Fixed-wing aircraft aerodynamic parameter intelligent fitting optimization method based on direct lift force

Abstract

The invention belongs to the technical field of aerodynamic parameter identification, and relates to an intelligent fitting optimization method for aerodynamic parameters of a fixed-wing aircraft based on direct lift force. According to the invention, a BP network is used to carry out fitting of a lift coefficient and an aerodynamic derivative of the lift coefficient to an attack angle on noiseless data. The input of the BP network comprises an attack angle, an elevator, a flap, a speed and a pitch angle speed, and is input into the BP network to obtain a prediction result when no noise influence exists, a loss function value is calculated, a gradient is calculated according to the loss function value, and then network parameters are updated according to a gradient descent algorithm to reduce the loss function value. When the loss function value is small, the difference between the prediction result of the network and the actual result is small, that is, the lift coefficient identification value output by the network is accurate in the BP network. The aerodynamic derivative obtained through calculation can be applied to a controller and has good control quality.

Description

Technical Field

[0001] The present invention belongs to the technical field of aerodynamic parameter identification, and relates to an intelligent fitting and optimization method for aerodynamic parameters of a fixed-wing aircraft based on direct lift. Background Art

[0002] The direct force control technology relies on the decoupling of control surfaces to generate direct force, and the decoupling deflection of control surfaces directly affects the direct force control effect. The decoupling design of control surfaces depends on a high-precision aerodynamic force model. Due to the deviation between the ground wind tunnel and the actual situation, it is necessary to study the fitting and correction of aerodynamic parameters based on data for the optimization design of control laws, so as to improve the decoupling control effect of maneuvering and reduce the pilot's maneuvering load.

[0003] Although the traditional recursive least squares method can perform fitting with high accuracy and speed, it has limitations in dealing with the non-linearity and time-variability of noise-free data, so the fitting result may deviate from the actual situation. With the rapid development of artificial intelligence and big data technologies, using intelligent methods such as machine learning and deep learning to process complex data provides new ideas and technical means for the fitting of direct force parameters. The BP network has strong non-linear modeling ability and can be effectively trained and learned to improve the prediction accuracy of the model. The intelligent fitting of the BP neural network is a widely used method. However, for the aerodynamic parameters identified by reasonably setting network parameters, the identification effect of aerodynamic parameters has not been greatly improved compared with the traditional recursive least squares result, but the identification error of aerodynamic derivatives is very large. In order to make the identification accuracy of aerodynamic parameters high and the fitting error of aerodynamic derivatives small.

[0004] Since the accuracy of flight test data will affect the accuracy of aerodynamic parameter identification, and the accuracy of aerodynamic parameter identification of an aircraft will greatly affect the decoupling control effect of maneuvering, it is very necessary to study an accurate identification method for aerodynamic parameters. Summary of the Invention

[0005] In the face of noise-free data, the present invention provides an intelligent fitting and optimization method for aerodynamic parameters of a fixed-wing aircraft based on direct lift. In order to improve the identification accuracy of the lift coefficient and the aerodynamic derivative of the lift coefficient with respect to the angle of attack, the present invention proposes to use BP (backpropagation neural network) to fit and optimize the lift coefficient and the aerodynamic derivative of the lift coefficient with respect to the angle of attack. After reasonably setting the network parameters, the error values of the lift coefficient and the aerodynamic derivative of the lift coefficient with respect to the angle of attack after fitting and optimizing the noise-free data by the BP network are greatly reduced compared with the traditional recursive least squares method.

[0006] The technical solution of the present invention is as follows:

[0007] An intelligent fitting and optimization method for aerodynamic parameters of a fixed-wing aircraft based on direct lift, the steps are as follows:

[0008] Step 1. Establishment of the aerodynamic model

[0009] The reference aircraft centroid dynamics equation can be expressed as:

[0010]

[0011] where m is the aircraft mass, V = [V x V y V z represents the components of the aircraft velocity in the body coordinate system, Ω = [p q r] represents the components of the aircraft angular velocity in the body coordinate system, and [F x F y F z represents the components of the resultant external force acting on the aircraft in the body coordinate system. The dot above a variable represents the derivative of that variable.

[0012] Combined with the aircraft force analysis, the aircraft centroid dynamics equation is finally expressed as follows:

[0013]

[0014] where G is the gravity acting on the aircraft, D is the drag, L is the lift, Z is the lateral force, φ T is the engine installation angle, F Ty is the component of the engine thrust in the O b y b axis, and [φ θ ψ] represents the roll angle, pitch angle, and yaw angle.

