Intelligent prediction method for separation trajectories of multiple external stores based on embedded neural network

Abstract

The present invention belongs to the fields of aerospace engineering and artificial intelligence, and discloses a method for intelligently predicting the separation trajectory of multiple external attachments based on an embedded neural network. The method for intelligently predicting the separation trajectory of multiple external attachments based on an embedded neural network of the present invention combines an embedded neural network with a six-degree-of-freedom motion equation, and by embedding a low-order model of the calculation data, improves the learning efficiency of the prediction model for the calculation data, accelerates the convergence of the neural network, and improves the accuracy of the intelligent prediction of the separation trajectory of multiple external attachments. In addition, by integrating the six-degree-of-freedom motion equation, it can more efficiently process the relationship between the two data sources, thereby improving the computational efficiency of the prediction model. The method for intelligently predicting the separation trajectory of multiple external attachments based on an embedded neural network of the present invention can be extended to apply to the aerodynamic design of carrier aircraft and multiple external attachments, performance analysis, multi-body separation characteristics and other fields, providing a new intelligent solution to the problem of predicting the separation trajectory of multiple external attachments.

Description

Technical Field

[0001] The present invention belongs to the fields of aerospace engineering and artificial intelligence, and in particular relates to an intelligent prediction method for the separation trajectories of multiple external stores based on an embedded neural network. Background Art

[0002] The carrier-external store model has a significant application background in the aerospace field. Due to varying mission requirements, the aerodynamic layout of multiple external stores has become increasingly diverse. Consequently, a key kinematic problem arises in the separation system of multi-body aircraft: multi-body separation dynamics. However, the complex and variable flow field characteristics under flight conditions, coupled with complex flow characteristics such as mutual aerodynamic interference during the separation process, lead to dramatic variations in the aerodynamic loads on the external stores, increasing the difficulty of studying the kinematic characteristics of multi-body separation. Furthermore, the safety analysis of the separation characteristics of multiple external stores requires studying various flight conditions within the flight envelope, including the incoming Mach number, flight altitude, incoming angle of attack and sideslip angle, and different spatial layouts. Consequently, the resulting flight conditions can reach thousands of combinations. Using numerical simulation methods or capture trajectory experiments to study these conditions sequentially would increase resource consumption and make project schedules difficult to control.

[0003] At present, it is necessary to carry out intelligent prediction of the separation trajectories of multiple external attachments and develop an intelligent prediction method for the separation trajectories of multiple external attachments based on embedded neural networks. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide an intelligent prediction method for the separation trajectory of multiple external attachments based on an embedded neural network, so as to overcome the limitation of low model training efficiency and improve the calculation efficiency and accuracy of the prediction model.

[0005] The present invention's method for intelligently predicting the separation trajectories of multiple external attachments based on an embedded neural network combines an embedded neural network with a six-degree-of-freedom motion equation. By embedding a low-order model in the neural network input layer, the learning efficiency of the prediction model for computational data is improved, the neural network convergence is accelerated, and the accuracy of intelligent prediction of the separation trajectories of multiple external attachments is increased. Furthermore, the integration of the six-degree-of-freedom motion equation enables more efficient processing of the relationship between the two data sources, thereby improving the computational efficiency of the prediction model.

[0006] The method for intelligently predicting the separation trajectories of multiple external attachments based on an embedded neural network of the present invention comprises the following steps:

[0007] S1. Obtain the required computational data through numerical simulation, select the input features of the neural network according to the requirements, and divide the obtained dataset into a training set and a test set;

[0008] S2. Based on the input features X and output features Y of the neural network, a low-order model Y with multiple external stores aerodynamic loads is established. LF The input feature X of the prediction model includes the spatial position of the external storage; the output feature Y of the prediction model is the aerodynamic load

[0009] S3. The prediction model uses a fully connected neural network structure. Hyperparameters, including the number of neural network layers, nodes, and activation functions, are determined, as well as the number and location of hidden layers.

