An aircraft takeoff mass estimation method based on improved simulated annealing algorithm

Abstract

The application discloses an aircraft take-off mass estimation method based on an improved simulated annealing algorithm, mainly comprising the following steps: step (1), based on an aircraft basic performance database (BADA), starting from a total energy equation of particle kinematics, considering the influence of wind, an aircraft take-off mass estimation model is constructed; step (2), aiming at the take-off mass estimation model constructed in step 1, considering the track points in the initial climb stage, a target function and a constraint condition are proposed; step (3), the tabu table function in the tabu search algorithm is introduced into the simulated annealing algorithm as an improved algorithm, and the improved algorithm is applied to solve the take-off mass estimation model. The method can establish a take-off mass estimation model based on historical track data, and the simulated annealing algorithm with the tabu search is used for optimization calculation, thereby providing technical support for high-precision track simulation work.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of aircraft performance analysis application, and particularly relates to an aircraft take-off mass estimation method based on an improved simulated annealing algorithm. BACKGROUND

[0002] In recent years, global aircrafts have developed rapidly, and with the proposal of the concept of trajectory based operation (TBO), high-precision four-dimensional trajectory prediction technology has become an important research content for improving air traffic predictability and management operation capacity. Aircraft mass is an important factor affecting the accuracy of trajectory prediction and has an important influence on the performance of each stage of flight.

[0003] However, aircraft mass belongs to the commercial operation data of airlines and is difficult to obtain through public channels. In actual research, the reference mass provided in the aircraft performance database is often applied to trajectory prediction, but the trajectory prediction based on the reference mass cannot reflect the actual flight situation.

[0004] Therefore, it is of great significance to estimate the aircraft mass based on historical trajectory data. SUMMARY

[0005] The purpose of the application is to provide an aircraft take-off mass estimation method based on an improved simulated annealing algorithm, which establishes an aircraft take-off mass iteration model, solves the model by improving the simulated annealing algorithm, and estimates the take-off mass of historical flights based on QAR data.

[0006] To achieve the above purpose, the application provides an aircraft take-off mass estimation method based on an improved simulated annealing algorithm, which comprises the following steps:

[0007] Step (1), based on the Base of Aircraft Data (BADA), starting from the total energy equation of particle kinematics, considering the influence of wind, an aircraft take-off mass estimation model is constructed;

[0008] Step (2), for the take-off mass estimation model constructed in step 1, the trajectory points in the initial climb stage are comprehensively considered, and the objective function and the constraint condition are proposed;

[0009] Step (3), the tabu table function in the tabu search algorithm is introduced into the simulated annealing algorithm as an improved algorithm, and the improved algorithm is applied to solve the take-off mass estimation model.

[0010] Further, the step (1) of constructing the aircraft take-off mass estimation model comprises the following steps:

[0011] Step (11), the barometric altitude H of each track point in the QAR is used as the basis p and the true airspeed V TAS Data, the calculation process of the resistance D and the thrust Thr of the aircraft during the climb is as follows:

[0012]

[0013] In the formula: D is the resistance, the unit is N; V TAS is the true airspeed, the unit is m / s; S is the wing area, the unit is m 2 ;

[0014] H p is the barometric altitude, the unit is ft; ρ is the atmospheric density at the barometric altitude H p , the unit is kg / m 3 ; C D is the resistance coefficient; C L is the lift coefficient; m is the mass of the aircraft, the unit is kg; g is the gravitational acceleration, the unit is m / s 2 , the value is 9.80665 m / s 2 ; is the flight slope angle, the unit is degree; Thr is the thrust, the unit is N; ΔT eff is the intermediate parameter, the unit is K; ΔT is the ISA temperature deviation, the unit is K; C D0 is the parasitic resistance coefficient, C D2 is the induced resistance coefficient, C D0 is the parasitic resistance coefficient, C D2 is the induced resistance coefficient, C1, C2, C3, C4, C5 are the climb thrust coefficients, all of which are derived from the BADA flight performance database;

[0015] Step (12), the fuel consumption rate η and the fuel flow rate FF during the climb of the aircraft are calculated according to the following formula:

[0016]

[0017] In the formula: η is the fuel consumption rate, the unit is kg / (min·kN); FF is the flow rate, the unit is kg / min; C f1 , C f2 are the thrust specific fuel consumption coefficients, derived from the BADA flight performance database;