[0015] The forces acting on a fixed-wing aircraft are related to the dynamic pressure Q of the oncoming flow, the characteristic area S of the airframe, and the characteristic length l (when analyzing the pitching moment M z , the characteristic length is taken as the mean aerodynamic chord length b a ; when analyzing the rolling moment M x and the yawing moment M y , the characteristic length is taken as the wingspan l). Therefore, the above aerodynamic forces and moments can be expressed as:

[0016]

[0017] where c x , c y , c z respectively represent the dimensionless moment coefficients of the lift coefficient, pitching moment coefficient, and rolling moment coefficient. When the fixed-wing aircraft is in cruise and normal maneuvering conditions, the dimensionless coefficients are defined as:

[0018]

[0019] where δ a represents the aileron deflection angle, δ rIndicates the rudder deflection angle, δ e Is the elevator deflection angle, δ f Is the flap deflection angle of the fixed-wing aircraft, c x0 Is the rolling moment coefficient caused by the shape asymmetry due to production errors, c y0 Is the lift coefficient when the angle of attack and the elevator deflection angle are both zero, c z0 The pitch moment coefficient when the angle of attack and the control surface deflection angle are both zero, Are all aerodynamic derivatives.

[0020] Among them, the lift coefficient offline identification aerodynamic derivative equation:

[0021]

[0022] In the process of establishing the aerodynamic parameter model of the aircraft, its core essence lies in using mathematical expressions to accurately express the relationship between the aerodynamic parameter values of the aircraft under specific flight conditions and the flight state, and then solving the corresponding aerodynamic force values, so as to provide a solid theoretical basis for subsequent dynamic performance analysis and controller design.

[0023] Set the input parameter x of the aerodynamic parameter model identification k To be:

[0024] x k =[α δ e δ f q V]

[0025] Output parameter To be:

[0026]

[0027] In summary, the lift coefficient offline identification aerodynamic derivative model derived by the present invention is:

[0028]

[0029] Step 2. BP network design

[0030] The number of neurons in the input layer corresponds to the number of input features. The hidden layer is responsible for extracting the non-linear relationships in the input features, and the activation function is used to introduce non-linearity so that the network can fit complex functional relationships. In the process of fitting the direct lift aerodynamic parameters, the inputs of the BP network are the angle of attack α, the elevator deflection angle δ e , the flap deflection angle δ f , the pitch angular velocity q and the velocity V; the output is the lift coefficient c y .

[0031] (1) Forward propagation

[0032] The input features enter the network through the input layer, undergo non-linear transformation in the hidden layer, and finally reach the output layer to obtain the predicted value of the lift coefficient.

[0033] Set the weights from the input layer to the hidden layer as v ih , and set the threshold of the h-th neuron in the hidden layer as γ h . There are d input neurons and a total of 5 input parameters, so d = 5. Set the weights from the hidden layer to the output layer as w hj , and represent the threshold of the j-th neuron in the output layer with θ j . There are q1 hidden neurons, and the number of nodes in the hidden layer can be set to 7, so q1 = 7. The network has a total of q1 hidden neuron thresholds and l output neuron thresholds, and the number of nodes in the output layer is 1, so l = 1. Now input the model parameter x k into the network:

[0034] ① From the input layer to the hidden layer:

[0035]

[0036] where α h is the net input vector of the hidden layer;

[0037] ② Through the activation function of the hidden layer:

[0038] b h = f(α h - γ h )

[0039] Activate the net input vector of the hidden layer to obtain b h , and b h is the activated net input vector of the hidden layer. The sigmoid function is used as the activation function:

[0040]

[0041] After activation, that is:

[0042] b h = φ(α h - γ h )

[0043] ③ From the hidden layer to the output layer:

[0044]

[0045] where β j is the net input vector of the output layer.

[0046] ④ Through the activation function of the output layer:

[0047]

[0048] After activation, i.e.:

[0049]

[0050] In the formula, is the fitted value of the output of the j-th neuron.

[0051] ⑤ Error formula:

[0052]

[0053] In the formula, the error formula uses the mean squared error to represent, and E k represents the mean squared error of the fitted value and the true value of the output lift coefficient.

[0054] (2) Backpropagation

[0055] Calculate the gap between the predicted value and the actual value according to the loss function, that is, the loss. Use the gradient descent algorithm or its variants to calculate the gradients of the loss function with respect to the weights and biases. Update the weights and biases according to the gradients to reduce the loss.

