Hypersonic aircraft dynamics correction method based on neural network

Abstract

The invention discloses a hypersonic aircraft dynamics correction method based on a neural network, and belongs to the technical field of aircraft dynamics. The problem that in the prior art, a traditional hypersonic aircraft dynamic correction method is low in correction precision is solved. The method comprises the following steps: S1, constructing a dynamic ideal model of the hypersonic flight vehicle according to characteristics and actual control requirements of the hypersonic flight vehicle; s2, setting a training sample according to actual data obtained by an experiment and prediction data obtained by the ideal dynamic model of the hypersonic flight vehicle, and constructing a correction relation between input and output of the ideal dynamic model of the hypersonic flight vehicle; and S3, constructing a neural network structure, training the ideal dynamic model of the hypersonic aircraft by adopting the neural network structure, and inputting a training sample to obtain an optimized correction relationship. The method improves the correction precision of the ideal dynamic model of the hypersonic aircraft, and can be applied to the correction of the state conversion quantity of the aircraft.

Description

Technical Field

[0001] The present invention relates to a hypersonic aircraft dynamics correction method, in particular to a hypersonic aircraft dynamics correction method based on a neural network, and belongs to the technical field of aircraft dynamics. Background Art

[0002] The dynamic model of hypersonic aircraft is an important basis for achieving high-precision hypersonic aircraft control, trajectory planning and guidance. However, there are often deviations between the artificially constructed dynamic model of hypersonic aircraft and the actual model. For aircraft that are often in a highly dynamic physical environment, their dynamic response is more sensitive to deviations, that is, smaller deviations may also bring larger disturbances, which will have an adverse effect on the planning and control of hypersonic aircraft.

[0003] In the prior art, the accuracy of dynamic model correction is related to the way of processing experimental data. Relevant practitioners often conduct corresponding experiments to correct the dynamic model. The technical challenges of the dynamic correction method of hypersonic aircraft are as follows: (1) Complex flow conditions: Hypersonic aircraft face extremely complex flow conditions, such as shock waves, boundary layer separation, etc. The above characteristics require the dynamic correction method to consider more nonlinear and unsteady effects; (2) Difficulty in accurate modeling: Accurate simulation of aerodynamic and thermodynamic effects at hypersonic speeds is a prerequisite for accurate modeling. The current correction method has the problem of insufficient accuracy in modeling, especially the limited prediction accuracy under extreme conditions; (3) Complexity of coupling effects: The dynamic correction of hypersonic aircraft not only involves aerodynamics, but also thermal effects, structural dynamics and coupling effects of control systems, which increases the complexity of system design and analysis; (4) Difficulty in experimental verification: Since the flow and thermodynamic effects under hypersonic conditions are difficult to fully simulate in ground laboratories, the reliability and accuracy of the dynamic correction method usually needs to rely on large-scale numerical simulations and wind tunnel experiments.

[0004] In summary, a hypersonic vehicle dynamics correction method with high correction accuracy is needed. Summary of the invention

[0005] A brief overview of the present invention is provided below in order to provide a basic understanding of certain aspects of the present invention. It should be understood that this overview is not an exhaustive overview of the present invention. It is not intended to identify key or important parts of the present invention, nor is it intended to limit the scope of the present invention. Its purpose is merely to present certain concepts in a simplified form as a prelude to a more detailed description discussed later.

[0006] In view of this, in order to solve the problem of low correction accuracy of traditional hypersonic aircraft dynamics correction methods in the prior art, the present invention provides a hypersonic aircraft dynamics correction method based on a neural network.

[0007] The technical solution is as follows: A hypersonic vehicle dynamics correction method based on a neural network specifically comprises the following steps:

[0008] S1. Construct an ideal dynamics model of hypersonic aircraft according to the characteristics of hypersonic aircraft and actual control requirements;

[0009] S2. According to the actual data obtained from the experiment and the predicted data obtained from the ideal model of hypersonic aircraft dynamics, the input of the ideal model of hypersonic aircraft dynamics is set as a training sample, and the correction relationship between its input and output is constructed;

[0010] S3. Construct a neural network structure, use the neural network structure to train the ideal model of hypersonic vehicle dynamics, input training samples, and obtain the optimized correction relationship.

