point 2 of the merged layer. The output point of the merged layer is connected to the fully connected layer 2, the fully connected layer 3, the fully connected layer 4, the renormalization layer, and the output layer in sequence.

[0075] The flattening layer reshapes the input data dimensions into a single dimension;

[0076] The mathematical expression for a fully connected layer is:

[0077] (4)

[0078] in, It is the input value of the i-th neuron; These are the weights connecting the i-th input neuron and the j-th output neuron; It is the bias of the j-th output neuron;

[0079] The output gate expression for a Long Short-Term Memory (LSTM) network layer is:

[0080] (5)

[0081] in, It is the output of the output gate at time step t; and These are the weight matrix and bias of the output gate, respectively; It is the output of the hidden state at time step t-1;

[0082] The data obtained in step 1 is organized into the input and output datasets required for training the trajectory prediction network model. The input dataset contains an external attachment shape coordinate matrix and an aerodynamic history matrix. The external attachment shape coordinate matrix is ​​an 80×256×2 matrix, representing 80 external attachment samples. Each sample is described by 256 point clouds, and the coordinate dimension of each point cloud is 2. The aerodynamic history matrix is ​​an 80×26×3 matrix, representing 80 external attachment samples. The separation time of each sample is described by 26 discrete time steps, and the aerodynamic data dimension of each time step is 3. The output dataset contains an external attachment trajectory matrix, which is also an 80×26×3 matrix, representing 80 external attachment samples. The separation time of each sample is described by 26 discrete time steps, and the trajectory data dimension of each time step is 3.

[0083] The trajectory prediction network model uses the mean squared error (MSE) as the loss function. MSE is defined as follows:

[0084] (6)

[0085] Where n is the number of data samples; It is the true value of the i-th data sample; It is the predicted value of the i-th data sample.

[0086] The optimal training method for the trajectory prediction network model is the Adam algorithm.

[0087] Step 4: Select an external attachment, initialize its trajectory history and aerodynamic history to 0, and use the external attachment's external coordinates and trajectory as input to predict and update the external attachment's aerodynamic history through a trained aerodynamic prediction network model; use the external attachment's external coordinates and aerodynamic history as input to predict and update the external attachment's trajectory through a trained trajectory prediction network model; iterate this process, predicting and updating the aerodynamic history and trajectory sequentially, until the preset number of iterations of 50 is reached; after the iteration is completed, the trajectory output by the trajectory prediction network model is the external attachment's deployment and separation trajectory.

[0088] The above steps were simulated using Python, and four test samples were selected for prediction and comparison to obtain the results. Figure 3 The trajectory prediction results shown in the figure are for four external attachment samples. The x and y coordinates of the center of gravity and the attitude angle of the external attachment are denoted as x, y, and Theta, respectively. The CFD calculation results are represented by straight lines, and the predicted values ​​are represented by dots. It can be seen that the method proposed in this application predicts the trajectory values ​​very closely to the actual values.

[0089] Comparative Example

[0090] The difference between the comparative example and Example 1 is that, instead of constructing an aerodynamic prediction network model, a trajectory prediction model is directly used, with the external object's shape coordinates as input for separation trajectory prediction. Specifically, the steps include:

[0091] Step 1: Select 80 external items. The shapes of all external items are as follows: Figure 2 As shown. The geometric model of the external attachment is imported into the mesh generation software, and the surface and flow field of the external attachment are meshed. Then, the coordinates of a total of 256 mesh points on the surface of the external attachment are extracted as the external attachment's shape coordinates. The flow field mesh of the external attachment is read using computational fluid dynamics software. Then, the deployment and separation conditions of the external attachment are set, including Mach number, angle of attack, sideslip angle, height, etc., and the aerodynamic forces on the external attachment at the current time step are calculated. The position of the external attachment at the next time step is updated according to the aerodynamic forces on the external attachment. This process is repeated until the separation motion simulation of all 26 time steps is completed. The separation trajectory is obtained by reading the horizontal and vertical coordinates of the center of gravity and the attitude angle of the external attachment at each time step.