[0056] Adjust the weights and thresholds to update the parameters by the gradient descent method:

[0057] ① Weight adjustment value from the hidden layer to the output layer:

[0058]

[0059] ② Weight adjustment value from the input layer to the hidden layer:

[0060]

[0061] ③ Threshold adjustment value from the hidden layer to the output layer:

[0062]

[0063] ④ Threshold adjustment value from the input layer to the hidden layer:

[0064]

[0065] According to the chain rule of differentiation, the following formula is finally obtained:

[0066]

[0067] Define the track angle rate dynamics equation of the fixed-wing aircraft as F(·), combine the aerodynamic moment network mapping result with the current flight state, for the input state x k =[α δ e δ f q V], after traversing all states, the loss function is obtained as follows:

[0068]

[0069] where: M is the number of samples; θ i ′ +1 represents the derivative of the threshold of the i-th neuron in the output layer.

[0070] The loss function is used to measure the gap between the network prediction result and the actual result. During the training process, the BP network adjusts the network parameters (including weights and biases) by continuously minimizing the loss function to make the network prediction result closer to the actual result. In the forward propagation stage, the input data passes through the network to obtain the prediction result and calculate the loss function value. In the backpropagation stage, the gradient is calculated based on the loss function value, and then the network parameters are updated according to the gradient descent algorithm to reduce the loss function value.

[0071] Advantages of the present invention:

[0072] The present invention uses a BP network to fit the lift coefficient and the aerodynamic derivative of the lift coefficient with respect to the angle of attack for noise-free data. The inputs of the BP network include the angle of attack, elevator, flap, speed, and pitch angular velocity. When there is no noise interference, the data is input into the BP network to obtain the prediction result and calculate the loss function value. The gradient is calculated based on the loss function value, and then the network parameters are updated according to the gradient descent algorithm to reduce the loss function value. When the loss function value is small, it indicates that the gap between the network prediction result and the actual result is small, that is, the identified value of the lift coefficient output by the network is relatively accurate in the BP network. The calculated aerodynamic derivative can be applied in the controller, having good control quality. Brief Description of the Drawings

[0073] Figure 1 is a schematic diagram of a BP neural network for aerodynamic parameter fitting;

[0074] Figure 2 is a comparison chart of the data before and after the angle of attack is processed;

[0075] Figure 3 is a comparison chart of the data before and after the elevator is processed;

[0076] Figure 4 is a comparison chart of the data before and after the flap is processed;

[0077] Figure 5 is a comparison chart of the data before and after the speed is processed;

[0078] Figure 6 is a comparison chart of the data before and after the pitch angular velocity is processed;

[0079] Figure 7is the mean square error of the derivative of the lift coefficient with respect to the angle of attack after recursive least squares fitting;

[0080] Figure 8 is the mean square error of the derivative of the lift coefficient with respect to the angle of attack after BP network fitting. Specific implementation manner

[0081] The specific implementation manner of the present invention will be further described below in conjunction with the accompanying drawings and technical solutions.

[0082] The intelligent fitting optimization method for the aerodynamic parameters of a fixed-wing aircraft based on direct lift is as follows:

[0083] (1) Establishment of the aerodynamic model

[0084] In the study of the orthogonalized aerodynamic parameter fitting model, it is first necessary to establish an aerodynamic model. The analysis of aerodynamic parameters affects the flight performance, stability, and controllability of the aircraft.

[0085] According to the motion characteristics and aerodynamic characteristics of the fixed-wing aircraft, reasonable assumptions are made to simplify the dynamic modeling process of the fixed-wing aircraft:

[0086] 1) Assume that the fixed-wing aircraft is a rigid body, ignore the influence of elastic deformation, and the mass is constant in the short-period attitude control.

[0087] 2) Assume that the ground is an inertial reference system, and ignore the rotation and revolution of the earth, that is, regard the earth as stationary.

[0088] 3) Ignore the curvature of the earth and regard the earth as a plane.

[0089] 4) Assume that the flight altitude does not affect the value of the gravitational acceleration.

[0090] (2) Filter the data

[0091] During the flight of the aircraft, it may encounter maneuvering operations that cause random acceleration changes, following a statistical distribution. Filtering can optimize the acceleration estimation and prediction, and improve the accuracy of the aircraft state estimation. By filtering state variables such as the angle of attack and elevator deflection angle, a more accurate fitting effect can be achieved.

