Online prediction method of flight envelope after fault based on radial basis function-back propagation neural network

Abstract

The present invention discloses an online safety envelope prediction method based on a radial basis function back-propagation neural network, which can prevent an aircraft from losing control after sudden structural damage and aerodynamic failure. First, commands from the onboard flight controller are sent to the aircraft actuators and sensors to monitor the health of the actuators. Then, a Kalman filter is used to estimate the aircraft state and sensor deviation based on the aircraft dynamics model, and the stability derivative is estimated using the recursive least squares method. Subsequently, aerodynamic effect modeling is performed to establish an aerodynamic model of the aircraft under normal and fault conditions. Finally, the calculated dimensionless forces and moments are used to initiate the online aerodynamic anomaly detection process by comparing the output of the normal flight model with the actual aircraft output measurements. The possible fault location and scale are determined based on the identified stability derivatives. Based on the estimated damage, a database retrieval scheme and interpolation algorithm are applied to obtain the safety envelope under the current fault condition.

Description

Technical Field

[0001] The present invention belongs to the technical field of fault diagnosis, and in particular relates to an online prediction method for a flight envelope after a fault based on a radial basis function-back propagation (RBF-BP) neural network. Background Art

[0002] Structural damage and aerodynamic failures are important factors that threaten the safe flight of aircraft. Research on flight envelope prediction under fault conditions is of great significance for ensuring the safe flight of aircraft. During normal flight, the safety envelope can provide a reference for pilots. However, when the aircraft suffers sudden structural damage, these envelopes may no longer be valid, because aircraft failures usually affect the aircraft's flight performance, resulting in a reduction in the aircraft's safe flight envelope. Therefore, when the aircraft suffers structural damage, it is necessary to perform real-time online prediction of the safety envelope, and the obtained safety envelope can be transmitted to the pilot in real time. However, the existing technology lacks real-time performance when predicting the safety envelope and cannot promptly feed back the new safety envelope to the pilot. Therefore, the present invention proposes fault diagnosis and safety envelope prediction based on an offline database, which greatly improves the efficiency of fault diagnosis and safety envelope prediction.

[0003] This paper proposes an online prediction method for the post-fault flight envelope based on a radial basis function (RBF)-backpropagation neural network. This method, based on an offline database modeled from the aerodynamic effects of damaged aircraft, uses offline neural network training to perform real-time online diagnosis of aircraft faults and generate a new safety envelope. Summary of the Invention

[0004] To achieve online prediction of the post-fault aircraft safety envelope, this paper provides an online post-fault flight envelope prediction method based on a radial basis function (RBF)-backpropagation neural network (BBP) to address the existing difficulties in predicting the flight envelope of damaged aircraft. With the help of an offline database, the challenges associated with obtaining a global model of the damaged aircraft and the high computational cost of safety envelope prediction can be overcome. Pattern classification techniques are employed, using locally estimated stability derivatives as classification features, to detect and identify the aircraft's damage state, thereby finding the correct database index.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] An online prediction of a post-fault flight envelope based on a radial basis function back propagation neural network comprises the following steps:

[0007] Step S1: Establish an aircraft health status monitoring module;

[0008] Step S2, aerodynamic parameter identification;

[0009] Step S3: Modeling of aerodynamic effects of structural damage and construction of a fault database;

[0010] Step S4, rbf-bp neural network training and real-time fault diagnosis;

[0011] Step S5: Establish a flight envelope database.

[0012] Preferably, in step S1, establishing an aircraft health status monitoring module includes the following steps:

[0013] (1) Command δ from the onboard flight controller cmd Received by the actuator;

[0014] (2) When a fault occurs, the actual output of the actuator δ abn and the expected value δ calculated according to its mathematical model nom Abnormal residuals between will be detected by the sensor;

[0015] (3) When a residual error occurs, the online aerodynamic anomaly detection process is initiated, and new measurements of the flight status and response are sent to the system identification module.

[0016] Preferably, in step S2, the aerodynamic parameter identification includes the following steps:

[0017] (1) Calculate the dimensionless forces and moments along each axis using sensor measurements or state values ​​estimated by the Kalman filter. The dimensionless aerodynamic forces and moments of the aircraft can be obtained by equations (1) and (2).