[0018] Step (13), the climb rate ROC is the rate of change of the barometric altitude with respect to time, expressed as:

[0019]

[0020] In the formula: T is the barometric altitude H pT is the temperature of the lower atmosphere in K; h is the geodetic height in ft, which is converted from the pressure altitude H p t is the time in s

[0021] Step (14), according to the aircraft basic performance database BADA, by analyzing the force of the aircraft mass point and the conversion relationship of potential energy and kinetic energy, considering the influence of wind, a total energy model is established:

[0022]

[0023] In the formula: V Wind is the wind speed in m / s; θ is the angle between the wind speed and the true airspeed in degrees;

[0024] The total energy equation can be expressed as follows:

[0025]

[0026] For convenience of description, P and Q are simplified:

[0027]

[0028] P is the power generated by the thrust and resistance in W; Q is an intermediate parameter in m 2 / s 3 ;

[0029] Step (15), by dynamically adjusting the mass m, the power P generated by the thrust and resistance acting on the aircraft is close to the power mQ obtained by the aircraft; based on the total energy equation, a function f(m) about the mass m of the aircraft is proposed:

[0030] f(m)=P-mQ

[0031] Substitute the climbing thrust and resistance calculation formula into P and Q, and the specific expression of f(m) is:

[0032] f(m)=a·m 2 +b·m+c

[0033] Where c=C D0 ρV TAS 2 S-Thr

[0034] Step (16), select n flight path points in the initial climbing stage, use uniform time interval Δt between adjacent flight path points, discretize the mass change process of the aircraft, and calculate the mass m i of the i th flight path point from the mass m0 of the initial flight path point:

[0035] m i= m0- δ i

[0036] wherein δ i is the fuel consumption from the initial waypoint to the i-th waypoint:

[0037]

[0038] Each waypoint i has a corresponding a i , b i , c i , which is a function of the takeoff mass m0:

[0039] f i (m0) = a i (m0- δ i ) 2 + b i (m0- δ i ) + c i .

[0040] Further, the step (2) of proposing the objective function and the constraints includes the following steps:

[0041] Step (21), for the n waypoints of the initial climb phase, sum the squares of the functions f i (m0) for each waypoint with respect to m0, and solve for the takeoff mass of the aircraft by minimizing the sum;

[0042] The objective function of the takeoff mass estimation model is:

[0043]

[0044] Step (22), the decision variable m0 must satisfy the mass constraint and the climb rate constraint:

[0045]

[0046] wherein m max , m min are the maximum operating mass and the minimum operating mass, respectively, in kg, and are derived from the BADA flight performance database; and fpm represents ft / min.

[0047] Further, the step (3) of applying the improved algorithm to solve the takeoff mass estimation model includes the following steps:

[0048] Step (31), initialize the parameters, set the initial temperature t0, the termination temperature t f , the cooling coefficient a, the number of neighborhood solutions Ca, and the maximum number of iterations N, and set the current temperature t = t0 and the current iteration number iter = 0;

[0049] Step (32), randomly generating an initial solution M0, setting the current solution m=M0 and the optimal solution m*=M0;

[0050] Step (33), generating Ca neighborhood solutions in the following way:

[0051] m near = m + (2r-1) x (m u -m l )

[0052] m near , m, m u , m l are upper and lower bounds of the solution; all neighborhood solutions constitute a neighborhood N*(m), and the solution with the minimum objective function value in the neighborhood is selected as a candidate solution m';

[0053] Step (34), calculating Δ=F(m')-F(m*); if Δ<0 and the quality constraint and the climb rate constraint are satisfied, accepting m' as the current solution, updating the tabu list, and turning to step (36), wherein F(m) is the objective function value; otherwise, turning to step (35);

[0054] Step (35), if exp(-Δ / t)>rand(0,1), accepting m' as the current solution, updating the tabu list, and turning to step (36); otherwise, turning to step (33);

[0055] Step (36), increasing the iteration number iter=iter+1, applying the cooling coefficient α in step (31), and updating the temperature t=αt;

[0056] Step (37), if t<t f or iter=N, stopping the algorithm and outputting the optimal solution m*; otherwise, returning to step (33).

[0057] The application has the advantages that the application starts from the total energy equation of aircraft mass point kinematics, establishes a takeoff mass iteration model according to BADA performance data, combines the tabu search algorithm with the simulated annealing algorithm, and has obvious advantages in searching for a global optimal solution and improves the operation efficiency. The average relative error is 3.45% when the takeoff mass of batch flights is estimated and compared with the real takeoff mass of QAR, which provides technical support for high-precision flight simulation.

