Multi-external store separation trajectory intelligent prediction method based on embedded neural network

Abstract

The invention belongs to the field of aerospace engineering and artificial intelligence, and discloses a multi-external store separation trajectory intelligent prediction method based on an embedded neural network. According to the multi-external store separation trajectory intelligent prediction method based on the embedded neural network, the embedded neural network and the six-degree-of-freedom motion equation are combined, the learning efficiency of the prediction model on the calculation data is improved through the low-order model of the embedded calculation data, the convergence of the neural network is accelerated, and the prediction precision is improved. According to the method, the precision of intelligent prediction of the separation track of the multiple external store is improved, the six-degree-of-freedom motion equation is fused, the relation between two data sources can be processed more efficiently, and therefore the calculation efficiency of a prediction model is improved. The multi-external store separation trajectory intelligent prediction method based on the embedded neural network can be popularized and applied to aerodynamic design, performance analysis, multi-body separation characteristics and other fields of aerial carriers and multi-external store, and a brand new intelligent solution is provided for the separation trajectory prediction problem of the multi-external store.

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 separation trajectories of multiple external attachments based on an embedded neural network. Background Art

[0002] The carrier-external store model has an important application background in the field of aerospace. Due to the different requirements of combat missions, the aerodynamic layout of multiple external stores has shown a diversified trend. Therefore, there is an important kinematic problem in the multi-body aircraft separation system: multi-body separation dynamics. However, the flow field characteristics under flight conditions are complex and changeable, and multi-body aircraft have complex flow characteristics such as mutual aerodynamic interference during the separation process, which leads to drastic changes in the aerodynamic load of external stores, increasing the difficulty of studying the motion characteristics of multi-body separation of external stores. In addition, the safety analysis of the separation characteristics of multiple external stores requires the study of various flight conditions within the flight envelope, including the incoming flow Mach number, flight altitude, incoming flow angle of attack and sideslip angle, different spatial layouts, etc. Therefore, the combined flight conditions are as high as thousands. If numerical simulation methods or capture trajectory tests are used to study them one by one, it will increase resource consumption and make the project progress 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 trajectories 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 method for intelligently predicting the separation trajectory of multiple external objects based on an embedded neural network of the present invention combines the embedded neural network with the six-degree-of-freedom motion equation. By embedding a low-order model in the input layer of the neural network, the learning efficiency of the prediction model for the calculation data is improved, the convergence of the neural network is accelerated, and the accuracy of the intelligent prediction of the separation trajectory of multiple external objects is increased. In addition, the six-degree-of-freedom motion equation is integrated, and the relationship between the two data sources can be processed more efficiently, thereby improving the calculation efficiency of the prediction model.

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

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

[0008] S2. According to the input features X and output features Y of the neural network, a low-order model Y with aerodynamic loads of multiple external stores 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 adopts a fully connected neural network structure, determines the hyperparameters including the number of layers, number of nodes, and activation function of the neural network, and determines the number and position of hidden layers;

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

[0011] S5. Based on step S1, define a loss function in combination with 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 of 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 input feature X and 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, and 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 a pneumatic 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 for 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 the aerodynamic moment M B , through the aerodynamic force f G , that is, the axial force, lateral force and normal force of the external attachment, and the center of mass velocity v in three directions of the rigid body is obtained by solving 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 three directions of the rigid body B ; Among them, the aerodynamic force f G , aerodynamic moment M B As input to the six-degree-of-freedom motion equations;

[0026] The output spatial position of the external attachment from the six-degree-of-freedom motion equation is used 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 rigid body's center of mass in the geodetic coordinate system, is 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, and f Gis the force on the rigid body. L is the inertia tensor, M B is the torque vector of the rigid body in the projectile coordinate system, ω B is the rigid body angular velocity, is the first-order 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 solve the linear (angular) velocity of the rigid body, and the formula is as follows:

[0031]

[0032] Among them, y n The state variable vector represents the state at the nth moment. It 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 objects or multiple airborne missiles.