[0010] S4. Add a new neuron to the input layer of the neural network and embed the low-order model Y in S2 LF , the new input feature of the prediction model is [X,Y LF ]; Improve the prediction accuracy of the prediction model by strengthening the training framework of the prediction model;

[0011] S5. Based on step S1, define a loss function based on the calculated data; and establish a prediction model;

[0012] S6. Train the prediction model and test the test set after the loss function converges to ensure that the prediction model achieves the required prediction accuracy and obtain the final embedded neural network prediction model;

[0013] S7. Based on step S6, determine the input characteristics of the current moment of the specific conditions, obtain the output characteristics of the prediction model, and couple the six-degree-of-freedom motion equation;

[0014] S8. Based on step S7, the fourth-order Runge-Kutta time marching method is used to obtain the input features at the next moment to iteratively predict the separation trajectory of the external attachment.

[0015] Furthermore, the low-order model Y described in S2 LF , is a polynomial regression model fitted based on the input feature X and the output feature Y. The polynomial formula is as follows:

[0016]

[0017] Among them, x i ,x j ,x k Represents each input feature; a i represents the coefficient of the fitted first-order polynomial; a ij represents the coefficient of the fitted second-order polynomial; a ijk represents the coefficient of the fitted third-order polynomial; a0 represents the constant term; Y LF Represents the aerodynamic load value of the low-order model.

[0018] Furthermore, the input features described in S2 have dimensional differences, so they are processed according to the linear normalization method. The normalization method is as follows:

[0019] y=(QQ min ) / (Q max -Q min )(2)

[0020] Among them, Q min and Q max Represent the minimum and maximum values ​​of the sample data points respectively.

[0021] Furthermore, the output characteristic Y described in S2 is aerodynamic load.

[0022] Furthermore, the new input features [X,Y LF ]Includes Mach number, multiple external storage channel spacing, external storage spatial posture and low-order models of calculation data.

[0023] Furthermore, the input feature described in S8 is the spatial posture of the external attachment.

[0024] Furthermore, the six-degree-of-freedom motion equations described in S7 are coupled with the output characteristics of the prediction model, specifically:

[0025] The output characteristic aerodynamic load of the prediction model is divided into aerodynamic force f G and aerodynamic torque M B , through the aerodynamic force f G , that is, the axial force, lateral force and normal force of the external attachment, and solve to obtain the center of mass velocity v in the three directions of the rigid body G , through the aerodynamic torque M B , namely the rolling moment, pitching moment and yaw moment of the external attachment, can be solved to obtain the angular velocity ω in the three directions of the rigid body B ; Among them, the aerodynamic force f G , aerodynamic torque M B As input to the six-degree-of-freedom motion equations;

[0026] The output of the six-degree-of-freedom motion equation is the spatial pose of the external attachment as the input feature of the prediction model.

[0027] Furthermore, the six-degree-of-freedom motion equations described in S7 are as follows:

[0028]

[0029] Among them, v G is the velocity of the center of mass of the rigid body in the geodetic coordinate system, is the first-order derivative of the velocity of the rigid body's center of mass with respect to time in the geodetic coordinate system, m is the rigid body's mass, and f Gis the force on the rigid body. L is the inertia tensor, M B is the moment vector acting on the rigid body in the projectile coordinate system, ω B is the angular velocity of the rigid body, is the first derivative of the angular velocity of the rigid body with respect to time.

[0030] Furthermore, the fourth-order Runge-Kutta time marching method described in S8 can be used to solve the linear (angular) velocity of the rigid body, as follows:

[0031]

[0032] Among them, y n The state variable vector at the nth moment is a collection of all variables describing the motion state of the rigid body in space, including the velocity, displacement, angular velocity, and Euler angle information in the six-degree-of-freedom equations. n+1 Represents the state variable vector at the next moment of the nth moment, k n It represents the intermediate value used to calculate the increment of the state variable in each time step, that is, the slope at the nth moment, h represents the time step, t n represents the time step at the nth moment.

[0033] Furthermore, the multiple external attachments are multiple auxiliary fuel tanks.

[0034] Furthermore, the multiple external attachments are replaced with multiple storage items or multiple airborne missiles.

[0035] Beneficial effects:

[0036] The present invention's intelligent prediction method for multiple external store separation trajectories based on an embedded neural network integrates two technologies: First, a low-order model is constructed based on the input and output features of the prediction model and embedded into the input layer of the neural network, overcoming the limitations of low neural network training efficiency and increasing the accuracy of neural network fitting and prediction. Second, based on the output features of the current moment of a specific task, the input features for the next moment are obtained by coupling the six-degree-of-freedom motion equations and employing a fourth-order Runge-Kutta time-marching method. This method then efficiently iterates the separation trajectory of the external stores, significantly improving the computational efficiency of the model and enabling rapid prediction of the motion trajectory of multiple stores during separation. Furthermore, the prediction model's input features, including the Mach number, the spacing between multiple external store channels, the spatial pose of the external stores, and the low-order model of the calculated data, can be flexibly adjusted according to specific circumstances and is applicable to different types of carrier aircraft-multiple store models. This method is particularly valuable in dynamic flow field environments, making the prediction of multiple store separation trajectories more accurate and reliable.