[0092] By filtering state variables such as the angle of attack, elevator deflection angle, flap deflection angle, pitch angular velocity, and speed, that is, filtering the network input data x k =[α δ e δ f q V], a more accurate fitting effect can be achieved.

[0093] From simulation Figure 2 to simulation Figure 6It can be concluded that after the angle of attack, flap, elevator, speed, and pitch angular velocity data are processed by the filter, the data becomes more concentrated, the abnormal data points are removed, and the accuracy of various state estimations is improved. Using the processed data as input to the two fitting models helps to improve the fitting accuracy of the aerodynamic parameters.

[0094] (2) BP neural network parameter setting

[0095] The present invention is applicable to fixed-wing aircraft, and the specific parameters are as follows in the table:

[0096] Parameter Name Parameter Value Aircraft Mass 9295.44 kg Wing Area <![CDATA[27.87m 2 > Wingspan 9.144m Angle of Attack 2° Pitch Angle 2°

[0097] The structure of the BP neural network is as Figure 1 shown.

[0098] Based on the derivation of the data processed by the filter and the BP neural network, the specific steps of the BP neural network fitting process are as follows:

[0099] a. Determine the neural network structure and the input-output structure: The input is x k = [α δ e δ f q V], and the output is

[0100] b. The number of neurons in each layer and the learning efficiency: The number of training times is set to 1000 times, the learning rate is set to 0.01, the minimum error of the training target is set to 0.0000001, the number of nodes in the input layer is 5, the number of nodes in the hidden layer is 7, and the number of nodes in the output layer is 1;

[0101] c. Put 90% of the training data into the neural network for training: In the established network model, the gradient descent method is used for training;

[0102] d. Normalize the sample data;

[0103] e. Use 10% of the data as the test set for model testing, and restore the simulated data to the original order of magnitude, that is, inverse normalization processing.

[0104] f. Calculate the error between the predicted value and the true value, save the fitted neural network, and output the fitted lift coefficient value.

[0105] g. Differentiate the angle of attack with the fitted lift coefficient value to solve the derivative value of the lift coefficient with respect to the angle of attack.

[0106] The BP network parameter settings are as follows:

[0107] Parameter Name Parameter Value Number of Nodes in the Input Layer 5 Number of Nodes in the Hidden Layer 7 Number of Nodes in the Output Layer 1

[0108] (4) RLS Recursive Least Squares Parameter Setting (using the RLS recursive least squares method as a comparison)

[0109] The parameter settings of the RLS recursive least squares method are as follows:

[0110] Parameter Name Parameter Value Forgetting Factor 1 Initial Length 40

[0111] (5) Explanation of Simulation Results

[0112] The mean squared error (MSE) is used to measure the progress of the method. MSE, full name Mean Squared Error, that is, the mean squared error, is a commonly used indicator to measure the performance of a prediction model. It is the average of the squares of the differences between the predicted values and the true values, and can be expressed as:

[0113]

[0114] where n is the number of test samples, y i is the true value of the i-th data point, is the predicted value of the i-th data point. In this embodiment, n is 900, y i is the true lift coefficient value of each data point, is the fitted value of the lift coefficient for each data point.

[0115] The ability of MSE to measure data fluctuations (i.e., errors), and the numerical size directly reflects the accuracy of the prediction.

[0116] From the simulation Figure 7 and the simulation Figure 8 it can be obtained that the simulation values of the lift coefficient with respect to the angle of attack in the recursive least squares and the BP network are stable at 1191.7937 and 327.7478 in the data points.

[0117] The specific values of the lift coefficient errors in the two methods are:

[0118]

[0119] From the simulation data, it can be seen that compared with the recursive least squares method, the performance difference shown by using the backpropagation neural network for lift coefficient identification is smaller. However, when identifying the influence of the small derivative of the angle of attack on the lift coefficient, the BP network shows better performance than the traditional recursive least squares method. Specifically, the application of the BP network significantly reduces the optimization error by 864.0459. The data optimized by the BP network not only has smaller errors, but also the fitted lift coefficient curve is smoother, enhancing the stability and reliability of the results.

