Civil aviation passenger plane fuel economy evaluation method based on Monte Carlo simulation

Abstract

The invention discloses a civil aircraft fuel economy evaluation method based on Monte Carlo simulation, and the method comprises the steps: constructing a comprehensive simulation model for the fuel economy evaluation of a civil aircraft, and designing a comprehensive simulation flight control law of the civil aircraft; establishing fuel economy evaluation indexes including fuel consumption and sideslip angle integral, and establishing a fuel influence factor uncertainty probability model based on a Monte Carlo method; a fuel economy evaluation statistical sample is established through multiple comprehensive simulation, analysis is performed in combination with Monte Carlo statistical characteristics, and the fuel economy of the civil aircraft under different flight conditions is accurately evaluated; according to the method, the credibility and the effectiveness of the evaluation result of the fuel economy of the civil aircraft are improved.

Description

Technical Field

[0001] The present invention relates to the field of civil aircraft performance evaluation, and in particular to a method for evaluating the fuel economy of civil aircraft based on Monte Carlo simulation. Background Art

[0002] As an important indicator of market competition, economic efficiency plays a key role in whether civil aircraft projects can achieve commercial success. Improving economic efficiency can significantly reduce the unit cost of an aircraft, thereby increasing the willingness of airlines to purchase aircraft and further enhancing the market competitiveness of civil aircraft. During the design and development stage of civil aircraft, direct operating costs have always been an important basis for evaluating the economic efficiency of civil aircraft. Fuel, as a non-renewable energy source, is of great significance in measuring the economic efficiency of civil aircraft.

[0003] The actual flight environment of civil aircraft is complex and changeable, and the factors affecting fuel consumption are diverse. It is difficult to distinguish and define the degree of influence of each factor and its combination on fuel consumption, which makes it difficult to accurately judge the fuel loading. There are currently two main research methods for the fuel economy evaluation of civil aircraft. One is to use the Quick Access Recorder (QAR) data to analyze and model the factors affecting the fuel consumption of civil aircraft through regression analysis; the other method is to use QAR data to study the relationship between the influencing factors and fuel consumption through neural networks and establish an aircraft fuel consumption model. However, both methods require a large amount of real flight data as support, and the required performance data is large and expensive. In addition, the performance, atmospheric environment and flight plan of civil aircraft may change during the flight. The traditional QAR data analysis method based on a single route or a single performance mostly relies on static model data and cannot fully consider complex flight dynamics and environmental changes. Therefore, in response to the urgent need for fuel economy evaluation of civil aircraft, a fuel economy evaluation method for civil aircraft based on Monte Carlo simulation was designed to analyze and explore the key influencing factors of fuel consumption during flight, which is of great significance in guiding the design, manufacture and control law optimization of civil aircraft. Summary of the invention

[0004] The purpose of the present invention is to provide a method for evaluating the fuel economy of civil aircraft based on Monte Carlo simulation, so as to improve the credibility and effectiveness of the evaluation results of the fuel economy of civil aircraft.

[0005] In order to achieve the above tasks, the present invention adopts the following technical solutions:

[0006] A method for evaluating fuel economy of civil aircraft based on Monte Carlo simulation comprises the following steps:

[0007] Step 1: Select the specific model of civil aircraft for which fuel economy evaluation is required to set the parameters of the civil aircraft, and set the engine parameters in combination with the engine model; construct a nonlinear dynamic model of the civil aircraft, including force and aerodynamic torque model, force equations, torque equations, and navigation equations; at the same time, construct an engine model, a sensor model, and a wind field model and integrate them with the nonlinear dynamics model to obtain a comprehensive simulation model for fuel economy evaluation;

[0008] Step 2, using the wind field model to correct the force and aerodynamic torque model formula to obtain a corrected comprehensive simulation model;