[0035] Beneficial effects:

[0036] The intelligent prediction method for the separation trajectory of multiple external attachments based on embedded neural network of the present invention integrates two technologies: first, a low-order model is constructed through the input and output features of the prediction model, and it is embedded in the input layer of the neural network, which overcomes the limitation of low efficiency of neural network training and increases the accuracy of neural network fitting and prediction. Secondly, according to the output features of the current moment of the specific task, by coupling the six-degree-of-freedom motion equation, the fourth-order Runge-Kutta time advancement method is used to solve the input features of the next moment, and the separation trajectory of the external attachment is efficiently iterated, which can better improve the calculation efficiency of the model and realize the rapid prediction of the motion trajectory of the multi-body separation of the external attachment. Moreover, the input features of the prediction model include Mach number, the spacing between the channels of multiple external attachments, the spatial posture of the external attachments, and the low-order model of the calculation data, which can be flexibly adjusted according to the specific situation and is suitable for different types of carrier-multiple external attachment models. It has important reference value especially when the dynamic flow field environment changes, making the prediction results of the separation trajectory of multiple external attachments more accurate and reliable.

[0037] In short, the intelligent prediction method for the separation trajectory of multiple external objects based on embedded neural network of the present invention combines the powerful nonlinear fitting ability of neural network with the credibility of calculation data, makes full use of the potential relationship between calculation data, embeds low-order models into the input layer of neural network, and enhances the robustness and convergence of prediction model. The use of neural network can better capture the complex and changeable aerodynamic characteristics of external objects and improve the accuracy of prediction; then coupled with the six-degree-of-freedom motion equation, and adopting the fourth-order Runge-Kutta method, the separation trajectory of external objects can be efficiently iterated, which improves the calculation efficiency and stability of the prediction model.

[0038] In summary, the method for intelligently predicting the separation trajectory of multiple external attachments based on embedded neural networks of the present invention combines embedded neural networks with six-degree-of-freedom motion equations, realizes highly accurate intelligent prediction of separation trajectories, can play a key role in the field of multi-body separation aircraft, provides a more accurate solution for the analysis of the separation trajectory of multiple external attachments, and provides an effective means for improving the efficiency and accuracy of the aerodynamic performance evaluation of advanced fighter aircraft carrying multiple external attachments and the multi-body separation safety analysis, promotes the development and application of the separation technology of multiple external attachments, and has a broad and important engineering application prospect. In particular, it can be promoted and applied to the aerodynamic design, performance analysis and other fields of carrier aircraft and multiple external attachments, and provides a new intelligent solution for the separation trajectory prediction problem of multiple external attachments. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a flow chart of the intelligent prediction method of multiple external attachment separation trajectories based on embedded neural network of the present invention;

[0040] Figure 2 This is a 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. 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 is described in detail below with reference to the accompanying drawings and embodiments.

[0049] Embodiment 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 calculation data through numerical simulation, select the input features of the neural network according to the requirements, and divide the obtained data set into a training set and a test set;

[0053] The key to S1 is to ensure that sufficient data is obtained to support the training and verification of the prediction model. In this embodiment, the large swept-wing fighter Su27 equipped with multiple external attachments is numerically simulated and analyzed by Ansys Fluent software to establish a data set of the motion characteristics of the multi-body separation of external attachments. The calculated data is shown in Table 1 below, and 80% of the data is divided into a training set to train the neural network, and 20% of the data is divided into a test set to test 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 position 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] Among them, x1 represents the Mach number; x2 represents the distance between the multiple external storage channels; x3, x4, and x5 represent the displacement of the external storage in the X, Y, and Z axis directions 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 Respectively represent the minimum and maximum values ​​of the sample data points in each input feature.

[0063] S3. The prediction model adopts a fully connected neural network structure, determines the hyperparameters including the number of layers, number of nodes, and activation function of the neural network, and determines the number and position of hidden layers;

[0064] For input features with fewer types, the number of hidden layers of the neural network is generally set to 2 to 4 layers, which can fit the complex nonlinear relationship of the calculation data. Usually, 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 more layers and nodes in the neural network, the more computing resources are consumed. S3 needs to comprehensively consider the complexity of the prediction model and the limitation of computing resources to obtain a high-performance fully connected neural network structure under the condition of limited economic cost.

