CN116127842A - Post-fault flight envelope online prediction method based on radial basis-counter propagation neural network - Google Patents
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Abstract
The invention discloses an online safety envelope prediction method based on a radial basis-counter propagation neural network, which can prevent an aircraft from being out of control after sudden structural damage and pneumatic faults occur. Commands for the on-board flight controller are first sent to the aircraft actuators and sensors to monitor the health of the actuators. Then, the aircraft state and sensor bias are estimated based on the aircraft dynamics model using a Kalman filter and the stability derivative is estimated using a recursive least squares method. And then, carrying out aerodynamic effect modeling, and establishing an aircraft aerodynamic model under normal and fault states. And finally, by utilizing the calculated dimensionless force and moment, the output of the normal flight model is compared with the actual aircraft output measured value, and an online aerodynamic anomaly detection process is started. The potential fault location and scale are determined based on the identified stability derivatives. And (3) applying a database retrieval scheme and an interpolation algorithm according to the estimated damage condition to obtain the safety envelope under the current fault condition.
Description
Technical Field
The invention belongs to the technical field of fault diagnosis, and particularly relates to an online prediction method of a post-fault flight envelope based on a radial basis-back propagation (Radial Basis Function-back propagation RBF-BP) neural network.
Background
Structural damage and aerodynamic faults are important factors threatening the safe flight of the aircraft, and the research of flight envelope prediction under the fault condition has important significance for ensuring the safe flight of the aircraft. The safety envelope may provide a reference to the pilot during normal flight. However, when sudden structural damage occurs to the aircraft, these envelopes may no longer be effective, as aircraft failure typically affects the aircraft's flight performance, resulting in a reduced safety flight envelope for the aircraft. Therefore, when an aircraft suffers structural damage, real-time online prediction of the safety envelope is required, and the resulting safety envelope can be transmitted to the pilot in real-time. However, the real-time performance of the safety envelope prediction in the prior art is insufficient, and a new safety envelope cannot be fed back to a pilot in time. Therefore, the invention provides the fault diagnosis and the safety envelope prediction based on the offline database, and the efficiency of the fault diagnosis and the safety envelope prediction is greatly improved.
The invention provides an online prediction method of a post-fault flight envelope based on a radial basis-counter propagation neural network. According to the method, based on an offline database obtained by modeling the aerodynamic effect of the damaged aircraft, the neural network is trained offline, so that the fault of the aircraft can be diagnosed online in real time, and a new safety envelope can be obtained online.
Disclosure of Invention
In order to complete the online prediction of the post-fault aircraft safety envelope, the invention provides an online prediction method of the post-fault flight envelope based on a radial basis-counter propagation neural network, which aims to solve the problem of difficult prediction of the damaged aircraft flight envelope in the prior art. With the help of the offline database, the challenges associated with the high computational cost of acquiring a global model and a safe envelope prediction of a damaged aircraft can be overcome. And detecting and identifying the damage state of the aircraft by using a mode classification technology and using the locally estimated stability derivative as a classification characteristic, so as to find a correct database index.
In order to achieve the above purpose, the invention adopts the following technical scheme:
an online prediction of post-fault flight envelope based on radial basis-counter propagating neural network, comprising the steps of:
s1, building an aircraft health state monitoring module;
s2, identifying pneumatic parameters;
s3, modeling the structural damage aerodynamic effect and constructing a fault database;
s4, training an rbf-bp neural network and diagnosing faults in real time;
and S5, establishing a flight envelope database.
Preferably, in the step S1, an aircraft health status monitoring module is established, including the following steps:
(1) Command delta from an on-board flight controller cmd Is received by an actuator;
(2) In the event of a fault, the actual output delta of the actuator abn And an expected value delta calculated from its mathematical model nom Abnormal residual errors between the two sensors are detected by the sensors;
(3) When a residual error occurs, an online aerodynamic anomaly detection process will be initiated, with new measurements of the flight status and response being sent to the system identification module.