[0058] Other features and advantages of the application will be set forth in the specification, and in part will become apparent from the specification, or can be learned by practice of the application. The objects and other advantages of the application will be realized and attained by the structure particularly pointed out in the specification as well as the appended drawings.

[0059] In order to make the above objectives, characteristics and advantages of the present application more apparent, clear and easy to understand, the following preferred embodiments are specifically described below with reference to the accompanying drawings. BRIEF DESCRIPTION OF DRAWINGS

[0060] In order to more clearly illustrate the specific embodiments of the present application or the technical solutions in the prior art, the following will briefly introduce the drawings needed to be used in the specific embodiments or the prior art description. Obviously, the drawings described below are some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0061] Figure 1 is a flow chart of the aircraft take-off mass estimation method based on the improved simulated annealing algorithm involved in the present application;

[0062] Figure 2 is a flow chart of the improved simulated annealing algorithm involved in the present application;

[0063] Figure 3 is a sample flight fuel flow rate comparison chart involved in the present application;

[0064] Figure 4 is a sample flight take-off mass comparison chart involved in the present application;

[0065] Figure 5 is a batch flight relative error absolute value distribution chart involved in the present application. DETAILED DESCRIPTION

[0066] In order to make the objectives, technical solutions and advantages of the embodiments of the present application more apparent, clear and easy to understand, the technical solutions of the present application will be described clearly and completely below with reference to the accompanying drawings. Obviously, the described embodiments are some of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0067] Currently, the commonly used flight path analysis data are Air Traffic Control Second Surveillance Radar (ATC SSR) or Automatic Dependent Surveillance-Broadcast (ADS-B), and the field information such as true airspeed, total temperature and wind is not included in these data. Since the field information in the Quick Access Recorder (QAR) is rich, contains various state monitoring data of the aircraft, and even provides quality data in each flight phase, therefore, based on the historical flight QAR data information, a takeoff quality iteration model can be established.

[0068] Embodiments

[0069] Figure 1 is a flowchart of the aircraft takeoff quality estimation method based on the improved simulated annealing algorithm.

[0070] As Figure 1 shown, the embodiment 1 provides an aircraft takeoff quality estimation method based on the improved simulated annealing algorithm, and the steps are as follows: step (1), based on the Base of Aircraft Data (BADA), starting from the total energy equation of particle kinematics, considering the influence of wind, an aircraft takeoff quality estimation model is constructed; step (2), for the takeoff quality estimation model constructed in step 1, the trajectory points in the initial climb phase are comprehensively considered, and a target function and a constraint condition are proposed; step (3), the tabu table function in the tabu search algorithm is introduced into the simulated annealing algorithm as an improved algorithm, and the improved algorithm is applied to solve the takeoff quality estimation model.

[0071] In the embodiment, the step (1) of constructing the aircraft takeoff quality estimation model includes:

[0072] Firstly, the QAR trajectory data is acquired, and the data is twice segmented to ensure that the flight information corresponds to the trajectory one by one; the twice segmented QAR trajectory is data cleaned to remove the noise points and repeated space-time records, so as to obtain the preprocessed trajectory. Table 1 is the field information of the used QAR data:

[0073] Table 1: QAR data field information

[0074]

[0075] The aircraft has a small fuel consumption during taxiing and takeoff phase, and the mass corresponding to the initial trajectory point in the initial climb phase is considered as the takeoff mass of the aircraft. Based on the changes of the aerodynamic configuration and the vertical motion situation of the aircraft, the aircraft operation phase is re-divided, and the trajectory point in the initial climb phase is selected as the research object.

[0076] The update interval of QAR data is 1 s. When the aircraft is disturbed by airflow, the barometric altitude will change temporarily, which will have a certain influence on the barometric altitude rate of change. However, this change cannot reflect the true flight intention. Therefore, in order to obtain more accurate and stable trajectory information, the QAR trajectory of the aircraft is selected at an interval of 4 s, and the extracted trajectory is preprocessed.