[0065] S4. Add a new neuron in the neural network input layer 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 settings 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 in combination with the calculated data; and establish a prediction model;

[0068] The loss function E in S5 r As shown below:

[0069]

[0070] in, To calculate the data, 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 needs to iterate and adjust the hyperparameters of the neural network, such as the number of layers, number of nodes, and number of embedded neurons of the neural network. Therefore, the neural network structure is optimized through a genetic algorithm. Generally speaking, the population size is set to 40-60, the crossover probability is set to 0.8-0.9, the mutation probability is set to 0.15, and the evolutionary generation is set to 40-60 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 through the six-degree-of-freedom motion equation. In the geodetic coordinate system, the translational motion formula of the center of mass of the external attachment 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 attachment.

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

[0078]

[0079] Where L is the inertia tensor, M B is the torque vector of the external attachment in the missile body coordinate system, ω B is the angular velocity of the external attachment, It 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 geodetic 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 geodetic coordinate system g Axis, Oy g Axis and Ox g axis.

[0081] This can be obtained through 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 of 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 represents the state at the nth moment. It 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 FIG. 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 diagram of the intelligent prediction of the lateral force of the external attachment is shown in FIG. Figure 4 It can be seen that the absolute error of the neural network in predicting the aerodynamic coefficient of the external attachment and calculating the high-fidelity data is within 10%, which meets the accuracy requirements.

[0094] This embodiment obtains Figure 5 The results of intelligent prediction of vertical displacement of external attachments are shown in the figure; 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 diagram of the intelligent prediction of the vertical displacement of the external attachment shown in FIG. Figure 6 It can be seen that the absolute error of the neural network in predicting the spatial posture 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 intelligent prediction results of the roll angle of the external attachment shown in FIG. 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 diagram 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 of the neural network in predicting the spatial posture of the external attachment and calculating the high-fidelity data is within 10%. Since the amplitude of the calculated data is relatively small, 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 specification and implementation modes. For those familiar with the art, all features disclosed in the present invention, or steps in all methods or processes disclosed, 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 objects based on embedded neural networks, characterized in that: The steps include: (1) Construct an embedded neural network prediction model; specifically including: S1. Obtain the required calculation data through numerical simulation, select the input features of the prediction model according to the requirements, and divide the obtained data set into a training set and a test set; S2. According to the input characteristics X and output characteristics Y of the prediction model, a low-order model Y with multiple external storage 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; S3. The prediction model adopts a fully connected neural network structure, determines the hyperparameters including the number of layers, number of nodes, and activation function of the neural network, and determines the number and position of hidden layers; S4. Add a new neuron in the neural network input layer 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 in combination with 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 position of the external storage at the next moment is calculated; the spatial position of the external storage 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 position of the external storage at each moment is iteratively predicted to obtain the separation trajectory.

2. The method for intelligently predicting the separation trajectory of multiple external objects based on embedded neural network according to claim 1 is characterized in that: 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 of the next moment to iteratively predict the separation trajectory of the external attachment.

3. The method for intelligently predicting the separation trajectory of multiple external objects based on embedded neural network according to claim 1 is characterized in that: 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 Represents the aerodynamic load value of the low-order model.

4. The method for intelligently predicting the separation trajectory of multiple external objects based on 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.

5. The method for intelligently predicting the separation trajectory of multiple external objects based on embedded neural network according to claim 2 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 loads, including the aerodynamic force f G and the aerodynamic moment 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 moment M B As input to the six-degree-of-freedom motion equations; The output spatial position of the external attachment from the six-degree-of-freedom motion equation is used as the input feature of the prediction model.

6. The method for intelligently predicting the separation trajectory of multiple external objects based on embedded neural network according to claim 2 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 storage 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 rigid body's center of mass in the geodetic coordinate system, represents the first-order derivative of the velocity of the center of mass of a 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., the aerodynamic force, L is the inertia tensor, M B is the moment vector of the rigid body in the missile coordinate system, i.e., the aerodynamic moment, ω B is the rigid body angular velocity, Represents the first-order derivative of the angular velocity of a rigid body with respect to time.

7. The method for intelligently predicting the separation trajectory of multiple external objects based on embedded neural network according to claim 2 is characterized in that: In S8, the differential equation is solved by the fourth-order Runge-Kutta method, specifically: k1=f(t n ,y n ) k4=f(t n +h,y n +k3) Among them, y n The state variable vector represents the state at the nth moment. It 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.

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

9. The method for intelligently predicting the separation trajectory of multiple external objects based on 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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