Gaussian process modeling method for controlled separation steerage of combined aircraft

Abstract

The invention discloses a Gaussian process modeling method for a controlled separation steerage of an assembly aircraft, and belongs to the technical field of aerodynamics. In order to achieve the steering aerodynamic force obtaining precision of the combined aircraft, the method comprises the steps that a steering aerodynamic force database of a secondary aircraft in a disturbing flow field in the separation process of the combined aircraft is obtained through a wind tunnel grid force measurement test; the obtained first-stage aircraft attack angle, second-stage aircraft attack angle, two-stage aircraft gap and second-stage aircraft rudder deflection angle are combined into an input feature matrix, and the obtained pitching rudder deflection moment of the second-stage aircraft in the interference flow field of the first-stage aircraft serves as an output vector to obtain a training set, a verification set and a test set; and importing the training set into a Gaussian process regression model, training the Gaussian process regression model, verifying the trained Gaussian process regression model by using the verification set, and then testing by using the test set to obtain the Gaussian process regression model of the controlled separation steerage of the combined aircraft to predict the steerage aerodynamic torque.

Description

Technical Field

[0001] The invention belongs to the technical field of aerodynamics, and in particular relates to a Gaussian process modeling method for a controlled separation rudder effect of a combined aircraft. Background Art

[0002] Hypersonic complex vehicles mainly include various types of aerospace complex vehicles, such as aerospace planes carrying orbiters, satellite radars, jammers, hypersonic missiles, high-energy laser interceptors and other new strategic weapons. In the problem of interstage separation of complex vehicles, the larger vehicle is called the first-stage vehicle, and the smaller vehicle is called the second-stage vehicle. The separation problem of complex vehicles is also called interstage separation.

[0003] In the interstage separation problem, as the distance between the two large aircraft increases, the two-stage interference flow field forms a channel flow. When the height of the separation channel between the first-stage aircraft and the second-stage aircraft is small, the two-stage head shock waves interfere with each other, and the second-stage aircraft causes a large flow separation on the first-stage aircraft. The flow separation generates a separation shock wave, and the separation shock wave interacts with the head shock wave. The flow in the channel is all subsonic. When the height of the separation channel is large, the shock waves of the first-stage aircraft and the second-stage aircraft head reflect back and forth in the channel to form a shock wave train. When the height of the separation channel is large to a certain extent, the shock waves of the first-stage aircraft and the second-stage aircraft head cannot form a shock wave train in the channel, but there are still shock waves and shock wave reflection waves. Due to the drastic changes in the channel flow, in the interstage separation problem with control law, the rudder effect characteristics of the second-stage aircraft are significantly different from those in the free flow field, and the rudder effect characteristics show complex nonlinear change characteristics.

[0004] In the conventional aircraft-missile separation problems such as aircraft external loadout and internal weapon launch with control law, the rudder effect of the dropped missile in the disturbance flow field is usually not much different from that in the free flow field. Therefore, the rudder effect in the free flow field can be used to replace the rudder effect in the disturbance flow field. The rudder effect in the free flow field usually changes linearly with the rudder deviation. Therefore, in the free flow field rudder effect database of dropped objects, linear interpolation can approximate its rudder effect in the interference flow field of the carrier aircraft. In the interstage separation problem, due to the obvious gap between the rudder effect characteristics of the second-stage aircraft and the rudder effect characteristics in the free flow field, its rudder effect in the free flow cannot be directly used to equate its rudder effect in the disturbance flow field. Moreover, the rudder effect characteristics of the second-stage aircraft in the disturbance flow field show complex nonlinear change characteristics. Therefore, the use of linear interpolation rudder effect modeling method will cause distortion of the rudder effect aerodynamic force, and a suitable rudder effect modeling method needs to be established. Summary of the invention

[0005] The problem to be solved by the present invention is to improve the accuracy of obtaining the aerodynamic force of the rudder effect of a combined aircraft, and a Gaussian process modeling method for the controlled separation rudder effect of a combined aircraft is proposed.