[0009] Step 3, applying the designed civil aircraft flight control law, including the longitudinal flight control law, the lateral flight control law and the automatic throttle control law, to the revised integrated simulation model, thereby obtaining a closed-loop flight control system for the civil aircraft, the input of which is the flight control command;

[0010] Step 4, constructing a sensor error probability model and a wind field impact area probability model;

[0011] Step 5, setting the number of Monte Carlo simulations, the duration of the full-process flight simulation, and the simulation step size, and using the sensor error probability model and the wind field influence area probability model to generate the sensor model parameter uncertainty sampling value and the wind field influence area uncertainty sampling value;

[0012] Step 6, performing a Monte Carlo simulation of the civil aircraft based on the revised comprehensive simulation model and the closed-loop flight control system of the civil aircraft;

[0013] When performing simulation, the uncertainty sampling value of the wind field impact area is used to set the specific time period in which different wind field models appear. The sampling matrix is ​​used to obtain the measurement error of each sensor model at each time step in each Monte Carlo simulation, and the measurement error is used as the zero-mean Gaussian noise of the three axes in the sensor model.

[0014] After each simulation is completed, the fuel consumption and the integral of the sideslip angle are calculated as the statistical samples obtained in this simulation;

[0015] After all simulations are completed, the fuel economy is evaluated by statistical characteristics of the statistical samples.

[0016] Furthermore, the civil aircraft parameters include the aircraft mass m, the moment of inertia I x ,I y and I z , reference area S, engine parameters including time constant τ, maximum static thrust at sea level F max , relative pressure ratio δ(h), thrust correction factor C T .

[0017] Furthermore, the wind field model is used to correct the force and aerodynamic torque model to obtain a corrected comprehensive simulation model; specifically, as follows:

[0018] The wind field can bring additional speed u Wg , ν Wg and w Wg , so that the aircraft has an additional angle of attack α W and the additional sideslip angle β W , which in turn affects the aerodynamic force and aerodynamic moment;

[0019] Among them, the flight speed under the action of wind field V represents the flight speed;

[0020] Therefore, the aerodynamic force and aerodynamic moment model under the action of wind field can be corrected as follows:

[0021]

[0022] In the formula, C L (α W ), C D (α W ), C Y (α W ,β W )、m z (α W ,β W )、m x (α W ,β W ) and m y (α W ) are the lift coefficient, drag coefficient, side force coefficient, yaw moment coefficient, roll moment coefficient and pitch moment coefficient brought by the additional angle of attack and sideslip angle, L t , D t , Y t is the corrected lift, drag and lateral force, M zt 、M xt 、M yt is the corrected three-axis moment.

[0023] Furthermore, the flight control instruction includes a pitch angle instruction θ c , height command h c , speed command V c , yaw angle command ψ c , lateral displacement command y c .

[0024] Furthermore, the construction of the sensor error probability model and the wind field impact area probability model includes:

[0025] The sensor error probability model is constructed as follows:

[0026]

[0027] In the formula, y ri Represents the output value of each sensor model, y mi represents the corresponding measured value; η i Represents the measurement error of each sensor model, and the measurement error obeys the zero-mean normal distribution, σ i is the standard deviation of the normal distribution;

[0028] The probability model of wind farm impact area is constructed as follows:

[0029]

[0030] Where W i Represents different wind field models such as quasi-steady wind and wind shear; P(W i = k) means that W appears exactly k times in the nth simulation i The probability of wind field action; c is W in each simulation i The probability of wind field action.