[0011] Furthermore, in S1, it is assumed that the hypersonic aircraft does not have sideslip, and the aerodynamic drag coefficient C D and the aerodynamic lift coefficient C L It is expressed as:

[0012] C D =d 00 +d 10 α+d 01 ma+d 11 α·ma+d 20 α 2 +d 02 ma 2

[0013] C L = l 00 +l 10 α+l 01 ma+l 11 α·ma+l 20 α 2 +l 02 ma 2

[0014] Where α is the angle of attack, ma is the Mach number, and d ij is the characterization parameter of the aerodynamic drag coefficient under the polynomial characterization method, l ij is the characterization parameter of the aerodynamic lift coefficient under the polynomial characterization method;

[0015] Considering the Earth's oblateness, Earth's rotation and gravitational perturbation, an ideal model M of hypersonic vehicle dynamics is constructed;

[0016] The ideal model M of hypersonic vehicle dynamics is expressed as:

[0017]

[0018] in, is the dimensionless distance from the center of the Earth, R0 is the average radius of the Earth, which represents the dimensionless distance from the center of the Earth. The dimensionless parameter of , r is the distance from the center of the earth, θ is the longitude, φ is the latitude, is the dimensionless velocity of the aircraft relative to the earth, g0 is the gravitational acceleration at sea level, γ is the path angle, ψ is the heading angle, is the dimensionless earth rotation angular velocity, σ is the aircraft roll angle, is the dimensionless lift, is the dimensionless drag acceleration.

[0019] Furthermore, in S3, according to the actual experimental conditions, time t k-1 The actual state quantity is x k-1 , time t k-1 The actual state change in the time interval Δt is Δx k-1,real , time t k The actual state quantity is x k,real , time t k The actual state change in the time interval Δt is Δx k,real , for the ideal model M' of hypersonic vehicle dynamics, at time t k-1 The predicted state change in the time interval Δt is Δx k-1,pre , time t k The predicted state change in the time interval Δt is Δx k,pre , time t k The predicted state change Δx k,pre and the actual state change Δx k,real The deviation is ΔX k ;

[0020] The state change amount includes speed V, path angle γ and heading angle ψ;

[0021] Set the time t k-1 The actual state x k-1 , actual state change Δx k-1,real and the predicted state change Δx k-1,pre As the input of the ideal model M of hypersonic vehicle dynamics, i.e., the training sample, the deviation ΔX k As the output of the hypersonic vehicle dynamics model M;

[0022] The input and output of the hypersonic vehicle dynamics model M are expressed as:

[0023] input:Δx k-1,real ,Δx k-1,pre ,x k-1

[0024] output:ΔX k =Δx k,real -Δx k,pre

[0025] Construct the correction relationship f between the input and output of the hypersonic vehicle dynamics model M * ;

[0026]

[0027] Furthermore, in S4, the neural network structure includes an input layer F input , fully connected layer F fcn 、Tanh activation layer F tan , LayerNorm normalization layer F layernorm , Relu activation layer F relu And the output layer F output ;

[0028] In the input layer F of the neural network structure input Input training samples, through the fully connected layer F fcn 、Tanh activation layer F tan and LayerNorm normalization layer F layernorm After that, it passes through the fully connected layer F fcn and Relu activation layer F relu The optimization cycle is repeated three times, and finally the fully connected layer F tan Then the output layer F output Output optimized correction relationship f * ;

[0029] The process of building a neural network structure is expressed as:

[0030] F input (x) = W input x+b input

[0031] F fcn (x) = W fcn x+b fcn

[0032] F output (x) = W output x+b output

[0033]

[0034] F relu (x)=max(0,x)

[0035]

[0036] μ=mean(x),σ=var(x)

[0037] Among them, W input The input layer F input The weight, W fcn is the fully connected layer F fcn The weight, W output The output layer F output The weight of b input The input layer F input The bias coefficient, b fcn is the fully connected layer F fcn The bias coefficient, b output The output layer F output The bias coefficient of γ' is the normalization layer F of LayerNorm layernorm The scaling factor of γ'=1, β is the LayerNorm normalization layer F layernorm The offset coefficient, β = 0, μ is the mean of the input x, mean is the mean function, σ is the variance of the input x, var is the variance function, max is the maximum value function, ∈ is a small amount to maintain numerical stability;

[0038] The input layer F input The sample nodes are determined by the input sample dimension, which is 24 dimensions. The 24 dimensions are composed of the six states of the ideal model of hypersonic vehicle dynamics and the time t k-1 The actual state x k-1 , actual state change Δx k-1,real and the predicted state change Δx k-1,pre Composition, fully connected layer F fcn It is a network structure where each node is connected to the nodes in the next layer. The output layer F output The sample nodes are determined by the output sample dimension, which is 6 dimensions.