[0018]

[0019]

[0020] Where C L 、C D 、C Y 、C l 、C m 、C n They are lift coefficient, drag coefficient, side force coefficient, rolling moment coefficient, pitching moment coefficient and yaw moment coefficient respectively, α is the angle of attack, β is the sideslip angle, m is the mass of the aircraft, A X 、A Y 、A Z are the acceleration components along the X, Y, and Z axes, ρ is the air density, V is the airspeed, S is the wing area, and I xx , I yy , I zz , I xzis the moment of inertia and rotational product, p, q, r are the roll, yaw and pitch angular velocities respectively, are the roll, yaw and pitch angular velocity derivatives, b, are wingspan and mean chord length respectively;

[0021] (2) Use recursive least squares method to estimate the aircraft stability derivative from the simulation data through equation (3);

[0022]

[0023] Where, They are the basic incremental coefficient of lift, the incremental coefficient related to lift and angle of attack, the incremental coefficient related to lift and yaw angle, and the incremental coefficient related to lift and elevator;

[0024] (3) The recursive least squares method with forgetting factor is used for parameter estimation. The structure of the recursive least squares method is as follows:

[0025]

[0026] is the parameter to be estimated, λ∈[0,1] is the forgetting factor, and the variable forgetting factor is used to enhance the influence of new data when the model parameters change suddenly and to reduce the saturation of the covariance matrix under steady-state conditions.

[0027] Preferably, in step S3, the aerodynamic effect modeling of structural damage and the construction of a fault database include the following steps:

[0028] (1) Based on a series of wind tunnel tests, each damage condition will produce a unique aerodynamic effect on the aircraft and change different stability derivatives. Damage to the horizontal stabilizer will cause changes in longitudinal stability, which can be determined by The damage to the vertical tail wing tip mainly leads to changes in lateral force and directional stability, which can be expressed by The changed value of .

[0029] (2) The change value under the damage degree can be obtained by the following formula:

[0030]

[0031] Where, ΔC, C d , C are the damage degree of the aircraft, the dimensionless aerodynamic coefficient of the damaged aircraft and the dimensionless aerodynamic coefficient of the intact aircraft respectively;

[0032] (3) By analyzing the wind tunnel data, it can be assumed that there is an approximately linear relationship between the variation range of each aerodynamic coefficient and the wingtip loss percentage. Based on the calculated damage degree variation scale, linear interpolation can be used to establish an aerodynamic damage model for each damage level, and a fault aerodynamic database including aerodynamic data and corresponding stability derivatives for horizontal stabilizer damage and vertical tail wingtip damage can be generated.

[0033] Preferably, in step S4, the rbf-bp neural network training and real-time fault diagnosis include the following steps:

[0034] (1) Determine the input variable x as the value of each Mach The output variables are the specific fault type and damage degree corresponding to the aerodynamic data;

[0035] (2) Before training the RBF-BP neural network, the data set was divided into a training set and a test set at a ratio of 7:3, and then the data was normalized to between [0, 1];

[0036] (3) Initialize the RBF network, select t different initial cluster centers, set the number of iterations to 1, and randomly select the input from the sample. The distance between the input sample and the cluster center is the shortest, which can be obtained by the following formula:

[0037] iX k =min||X k -C i (m)||, i=1,2,...,t, k=1,2,...,n (6)

[0038] (4) Calculate and adjust the center of the hidden layer nodes:

[0039]

[0040] When C i (m+1)=C i (m), the clustering process ends, and the width of the hidden layer nodes can be determined based on the cluster center. If the two are not equal, the distance between the input sample and the center is recalculated until the learning process is complete. The mean square error target is set to 0.05, the radial basis expansion rate is 1, and the maximum number of neurons defaults to 25.

[0041] (5) For the BP neural network, set the number of input neurons n = 6, the number of output neurons m = 10, the number of training times E = 1000, the number of hidden layer neurons h = 13, and the activation function uses logsig and purelin functions. The number of hidden layer neurons h is obtained by the following formula:

[0042]

[0043] Where α is any integer between 1 and 10.

[0044] Preferably, in step S5, establishing a flight envelope database includes the following steps:

[0045] (1) The maximum speed of an aircraft in level flight can be obtained from the following formula:

[0046]

[0047] T max is the thrust, ρ(H) is the air density related to the altitude, C xmin is the drag coefficient, S is the wing area;

[0048] (2) The minimum speed of an aircraft in level flight can be obtained from the following formula:

[0049]

[0050] G is the weight of the aircraft, C zmax is the lift coefficient;

[0051] (3) The maximum altitude ceiling for an aircraft to maintain constant speed straight and level flight can be obtained from the following formula:

[0052]