[0092] Step 2: Create a trajectory prediction network model, which specifically includes:

[0093] The outer shape coordinate input layer, flattening layer, fully connected layer 1, fully connected layer 2, fully connected layer 3, fully connected layer 4, reshaping layer, and output layer;

[0094] The flattening layer reshapes the input data dimensions into a single dimension;

[0095] The mathematical expression for a fully connected layer is:

[0096] (1)

[0097] in, It is the input value of the i-th neuron; These are the weights connecting the i-th input neuron and the j-th output neuron; It is the bias of the j-th output neuron;

[0098] The output gate expression for a Long Short-Term Memory (LSTM) network layer is:

[0099] (2)

[0100] in, It is the output of the output gate at time step t; and These are the weight matrix and bias of the output gate, respectively; It is the output of the hidden state at time step t-1;

[0101] The data obtained in step 1 is organized into the input and output datasets required for training the trajectory prediction network model. The input dataset contains the external attachment shape coordinate matrix. This matrix is ​​80×256×2, representing 80 external attachment samples. Each sample is described by 256 point clouds, and each point cloud has a coordinate dimension of 2. The output dataset contains the external attachment trajectory matrix, which is 80×26×3, representing 80 external attachment samples. The separation time of each sample is described by 26 discrete time steps, and the trajectory data dimension of each time step is 3.

[0102] The trajectory prediction network model uses the mean squared error (MSE) as the loss function. MSE is defined as follows:

[0103] (3)

[0104] Where n is the number of data samples; It is the true value of the i-th data sample; It is the predicted value of the i-th data sample.

[0105] The optimal training method for the trajectory prediction network model is the Adam algorithm.

[0106] Step 3: Select an external object, take the external object's shape coordinates as input, and use the trained trajectory prediction network model to predict the trajectory of the external object. The trajectory output by the trajectory prediction network model is the deployment and separation trajectory of the external object.

[0107] The above steps were simulated using Python, and four test samples were selected for prediction and comparison to obtain the results. Figure 4 The trajectory prediction results shown in the figure are for four external attachment samples. The x and y coordinates of the attachment's center of gravity and its attitude angle are denoted as x, y, and Theta, respectively. CFD calculation results are represented by straight lines, and predicted values ​​are represented by dots. It can be seen that the comparative method has a large error between the predicted and actual trajectories. Compared with the comparative method, the method described in this invention has higher prediction accuracy.

Claims

1. A method for predicting the separation trajectory of deployed external objects based on a small sample size, characterized in that, The specific steps include: Step 1: Select N attachments and obtain the external coordinates of each attachment through experimental testing or numerical simulation, as well as the separation trajectory and aerodynamic history of the attachment during the Nt separation time steps. The separation trajectory is the coordinates of the attachment's center of gravity for each Nt separation time step; the aerodynamic history is the collection of aerodynamic forces of the attachment at each time step. Step 2: Create an aerodynamic prediction network model. Use the external object's shape coordinates and trajectory obtained in Step 1 as inputs and the aerodynamic history of the external object as outputs to train the aerodynamic prediction network model. Step 3: Create a trajectory prediction network model. Use the external object's shape coordinates and aerodynamic history obtained in Step 1 as inputs and the external object's trajectory as output to train the trajectory prediction network model. Step 4: Select an external attachment, initialize its trajectory history and aerodynamic history to 0, and use the external attachment's external coordinates and trajectory as input to predict and update the external attachment's aerodynamic history through a trained aerodynamic prediction network model; use the external attachment's external coordinates and aerodynamic history as input to predict and update the external attachment's trajectory through a trained trajectory prediction network model; iterate this process, predicting and updating the aerodynamic history and trajectory sequentially, until the preset number of iterations is reached; after the iteration is completed, the trajectory output by the trajectory prediction network model is the external attachment's deployment and separation trajectory.

2. The method for predicting the separation trajectory of external objects based on a small sample size according to claim 1, characterized in that, N does not exceed 100.

3. The method for predicting the separation trajectory of external objects based on a small sample size according to claim 1, characterized in that, The specific process of obtaining external shape coordinates through numerical simulation includes: Import the geometric model of the external attachment into the mesh generation software, perform mesh generation on the surface and flow field of the external attachment, and then extract the coordinates of the mesh points on the surface of the external attachment as the external attachment's shape coordinates.

4. The method for predicting the separation trajectory of external objects based on a small sample size according to claim 1, characterized in that, The specific process of obtaining the separation trajectory and aerodynamic history of the attachment during the separation process through numerical simulation includes: reading the flow field mesh of the attachment using computational fluid dynamics software; then setting the deployment and separation conditions of the attachment, calculating the aerodynamic forces acting on the attachment at the current time step, and updating the position of the attachment at the next time step based on the aerodynamic forces acting on the attachment; repeating this process until the separation motion simulation of all Nt time steps is completed; reading the coordinates of the center of gravity of the attachment at each time step to obtain the separation trajectory; and reading the aerodynamic forces acting on the attachment at each time step as the aerodynamic history of the attachment during the separation process.