[0037] In short, the present invention's intelligent prediction method for multiple external store separation trajectories based on an embedded neural network combines the powerful nonlinear fitting capabilities of neural networks with the reliability of computational data. It fully exploits the potential relationships between computational data and embeds low-order models into the neural network's input layer, enhancing the robustness and convergence of the prediction model. The use of neural networks better captures the complex and ever-changing aerodynamic characteristics of external stores, improving prediction accuracy. Furthermore, by coupling the six-degree-of-freedom equations of motion and employing the fourth-order Runge-Kutta method, the separation trajectories of the external stores can be efficiently iterated, improving the computational efficiency and stability of the prediction model.

[0038] In summary, the present invention's embedded neural network-based intelligent prediction method for multiple external store separation trajectories combines embedded neural networks with six-degree-of-freedom motion equations to achieve highly accurate intelligent prediction of separation trajectories. This method can play a key role in the field of multi-body separation aircraft, providing a more accurate solution for analyzing the separation trajectories of multiple external stores. It also offers an effective means for improving the efficiency and accuracy of aerodynamic performance assessments of multiple stores mounted on advanced fighter aircraft, as well as for multi-body separation safety analysis. This method promotes the development and application of multiple store separation technology, and has broad and important engineering application prospects. In particular, it can be applied to carrier aircraft and multiple store aerodynamic design, performance analysis, and other fields, providing a new intelligent solution to the problem of multiple store separation trajectory prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is a flow chart of the method for intelligently predicting the separation trajectories of multiple external attachments based on an embedded neural network according to the present invention;

[0040] Figure 2 Schematic diagram of embedding a low-order model in neurons of the input layer of a neural network in Example 1;

[0041] Among them, Y LF is a low-order model. The gray circles represent the neurons in the input layer that are embedded in the low-order model. The white circles represent the original neurons in the neural network. x1, x2,…, x i represents the input features, i represents the number of neurons in the input layer, and Y represents the output features of the embedded neural network;

[0042] Figure 3 This is a comparison chart of the results of the intelligent prediction of the lateral force of the external attachment obtained in Example 1;

[0043] Figure 4 This is a schematic diagram of the absolute error percentage of the intelligent prediction of the lateral force of the external attachment obtained in Example 1;

[0044] Figure 5 This is a comparison chart of the results of intelligent prediction of vertical displacement of external attachments obtained in Example 1;

[0045] Figure 6 Schematic diagram of the absolute error percentage of the intelligent prediction of the vertical displacement of the external attachment obtained in Example 1.

[0046] Figure 7 This is a comparison chart of the results of the intelligent prediction of the roll angle of the external attachment obtained in Example 1;

[0047] Figure 8 Schematic diagram of the absolute error percentage of the intelligent prediction of the roll angle of the external attachment obtained in Example 1. DETAILED DESCRIPTION

[0048] The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0049] Example 1:

[0050] The multiple external attachments in this embodiment are multiple auxiliary fuel tanks.

[0051] like Figure 1 As shown, the method for intelligently predicting the separation trajectories of multiple external attachments based on an embedded neural network in this embodiment includes the following steps:

[0052] S1. Obtain the required computational data through numerical simulation, select the input features of the neural network as required, and divide the obtained dataset into a training set and a test set;

[0053] The key to S1 is ensuring sufficient data to support the training and validation of the prediction model. This example uses Ansys Fluent software to perform numerical simulation analysis on the Su-27 large-swept-wing fighter aircraft equipped with multiple external stores. This establishes a dataset of the kinematic characteristics of the multiple stores separated by the stores. The calculated data is shown in Table 1 below. 80% of the data is divided into a training set for training the neural network, and 20% of the data is divided into a test set for testing the accuracy of the neural network.