[0039] The beneficial effects of the present invention are as follows: the present invention first establishes a three-degree-of-freedom dynamics model of a hypersonic aircraft, namely, an ideal model of hypersonic aircraft dynamics, and then obtains real data of the aircraft through experiments, compares the real data with the output data of the ideal model of hypersonic aircraft dynamics, namely, the state change quantity, and finally uses a self-constructed neural network structure to mine the deviation relationship between the experimental data and the model data, and corrects the ideal model of hypersonic aircraft dynamics. The output of the hypersonic aircraft dynamics model, namely, the corrected state change quantity, can be obtained through the correction relationship, thereby realizing precise hypersonic aircraft dynamics correction; the present invention further verifies the effectiveness of the correction by constructing an artificial model M2 of hypersonic aircraft dynamics for numerical simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0041] Figure 1 It is a flowchart of a hypersonic vehicle dynamics correction method based on a neural network;

[0042] Figure 2 It is a schematic diagram of the neural network structure;

[0043] Figure 3 Schematic diagram of training loss for ;

[0044] Figure 4 Schematic diagram of verification loss for ;

[0045] Figure 5 This is a schematic diagram of speed correction comparison;

[0046] Figure 6 This is a schematic diagram of path angle correction comparison;

[0047] Figure 7 This is a schematic diagram for comparing heading angle corrections;

[0048] Figure 8 It is a schematic diagram of speed deviation;

[0049] Fig. 9 is a schematic diagram of path angle deviation;

[0050] Fig.10 Schematic diagram of heading angle deviation. DETAILED DESCRIPTION

[0051] In order to make the technical solutions and advantages of the embodiments of the present invention more clearly understood, the exemplary embodiments of the present invention are further described in detail below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than an exhaustive list of all the embodiments. It should be noted that the embodiments of the present invention and the features in the embodiments can be combined with each other without conflict.

[0052] refer to Figure 1-Figure 10 The present embodiment is described in detail, a method for correcting hypersonic vehicle dynamics based on a neural network, specifically comprising the following steps:

[0053] S1. Construct an ideal dynamics model of hypersonic aircraft according to the characteristics of hypersonic aircraft and actual control requirements;

[0054] S2. According to the actual data obtained from the experiment and the predicted data obtained from the ideal model of hypersonic aircraft dynamics, the input of the ideal model of hypersonic aircraft dynamics is set as a training sample, and the correction relationship between its input and output is constructed;

[0055] S3. Construct a neural network structure, use the neural network structure to train the ideal model of hypersonic vehicle dynamics, input training samples, and obtain the optimized correction relationship.

[0056] Furthermore, in S1, it is assumed that the hypersonic aircraft does not have sideslip, and the aerodynamic drag coefficient C D and the aerodynamic lift coefficient C L It is expressed as:

[0057] C D =d 00 +d 10 α+d 01 ma+d 11 α·ma+d 20 α 2 +d 02 ma 2

[0058] C L = l 00 +l 10 α+l 01 ma+l 11 α·ma+l 20 α 2 +l 02 ma 2

[0059] Where α is the angle of attack, ma is the Mach number, and d ij is the characterization parameter of the aerodynamic drag coefficient under the polynomial characterization method, l ijis the characterization parameter of the aerodynamic lift coefficient under the polynomial characterization method;

[0060] Considering the Earth's oblateness, Earth's rotation and gravitational perturbation, an ideal model M of hypersonic vehicle dynamics is constructed;

[0061] The ideal model M of hypersonic vehicle dynamics is expressed as:

[0062]

[0063] in, is the dimensionless distance from the center of the Earth, R0 is the average radius of the Earth, which represents the dimensionless distance from the center of the Earth. The dimensionless parameter of , r is the distance from the center of the earth, θ is the longitude, φ is the latitude, is the dimensionless velocity of the aircraft relative to the earth, g0 is the gravitational acceleration at sea level, γ is the path angle, ψ is the heading angle, is the dimensionless earth rotation angular velocity, σ is the aircraft roll angle, is the dimensionless lift, is the dimensionless drag acceleration.