[0077] In this embodiment, the step (1) of constructing the aircraft takeoff mass estimation model comprises the following steps:

[0078] In step (11), based on the barometric altitude H p and true airspeed V TAS data of each trajectory point in QAR, the calculation process of the drag D and the thrust Thr of the aircraft during the climb is as follows:

[0079]

[0080] In the formula: D is the drag, the unit is N; V TAS is the true airspeed, the unit is m / s; S is the wing area, the unit is m 2 ;

[0081] H p is the barometric altitude, the unit is ft; p is the atmospheric density under the barometric altitude H p , the unit is kg / m 3 ; C D is the drag coefficient; C L is the lift coefficient; m is the mass of the aircraft, the unit is kg; g is the gravitational acceleration, the unit is m / s 2 , the value is 9.80665 m / s 2 ; is the flight slope angle, the unit is degree; Thr is the thrust, the unit is N; AT eff is an intermediate parameter, the unit is K; AT is the ISA temperature deviation, the unit is K; C D0 is the parasitic drag coefficient, C D2 is the induced drag coefficient, C D0 is the parasitic drag coefficient, C D2 is the induced drag coefficient, C1, C2, C3, C4, C5 are the climb thrust coefficients, all of which are derived from the BADA flight performance database;

[0082] Step (12), the fuel consumption rate η and the fuel flow rate FF during the aircraft climb are calculated as follows:

[0083]

[0084] wherein: η is the fuel consumption rate, in kg / (min·kN); FF is the flow rate, in kg / min; C f1 , C f2 is the thrust specific fuel consumption coefficient, which is derived from the BADA flight performance database;

[0085] Step (13), the climb rate ROC is the rate of change of the barometric altitude with respect to time, expressed as:

[0086]

[0087] wherein: T is the atmospheric temperature at the barometric altitude H p , in K; h is the geodetic altitude, in ft, which is obtained by converting the barometric altitude H p ; t is time, in s;

[0088] Step (14), according to the aircraft basic performance database BADA, by analyzing the force acting on the aircraft mass and the conversion relationship between potential energy and kinetic energy, and considering the influence of wind, a total energy model is established:

[0089]

[0090] wherein: V Wind is the wind speed, in m / s; θ is the angle between the wind speed and the true airspeed, in degrees;

[0091] The total energy equation can be expressed as follows:

[0092]

[0093] For convenience, P and Q are simplified as follows:

[0094]

[0095] P is the power generated by the thrust and the resistance, in W; Q is an intermediate parameter, in m 2 / s 3 ;

[0096] Step (15), by dynamically adjusting the mass m, the power P generated by the thrust and the resistance acting on the aircraft is close to the power mQ obtained by the aircraft; based on the total energy equation, a function f(m) about the mass m of the aircraft is proposed:

[0097] f(m) = P - mQ

[0098] The climbing thrust and resistance calculation formula is substituted into P and Q, and f(m) has a specific expression form as follows:

[0099] f(m) = a·m 2 +b·m+c

[0100] wherein c = C D0 ρV TAS 2 S-Thr

[0101] Step (16), n track points in the initial climb phase are selected, and a uniform time interval Δt is used between adjacent track points to discretize the aircraft mass change process. The mass m of the i-th track point is calculated based on the mass m0 of the initial track point. i :

[0102] m i =m0-δ i

[0103] In the formula, δ i is the fuel consumption from the initial track point to the i-th track point:

[0104]

[0105] Each track point i has corresponding a i , b i , and c i , and the function of point i with respect to the takeoff mass m0 is:

[0106] f i (m0) = a i (m0-δ i ) 2 +b i (m0-δ i )+c i .

[0107] In this embodiment, the objective function and the constraint conditions proposed in step (2) include:

[0108] Step (21), for the n track points in the initial climb phase, the sum of squares of the function f i (m0) of each point with respect to m0 is minimized to obtain the takeoff mass of the aircraft;

[0109] The objective function of the aircraft takeoff mass estimation model is:

[0110]

[0111] Step (22), the decision variable m0 needs to satisfy the mass constraint and the climb rate constraint condition:

[0112]

[0113] wherein m max , m min are the maximum and minimum operating mass, respectively, in kg, from the BADA flight performance database; and fpm denotes ft / min.