[0006] To achieve the above object, the present invention is implemented through the following technical solutions: A Gaussian process modeling method for controlled separation rudder effect of a combined aircraft comprises the following steps: S1. Obtain the rudder effect aerodynamic database of the secondary vehicle under the interference flow field during the separation process of the combined vehicle through wind tunnel grid force measurement test; S2. The first-stage aircraft angle of attack, the second-stage aircraft angle of attack, the clearance between the two-stage aircraft and the second-stage aircraft rudder deflection angle obtained in the rudder effect aerodynamic database of the second-stage aircraft under the interference flow field in step S1 are combined into an input feature matrix, and the pitch rudder deflection moment of the second-stage aircraft in the first-stage aircraft interference flow field is obtained as an output vector to construct a rudder effect aerodynamic data set, and the data set is divided into a training set, a validation set and a test set in a ratio of 8:1:1; S3. Import the training set obtained in step S2 into the Gaussian process regression model, train the Gaussian process regression model, verify the trained Gaussian process regression model using the validation set, and then test it using the test set to obtain the Gaussian process regression model of the controlled separation rudder effect of the combined aircraft to predict the rudder effect aerodynamic torque.

[0007] Furthermore, during the separation process between the first-stage aircraft and the second-stage aircraft in step S1, the pitch moment of the second-stage aircraft is a nonlinear function of the first-stage aircraft angle of attack, the second-stage aircraft angle of attack, the clearance between the two-stage aircraft and the pitch rudder angle of the second-stage aircraft, as shown in the following formula: ; in, is the pitch moment coefficient of the secondary vehicle, is the first-stage vehicle angle of attack, is the secondary vehicle angle of attack, is the clearance between the two-stage aircraft, It is the pitch rudder deflection angle of the secondary aircraft.

[0008] Furthermore, during the wind tunnel grid force measurement test in step S1, four parameters, namely the first-stage aircraft angle of attack, the second-stage aircraft angle of attack, the two-stage aircraft clearance and the second-stage aircraft pitch rudder deflection angle, are arranged and combined to form a test condition, wherein the first-stage aircraft angle of attack is set to 0°, the second-stage aircraft pitch control surface only performs positive deflection, the second-stage rudder deflection angle is selected to be 0°, 5°, 10°, 15, the second-stage aircraft angle of attack is selected to be 0°, 1°, 2°, 3°, and the center of mass distance of the two-stage aircraft is selected to be 5 meters, 5.5 meters, 6 meters, 7 meters, 8 meters, 10 meters, and 13 meters, which are combined into the grid point state of the second-stage aircraft rudder effect grid force measurement test, and the pitch moment of the second-stage aircraft measured in the test is the pitch rudder effect aerodynamic force of the second-stage aircraft.

[0009] Furthermore, the solution of the Gaussian process in step S3 includes the solution of the mean function and the solution of the covariance function. The expressions of the mean function and the covariance function are as follows: ; in, Enter the first variable into the model, Enter the second variable into the model, is the model expression function, E is the mathematical expectation operator, which means to find the mathematical expectation of the function in the brackets. is the mean function, which describes the average trend of the model output when the input is x. is the covariance function, which is used to measure the model under different input and The correlation between the following outputs; The variables in the input space are the normal position of the secondary aircraft, the angle of attack of the primary aircraft, and the vector combination of the angle of attack of the secondary aircraft and the pitch rudder angle of the secondary aircraft; The Gaussian process is expressed as: ; in, represents a Gaussian process.

[0010] Furthermore, in step S3, based on the Gaussian process The following regression model is established: ; in, is the observation result of the pitch and rudder effect aerodynamic force of the second-stage aircraft, is the noise term, ; represents a normal distribution, is the noise term The standard deviation is used to measure the dispersion of noise; The aerodynamic observation results of the pitch and rudder effect of the second-stage aircraft were obtained. The prior distribution of is: ; in, is an n-order identity matrix, whose main diagonal elements are all 1 and the rest are all 0. The covariance matrix of the training input X itself is used to describe the correlation between different samples in the training set.

[0011] Further, the pitch rudder effect aerodynamic observation result of the secondary aircraft in step S3 The prediction results of the pitch and rudder aerodynamic force of the second-stage aircraft The associated prior distribution of is: ; in, Input for training Its own covariance matrix, Input for training With test input The covariance matrix established between For test input With training input The covariance matrix established between For test input Its own covariance matrix; Aerodynamic observation results based on the pitch and rudder effect of a two-stage aircraft The prediction results of the pitch and rudder aerodynamic force of the second-stage aircraft The associated prior distribution of the pitch rudder effect aerodynamic prediction results of the second-stage aircraft are deduced The posterior distribution of is: ; in, Given training data and test input Under the condition of , the average value of the prediction results of the pitch rudder effect aerodynamic force of the secondary aircraft is, For test input The variance of the corresponding prediction results reflects the degree of dispersion of the predicted values ​​around the mean. The larger the variance, the higher the uncertainty of the predicted value. ; ; in, The prediction results of the pitch and rudder aerodynamic force of the second-stage aircraft The covariance of is used to measure the dispersion of the predicted values ​​and the correlation between the dimensions.