[0053] v z is the maximum climb rate of the aircraft, K is the lift-to-drag ratio, and v is the level flight speed;

[0054] (4) The steps to establish the flight envelope database are as follows:

[0055] Constraints:

[0056]

[0057] Level flight conditions:

[0058]

[0059] Basic trim control parameters:

[0060] λ=[θ,ψ,δ T ,δ e ,δ r ] (14)

[0061] Optimization objective function:

[0062]

[0063] Among them, AI is the optimization parameter, Dr is the drag, L is the lift, T is the thrust along the body, φ, ψ, θ are the roll angle, yaw angle and pitch angle respectively, are the roll, yaw and pitch angle derivatives respectively, p, q, r are the roll, yaw and pitch angular velocities respectively, are the roll, yaw and pitch angular velocity derivatives, V is the flight speed, h is the altitude, V0 and h0 are the speed and altitude when the horizontal tail deflection angle is 0°, β is the sideslip angle, is the sideslip angle derivative, α is the angle of attack, is the angle of attack derivative, m and g are the mass of the aircraft and the acceleration of gravity, δ T , δ e , δ r is the rudder deflection angle caused by thrust, the elevon deflection angle, and the rudder deflection angle caused by drag, is the height derivative, is the velocity derivative;

[0064] When an aircraft malfunctions, a set of different drag and lift coefficients will be obtained by trimming the aircraft at each specified altitude and speed. According to equations (1) to (3), the maximum and minimum speeds and ceilings at this time can be estimated. Based on a series of such estimation results, the flight envelope under this malfunction condition can be obtained, and then a flight envelope database under various malfunction conditions can be obtained.

[0065] Compared with the prior art, the present invention has the following beneficial effects:

[0066] This method models the aerodynamic effects of a faulty aircraft, obtains aerodynamic data, and establishes a database. A radial basis function back-propagation neural network is trained using the database to generate a classifier and a decision surface. The classification results are used to estimate the flight envelope in real time, and a new flight envelope is generated based on the offline database. Compared to conventional dynamic envelope estimation methods, this method, which utilizes an offline database and performs real-time fault diagnosis and safety envelope generation, avoids the curse of dimensionality and significantly reduces computation time. Finally, simulations demonstrate the feasibility and efficiency of this method. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 This is the overall framework diagram of the flight envelope prediction system;

[0068] Figure 2 It is the flow chart of aerodynamic parameter identification;

[0069] Figure 3 It is a schematic diagram of the fault diagnosis process;

[0070] Figure 4 This is a schematic diagram of the RBF-BP neural network learning process;

[0071] Figure 5 It is a schematic diagram of fault diagnosis accuracy with different sample numbers;

[0072] Figure 6 It is a schematic diagram of the aerodynamic effects of different degrees of wing damage;

[0073] Figure 7 Is the rbf-bp network under different ma Prediction diagram of . DETAILED DESCRIPTION

[0074] The present invention will be further described below in conjunction with the embodiments.

[0075] Addressing the difficulty in predicting the safety envelope of a faulty aircraft, this paper proposes an online prediction method for the post-fault flight envelope based on an RBF-BP neural network. This method allows for real-time online diagnosis of various faults and generates a new safety envelope using an offline database. The method first uses sensors to monitor the health of the actuators. If any fault occurs, abnormal residuals between the actual actuator output and the expected value quickly detect the fault. A Kalman filter or other advanced state estimator is then used to estimate the aircraft state and sensor biases based on the aircraft dynamics model. The estimated state and sensor information are then used to calculate dimensionless forces and moments on each axis, providing input for the second step of a two-step approach: estimating stability derivatives using a recursive least squares method. Finally, the calculated dimensionless forces and moments are used to initiate online aerodynamic anomaly detection by comparing the outputs of the normal flight model with the actual aircraft output measurements. Simultaneously, based on the newly identified stability derivatives, an alert is generated, triggering fault classification and determining the likely fault location and magnitude. Once the damage estimate is generated, this information is indexed into the database. Database retrieval schemes and interpolation algorithms are then applied to obtain a unique safe flight envelope that best approximates the current fault scenario. The resulting safe flight envelope can be presented to the pilot and used to generate new control laws using a fault-tolerant controller. Simulation results demonstrate the feasibility of this approach, successfully detecting and classifying two impairment scenarios.