[0114] In this embodiment, step (3) applies an improved algorithm to solve the takeoff mass estimation model, which comprises:

[0115] Step (31), initialize parameters, set initial temperature t0, termination temperature t f , cooling coefficient a, number of neighborhood solutions Ca, maximum iteration number N, let current temperature t = t0, current iteration number iter = 0;

[0116] Step (32), randomly generate an initial solution M0, let current solution m = M0, optimal solution m* = M0;

[0117] Step (33), generate Ca neighborhood solutions in the following manner:

[0118] m near = m + (2r-1)×(m u -m l )

[0119] wherein m near is a neighborhood solution; m is the current solution; r is a random number in the range of (0, 1); m u , m l are the upper and lower boundaries of the solution; all neighborhood solutions constitute a neighborhood N*(m), and the solution with the minimum objective function value in the neighborhood is selected as a candidate solution m';

[0120] Step (34), calculate Δ = F(m') - F(m*); if Δ < 0 and the mass constraint and the climb rate constraint are satisfied, accept m' as the current solution, update the tabu list, and go to step (36), wherein F(m) is the objective function value; otherwise, go to step (35);

[0121] Step (35), if exp(-Δ / t) > rand(0, 1), accept m' as the current solution, update the tabu list, and go to step (36); otherwise, go to step (33);

[0122] Step (36), increase the iteration number iter = iter + 1, update the temperature t = at according to the cooling coefficient a in step (31);

[0123] Step (37), if t < t for iter = N, then stop the algorithm and output the optimal solution m*, otherwise return to step (33).

[0124] Figure 2 is the flow chart of the improved simulated annealing algorithm.

[0125] Table 2 is the parameter setting of the improved simulated annealing algorithm.

[0126] Table 2: Parameter setting of the improved simulated annealing algorithm

[0127]

[0128] The classical simulated annealing algorithm has the advantages of simple algorithm and being able to accept deteriorated solutions with a certain probability, but the algorithm still has defects such as lack of memory function leading to repeated calculation, long algorithm running time and the like. The present application introduces the taboo table function of the taboo search algorithm, increases the memory capacity and improves the running efficiency, while avoiding the loss of optimal solution due to accepting inferior solution.

[0129] The take-off mass of a typical sample flight and a batch flight is estimated, and the mass field in the QAR is taken as the true value of the take-off mass for comparison, the relative error RE and the average relative error MRE are selected as evaluation indexes, and the accuracy of the calculation result of the method is analyzed.

[0130]

[0131]

[0132] In the formula, m* is the model estimated aircraft take-off mass, m QAR is the actual take-off mass.

[0133] Firstly, a departure flight (A320) on a certain day is selected as a sample flight, the actual take-off mass of the sample flight is 67297 kg, and the take-off mass calculated by the method is 69278 kg, the relative error RE of the estimation result and the actual value is 2.94%. In order to verify the accuracy of the fuel calculation model, the fuel flow rate values at each time in the climbing stage are calculated according to the BADA model, as shown in the table. Figure 3 It can be seen that the change trend of the fuel flow rate calculated by the BADA model is the same as the real change trend recorded in the QAR, and the size is similar, the average relative error MRE of the BADA model estimated fuel flow rate is 2.06%, which can meet the accuracy requirement.

[0134] In order to better reflect the change of the aircraft mass with time, the mass at each track point in the climbing stage is calculated by using the method, as shown in the table. Figure 4 The average relative error MRE of the estimated aircraft mass of all track points is 3.07%, and the overall estimation accuracy is within the acceptable range.

[0135] To verify the universality of the model for estimating the takeoff mass of the aircraft, data of 15 types of aircraft and 26735 flights were collected. The trajectory data of the initial climb phase of each flight was input into the takeoff mass iterative model, and the takeoff mass was estimated by improving the simulated annealing algorithm. The estimated mass value was compared with the mass field value in the QAR, and the distribution of the relative error of the batch flights is shown in Table 3.

[0136] Table 3: Distribution of relative error of batch flights

[0137]

[0138] The results show that the absolute value RE of the relative error of the estimated mass of 97.67% of the flights is within 10%, and the absolute value RE of the relative error of the estimated mass of 75.30% of the flights is within 5%. This paper involves 15 types of aircraft, and the RE of the estimated mass of more than 60% of the flights in each type is less than 5%, and the average absolute value MRE of the relative error of each type is distributed between 3% and 5%.