[0054] Table 1 Calculation data table

[0055]

[0056] S2. According to the input features and output features required by the prediction model, establish Figure 2 The embedded low-order model Y shown LF A neural network prediction model; the input feature X of the prediction model includes the spatial posture of the external storage; the output feature Y of the prediction model is the aerodynamic load;

[0057] Low-order model Y LF It is a polynomial regression model fitted by input feature X and output feature Y. The polynomial formula is as follows:

[0058]

[0059] Where x1 represents the Mach number; x2 represents the distance between the multiple external stores; x3, x4, and x5 represent the displacement of the external stores in the X, Y, and Z axes, respectively; a i represents the coefficient of the fitted first-order polynomial; a ij represents the coefficient of the fitted second-order polynomial; a ijk represents the coefficient of the fitted third-order polynomial; a0 represents the constant term; Y LF Represents the aerodynamic load value of the low-order model.

[0060] Since there are dimensional differences among the input features, they are processed according to the linear normalization method. The normalization method is as follows:

[0061] y=(QQ min ) / (Q max -Q min )(2)

[0062] Among them, Q min and Q max Represent the minimum and maximum values ​​of the sample data points in each input feature respectively.

[0063] S3. The prediction model uses a fully connected neural network structure. Hyperparameters, including the number of neural network layers, nodes, and activation functions, are determined, as well as the number and location of hidden layers.

[0064] For input features with a limited variety, the number of hidden layers in the neural network is generally set to 2 to 4, which is sufficient to fit complex nonlinear relationships in the computational data. Typically, the number of hidden layer nodes is set to 20 to 50, the activation function uses the Tansig function, and the initial learning rate is set to 0.015. The greater the number of layers and nodes in the neural network, the greater the computing resources consumed. S3 needs to comprehensively consider the complexity of the prediction model and the limitations of computing resources to achieve a high-performance fully connected neural network structure within a limited economic cost.

[0065] S4. Add a new neuron to the input layer of the neural network and embed the low-order model Y in S2 LF ; At this time, the new input feature of the prediction model is [X,Y LF ];

[0066] The number of neurons in S4 will affect the complexity and fitting ability of the prediction model, so reasonable setting and optimization are required to improve the prediction accuracy of the prediction model by strengthening the training framework of the prediction model.

[0067] S5. Based on step S1, define a loss function based on the calculated data; and establish a prediction model;

[0068] The loss function E in S5 r As shown in the following formula:

[0069]

[0070] in, To calculate the data, is the prediction data of the prediction model.

[0071] S6. Train the prediction model and test the test set after the loss function converges to ensure that the prediction model achieves the required prediction accuracy and obtain the final embedded neural network prediction model;

[0072] S6 requires repeated iteration and adjustment of the neural network's hyperparameters, such as the number of layers, nodes, and embedded neurons. Therefore, the neural network structure is optimized through a genetic algorithm. Generally speaking, the population size is set to 40 to 60, the crossover probability is set to 0.8 to 0.9, the mutation probability is set to 0.15, and the evolutionary generations are set to 40 to 60 to ensure that the accuracy of the prediction model reaches the expected level.

[0073] S7. Based on step S6, determine the input characteristics of the current moment of the specific conditions, obtain the output characteristics of the prediction model, and couple the six-degree-of-freedom motion equation;

[0074] In S7, the linear (angular) acceleration of the external attachment needs to be solved by the six-degree-of-freedom motion equation. In the geodetic coordinate system, the translational motion formula of the external attachment's center of mass is:

[0075]

[0076] Among them, v G is the velocity of the external mass center in the geodetic coordinate system, is the first-order derivative of the velocity of the external material center with respect to time in the geodetic coordinate system, m is the mass of the external material, and f G The aerodynamic force acting on the external attachments.

[0077] The formula for the angular motion of the external attachment in the missile body coordinate system is:

[0078]

[0079] Where L is the inertia tensor, M B is the moment vector of the external attachment in the missile body coordinate system, ω B is the angular velocity of the external attachment, is the first-order derivative of the angular velocity of the external storage with respect to time.

[0080] In order to convert the torque of the external attachment from the earth coordinate system to the missile body coordinate system, it is divided into three steps, rotating three times around the corresponding axis, rotating through ψ, θ and φ in turn, that is, Oz in the earth coordinate system g Axis, Oy g Axis and Ox g axis.

[0081] This can be obtained by the following formula:

[0082] M B =RM G (6)

[0083] Among them, M G represents the moment vector of the external attachment in the geodetic coordinate system, and R represents the coordinate transformation matrix.