[0031] Furthermore, the method of using the sensor error probability model and the wind field influence area probability model to generate the sensor model parameter uncertainty sampling value and the wind field influence area uncertainty sampling value includes:

[0032] The sensor model includes the accelerometer model, the gyroscope model and the pressure measurement sensor model; the size of N×t can be obtained by sampling the sensor error probability model a / t s The sampling matrix M of the Monte Carlo simulation is N times, and the duration of the full-process flight simulation is t. a seconds, the simulation step is t s ;

[0033] For the pressure measurement sensor model, the corresponding sampling matrix M a The element in the mth row and nth column represents the measurement error of the pressure measurement sensor model at the nth time step in the mth Monte Carlo simulation, m=1,2...,N, n=1,2...t a / t s ;

[0034] Set the wind farm impact duration to t w seconds, the total area affected by the wind farm is t a / t w Set the number of quasi-steady wind, wind shear, and gusts to n1, n2, and n3, respectively, and n1+n2+n3=ta / t w ; For quasi-steady wind, if the probability of its occurrence is p1, it is necessary to generate an N×n1 probability distribution matrix. The distribution characteristics of each row of the matrix are binomial distribution, and the distribution law is B(n1,p1); finally, according to the probability model of the wind field impact area, the uncertainty sampling value of the impact area is generated, and the sampling value is the specific time period when the set wind field model appears.

[0035] Furthermore, the fuel consumption F c The calculation of is as follows:

[0036] sfc=C SFC (C T ,Ma)·SFC

[0037] Where sfc is the fuel consumption rate under unit thrust, SFC is the fuel efficiency benchmark value of the engine under standard sea level conditions, C SFC It is the fuel consumption rate correction value related to altitude and speed under actual flight conditions;

[0038] By defining the fuel consumption rate C s =T·sfc, the fuel consumption can be obtained by integrating the fuel consumption rate over time t, specifically:

[0039] F c =∫C s dt=∫T·sfcdt

[0040] Where T represents the engine thrust.

[0041] Furthermore, the sideslip angle integral β is the sideslip angle, t final Indicates flight duration.

[0042] Furthermore, the statistical characteristics include mean, variance, skewness and kurtosis.

[0043] Compared with the prior art, the present invention has the following technical features:

[0044] 1) The present invention constructs a comprehensive simulation model for fuel economy evaluation of civil aircraft, introduces engine model, sensor model and wind field model on the basis of traditional civil aircraft dynamics model, so as to clearly characterize the system dynamic characteristics of civil aircraft under complex flight conditions; 2) The fuel economy evaluation method based on Monte Carlo simulation designed by the present invention can effectively simulate the randomly changing wind field environment and sensor error, thereby improving the validity and credibility of the fuel economy evaluation results of civil aircraft; 3) The present invention can guide the design and optimization of flight control laws of civil aircraft through the fuel economy evaluation results, thereby improving the economic benefits of civil aircraft in control law design. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a schematic diagram of the principle of the method of the present invention;

[0046] Figure 2 It is a schematic diagram of the overall framework of the method of the present invention;

[0047] Figure 3 is a schematic diagram of the process of this method;

[0048] Figure 4 A three-dimensional flight trajectory diagram in an embodiment of the present invention;

[0049] Figure 5 A curve diagram of an aircraft control surface in an embodiment of the present invention;

[0050] Figure 6 The engine parameter variation curve diagram in the embodiment of the present invention;

[0051] Figure 7 Schematic diagram of the wind field influence area in the embodiment of the present invention (taking quasi-steady wind as an example);

[0052] Figure 8 is the error sampling value of the sideslip angle sensor according to the embodiment of the present invention;

[0053] Fig. 9 The wind speed sampling simulation histogram of the embodiment of the present invention;

[0054] Fig.10 is a simulation flow chart of an embodiment of the present invention;

[0055] Fig.11 A fuel consumption distribution histogram according to an embodiment of the present invention;

[0056] Fig.12 This is a scatter plot of fuel consumption according to an embodiment of the present invention. DETAILED DESCRIPTION

[0057] The present invention discloses a method for evaluating the fuel economy of a civil aircraft based on Monte Carlo simulation. Firstly, a comprehensive simulation model for fuel economy evaluation is constructed, and a comprehensive simulation flight control law for the civil aircraft is designed; fuel economy evaluation indicators including fuel consumption and sideslip angle integral are established, and an uncertainty probability model of fuel influencing factors is established based on the Monte Carlo method; a fuel economy evaluation statistical sample is established through multiple comprehensive simulations, and the analysis is performed in combination with Monte Carlo statistical characteristics to accurately evaluate the fuel economy of the civil aircraft under different flight conditions.