[0076] Example 1

[0077] Step S1, establish the aircraft health status monitoring module: input data δ nom , δ abn is the expected value calculated according to its normal aerodynamic model and the actual output of the actuator, such as Figure 1 The command δ from the onboard flight controller is shown as cmd Received by the actuator, when a fault occurs, the actual output of the actuator δ abn and the expected value δ calculated according to its mathematical model nom Abnormal residuals between the two are quickly detected by the sensors. When a residual occurs, the online aerodynamic anomaly detection process is initiated, and new measurements of the flight state and response are sent to the system identification module.

[0078] Step S2, aerodynamic parameter identification: Figure 2 As shown, firstly, the dimensionless aerodynamic force and moment of the aircraft are calculated by equations (1) and (2);

[0079]

[0080]

[0081] Where C L 、C D 、C Y are lift coefficient, drag coefficient and side force coefficient respectively, C l 、C m 、C n They are the rolling moment coefficient, pitching moment coefficient and yaw moment coefficient respectively, α is the angle of attack, β is the sideslip angle, m is the aircraft mass, A X 、A Y 、A Z are the acceleration components along the X, Y, and Z axes, ρ is the air density, V is the airspeed, S is the wing area, and I xx , I yy , I zz , I xz is the moment of inertia and rotational product, p, q, r are the roll, yaw and pitch angular velocities respectively, b, are wingspan and mean chord length respectively. C L 、C D 、C Y 、C l 、C m 、C n is the required unknown quantity, and the remaining parameters are known or can be obtained from onboard sensors. The model structure is estimated based on the input-output model of formula (3):

[0082]

[0083] Where, These are the basic lift increment coefficient, the lift increment coefficient related to the angle of attack, the lift increment coefficient related to the yaw angle, and the lift increment coefficient related to the elevator. The remaining coefficients are the same as above. The estimation method used in this paper is the recursive least squares method. When model parameters change abruptly, a variable forgetting factor is used to enhance the impact of new data and to reduce covariance matrix saturation under steady-state conditions. is the parameter to be estimated, the forgetting factor α ranges from 0.95 to 0.99, and the initial value is the stability derivative of the aircraft under normal conditions. The recursive least squares method structure is shown in formula (4):

[0084]

[0085] In step S3, the aerodynamic effects of structural damage are modeled and the fault database is constructed:

[0086] Based on a series of wind tunnel tests, each damage condition will produce a unique aerodynamic effect on the aircraft and change different stability derivatives. Damage to the horizontal stabilizer will cause changes in longitudinal stability, which can be determined by The damage to the vertical tail wing tip mainly leads to changes in lateral force and directional stability, which can be expressed by The change value of the damage degree can be expressed as follows:

[0087]

[0088] Where, ΔC, C d , C are the damage degree of the fuselage, the dimensionless aerodynamic coefficient of the damaged fuselage, and the dimensionless aerodynamic coefficient of the intact fuselage, respectively. By analyzing the wind tunnel data, it can be assumed that there is an approximate linear relationship between the variation range of each aerodynamic coefficient and the percentage of wingtip loss. According to the calculated damage degree variation scale, linear interpolation can be used to establish an aerodynamic damage model for each damage level, and generate a fault aerodynamic database including aerodynamic data and corresponding stability derivatives for horizontal stabilizer damage and vertical tail wingtip damage. Figure 3 As shown, the established fault aerodynamic database will be used to train the neural network.

[0089] Step S4, rbf-bp neural network training and real-time fault diagnosis:

[0090] The input variable x is determined to be the specific fault type and damage level at each Mach number, and the output variable is the specific fault type and damage level corresponding to the aerodynamic data. Before training the RBF-BP neural network, the dataset is divided into a training set and a test set at a ratio of 7:3. The data is then normalized to the range [0, 1]. The RBF network is initialized, t different initial cluster centers are selected, the number of iterations is set to 1, and the input is randomly selected from the sample. The distance between the input sample and the cluster center is minimized, which can be obtained by the following formula:

[0091] iX k =min||X k -C i (m)||, i=1,2,...,t, k=1,2,...,n (6)

[0092] The calculation and adjustment of the center of the hidden layer nodes can be obtained by formula (7),

[0093]

[0094] When C i (m+1)=Ci (m), the clustering process ends, and the width of the hidden layer node can be determined based on the cluster center. If the two are not equal, the distance between the input sample and the center is recalculated until the learning process is completed. The neural network training process is as follows Figure 4 As shown in the figure. The mean square error target is set to 0.05, the radial basis expansion rate is 1, and the maximum number of neurons is 25 by default. For the BP neural network, the number of input neurons n is set to 12, the number of output neurons m is set to 10, the number of training times E is set to 1000, the activation function uses the logsig and purelin functions, and the number of hidden layer neurons h is 13, which is obtained by the following formula:

[0095]

[0096] Where α is any integer between 1 and 10. Figure 5 、 6 The results shown in Figure 7 demonstrate the effectiveness of the algorithm proposed in this paper.