[0084]

[0085] Among them, C χ =cos(χ),S χ =sin(χ).

[0086] The combined equations (4) and (5) can be used to calculate the linear (angular) velocity of the external attachment.

[0087] S8. Based on step S7, the fourth-order Runge-Kutta time marching method is used to obtain the input features at the next moment to iteratively predict the separation trajectory of the external attachment.

[0088] The formula for the fourth-order Runge-Kutta method in S8 is:

[0089]

[0090] Among them, y n The state variable vector at the nth moment is a collection of all variables describing the motion state of the rigid body in space, including the velocity, displacement, angular velocity, and Euler angle information in the six-degree-of-freedom equations. n+1 Represents the state variable vector at the next moment of the nth moment, k n It represents the intermediate value used to calculate the increment of the state variable in each time step, that is, the slope at the nth moment, h represents the time step, t n represents the time step at the nth moment.

[0091] According to this method, the linear (angular) velocity of the external attachment can be solved, thereby obtaining its spatial displacement and posture change.

[0092] This embodiment obtains Figure 3 The comparison chart of the results of intelligent prediction of the lateral force of the external attachments shown in the figure; Figure 3It can be seen that the neural network can accurately predict the aerodynamic coefficients of the external attachments, which is in good agreement with the high-fidelity data.

[0093] This embodiment obtains Figure 4 The absolute error percentage of the intelligent prediction of the lateral force of the external storage is shown in the figure; Figure 4 It can be seen that the absolute error between the neural network's prediction of the aerodynamic coefficient of the external attachment and the calculation of high-fidelity data is within 10%, which meets the accuracy requirements.

[0094] This embodiment obtains Figure 5 The comparison chart of the results of intelligent prediction of vertical displacement of external attachments shown in FIG. Figure 5 It can be seen that the neural network can accurately predict the spatial position of the external attachment, which is consistent with the high-fidelity data.

[0095] This embodiment obtains Figure 6 The absolute error percentage of the intelligent prediction of the vertical displacement of the external attachment is shown in FIG. Figure 6 It can be seen that the absolute error of the neural network in predicting the spatial pose of the external attachment and calculating the high-fidelity data is within 5%, which meets the accuracy requirements.

[0096] This embodiment obtains Figure 7 The comparison chart of the roll angle intelligent prediction results of the external storage shown in the figure; Figure 7 It can be seen that the neural network can accurately predict the spatial position of the external attachment, which is consistent with the high-fidelity data.

[0097] This embodiment obtains Figure 8 The absolute error percentage of the intelligent prediction of the roll angle displacement of the external storage shown in FIG. Figure 8 It can be seen that the absolute error between the neural network's prediction of the external attachment's spatial posture and the calculation of high-fidelity data is within 10%. Due to the small amplitude of the calculated data, the error fluctuation will increase, but it still meets the accuracy requirements.

[0098] Although the embodiments of the present invention have been disclosed as above, they are not limited to the applications listed in the description and implementation methods. For those familiar with the art, all features disclosed in the present invention, or all steps in the disclosed methods or processes, except for mutually exclusive features and / or steps, can be combined in any way without departing from the principles of the present invention. The present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. An intelligent prediction method for separation trajectories of multiple external stores based on an embedded neural network, characterized in that: The steps include: (1) Constructing an embedded neural network prediction model; specifically including: S1. Obtain the required computational data through numerical simulation, select the input features of the prediction model based on the requirements, and divide the obtained dataset into a training set and a test set; S2. Based on the input features X and output features Y of the prediction model, a low-order model Y with multiple external stores aerodynamic loads is established. LF The input feature X of the prediction model includes the spatial position of the external storage; the output feature Y of the prediction model is the aerodynamic load; the low-order model Y described in S2 LF , is a polynomial regression model fitted according to the original input feature X and output feature Y, and embedded into the input layer of the neural network to form a new input feature [X,Y LF ], the polynomial formula is as follows: Among them, x i ,x j ,x k Represents each input feature; a i represents the coefficient of the fitted first-order polynomial; a ij represents the coefficient of the fitted second-order polynomial; a ijk represents the coefficient of the fitted third-order polynomial; a0 represents the constant term; Y LF Indicates the aerodynamic load value of the low-order model; S3. The prediction model uses a fully connected neural network structure. Hyperparameters, including the number of neural network layers, nodes, and activation functions, are determined, as well as the number and location of hidden layers. S4. Add a new neuron to the input layer of the neural network and embed the low-order model Y in S2 LF , the new input feature of the prediction model is [X,Y LF ]; S5. Based on step S1, define a loss function based on the calculated data; and establish a prediction model; S6. Train the prediction model and test the test set after the loss function converges to ensure that the prediction model achieves the required prediction accuracy and obtain the final embedded neural network prediction model; (2) Based on the aerodynamic load output by the embedded neural network prediction model, the spatial posture of the external attachment at the next moment is calculated; the spatial posture of the external attachment at the next moment is used as the input feature of the embedded neural network prediction model to obtain the aerodynamic load at the next moment; the spatial posture of the external attachment at each moment is iteratively predicted to obtain the separation trajectory. Step (2) specifically includes: S7. Based on step S6, determine the input characteristics of the current moment of the specific conditions, obtain the output characteristics of the prediction model, and couple the six-degree-of-freedom motion equation; S8. Based on step S7, the fourth-order Runge-Kutta time marching method is used to obtain the input features at the next moment to iteratively predict the separation trajectory of the external attachment.