[0058] 1. Nonlinear dynamics model of civil aircraft

[0059] The classic equations of aircraft modeling are used to describe the dynamics and kinematics of civil aircraft. The center of mass of the aircraft is defined as the origin of the body coordinate system. The x-axis is in the symmetry plane of the aircraft, parallel to the theoretical longitudinal axis of the aircraft and pointing to the head. The y-axis is perpendicular to the symmetry plane of the aircraft and points to the right of the aircraft fuselage. The z-axis is in the symmetry plane of the aircraft, perpendicular to the x-axis and pointing to the bottom of the fuselage.

[0060] Define the state variables of a civil airliner as: [u,v,w,φ,θ,ψ,p,q,r,x g ,y g ,h], the system input is: [δ e ,δ r ,δ a ,δ T ]; u, v and w represent the velocity components of the civil aircraft in the body coordinate system x, y and z axes respectively, φ, θ and ψ represent the roll angle, pitch angle and yaw angle in the body coordinate system respectively, p, q and r represent the roll angular velocity, pitch angular velocity and yaw angular velocity in the body coordinate system respectively, x g ,y g are the displacement coordinates in the ground coordinate system, h is the flight altitude of the civil aircraft; δ e ,δ r ,δ a and δ T They are the elevator angle, rudder angle, aileron angle and throttle stick input respectively.

[0061] The aerodynamic force and aerodynamic moment model of civil aircraft is as follows:

[0062]

[0063] Where Q, S and c are dynamic pressure, reference area and average aerodynamic chord length respectively; L, D and Y represent lift, drag and lateral force respectively, C L , C D , C Y are the aerodynamic coefficients corresponding to L, D and Y respectively; M z 、M x and M y They are the three-axis moments of the civil aircraft in the body coordinate system, m z 、m x and m y M z 、M x and M y The corresponding aerodynamic coefficient.

[0064] The following civil aviation aircraft force equations can be further established:

[0065]

[0066] Where m and g represent the mass of the civil aircraft and the acceleration of gravity, respectively; the dot above the parameter represents its first-order derivative, the same below; F x 、F y and F z They respectively represent the xyz three-axis forces acting on the aircraft in the body coordinate system.

[0067] The moment equations for civil aircraft are:

[0068]

[0069] In the formula, c1=(I x -I y +I z )I xz / Σ,c3=I z / Σ,c4=I xz / Σ, c5=I z -I x / I y , c6=I xz / I y , c8=I x / Σ, I x ,I y and I z are the moments of inertia of the xyz axes in the body coordinate system, I xz is the product of inertia between the x-axis and the z-axis in the body coordinate system.

[0070] The navigation equation for civil airliners is:

[0071]

[0072] 2. Engine model

[0073] The civil aircraft engine model including stable working state and transitional working state is as follows:

[0074]

[0075] Where T is the engine thrust, the engine characteristics can be approximately described by the first-order inertia link 1 / (τs+1), τ is the engine time constant, s is the Laplace operator, and F max is the maximum static thrust at sea level, δ(h) is the relative pressure ratio, C T is the throttle lever input δ T Thrust correction factor related to Mach number Ma.

[0076] 3. Sensor Model

[0077] A sensor error model including systematic error and random error is established to facilitate the simulation of subsequent fuel economy evaluation. First, the accelerometer can be modeled as:

[0078]

[0079] In the formula, y accel,x ,y accel,y and accel,z are the three-axis numerical output values ​​of the accelerometer respectively; η accel,x , η accel,y and η accel,z are zero-mean Gaussian noises of the three axes.