[0064] Furthermore, in S3, according to the actual experimental conditions, time t k-1 The actual state quantity is x k-1 , time t k-1 The actual state change in the time interval Δt is Δx k-1,real , time t k The actual state quantity is x k,real , time t k The actual state change in the time interval Δt is Δx k,real , for the ideal model M' of hypersonic vehicle dynamics, at time t k-1 The predicted state change in the time interval Δt is Δx k-1,pre , time t k The predicted state change in the time interval Δt is Δx k,pre , time t k The predicted state change Δx k,pre and the actual state change Δx k,real The deviation is ΔX k ;

[0065] The state change amount includes speed V, path angle γ and heading angle ψ;

[0066] Set the time t k-1 The actual state x k-1 , actual state change Δx k-1,real and the predicted state change Δxk-1,pre As the input of the ideal model M of hypersonic vehicle dynamics, i.e., the training sample, the deviation ΔX k As the output of the hypersonic vehicle dynamics model M;

[0067] The input and output of the hypersonic vehicle dynamics model M are expressed as:

[0068] input:Δx k-1,real ,Δx k-1,pre ,x k-1

[0069] output:ΔX k =Δx k,real -Δx k,pre

[0070] Construct the correction relationship f between the input and output of the hypersonic vehicle dynamics model M * ;

[0071]

[0072] Furthermore, in S4, the neural network structure includes an input layer F input , fully connected layer F fcn 、Tanh activation layer F tan , LayerNorm normalization layer F layernorm , Relu activation layer F relu And the output layer F output ;

[0073] In the input layer F of the neural network structure input Input training samples, through the fully connected layer F fcn 、Tanh activation layer F tan and LayerNorm normalization layer F layernorm After that, it passes through the fully connected layer F fcn and Relu activation layer F relu The optimization cycle is repeated three times, and finally the fully connected layer F fcn Then the output layer F output Output optimized correction relationship f * ;

[0074] The process of building a neural network structure is expressed as:

[0075] F input (x) = W input x+b input

[0076] F fcn (x) = W fcn x+bfcn

[0077] F output (x) = W output x+b output

[0078]

[0079] F relu (x)=max(0,x)

[0080]

[0081] μ=mean(x),σ=var(x)

[0082] Among them, W input The input layer F input The weight, W fcn is the fully connected layer F fcn The weight, W output The output layer F output The weight of b input The input layer F input The bias coefficient, b fcn is the fully connected layer F fcn The bias coefficient, b output The output layer F output The bias coefficient of γ' is the normalization layer F of LayerNorm layernorm The scaling factor of γ'=1, β is the LayerNorm normalization layer F layernorm The offset coefficient, β = 0, μ is the mean of the input x, mean is the mean function, σ is the variance of the input x, var is the variance function, max is the maximum value function, ∈ is a small amount to maintain numerical stability;

[0083] The input layer F input The sample nodes are determined by the input sample dimension, which is 24 dimensions, which is determined by the dimensionless distance from the center of the earth of the ideal model of hypersonic vehicle dynamics. Longitude θ, latitude φ, dimensionless speed Path angle γ, heading angle ψ and time t k-1 The actual state x k-1 , actual state change Δx k-1,real and the predicted state change Δx k-1,pre Composition, fully connected layer F fcn It is a network structure where each node is connected to the nodes in the next layer. The output layer F output The sample nodes are determined by the output sample dimension, which is 6 dimensions;

[0084] Specifically, in this embodiment, the hyperparameters of the neural network structure include a learning rate of 0.0001, an optimization algorithm using the Adam optimizer, a hidden layer node of 500, where the hidden layer is all fully connected layers except the input layer and the output layer, a batch size of 256, a training sample size of 10,000, and a training iteration number of 100;

[0085] The ideal model M of hypersonic aircraft dynamics constructed in step S1 is used as the actual model M1 of hypersonic aircraft dynamics, and the state quantity and state quantity transformation quantity returned by the actual model M1 of hypersonic aircraft dynamics are set to the actual data obtained from the experiment;

[0086] Construct an artificial model M2 of hypersonic aircraft dynamics, which does not consider the rotation of the earth and gravitational perturbation. The aerodynamic lift coefficient is 0.8 times the nominal value of the actual model M1 of hypersonic aircraft dynamics, and the aerodynamic drag coefficient is 1.3 times the nominal value of the actual model M1 of hypersonic aircraft dynamics. Affected by the mass deviation, the velocity increment δV(mass), path angle increment δγ(mass), and heading angle increment δψ(mass) of the artificial model M2 of hypersonic aircraft dynamics are increased by an offset of 0.1 based on the actual model M1 of hypersonic aircraft dynamics.