2. The method for intelligently predicting the separation trajectory of multiple external attachments based on an embedded neural network according to claim 1 is characterized in that: The new input features [X,Y LF ]Including Mach number, multi-external storage channel spacing, external storage spatial posture and low-order model of calculation data, linear normalization is performed to ensure the dimensional consistency of each input feature.

3. The method for intelligently predicting the separation trajectory of multiple external attachments based on an embedded neural network according to claim 1 is characterized in that: The six-degree-of-freedom motion equations described in S7 are coupled to the output features of the prediction model, specifically: The output of the prediction model is the characteristic aerodynamic load, including the aerodynamic force f G and aerodynamic torque M B , through the aerodynamic force f G Solve to obtain the center of mass velocity v of the rigid body in three directions G , through the aerodynamic torque M B Solve to obtain the angular velocity ω of the rigid body in three directions B ; Among them, the aerodynamic force f G , aerodynamic torque M B As input to the six-degree-of-freedom motion equations; The output of the six-degree-of-freedom motion equation is the spatial pose of the external attachment as the input feature of the prediction model.

4. The method for intelligently predicting the separation trajectory of multiple external attachments based on an embedded neural network according to claim 1 is characterized in that: The output features of the prediction model described in S7 are used as input features of the six-degree-of-freedom motion equation, and the output feature of the six-degree-of-freedom motion equation, the external attachment spatial posture, is used as the input feature of the prediction model, wherein the six-degree-of-freedom motion equation is: Among them, v G is the velocity of the center of mass of the rigid body in the geodetic coordinate system, represents the first-order derivative of the velocity of the center of mass of the rigid body with respect to time in the geodetic coordinate system; m is the mass of the rigid body, f G is the force on the rigid body, i.e., aerodynamic force, L is the inertia tensor, M B is the moment vector acting on the rigid body in the missile coordinate system, i.e., the aerodynamic moment, ω B is the angular velocity of the rigid body, Represents the first-order derivative of the rigid body's angular velocity with respect to time.

5. The method for intelligently predicting the separation trajectory of multiple external attachments based on an embedded neural network according to claim 1 is characterized in that: In S8, the fourth-order Runge-Kutta method is used to solve the differential equation, specifically: k1=f(t n ,y n ) k4=f(t n +h,y n +k3) Among them, y n The state variable vector at the nth moment is a collection of all variables describing the motion state of the rigid body in space, including the velocity, displacement, angular velocity, and Euler angle information in the six-degree-of-freedom equations. n+1 Represents the state variable vector at the next moment of the nth moment, k n It represents the intermediate value used to calculate the increment of the state variable in each time step, that is, the slope at the nth moment, h represents the time step, t n represents the time step at the nth moment.

6. The method for intelligently predicting the separation trajectory of multiple external attachments based on an embedded neural network according to claim 1 is characterized in that: The multiple external attachments are multiple auxiliary fuel tanks.

7. The method for intelligently predicting the separation trajectory of multiple external attachments based on an embedded neural network according to claim 1 is characterized in that: The multiple external attachments are replaced with multiple storage objects or multiple airborne missiles.

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