[0097] In step S5, a flight envelope database is established:

[0098] The maximum speed of the aircraft in level flight, the minimum speed in level flight, and the maximum altitude ceiling for maintaining a constant speed straight and level flight can be obtained from equations (6), (7), and (8):

[0099]

[0100]

[0101]

[0102] T max is the thrust, ρ(H) is the air density related to the altitude, C xmin is the drag coefficient; G is the weight of the aircraft, C zmax is the lift coefficient. z is the maximum climb rate of the aircraft, and K is the lift-to-drag ratio.

[0103] Then build the flight envelope database:

[0104] Constraints:

[0105]

[0106] Level flight conditions:

[0107]

[0108] Basic trim control parameters:

[0109]

[0110] Optimization objective function:

[0111]

[0112] Among them, AI is the optimization parameter, Dr is the drag, L is the lift, T is the thrust along the body, φ, ψ, θ are the roll angle, yaw angle and pitch angle respectively, are the roll, yaw and pitch angle derivatives respectively, p, q, r are the roll, yaw and pitch angular velocities respectively, are the roll, yaw and pitch angular velocity derivatives, V is the flight speed, h is the altitude, V0 and h0 are the speed and altitude when the horizontal tail deflection angle is 0°, β is the sideslip angle, is the sideslip angle derivative, α is the angle of attack, is the angle of attack derivative, m and g are the mass of the aircraft and the acceleration of gravity, δ T , δ e , δ r is the rudder deflection angle caused by thrust, the elevon deflection angle, and the rudder deflection angle caused by drag, is the height derivative, is the velocity derivative;

[0113] Aircraft trimming is an optimization problem that satisfies initial values ​​and constraints. When an aircraft malfunctions, trimming the aircraft at each specified altitude and speed yields a different set of drag and lift coefficients. Using equations (1) to (3), we can estimate the maximum and minimum speeds and ceiling at that point. Based on a series of these estimates, we can derive the flight envelope for that particular malfunction, and thus a database of flight envelopes for various malfunctions.

[0114] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A post-fault flight envelope online prediction method based on radial basis function back propagation neural network, characterized in that: The following steps are involved: Step S1: Establish an aircraft health status monitoring module; Step S2, aerodynamic parameter identification; Step S3: Modeling of aerodynamic effects of structural damage and construction of a fault database; Step S4, rbf-bp neural network training and real-time fault diagnosis; Step S5: Establishing a flight envelope database; In step S2, the aerodynamic parameter identification includes the following steps: (1) Calculate the dimensionless forces and moments along each axis using sensor measurements or state values ​​estimated by the Kalman filter. The dimensionless aerodynamic forces and moments of the aircraft are obtained by equations (1) and (2). Where C L 、C D 、C Y 、C l 、C m 、C n They are lift coefficient, drag coefficient, side force coefficient, rolling moment coefficient, pitching moment coefficient and yaw moment coefficient respectively, α is the angle of attack, β is the sideslip angle, m is the mass of the aircraft, A X 、A Y 、A Z are the acceleration components along the X, Y, and Z axes, ρ is the air density, V is the airspeed, S is the wing area, and I xx , I yy , I zz , I xz is the moment of inertia and rotational product, p, q, r are the roll, yaw and pitch angular velocities respectively, are the roll, yaw and pitch angular velocity derivatives, b, are wingspan and mean chord length respectively; (2) Use recursive least squares method to estimate the aircraft stability derivative from the simulation data through equation (3); Where, They are the basic incremental coefficient of lift, the incremental coefficient related to lift and angle of attack, the incremental coefficient related to lift and yaw angle, and the incremental coefficient related to lift and elevator; (3) The recursive least squares method with forgetting factor is used for parameter estimation. The structure of the recursive least squares method is as follows: is the parameter to be estimated, λ∈[0,1] is the forgetting factor, and the variable forgetting factor is used to enhance the influence of new data when the model parameters change suddenly and to reduce the saturation of the covariance matrix under steady-state conditions; In step S3, the aerodynamic effect modeling of structural damage and the construction of a fault database include the following steps: (1) Damage to the horizontal stabilizer will cause changes in longitudinal stability. The damage to the vertical tail wing tip causes changes in lateral force and directional stability, which is represented by The change value of (2) The change value under the damage degree is obtained by the following formula; Where, ΔC, C d , C are the damage degree of the aircraft, the dimensionless aerodynamic coefficient of the damaged aircraft and the dimensionless aerodynamic coefficient of the intact aircraft respectively; (3) Assuming that there is an approximately linear relationship between the variation range of each aerodynamic coefficient and the wingtip loss percentage; using linear interpolation based on the calculated damage degree variation scale, an aerodynamic damage model is established for each damage level, and a fault aerodynamic database including aerodynamic data and corresponding stability derivatives for horizontal stabilizer damage and vertical tail wingtip damage is generated.