Preferably, in the step S2, the identifying of the aerodynamic parameters includes the following steps:
(1) Calculating dimensionless forces and moments along each axis using the sensor measurements or state values estimated by the kalman filter, the dimensionless aerodynamic forces and moments of the aircraft being obtainable from equations (1) and (2);
wherein C is L 、C D 、C Y 、C l 、C m 、C n Respectively a lift coefficient, a drag coefficient, a side force coefficient, a roll moment coefficient, a pitch moment coefficient and a yaw moment coefficient, alpha is an attack angle, beta is a sideslip angle, m is aircraft mass, A X 、A Y 、A Z Acceleration components along X, Y, Z axis, ρ is air density, V is airspeed, S is wing area, I xx 、I yy 、I zz 、I xz For moment of inertia and moment of product, p, q, r are roll, yaw and pitch rates respectively,derivatives for roll, yaw and pitch rates, b, etc.>The span and average chord length are respectively;
(2) Estimating a stability derivative of the aircraft from the simulation data using a recursive least squares method by equation (3);
in the method, in the process of the invention,the basic increment coefficient of the lifting force, the increment coefficient related to the lifting force and the attack angle, the increment coefficient related to the lifting force and the yaw angle and the increment coefficient related to the lifting force and the elevator are respectively;
(3) Parameter estimation is carried out by adopting a recursive least square method with forgetting factors, and the recursive least square method has the following structure:
for the parameter to be estimatedNumber lambda E [0,1]]As a forgetting factor, a variable forgetting factor is used to enhance the effect of new data when model parameters change suddenly and reduce covariance matrix saturation under steady-state conditions.
Preferably, in the step S3, the modeling of the structural damage aerodynamic effect and the construction of the fault database include the following steps:
(1) According to a series of wind tunnel experiments, each damage condition can generate a unique aerodynamic effect on the aircraft and change different stability derivatives. Horizontal stabilizer damage can lead to changes in longitudinal stability, which can be determined byA representation; vertical tail wing tip damage mainly results in changes in lateral force and directional stability, which can be determined byIs represented by a change value of (c).
(2) The change value at the damage degree can be obtained by the following formula;
in the formula, delta C, C d C is the degree of damage of the body, the dimensionless aerodynamic coefficient of the damaged body and the dimensionless aerodynamic coefficient of the complete body respectively;
(3) By analyzing the wind tunnel data, an approximate linear relationship between the range of variation of each aerodynamic coefficient and the percent loss of wing tip can be assumed; according to the calculated damage degree variation scale, a linear interpolation is used, a pneumatic damage model under each damage level can be established, and a fault pneumatic database comprising pneumatic data and corresponding stability derivative of the horizontal stabilizer damage and the vertical tail wing tip damage is generated.
Preferably, in the step S4, the rbf-bp neural network training and the real-time fault diagnosis include the following steps:
(1) Determining the input variable x as at each MachThe output variable is the specific fault type and damage degree corresponding to the pneumatic data;
(2) Prior to rbf-bp neural network training, the dataset was run at 7:3, dividing the data into a training set and a testing set, and then normalizing the data to be between [0,1 ];
(3) Initializing an rbf network, selecting t different initial clustering centers, setting the iteration step number to be 1, and immediately selecting the input from the samples. The closest distance between the input sample and the cluster center can be obtained by the following formula:
iX k =min||X k -C i (m)||,i=1,2,...,t,k=1,2,...,n (6)
(4) Calculating and adjusting the center of hidden layer nodes:
when C i (m+1)=C i And (m) ending the clustering process, and determining the width of the hidden layer node according to the clustering center. If the input sample and the center distance are not equal, the calculation of the input sample and the center distance is carried out again until the learning process is completed. The mean square error target was set to 0.05, the radial basis expansion rate was 1, and the maximum neuron number was set to 25 by default.
(5) For a bp neural network, setting the number of input neurons n=6, the number of output neurons m=10, the training frequency e=1000, the hidden layer neuron number h=13, and using log sig and purelin functions as an activation function, wherein the hidden layer neuron number h is obtained by the following formula:
where α is any integer between 1 and 10.