[0139] Figure 5 is the relative error absolute value distribution diagram of the batch flights involved in the present application. From the Figure 5 It can be seen from the box plot inside that the quartile range (25th percentile-75th percentile) of the relative error absolute value of the common aircraft is mainly concentrated in 2%-6%, and the median of the relative error absolute value is between 3%-4%. Figure 5 The kernel density plot outside shows the distribution density of the relative error value. The absolute value of the relative error of most of the estimated mass of the flights is less than 10%, and only a small number of flights have an absolute value of the relative error of the estimated mass greater than 10%, which is caused by a small amount of data deviation in the QAR trajectory and the accuracy error of the BADA performance model itself. For example, BADA provides the aerodynamic configuration aerodynamic parameter value of each aircraft type in the initial climb phase, and the aircraft will use different flap and slot positions, i.e., the aerodynamic configuration is not fixed, during the actual initial climb process according to the running environment (takeoff mass, airport conditions, surrounding obstacles, etc.).

[0140] In summary, the application provides an aircraft take-off mass estimation method based on an improved simulated annealing algorithm, comprising: obtaining QAR track data, extracting the required field information for preprocessing; constructing an aircraft performance model based on an aircraft basic performance database BADA; considering the track points of the initial climb phase, proposing a target function and constraint condition based on the total energy equation of aircraft particle kinematics, and establishing a take-off mass iterative model; introducing the tabu table function in the tabu search algorithm into the simulated annealing algorithm, and applying the improved algorithm to solve the take-off mass iterative model; and estimating the take-off mass for sample flights and batch flights to test the calculation accuracy. The application as an aircraft take-off mass estimation method can fill the gap in aircraft mass estimation in China and effectively improve the accuracy of flight performance estimation and track prediction.

[0141] In the embodiments provided in the present application, it should be understood that the disclosed method can also be implemented in other manners. The flowchart and block diagram in the accompanying drawings illustrate the possible implementation architectures, functions and operation of the method and computer program product according to the embodiments of the present application. In this regard, each block in the flowchart or block diagram can represent a module, a program segment or a part of code, which contains one or more executable instructions for implementing the specified logic function. It should also be noted that in some alternative implementations, the functions noted in the blocks can occur in a different order than that noted in the accompanying drawings. For example, two consecutive blocks can actually be executed substantially in parallel, and sometimes they can be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagram and / or flowchart, and the combination of blocks in the block diagram and / or flowchart, can be implemented by a dedicated hardware-based system that performs the specified functions or actions, or can be implemented by a combination of special-purpose hardware and computer instructions.

[0142] In addition, each functional module in the various embodiments of the present application can be integrated together to form an independent part, or each module can exist independently, or two or more modules can be integrated to form an independent part.

[0143] If the functions are implemented in the form of software function modules and sold or used as independent products, they can be stored in a computer readable storage medium. Based on this understanding, the technical solutions of the present application or the parts of the present application that essentially contribute to the prior art or the parts of the technical solutions can be embodied in the form of software products. The computer software product is stored in a storage medium and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in the various embodiments of the present application. The aforementioned storage medium includes a U disk, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a magnetic disk or an optical disk, and various media that can store program codes.

[0144] Based on the above ideal embodiments according to the present application, through the above description, relevant personnel can make various changes and modifications without deviating from the technical idea of the present application. The technical scope of the present application is not limited to the contents of the specification, and must be determined according to the scope of the claims.