2. The post-fault flight envelope online prediction method based on radial basis function back propagation neural network according to claim 1, characterized in that: In step S1, establishing an aircraft health status monitoring module includes the following steps: (1) Command δ from the onboard flight controller cmd Received by the actuator; (2) When a fault occurs, the actual output of the actuator δ abn and the expected value δ calculated according to its mathematical model nom Abnormal residuals between will be detected by the sensor; (3) When a residual error occurs, the online aerodynamic anomaly detection process is initiated, and new measurements of the flight status and response are sent to the system identification module.

3. The post-fault flight envelope online prediction method based on radial basis function back propagation neural network according to claim 1, characterized in that: In step S4, the RBF-BP neural network training and real-time fault diagnosis include the following steps: (1) Determine the input variable x as the value of each Mach The output variables are the specific fault type and damage degree corresponding to the aerodynamic data; (2) Before training the RBF-BP neural network, the data set is divided into a training set and a test set, and then the data is normalized to between [0, 1]; (3) Initialize the RBF network, select t different initial cluster centers, set the number of iterations, and randomly select the input from the sample; make the distance between the input sample and the cluster center as short as possible, which is obtained by the following formula: iX k =min||X k -C i (m)||,i=1,2,...,t,k=1,2,...,n (6) (4) Calculate and adjust the center of the hidden layer nodes: When C i (m+1)=C i (m), the clustering process ends, and the width of the hidden layer node is determined according to the cluster center; if the two are not equal, the distance between the input sample and the center is recalculated until the learning process is completed; (5) For the BP neural network, set the number of input neurons n, the number of output neurons m, the number of training times E, the activation function uses the logsig and purelin functions, and the number of hidden layer neurons h is obtained by the following formula: Where α is any integer between 1 and 10.

4. The post-fault flight envelope online prediction method based on radial basis function back propagation neural network according to claim 1, characterized in that: In step S5, establishing a flight envelope database includes the following steps: (1) The maximum speed of an aircraft in level flight is obtained from the following formula: T max is the thrust, ρ(H) is the air density related to the altitude, C xmin is the drag coefficient; (2) The minimum speed of the aircraft in level flight is obtained by the following formula: G is the weight of the aircraft, C zmax is the lift coefficient; (3) The maximum altitude ceiling for an aircraft to maintain constant speed straight and level flight is obtained from the following formula: v z is the maximum climb rate of the aircraft, K is the lift-to-drag ratio; (4) The steps to establish the flight envelope database are as follows: Constraints: Level flight conditions: Dr=Tcosα L-mg=Tsinα (13) Basic trim control parameters: Optimization objective function: Among them, AI is the optimization parameter, Dr is the drag, L is the lift, T is the thrust along the body, φ, ψ, θ are the roll angle, yaw angle and pitch angle respectively, are the roll, yaw and pitch angle derivatives respectively, p, q, r are the roll, yaw and pitch angular velocities respectively, are the roll, yaw and pitch angular velocity derivatives, V is the flight speed, h is the altitude, V0 and h0 are the speed and altitude when the horizontal tail deflection angle is 0°, β is the sideslip angle, is the sideslip angle derivative, α is the angle of attack, is the angle of attack derivative, m and g are the mass of the aircraft and the acceleration of gravity, δ T , δ e , δ r is the rudder deflection angle caused by thrust, the elevon deflection angle, and the rudder deflection angle caused by drag, is the height derivative, is the velocity derivative; When an aircraft malfunctions, a set of different drag and lift coefficients will be obtained by trimming the aircraft at each specified altitude and speed. According to equations (1) to (3), the maximum and minimum speeds and ceilings at this time are estimated. Based on a series of such estimation results, the flight envelope under this malfunction condition is obtained, and then a flight envelope database under various malfunction conditions is obtained.

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