Preferably, in the step S5, a flight envelope database is established, including the following steps:
(1) The plane maximum speed can be obtained by:
T max for thrust, ρ (H) is the air density in relation to altitude, C xmin S is the wing area, which is the drag coefficient;
(2) The plane fly minimum speed can be obtained by:
g is the weight of the aircraft, C zmax Is the lift coefficient;
(3) The maximum altitude rise of an aircraft in constant velocity straight line fly can be obtained by:
v z the maximum rise rate of the aircraft is represented by K, the lift-drag ratio is represented by K, and the flat flying speed is represented by v;
(4) The step of establishing a flight envelope database is as follows:
constraint conditions:
flat flight conditions:
basic trim control parameters:
λ=[θ,ψ,δ T ,δ e ,δ r ] (14)
optimizing an objective function:
wherein A-I is an optimized parameter, dr is resistance, L is lift force, T is thrust along the machine body, phi, psi and theta are rolling angle, yaw angle and pitch angle respectively,the roll angle and yaw and pitch angle derivatives, respectively, p, q, r are roll, yaw and pitch rates, respectively,/->Derivatives of roll, yaw and pitch rates, V is the flight speed, h is the altitude, V 0 And h 0 For a speed and height at a horizontal tail offset angle of 0 DEG, beta is the sideslip angle, +.>Is the derivative of sideslip angle, alpha is the angle of attack, +.>Is the derivative of angle of attack, m and g are the mass of the aircraft and the acceleration of gravity, delta T 、δ e 、δ r Rudder deflection angle caused by thrust, elevating aileron deflection angle, rudder deflection angle caused by resistance,/->Is a high derivative>Is the speed derivative;
when the aircraft fails, balancing the aircraft at each designated altitude and speed, a set of different drag and lift coefficients are obtained; from equations (1) - (3), the maximum and minimum speeds and the rise limit at this time can be estimated; based on a series of such estimations, a flight envelope for such fault conditions is obtained, which in turn results in a database of flight envelopes for various fault conditions.
Compared with the prior art, the invention has the following beneficial effects:
according to the method, aerodynamic effect modeling is carried out on the fault aircraft, aerodynamic data of the damaged aircraft are obtained, and a database is built. The radial basis-backpropagation neural network is trained in conjunction with a database to generate classifiers and to generate decision surfaces. And estimating the flight envelope in real time by applying the classification result, and generating a new flight envelope according to the offline database. Compared with the conventional dynamic envelope prediction method, the method adopts the mode of establishing an offline database, carrying out fault diagnosis and generating a safety envelope in real time, avoids dimension disasters and greatly reduces calculation time. Finally, the feasibility and the efficiency of the method are proved through simulation verification.
Drawings
FIG. 1 is an overall frame diagram of a flight envelope prediction system;
FIG. 2 is a pneumatic parameter identification flow chart;
FIG. 3 is a schematic diagram of a fault diagnosis flow;
FIG. 4 is a schematic diagram of a rbf-bp neural network learning process;
FIG. 5 is a schematic diagram of fault diagnosis accuracy for different sample numbers;
FIG. 6 is a schematic illustration of aerodynamic effects of different degrees of wing damage;
Detailed Description
The invention will be further illustrated with reference to examples.
Aiming at the characteristic that the safety envelope of the fault aircraft is difficult to predict, the invention provides an online prediction method of the post-fault flight envelope based on an rbf-bp neural network, which can diagnose various faults on line in real time through an offline database and generate a new safety envelope. The method first utilizes sensors to monitor the health of the actuator. If any failure occurs, an abnormal residual between the actual output of the actuator and the expected value will soon detect the failure. The aircraft state and sensor bias are then estimated based on the aircraft dynamics model using a kalman filter or other advanced state estimator. And secondly, calculating dimensionless forces and moments on each shaft by using the estimated states and the sensor information, and providing input for the second step of the two-step method, namely estimating the stability derivative by using a recursive least squares method. And finally, by utilizing the calculated dimensionless force and moment, the output of the normal flight model is compared with the actual aircraft output measured value, and an online aerodynamic anomaly detection process is started. At the same time, an alarm is generated based on the newly identified stability derivative, a fault classification is triggered, and the likely location and scale of the fault is determined. Once the damage condition is estimated, this information is provided as an index to a database, and a database retrieval scheme and interpolation algorithm are applied to obtain the unique safe flight envelope closest to the current fault condition. The resulting safe flight envelope may be presented to the pilot and used by the fault tolerant controller to generate a new control law. Simulation results demonstrate the feasibility of this approach, successfully detecting and classifying two damage conditions.
Example 1
Step S1, building an aircraft health status monitoring module: input data delta nom 、δ abn For the expected values calculated from its normal pneumatic model and the actual output of the actuator, as shown in fig. 1. Command delta from an on-board flight controller cmd Is received by the actuator, and when a fault occurs, the actual output delta of the actuator abn And an expected value delta calculated from its mathematical model nom The anomaly residual between them can be detected quickly by the sensor. When the residual error occurs, an online aerodynamic anomaly detection process is started, and new measurement values of the flight state and response are sent to a system identification module.