5. The method for predicting the separation trajectory of external objects based on a small sample size according to claim 1, characterized in that, The aerodynamic prediction network model specifically includes: The shape coordinate input layer, flattening layer, fully connected layer 1, and then the input point 1 of the merge layer is connected. The trajectory input layer is connected to the long short-term memory network layer, and then the input point 2 of the merge layer is connected. The output point of the merge layer is connected to fully connected layer 2, fully connected layer 3, fully connected layer 4, renormalization layer and output layer in sequence. The flattening layer reshapes the input data dimensions into a single dimension; The mathematical expression for a fully connected layer is: (1) in, It is the input value of the i-th neuron; These are the weights connecting the i-th input neuron and the j-th output neuron; It is the bias of the j-th output neuron; The output gate expression for a Long Short-Term Memory (LSTM) network layer is: (2) in, It is the output of the output gate at time step t; and These are the weight matrix and bias of the output gate, respectively; It is the hidden state output at time step t-1; the remodeling layer remodels the data dimensions to be consistent with the output layer dimensions.

6. The method for predicting the separation trajectory of external objects based on a small sample size according to claim 1, characterized in that, The trajectory prediction network model specifically includes: The external coordinate input layer is connected to the flattening layer and the fully connected layer 1. Then, the input point 1 of the merged layer is connected. The aerodynamic history input layer is connected to the long short-term memory network layer and then to the input point 2 of the merged layer. The output point of the merged layer is connected to the fully connected layer 2, the fully connected layer 3, the fully connected layer 4, the renormalization layer, and the output layer in sequence. The flattening layer reshapes the input data dimensions into a single dimension; The mathematical expression for a fully connected layer is: (3) in, It is the input value of the i-th neuron; These are the weights connecting the i-th input neuron and the j-th output neuron; It is the bias of the j-th output neuron; The output gate expression for a Long Short-Term Memory (LSTM) network layer is: (4) in, It is the output of the output gate at time step t; and These are the weight matrix and bias of the output gate, respectively; It is the hidden state output at time step t-1.

7. The method for predicting the separation trajectory of external objects based on a small sample size according to claim 1, characterized in that, In step 2, the data obtained in step 1 is organized into the input and output datasets required for training the aerodynamic prediction network model. The input dataset contains the external attachment shape coordinate matrix and the separation trajectory history matrix. The external attachment shape coordinate matrix is ​​an N×Np×n matrix, representing N external attachment samples. Each sample is described by Np point clouds, and the coordinate dimension of each point cloud is n. For two-dimensional cases, n=2, and for three-dimensional cases, n=3. The separation trajectory matrix is ​​an N×Nt×m matrix, representing N external attachment samples. The separation time of each sample is described by Nt discrete time steps, and the trajectory data dimension of each time step is m. For two-dimensional cases, m=3, and for three-dimensional cases, m=6. The output dataset contains the external attachment aerodynamic history matrix, which is also an N×Nt×m matrix, representing N external attachment samples. The separation time of each sample is described by Nt discrete time steps, and the aerodynamic data dimension of each time step is m. For two-dimensional cases, m=3, and for three-dimensional cases, m=6.

8. The method for predicting the separation trajectory of external objects based on a small sample size according to claim 1, characterized in that, In step 2, the aerodynamic prediction network model uses the mean squared error (MSE) as the loss function. MSE is defined as: (5) Where n is the number of data samples; It is the true value of the i-th data sample; It is the predicted value of the i-th data sample.

9. The method for predicting the separation trajectory of external objects based on a small sample size according to claim 1, characterized in that, In step 3, the data obtained in step 1 is organized into the input and output datasets required for training the trajectory prediction network model. The input dataset includes the external attachment shape coordinate matrix and the aerodynamic history matrix. The external attachment shape coordinate matrix is ​​an N×Np×n matrix, representing N external attachment samples. Each sample is described by Np point clouds, and the coordinate dimension of each point cloud is n. For two-dimensional cases, n=2, and for three-dimensional cases, n=3. The aerodynamic history matrix is ​​an N×Nt×m matrix, representing N external attachment samples. The separation time of each sample is described by Nt discrete time steps, and the aerodynamic data dimension of each time step is m. For two-dimensional cases, m=3, and for three-dimensional cases, m=6. The output dataset includes the external attachment trajectory matrix, which is an N×Nt×m matrix, representing N external attachment samples. The separation time of each sample is described by Nt discrete time steps, and the trajectory data dimension of each time step is m. For two-dimensional cases, m=3, and for three-dimensional cases, m=6.

10. The method for predicting the separation trajectory of external objects based on a small sample size according to claim 1, characterized in that, In step 3, the trajectory prediction network model uses the mean squared error (MSE) as the loss function. MSE is defined as: (6) Where n is the number of data samples; It is the true value of the i-th data sample; It is the predicted value of the i-th data sample.

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