[0012] Beneficial effects of the present invention: The Gaussian process modeling method for the controlled separation rudder effect of a combined aircraft described in the present invention is based on the Gaussian process regression method in the traditional machine learning method. It takes the different normal positions of the secondary aircraft in the interference flow field of the first-stage aircraft, different first-stage and second-stage aircraft angles of attack, and different second-stage aircraft pitch and rudder deflections as input objects. When the second-stage aircraft is in the interference flow field of the first-stage aircraft, the accurate prediction of the pitch and rudder deflection moment of the second-stage aircraft can be achieved.

[0013] The Gaussian process modeling method for the controlled separation rudder effect of a combined aircraft described in the present invention can effectively capture the nonlinear characteristics of the aerodynamic force of the rudder effect of the secondary aircraft through the Gaussian process modeling method, and avoid the distortion problem caused by the linear assumption of the traditional interpolation method. At the same time, through the flexible selection of the kernel function, the model can accurately fit the complex aerodynamic data distribution, and the prediction accuracy is significantly improved. In terms of the uncertainty quantification of the predicted value, the Gaussian process not only provides the predicted value, but also outputs the confidence interval of the predicted result, quantifies the uncertainty of the prediction, and provides more reliable data support for engineering decision-making. In terms of cost and efficiency, by adjusting the hyperparameters through the optimization algorithm, the model significantly reduces the computational cost and complexity while ensuring accuracy, and is suitable for real-time or near real-time engineering application scenarios. Through the above technical solution, the present invention can significantly improve the prediction accuracy of the pitch rudder moment of the secondary aircraft, provide more accurate aerodynamic data support for the controlled separation of the combined aircraft, thereby effectively improving the safety and reliability of the aircraft separation process. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a flow chart of a Gaussian process modeling method for a controlled separation rudder effect of a combined aircraft according to the present invention; Figure 2 This is a training block diagram of the Gaussian process regression model described in the present invention. DETAILED DESCRIPTION

[0015] In order to make the purpose, technical solution and advantages of the present invention more clear, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention, that is, the specific embodiments described are only part of the embodiments of the present invention, rather than all of the specific embodiments. The components of the specific embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations, and the present invention can also have other embodiments.

[0016] Therefore, the following detailed description of the specific embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents the selected specific embodiments of the present invention. Based on the specific embodiments of the present invention, all other specific embodiments obtained by those skilled in the art without making creative work are within the scope of protection of the present invention.

[0017] In order to further understand the content, features and effects of the present invention, the following specific implementation methods are given as examples, and the attached Figure 1 and attached Figure 2 The detailed instructions are as follows:

[0018] Embodiment 1: A Gaussian process modeling method for controlled separation rudder effect of a combined aircraft comprises the following steps: S1. Obtain the rudder effect aerodynamic database of the secondary vehicle under the interference flow field during the separation process of the combined vehicle through wind tunnel grid force measurement test; Furthermore, during the separation process between the first-stage aircraft and the second-stage aircraft in step S1, the pitch moment of the second-stage aircraft is a nonlinear function of the first-stage aircraft angle of attack, the second-stage aircraft angle of attack, the clearance between the two-stage aircraft and the pitch rudder angle of the second-stage aircraft, as shown in the following formula: ; in, is the pitch moment coefficient of the secondary vehicle, is the first-stage vehicle angle of attack, is the secondary vehicle angle of attack, is the clearance between the two-stage aircraft, is the pitch rudder deflection angle of the secondary aircraft; Further, in step S1, during the wind tunnel grid force measurement test, four parameters, namely, the first-stage aircraft angle of attack, the second-stage aircraft angle of attack, the two-stage aircraft clearance, and the second-stage aircraft pitch rudder deflection angle, are arranged and combined to form a test condition, the first-stage aircraft angle of attack is set to 0°, the second-stage aircraft pitch control surface is only positively deflected, the second-stage rudder deflection angle is selected as 0°, 5°, 10°, 15°, the second-stage aircraft angle of attack is selected as 0°, 1°, 2°, 3°, the two-stage aircraft center of mass distance is selected as 5 meters, 5.5 meters, 6 meters, 7 meters, 8 meters, 10 meters, 13 meters, and the combination is a grid point state of the second-stage aircraft rudder effect grid force measurement test, and the pitch moment of the second-stage aircraft measured in the test is the pitch rudder effect aerodynamic force of the second-stage aircraft; The database is mainly composed of the aircraft position information and attitude angle, and the pitch rudder aerodynamic force of the secondary aircraft. The position information and attitude angle mainly include the normal position distribution of the secondary aircraft in the interference flow field of the first aircraft, the first aircraft angle of attack, the second aircraft angle of attack and the second aircraft pitch rudder deflection angle, forming the test conditions, and the pitch moment of the second aircraft measured by the test is the pitch rudder aerodynamic force of the second aircraft.