Step S2, identifying pneumatic parameters: as shown in fig. 2, first, dimensionless aerodynamic force and moment of the aircraft are calculated by the formula (1) and the formula (2);
wherein C is L 、C D 、C Y C is the lift coefficient, the drag coefficient and the side force coefficient respectively l 、C m 、C n Respectively a roll moment coefficient, a pitch moment coefficient and a yaw moment coefficient, alpha is an attack angle, beta is a sideslip angle, m is aircraft mass, A X 、A Y 、A Z Acceleration components along X, Y, Z axis, ρ is air density, V is airspeed, S is wing area, I xx 、I yy 、I zz 、I xz For moment of inertia and moment of product, p, q, r are roll, yaw and pitch rates, b,The span and average chord lengths, respectively. C (C) L 、C D 、C Y 、C l 、C m 、C n The remaining parameters are known or can be obtained by an on-board sensor for the required unknowns. Estimating a model structure based on the input-output model of formula (3):
in the method, in the process of the invention,the basic increment coefficient of the lifting force, the increment coefficient related to the lifting force and the attack angle, the increment coefficient related to the lifting force and the yaw angle and the increment coefficient related to the lifting force and the elevator are respectively as above. The estimation method employed herein is the recursive least squares method. When model parameters change suddenly, a variable forgetting factor is used to enhance the effect of new data and reduce covariance matrix saturation under steady-state conditions. />And as the parameter to be estimated, the value range of the forgetting factor alpha is 0.95-0.99, and the initial value is the stability derivative value of the aircraft in the normal state. The recursive least square method has the structure shown in the formula (4):
in step S3, modeling of structural damage aerodynamic effect and construction of a fault database:
according to a series of wind tunnel experiments, each damage condition can generate a unique aerodynamic effect on the aircraft and change different stability derivatives. Horizontal stabilizer damage can lead to changes in longitudinal stability, which can be determined byA representation; vertical tail wing tip damage mainly results in changes in lateral force and directional stability, which can be determined byIs represented by a change value of (c). The scale of variation in the extent of damage can be obtained from the following formula;
in the formula, delta C, C d C is the degree of damage to the body, the dimensionless aerodynamic coefficient of the damaged body and the dimensionless aerodynamic coefficient of the complete body, respectively. By analyzing the wind tunnel data, an approximately linear relationship between the range of variation of each aerodynamic coefficient and the percent tip loss can be assumed. According to the calculated damage degree variation scale, a linear interpolation is used, a pneumatic damage model under each damage level can be established, and a fault pneumatic database comprising pneumatic data and corresponding stability derivative of the horizontal stabilizer damage and the vertical tail wing tip damage is generated. As shown in fig. 3, the established fault pneumatic database will be used to train the neural network.
S4, training an rbf-bp neural network and diagnosing faults in real time:
and determining the input variable x as the specific fault type and damage degree corresponding to the pneumatic data under each Mach number, and determining the output variable x as the specific fault type and damage degree corresponding to the pneumatic data. Prior to rbf-bp neural network training, the dataset was run at 7:3 is divided into a training set and a testing set, and then normalization processing is carried out on the data, so that the data is normalized to be between [0,1 ]. Initializing an rbf network, selecting t different initial clustering centers, setting the iteration step number to be 1, and immediately selecting the input from the samples. The closest distance between the input sample and the cluster center can be obtained by the following formula:
iX k =min||X k -C i (m)||,i=1,2,...,t,k=1,2,...,n (6)
the center of calculating and adjusting hidden layer nodes can be obtained by equation (7),
when C i (m+1)=C i And (m) ending the clustering process, and determining the width of the hidden layer node according to the clustering center. If the input sample and the center distance are not equal, the calculation of the input sample and the center distance is carried out again until the learning process is completed. The neural network training process is shown in fig. 4. The mean square error target was set to 0.05, the radial basis expansion rate was 1, and the maximum neuron number was set to 25 by default. For bp neural network, set the input neuron number n=12, output neuron number m=10, training frequency e=1000, activation function uses log sig and purelin functions, hidden layer neuron number h=13 is obtained by the following formula:
where α is any integer between 1 and 10. The results shown in fig. 5, 6 and 7 show the effectiveness of the algorithm proposed by the present invention.
In step S5, a flight envelope database is established:
the maximum and minimum speeds of the plane and the maximum height rise of the plane in the constant speed straight line can be obtained by the formulas (6), (7) and (8):
T max for thrust, ρ (H) is the air density in relation to altitude, C xmin Is the resistance coefficient; g is the weight of the aircraft, C zmax Is the lift coefficient. v z K is the lift-drag ratio, which is the maximum lift-off rate of the aircraft.