Claims

1. An intelligent fitting and optimization method for the aerodynamic parameters of a fixed-wing aircraft based on direct lift, characterized in that, The steps are as follows: Step 1: Establish the aerodynamic model The reference aircraft centroid dynamics equation is expressed as: Where m is the mass of the aircraft, V = [V x V y V z represents the components of the aircraft velocity in the body coordinate system, Ω = [p q r] represents the components of the aircraft angular velocity in the body coordinate system, [F x F y F z represents the components of the resultant external force acting on the aircraft in the body coordinate system; a dot superscript on a variable represents the derivative of that variable; Combined with the aircraft force analysis, the aircraft centroid dynamics equation is finally expressed as follows: Wherein, G is the gravity acting on the aircraft, D is the drag force, L is the lift force, Z is the lateral force, and φ T is the engine installation angle, and F Ty is the component of the engine thrust in the O b y b axis, and [φ θ ψ] represents the roll angle, pitch angle, and yaw angle; The forces acting on a fixed-wing aircraft are related to the dynamic pressure Q of the oncoming flow, the characteristic area S of the airframe, and the characteristic length l. Therefore, the aerodynamic force and moment are expressed as: where c x , c y , c z respectively represent the dimensionless moment coefficients of the lift coefficient, pitch moment coefficient, and roll moment coefficient. When the fixed-wing aircraft is in cruise and normal maneuvering conditions, the dimensionless coefficients are defined as: where δ a represents the aileron deflection angle, δ r represents the rudder deflection angle, δ e is the elevator deflection angle, δ f is the flap deflection angle of the fixed-wing aircraft, c x0 is the rolling moment coefficient caused by the shape asymmetry due to production errors, c y0 is the lift coefficient when the angle of attack and the elevator deflection angle are both zero, c z0 is the pitch moment coefficient when the angle of attack and the control surface deflection angles are both zero, are all aerodynamic derivatives; Among them, the lift coefficient offline identification aerodynamic derivative equation: Set the input parameter x for pneumatic parameter model identification k as follows: x k = [α δ e δ f q V] Output parameter is as follows: Therefore, the lift coefficient offline identification aerodynamic derivative model is: Step 2: Design the BP network During the process of fitting the direct lift aerodynamic parameters, the inputs of the BP network are the angle of attack α, the elevator deflection angle δ e , the flap deflection angle δ f , the pitch angular velocity q, and the velocity V; the output is the lift coefficient c y ; (1) Forward propagation The input features enter the network through the input layer, undergo non-linear transformation in the hidden layer, and finally reach the output layer to obtain the predicted value of the lift coefficient; Set the weight from the input layer to the hidden layer as v ih , and set the threshold of the h-th neuron in the hidden layer as γ h , there are d input neurons and a total of 5 input parameters, so d = 5; set the weight from the hidden layer to the output layer as w hj , and use θ to represent the threshold of the j-th neuron in the output layer j , there are q1 hidden neurons, and the number of nodes in the hidden layer is set to 7, so q1 = 7; the network has a total of q1 hidden neuron thresholds and l output neuron thresholds, and the number of nodes in the output layer is 1, so l = 1; now input the model parameter x k into the network: ① From the input layer to the hidden layer: where α h is the net input vector of the hidden layer; ② Through the activation function of the hidden layer: b h = f(α h - γ h ) Activate the net input vector of the hidden layer to obtain b h , b h is the net input vector of the activated hidden layer; the activation function uses the sigmoid function: After activation, that is: b h = φ(α h - γ h ) ③ From the hidden layer to the output layer: where β j is the net input vector of the output layer; ④ Through the activation function of the output layer: After activation, that is: Wherein, is the fitted value output by the j-th neuron; ⑤ Error formula: In the formula, the error formula is expressed using the mean square error, E k represents the mean square error of the output lift coefficient fitting value and the true value; (2) Backward propagation Calculate the gap between the predicted value and the actual value according to the loss function, that is, the loss; use the gradient descent algorithm or its variant to calculate the gradient of the loss function with respect to the weights and biases; update the weights and biases according to the gradient to reduce the loss; Adjust the weights and thresholds to update the parameters through the gradient descent method: ① The weight adjustment value from the hidden layer to the output layer: ② The weight adjustment value from the input layer to the hidden layer: ③ The threshold adjustment value from the hidden layer to the output layer: ④ The threshold adjustment value from the input layer to the hidden layer: According to the chain rule of differentiation, the following formula is finally obtained:

2. The intelligent fitting and optimization method for aerodynamic parameters of a fixed-wing aircraft based on direct lift according to claim 1, wherein In step 2, define the fixed-wing aircraft track angle rate dynamics equation as F(·). Combining the aerodynamic moment network mapping result and the current flight state, for the input state x k =[α δ e δ f q V], after traversing all states, the loss function is obtained as follows: Where: M is the number of samples; θ i ′ +1 represents the derivative of the threshold of the i-th neuron in the output layer.

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