[0019] S2. The first-stage aircraft angle of attack, the second-stage aircraft angle of attack, the clearance between the two-stage aircraft and the second-stage aircraft rudder deflection angle obtained in the rudder effect aerodynamic database of the second-stage aircraft under the interference flow field in step S1 are combined into an input feature matrix, and the pitch rudder deflection moment of the second-stage aircraft in the first-stage aircraft interference flow field is obtained as an output vector to construct a rudder effect aerodynamic data set, and the data set is divided into a training set, a validation set and a test set in a ratio of 8:1:1; Furthermore, in step S2, a data set is constructed for the Gaussian process modeling method of the controlled separation rudder effect of the combined aircraft. Specifically, by defining the normal position distribution of the secondary aircraft in the interference flow field of the first-stage aircraft (i.e., the vertical distance variation range of the secondary aircraft relative to the first-stage aircraft), the variation range of the angle of attack of the first-stage aircraft, the variation range of the angle of attack of the second-stage aircraft, and the distribution of the pitch rudder deflection angle of the second-stage aircraft as input objects, a 5-channel data set is generated. Among them, the first 4 channels correspond to: the normal position of the secondary aircraft (relative to the vertical distance of the first-stage aircraft), the angle of attack of the first-stage aircraft, the angle of attack of the second-stage aircraft, and the pitch rudder deflection angle of the second-stage aircraft. The fifth channel, as the output of the Gaussian process regression model, corresponds to the pitch rudder deflection moment of the secondary aircraft (i.e., the aerodynamic moment generated by the pitch rudder deflection). By modeling the rudder effect characteristics of the secondary aircraft in the interference flow field, a fitting function of the nonlinear characteristics of the rudder effect of the secondary aircraft is constructed. As shown in the following formula: ; in, is the predicted value of the pitch moment coefficient of the secondary aircraft, The model can accurately predict the variation law of the pitch rudder moment of the secondary aircraft under the conditions of normal position distribution, the range of attack angles of the first and second aircraft, and the distribution of pitch rudder angles.

[0020] S3. Import the training set obtained in step S2 into the Gaussian process regression model, train the Gaussian process regression model, verify the trained Gaussian process regression model using the validation set, and then test it using the test set to obtain the Gaussian process regression model of the controlled separation rudder effect of the combined aircraft to predict the rudder effect aerodynamic torque.

[0021] Furthermore, in step S3, the Gaussian process is a non-parametric machine learning method based on Bayesian reasoning. It infers the uncertainty of data by defining a Gaussian process in the function space, and uses a kernel function to describe the similarity between input data points, and can provide a probability distribution of the prediction results, and quantify the uncertainty of the model prediction. The overall prediction process of the Gaussian process model is described as follows: First, the current data set is preprocessed, including cleaning (processing missing values ​​and outliers), feature selection and scaling, and the data set is divided into a training set and a test set; second, the kernel function of the Gaussian process model is selected. The core of the Gaussian process is the kernel function (also called the covariance function), which defines the correlation and similarity between data points. At this stage, it is necessary to select a suitable kernel function according to the characteristics of the data itself, such as a square exponential kernel, a radial basis function kernel, or a custom kernel; second, the training set is used to train the Gaussian process model. At this stage, the model will calculate the kernel matrix and adjust the hyperparameters based on the kernel matrix and training data through optimization algorithms (such as gradient ascent or Bayesian optimization) to maximize the marginal likelihood of the training data, thereby improving the predictive performance of the model; finally, the test data set is predicted, and the Gaussian process not only provides the prediction mean, but also provides an estimate of the uncertainty of the prediction. The mean square error (MSE), mean absolute error (MAE) or other related indicators are usually used to measure the accuracy of the prediction.