And then establishing a flight envelope database:
constraint conditions:
flat flight conditions:
basic trim control parameters:
optimizing an objective function:
wherein A-I is an optimization parameter, dr is resistanceForce L is lift force, T is thrust along the machine body, phi and theta are roll angle, yaw angle and pitch angle respectively,the roll angle and yaw and pitch angle derivatives, respectively, p, q, r are roll, yaw and pitch rates, respectively,/->Derivatives of roll, yaw and pitch rates, V is the flight speed, h is the altitude, V 0 And h 0 For a speed and height at a horizontal tail offset angle of 0 DEG, beta is the sideslip angle, +.>Is the derivative of sideslip angle, alpha is the angle of attack, +.>Is the derivative of angle of attack, m and g are the mass of the aircraft and the acceleration of gravity, delta T 、δ e 、δ r Rudder deflection angle caused by thrust, elevating aileron deflection angle, rudder deflection angle caused by resistance,/->Is a high derivative>Is the speed derivative;
the trim of an aircraft is an optimization problem that satisfies initial values and constraint limits. When an aircraft fails, trimming the aircraft at each designated altitude and speed results in a set of different drag and lift coefficients. From equations (1) - (3), the maximum and minimum speeds and the rise limit at this time can be estimated. Based on a series of such estimations, a flight envelope for such fault conditions is obtained, which in turn results in a database of flight envelopes for various fault conditions.
The foregoing is only a preferred embodiment of the invention, it being noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the present invention, and such modifications and adaptations are intended to be comprehended within the scope of the invention.
Claims (6)
1. The post-fault flight envelope on-line prediction method based on the radial basis-counter propagation neural network is characterized by comprising the following steps of:
s1, building an aircraft health state monitoring module;
s2, identifying pneumatic parameters;
s3, modeling the structural damage aerodynamic effect and constructing a fault database;
s4, training an rbf-bp neural network and diagnosing faults in real time;
and S5, establishing a flight envelope database.
2. The method for online prediction of post-fault flight envelope based on radial basis-counter-propagating neural network according to claim 1, wherein in step S1, an aircraft health status monitoring module is established, comprising the steps of:
(1) Command delta from an on-board flight controller cmd Is received by an actuator;
(2) In the event of a fault, the actual output delta of the actuator abn And an expected value delta calculated from its mathematical model nom Abnormal residual errors between the two sensors are detected by the sensors;
(3) When a residual error occurs, an online aerodynamic anomaly detection process will be initiated, with new measurements of the flight status and response being sent to the system identification module.
3. The method for online prediction of post-fault flight envelope based on radial basis-counter-propagating neural network according to claim 1, wherein in step S2, the aerodynamic parameter identification comprises the following steps:
(1) Calculating dimensionless forces and moments along each axis using the sensor measurements or state values estimated by the kalman filter, the dimensionless aerodynamic forces and moments of the aircraft being derived from equations (1) and (2);
wherein C is L 、C D 、C Y 、C l 、C m 、C n Respectively a lift coefficient, a drag coefficient, a side force coefficient, a roll moment coefficient, a pitch moment coefficient and a yaw moment coefficient, alpha is an attack angle, beta is a sideslip angle, m is aircraft mass, A X 、A Y 、A Z Acceleration components along X, Y, Z axis, ρ is air density, V is airspeed, S is wing area, I xx 、I yy 、I zz 、I xz For moment of inertia and moment of product, p, q, r are roll, yaw and pitch rates respectively,derivatives of roll, yaw and pitch rates, b +.>The span and average chord length are respectively;
(2) Estimating a stability derivative of the aircraft from the simulation data using a recursive least squares method by equation (3);
in the method, in the process of the invention,the basic increment coefficient of the lifting force, the increment coefficient related to the lifting force and the attack angle, the lifting force and the deflection are respectivelyIncrement coefficient related to the aviation angle and increment coefficient related to lift and elevator;
(3) Parameter estimation is carried out by adopting a recursive least square method with forgetting factors, and the recursive least square method has the following structure:
4. The method for online prediction of post-fault flight envelope based on radial basis-counter-propagating neural network according to claim 1, wherein in step S3, the structural damage aerodynamic effect modeling and the fault database construction comprise the following steps:
(1) Horizontal stabilizer damage can lead to changes in longitudinal stability, due toA representation; vertical tail wing tip damage causes a change in lateral force and directional stability, consisting of +.>Is represented by a change value of (a);
(2) The change value under the damage degree is obtained by the following formula;
in the formula, delta C, C d C is the degree of injury of the body, the dimensionless aerodynamic coefficient of the damaged body and the dimensionless of the complete body respectivelyAerodynamic coefficient of the line;
(3) Assuming an approximately linear relationship between the range of variation of each aerodynamic coefficient and the percent loss of wing tip; and according to the calculated damage degree variation scale, using linear interpolation to establish a pneumatic damage model under each damage level, and generating a fault pneumatic database comprising pneumatic data and corresponding stability derivative of the horizontal stabilizer damage and the vertical tail wing tip damage.