[0087] The artificial model M2 of hypersonic vehicle dynamics is expressed as:

[0088]

[0089] The present invention is used to correct the artificial model M2 of hypersonic aircraft dynamics. Since the deviation of the artificial model M2 of hypersonic aircraft dynamics relative to the actual model M1 of hypersonic aircraft dynamics will only affect the state change of the speed V, the path angle γ and the heading angle ψ, only the above three quantities are analyzed. The present invention can effectively correct the state change of the artificial model M2 of hypersonic aircraft dynamics, and the data of the corrected artificial model M2 of hypersonic aircraft dynamics is very close to the data of the original dynamics model.

[0090] refer to Figure 3 , the training loss result is obtained by training the training samples in step S2 through the neural network structure;

[0091] refer to Figure 4 ,The validation loss result is obtained by training the neural network structure with the test set constructed by the real ,experimental data;

[0092] refer to Figure 5 , V real is the velocity of the actual model M1 of the hypersonic vehicle dynamics, V fakeis the predicted speed after neural network correction, V fakewithoutoffset is the predicted speed without neural network correction;

[0093] refer to Figure 6 , γ real is the path angle of the actual model M1 of the hypersonic vehicle dynamics, γ fake is the predicted path angle after neural network correction, γ fakewithoutoffset is the predicted path angle without neural network correction;

[0094] refer to Figure 7 , ψ real is the heading angle of the actual model M1 of the hypersonic vehicle dynamics, ψ fake is the predicted heading angle after neural network correction, ψ fakewithoutoffset is the predicted heading angle without neural network correction;

[0095] refer to Figure 8 , V bias withoutoffset is the uncorrected velocity of the artificial model M2 of the hypersonic vehicle dynamics, V bias withoffset is the corrected speed of the artificial model M2 of the hypersonic vehicle dynamics;

[0096] refer to Fig. 9 , γ bias Withoutoffset is the uncorrected path angle of the artificial model M2 of hypersonic vehicle dynamics, γ bias withoffset The corrected path angle of the artificial model M2 of hypersonic vehicle dynamics;

[0097] refer to Fig.10 , ψ bias Withoutoffset is the uncorrected heading angle of the artificial model M2 of the hypersonic vehicle dynamics, ψ bias withoffset is the corrected heading angle of the artificial model M2 of the hypersonic vehicle dynamics.

[0098] Although the present invention has been described according to a limited number of embodiments, it will be apparent to those skilled in the art, with the benefit of the above description, that other embodiments may be envisioned within the scope of the invention thus described. In addition, it should be noted that the language used in this specification is selected primarily for readability and teaching purposes, rather than for explaining or defining the subject matter of the present invention. Therefore, many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the appended claims. The disclosure of the present invention is illustrative, not restrictive, with respect to the scope of the present invention, which is defined by the appended claims.

Claims

1. A hypersonic vehicle dynamics correction method based on neural network, characterized in that: The following steps are involved: S1. Construct an ideal dynamics model of hypersonic aircraft according to the characteristics of hypersonic aircraft and actual control requirements; S2. According to the actual data obtained from the experiment and the predicted data obtained from the ideal model of hypersonic aircraft dynamics, the input of the ideal model of hypersonic aircraft dynamics is set as a training sample, and the correction relationship between its input and output is constructed; S3. Construct a neural network structure, use the neural network structure to train the ideal model of hypersonic vehicle dynamics, input training samples, and obtain the optimized correction relationship.