[0022] Furthermore, the solution of the Gaussian process in step S3 includes the solution of the mean function and the solution of the covariance function. The expressions of the mean function and the covariance function are as follows: ; in, Enter the first variable into the model, Enter the second variable into the model, is the model expression function, E is the mathematical expectation operator, which means to find the mathematical expectation of the function in the brackets. is the mean function, which describes the average trend of the model output when the input is x. is the covariance function, which is used to measure the model under different input and The correlation between the following outputs; The variables in the input space are the normal position of the secondary aircraft, the angle of attack of the primary aircraft, and the vector combination of the angle of attack of the secondary aircraft and the pitch rudder angle of the secondary aircraft; The Gaussian process is expressed as: ; in, represents a Gaussian process.

[0023] Furthermore, in step S3, based on the Gaussian process The following regression model is established: ; in, is the observation result of the pitch and rudder effect aerodynamic force of the second-stage aircraft, is the noise term, ; Represents normal distribution. is the noise term The standard deviation is used to measure the dispersion of noise; The aerodynamic observation results of the pitch and rudder effect of the second-stage aircraft were obtained. The prior distribution of is: ; in, It is an n-order unit matrix, whose main diagonal elements are all 1 and the rest of the elements are all 0. It plays a role similar to the number 1 in multiplication operations in matrix operations. Any matrix multiplied by the unit matrix is ​​equal to itself. The covariance matrix of the training input X itself is used to describe the correlation between different samples in the training set.

[0024] Further, the pitch rudder effect aerodynamic observation result of the secondary aircraft in step S3 The prediction results of the pitch and rudder aerodynamic force of the second-stage aircraft The associated prior distribution of is: ; in, Input for training Its own covariance matrix, Input for training With test input The covariance matrix established between For test input With training input The covariance matrix established between For test input Its own covariance matrix; Aerodynamic observation results based on the pitch and rudder effect of a two-stage aircraft The prediction results of the pitch and rudder aerodynamic force of the second-stage aircraft The associated prior distribution of the pitch rudder effect aerodynamic prediction results of the second-stage aircraft are deduced The posterior distribution of is: ; in, Given training data and test input Under the condition of , the average value of the prediction results of the pitch rudder effect aerodynamic force of the secondary aircraft is, For test input The variance of the corresponding prediction results reflects the degree of dispersion of the predicted values ​​around the mean. The larger the variance, the higher the uncertainty of the predicted value. ; ; in, The prediction results of the pitch and rudder aerodynamic force of the second-stage aircraft The covariance of is used to measure the dispersion of the predicted values ​​and the correlation between the dimensions.

[0025] It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0026] Although the present application has been described above with reference to specific embodiments, various modifications may be made thereto and parts thereof may be replaced with equivalents without departing from the scope of the present application. In particular, as long as there is no structural conflict, the various features in the specific embodiments disclosed in the present application may be used in combination with each other in any manner, and the fact that these combinations are not exhaustively described in this specification is only for the sake of omitting space and saving resources. Therefore, the present application is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A Gaussian process modeling method for the controlled separation rudder effect of a composite aircraft, characterized in that: The steps include: S1. Obtain the rudder effect aerodynamic database of the secondary vehicle under the interference flow field during the separation process of the combined vehicle through wind tunnel grid force measurement test; S2. The first-stage aircraft angle of attack, the second-stage aircraft angle of attack, the clearance between the two-stage aircraft and the second-stage aircraft rudder deflection angle obtained in the rudder effect aerodynamic database of the second-stage aircraft under the interference flow field in step S1 are combined into an input feature matrix, and the pitch rudder deflection moment of the second-stage aircraft in the first-stage aircraft interference flow field is obtained as an output vector to construct a rudder effect aerodynamic data set, and the data set is divided into a training set, a validation set and a test set in a ratio of 8:1:1; S3. Import the training set obtained in step S2 into the Gaussian process regression model, train the Gaussian process regression model, verify the trained Gaussian process regression model using the validation set, and then test it using the test set to obtain the Gaussian process regression model of the controlled separation rudder effect of the combined aircraft to predict the rudder effect aerodynamic torque.