5. The method for online prediction of post-fault flight envelope based on radial basis-counter-propagating neural network according to claim 4, wherein in step S4, rbf-bp neural network training and real-time fault diagnosis comprises the following steps:
(1) Determining the input variable x as at each MachThe output variable is the specific fault type and damage degree corresponding to the pneumatic data;
(2) Before rbf-bp neural network training is carried out, dividing a data set into a training set and a testing set, and then carrying out normalization processing on the data to normalize the data to be between [0,1 ];
(3) Initializing an rbf network, selecting t different initial clustering centers, setting iteration steps, and inputting and then selecting from samples; the closest distance between the input sample and the cluster center is obtained by the following formula:
iX k =min||X k -C i (m)||,i=1,2,...,t,k=1,2,...,n (6)
(4) Calculating and adjusting the center of hidden layer nodes:
when C i (m+1)=C i (m) when the clustering process is finished, determining the width of hidden layer nodes according to a clustering center; if the two are not equal, the input sample and the center distance are re-performedCalculating the distance until the learning process is completed;
(5) For the bp neural network, setting the number n of input neurons, the number m of output neurons and the training frequency E, wherein the activation function uses log sig and purelin functions, and the number h of hidden layer neurons is obtained by the following formula:
where α is any integer between 1 and 10.
6. The method for online prediction of post-fault flight envelope based on radial basis-counter-propagating neural network according to claim 1, wherein in step S5, a flight envelope database is built, comprising the steps of:
(1) The plane maximum speed is obtained by the following formula:
T max for thrust, ρ (H) is the air density in relation to altitude, C xmin Is the resistance coefficient;
(2) The plane fly minimum speed is obtained by:
g is the weight of the aircraft, C zmax Is the lift coefficient;
(3) The maximum altitude rise limit for an aircraft to maintain a constant velocity straight line flat flight is obtained by:
v z the maximum rise rate of the aircraft is shown, and K is the lift-drag ratio;
(4) The step of establishing a flight envelope database is as follows:
constraint conditions:
flat flight conditions:
basic trim control parameters:
optimizing an objective function:
wherein A-I is an optimized parameter, dr is resistance, L is lift force, T is thrust along the machine body, phi, psi and theta are rolling angle, yaw angle and pitch angle respectively,the roll angle and yaw and pitch angle derivatives, respectively, p, q, r are roll, yaw and pitch rates, respectively,/->Derivatives of roll, yaw and pitch rates, V is the flight speed, h is the altitude, V 0 And h 0 For a speed and height at a horizontal tail offset angle of 0 DEG, beta is the sideslip angle, +.>Is the derivative of sideslip angle, alpha is the angle of attack, +.>Is the derivative of angle of attack, m and g are the mass of the aircraft and the acceleration of gravity, delta T 、δ e 、δ r Is the rudder deflection angle caused by thrust, the aileron deflection angle and the rudder deflection angle caused by resistance,is a high derivative>Is the speed derivative;
when the aircraft fails, balancing the aircraft at each designated altitude and speed, a set of different drag and lift coefficients are obtained; estimating the maximum and minimum speeds and the rise limit at this time according to the formulas (1) - (3); based on a series of such estimations, a flight envelope for such fault conditions is obtained, which in turn results in a database of flight envelopes for various fault conditions.
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CN116702030B (en) * | 2023-05-31 | 2024-01-23 | 浙江大学 | Blast furnace state monitoring method and device based on sensor reliability analysis |
CN116552804A (en) * | 2023-07-10 | 2023-08-08 | 四川腾盾科技有限公司 | Test flight planning method for verifying practical limit rise index of low-speed unmanned aerial vehicle |
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