2. The method for correcting hypersonic vehicle dynamics based on a neural network according to claim 1, characterized in that: In S1, it is assumed that the hypersonic aircraft does not have sideslip, and the aerodynamic drag coefficient C D and the aerodynamic lift coefficient C L It is expressed as: C D =d 00 +d 10 α+d 01 ma+d 11 α·ma+d 20 alpha 2 +d 02 my 2 C L l 00 +l 10 α+l 01 ma+l 11 α·ma+l 20 alpha 2 +l 02 my 2 Where α is the angle of attack, ma is the Mach number, and d ij is the characterization parameter of the aerodynamic drag coefficient under the polynomial characterization method, l ij is the characterization parameter of the aerodynamic lift coefficient under the polynomial characterization method; Considering the Earth's oblateness, Earth's rotation and gravitational perturbation, an ideal model M of hypersonic vehicle dynamics is constructed; The ideal model M of hypersonic vehicle dynamics is expressed as: in, is the dimensionless distance from the center of the Earth, R0 is the average radius of the Earth, which represents the dimensionless distance from the center of the Earth. The dimensionless parameter of , r is the distance from the center of the earth, θ is the longitude, φ is the latitude, is the dimensionless velocity of the aircraft relative to the earth, g0 is the gravitational acceleration at sea level, γ is the path angle, ψ is the heading angle, is the dimensionless earth rotation angular velocity, σ is the aircraft roll angle, is the dimensionless lift, is the dimensionless drag acceleration.

3. The method for correcting hypersonic vehicle dynamics based on a neural network according to claim 2, characterized in that: In S3, according to the actual experimental conditions, time t k-1 The actual state quantity is x k-1 , time t k-1 The actual state change in the time interval Δt is Δx k-1,real , time t k The actual state quantity is x k,real , time t k The actual state change in the time interval Δt is Δx k,real , for the ideal model M' of hypersonic vehicle dynamics, at time t k-1 The predicted state change in the time interval Δt is Δx k-1,pre , time t k The predicted state change in the time interval Δt is Δx k,pre , time t k The predicted state change Δx k,pre and the actual state change Δx k,real The deviation is ΔX k ; The state change amount includes speed V, path angle γ and heading angle ψ; Set the time t k-1 The actual state x k-1 , actual state change Δx k-1,real and the predicted state change Δx k-1,pre As the input of the ideal model M of hypersonic vehicle dynamics, i.e., the training sample, the deviation ΔX k As the output of the hypersonic vehicle dynamics model M; The input and output of the hypersonic vehicle dynamics model M are expressed as: input:Δx k-1,real ,Δx k-1,pre ,x k-1 output:ΔX k =Δx k,real -Δx k,pre Construct the correction relationship f between the input and output of the hypersonic vehicle dynamics model M * ; 4. The method for correcting hypersonic vehicle dynamics based on a neural network according to claim 3, characterized in that: In S4, the neural network structure includes an input layer F input , fully connected layer F fcn 、Tanh activation layer F tan , LayerNorm normalization layer F layernorm , Relu activation layer F relu And the output layer F output ; In the input layer F of the neural network structure input Input training samples, through the fully connected layer F fcn 、Tanh activation layer F tan and LayerNorm normalization layer F layernorm After that, it passes through the fully connected layer F fcn and Relu activation layer F relu The optimization cycle is repeated three times, and finally the fully connected layer F tan Then the output layer F output Output optimized correction relationship f * ; The process of building a neural network structure is expressed as: F input (x)=W input x+b input F fcn (x)=W fcn x+b fcn F output (x)=W output x+b output F relu (x)=max(0,x) μ=mean(x),σ=var(x) Among them, W input The input layer F input The weight, Wf cn is the fully connected layer F fcn The weight, W output The output layer F output The weight of b input The input layer F input The bias coefficient, b fcn is the fully connected layer F fcn The bias coefficient, b output The output layer F output The bias coefficient of γ' is the normalization layer F of LayerNorm layernorm The scaling factor of γ'=1, β is the LayerNorm normalization layer F layernorm The offset coefficient, β = 0, μ is the mean of the input x, mean is the mean function, σ is the variance of the input x, var is the variance function, max is the maximum value function, ∈ is a small amount to maintain numerical stability; The input layer F input The sample nodes are determined by the input sample dimension, which is 24 dimensions. The 24 dimensions are composed of the six states of the ideal model of hypersonic vehicle dynamics and the time t k-1 The actual state x k-1 , actual state change Δx k-1,real and the predicted state change Δx k-1,pre Composition, fully connected layer F fcn It is a network structure where each node is connected to the nodes in the next layer. The output layer F output The sample nodes are determined by the output sample dimension, which is 6 dimensions.

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