Claims

1. A method for estimating aircraft takeoff mass based on an improved simulated annealing algorithm, characterized in that, Includes the following steps: Step (1): Based on the aircraft basic performance database BADA, starting from the total energy equation of particle kinematics and considering the influence of wind, construct an aircraft takeoff mass estimation model. Step (2): Based on the takeoff mass estimation model constructed in Step 1, the objective function and constraints are proposed, taking into account the track points in the initial climb phase. Step (3) introduce the tabu table function in the tabu search algorithm into the simulated annealing algorithm as an improved algorithm, and apply the improved algorithm to solve the takeoff mass estimation model; The steps in step (1) of constructing the aircraft takeoff mass estimation model include the following steps: Step (11), based on the barometric altitude H of each track point in QAR p and vacuum velocity V TAS The calculation process for drag D and thrust Thr during an aircraft's climb is as follows: In the formula: D is the resistance, in N; V TAS Void velocity is given in m / s; S is the wing area in m². 2 H p ρ is the air pressure altitude, in feet; H is the air pressure altitude. p Atmospheric density at this time of year, in kg / m³ 3 C D C is the drag coefficient; L ρ is the lift coefficient; m is the aircraft mass in kg; g is the acceleration due to gravity in m / s². 2 The value is 9.80665 m / s 2 φ is the bank angle, in degrees; Thr is the thrust, in N; ΔT eff The intermediate parameter is K; ΔT is the ISA temperature deviation, in K; C D0 C is the parasitic drag coefficient. D2 C is the induced drag coefficient. D0 C is the parasitic drag coefficient. D2 C1, C2, C3, C4, and C5 are the induced drag coefficients, and all are derived from the BADA flight performance database. Step (12), the formulas for calculating the fuel consumption rate η and fuel flow rate FF during the aircraft's climb are as follows: In the formula: η is the fuel consumption rate, in kg / (min·kN); FF is the flow rate, in kg / min; C f1 C f2 The thrust-to-fuel ratio is derived from the BADA flight performance database; Step (13), the rate of ascent (ROC) is the rate of change of air pressure altitude over time, expressed as: In the formula: T is the air pressure altitude H p The atmospheric temperature is expressed in Kelvin (K); h is the geodetic altitude, expressed in feet (ft), derived from the atmospheric pressure altitude (H). p The result is obtained through conversion; t represents time, in seconds (s). Step (14): Based on the aircraft basic performance database BADA, by analyzing the forces acting on the aircraft mass and the relationship between potential and kinetic energy conversion, and considering the influence of wind, a full energy model is established: In the formula: V Wind θ is the wind speed, in m / s; θ is the angle between the wind speed and the vacuum velocity, in degrees. The total energy equation can be expressed in the following form: For ease of explanation, we will simplify P and Q: P represents the power generated by thrust and drag, measured in W; Q is an intermediate parameter, measured in m. 2 / s 3 ; Step (15), by dynamically adjusting the quality This makes the power P generated by the thrust and drag acting on the aircraft close to the power mQ obtained by the aircraft; based on the total energy equation, a function f(m) of the aircraft mass m is proposed: Substituting the formulas for climbing thrust and drag into P and Q, the specific expression for f(m) is as follows: in , , Step (16): Select n waypoints for the initial climb phase, with a uniform time interval Δt between adjacent waypoints. Discretize the aircraft mass change process and calculate the mass m of the i-th waypoint from the mass m0 of the initial waypoint. i : In the formula, δ i The amount of fuel consumed from the initial waypoint to the i-th waypoint: trackpoints Each has a corresponding a i b i c i The function of point i with respect to takeoff mass m0 is: 。 2. The aircraft takeoff mass estimation method based on the improved simulated annealing algorithm as described in claim 1, characterized in that, The steps in step (2) to propose the objective function and constraints include the following steps: Step (21): For the n waypoints in the initial climb phase, calculate the function f for each point with respect to m0. i Sum the squares of (m0) and minimize the summation to find the takeoff mass of the aircraft. The objective function of the aircraft takeoff mass estimation model is: Step (22) requires that the decision variable m0 satisfy the quality constraint and the rate of increase constraint: Where: m max m min Maximum and minimum operational mass, in kg, derived from the BADA flight performance database; fpm represents ft / min.

3. The aircraft takeoff mass estimation method based on the improved simulated annealing algorithm as described in claim 2, characterized in that, Step (3) involves applying the improved algorithm to solve the takeoff mass estimation model, including the following steps: Step (31): Initialize parameters, set initial temperature t0 and termination temperature t f , Cooling coefficient α, Number of neighborhood solutions Ca, Maximum number of iterations N, Let the current temperature t=t0 and the current number of iterations iter=0; Step (32): Randomly generate an initial solution M0, and set the current solution m = M0 and the optimal solution m* = M0; Step (33) generates Ca neighborhood solutions as follows: Where: m near The neighborhood solution is m; the current solution is m; r is a random number in the range (0, 1); m u m l The upper and lower boundaries of the solution; all neighborhood solutions constitute a neighborhood N*(m), and the solution with the smallest objective function value in the neighborhood is selected as the candidate solution m'; Step (34): Calculate Δ = F(m') - F(m*); if Δ < 0 and satisfies the quality constraint and climb rate constraint, then accept m' as the current solution, update the tabu list, and go to step (36), where F(m) is the objective function value; otherwise, go to step (35). Step (35): If exp(-Δ / t) > rand(0,1), then accept m' as the current solution, update the tabu list, and go to step (36); otherwise, go to step (33). Step (36): Increase the iteration number by iter = iter + 1, apply the cooling coefficient α from step (31), and update the temperature t = αt; Step (37), if t <t f If iter=N, then stop the algorithm and output the optimal solution m*; otherwise, return to step (33).

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