2. The Gaussian process modeling method for the controlled separation rudder effect of a combined aircraft according to claim 1 is characterized in that: During the separation process between the first-stage aircraft and the second-stage aircraft in step S1, the pitch moment of the second-stage aircraft is a nonlinear function of the first-stage aircraft angle of attack, the second-stage aircraft angle of attack, the clearance between the two-stage aircraft and the pitch rudder angle of the second-stage aircraft, as shown in the following formula: ； in, is the pitch moment coefficient of the secondary vehicle, is the first-stage vehicle angle of attack, is the secondary vehicle angle of attack, is the clearance between the two-stage aircraft, It is the pitch rudder deflection angle of the secondary aircraft.

3. The Gaussian process modeling method for the controlled separation rudder effect of a composite aircraft according to claim 2, characterized in that: During the wind tunnel grid force measurement test in step S1, four parameters of the first-stage aircraft angle of attack, the second-stage aircraft angle of attack, the two-stage aircraft clearance and the second-stage aircraft pitch rudder deflection angle are arranged and combined to form a test condition, the first-stage aircraft angle of attack is set to 0°, the second-stage aircraft pitch control surface is only positively deflected, the second-stage rudder deflection angle is selected as 0°, 5°, 10°, 15°, the second-stage aircraft angle of attack is selected as 0°, 1°, 2°, 3°, the two-stage aircraft center of mass distance is selected as 5 meters, 5.5 meters, 6 meters, 7 meters, 8 meters, 10 meters, 13 meters, and the combination is formed into a grid point state of the second-stage aircraft rudder effect grid force measurement test, and the pitch moment of the second-stage aircraft measured in the test is the pitch rudder effect aerodynamic force of the second-stage aircraft.

4. The Gaussian process modeling method for the controlled separation rudder effect of a composite aircraft according to claim 3 is characterized in that: In step S3, solving the Gaussian process includes solving the mean function and the covariance function. The expressions of the mean function and the covariance function are as follows: ； in, Enter the first variable into the model, Enter the second variable into the model, is the model expression function, E is the mathematical expectation operator, which means to find the mathematical expectation of the function in the brackets. is the mean function, which describes the average trend of the model output when the input is x. is the covariance function, which is used to measure the model under different input and The correlation between the following outputs; The variables in the input space are the normal position of the secondary aircraft, the angle of attack of the primary aircraft, and the vector combination of the angle of attack of the secondary aircraft and the pitch rudder angle of the secondary aircraft; The Gaussian process is expressed as: ； in, represents a Gaussian process.

5. The Gaussian process modeling method for the controlled separation rudder effect of a composite aircraft according to claim 4, characterized in that: Step S3 is based on the Gaussian process. The following regression model is established: ； in, is the observation result of the pitch and rudder aerodynamic force of the second-stage aircraft, is the noise term, ;in, represents a normal distribution, is the noise term The standard deviation is used to measure the dispersion of noise; The aerodynamic observation results of the pitch and rudder effect of the second-stage aircraft were obtained. The prior distribution of is: ； in, is an n-order identity matrix, whose main diagonal elements are all 1 and the rest are all 0. The covariance matrix of the training input X itself is used to describe the correlation between different samples in the training set.

6. The Gaussian process modeling method for the controlled separation rudder effect of a composite aircraft according to claim 5, characterized in that: The aerodynamic observation results of the pitch and rudder effect of the secondary aircraft in step S3 The prediction results of the pitch and rudder aerodynamics of the second-stage aircraft The associated prior distribution of is: ； in, Input for training Its own covariance matrix, Input for training With test input The covariance matrix established between For test input With training input The covariance matrix established between For test input Its own covariance matrix; Aerodynamic observation results based on the pitch and rudder effect of a two-stage aircraft The prediction results of the pitch and rudder aerodynamics of the second-stage aircraft The associated prior distribution of the pitch rudder effect aerodynamic prediction results of the second-stage aircraft are deduced The posterior distribution of is: ； in, Given training data and test input Under the condition of , the average value of the prediction results of the pitch rudder effect aerodynamic force of the secondary aircraft is, For test input The variance of the corresponding prediction results reflects the degree of dispersion of the predicted values ​​around the mean. The larger the variance, the higher the uncertainty of the predicted value. ； ； in, The prediction results of the pitch and rudder aerodynamic force of the second-stage aircraft The covariance of is used to measure the dispersion of the predicted values ​​and the correlation between the dimensions.

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