[0080] The gyroscope model can be modeled as:

[0081]

[0082] In the formula, y gyro,x ,y gyro,y and gyro,z are the gyroscope output values ​​respectively; η gyro,x , η gyro,y and η gyro,z are zero-mean Gaussian noises of the three axes.

[0083] The pressure measurement sensor model can be modeled as:

[0084]

[0085] Where ρ is the atmospheric density, V a is the true value of airspeed; y h ,y Va and α are the output values ​​of altitude, airspeed and angle of attack respectively; k α is the measurement gain of the angle of attack α, which is determined by the sensor installation position; β abs,pres and η abs,pres They are pressure measurement bias drift and three-axis zero-mean Gaussian noise, respectively.

[0086] 4. Wind field model

[0087] As the main disturbance source of civil aircraft flight, the wind field has an impact on the performance of civil aircraft that cannot be ignored. Considering various wind field models such as quasi-constant length wind, wind shear, atmospheric turbulence, gusts and random wind, we have:

[0088]

[0089] In the formula, u Wg , ν Wg and w Wg are the velocity components of the wind field model on the x-axis, y-axis and z-axis of the ground coordinate system, Vw is the wind speed vector under different wind field models, θ w and φ w are the angles that the wind speed vector rotates clockwise from the x-axis and z-axis of the geographic coordinate system, respectively; where:

[0090] 1) The quasi-steady wind speed vector can be described in the ground coordinate system as: V w =[u Wg ,ν Wg ,ω Wg ] T .

[0091] 2) The wind shear model can be described as: V w =W 20 (ln(h / z0)) / (ln(20 / z0)),3ft<h<1000ft, W 20 is the wind speed at 20 feet. When the aircraft is in the C-type flight phase (terminal flight phase), z0=0.15, and when the aircraft is in the remaining flight phases, z0=2.0.

[0092] 3) The gust model can be described as: V w =V max h / d m ,(0≤h≤d m ), V w =V max (2d m -h) / d m , (d m ≤h≤2d m );V max is the gust amplitude, d m It is the half thickness of the gust layer.

[0093] 4) Probability density function of random wind: μ w is the mean wind speed of random wind, σ w is the standard deviation of the random wind speed.

[0094] The nonlinear dynamic model of civil aircraft constructed above, including equations (2), (3), (4), as well as the engine model equation (5), sensor model equations (6), (7), (8), and wind field model equation (9), are integrated to obtain a comprehensive simulation model for fuel economy evaluation.

[0095] 5. Flight control laws of civil aircraft

[0096] Design control laws for typical flight modes of civil airliners to ensure the stability of the flight control system and establish a control foundation for subsequent Monte Carlo comprehensive simulation test analysis.

[0097] (1) Longitudinal flight control law design

[0098] The longitudinal flight control law design is based on the longitudinal trim state of the aircraft, and adopts the proportional-integral strategy to design the longitudinal pitch angle and altitude tracking control law:

[0099]

[0100] Where t is the time parameter, Δδ eθ , Δδ eh are the elevator input values ​​under pitch angle and altitude tracking commands respectively; θ c and h c are the pitch angle and height tracking instructions respectively; Δθ and are the pitch angle deviation and pitch angle rate deviation, Δh and is the height change amount and height change rate, L θ , L θ / T θ , L θ are the feedback control gain, integral gain and differential gain of the pitch angle PID control channel respectively, T c is the time constant of the integral part; and They are the pitch angle feedback control gain, pitch angle differential gain, altitude feedback control gain, and altitude differential gain of the altitude hold PID channel respectively.

[0101] (2) Lateral flight control law design

[0102]

[0103] In the formula, δ a ,δ r are the aileron and rudder inputs respectively; ψ c and c are heading instruction and lateral displacement instruction respectively, y represents the lateral displacement of the aircraft, L φ , L ψ , L y are the roll angle feedback control gain, roll angle differential gain, yaw angle feedback control gain and yaw displacement control gain of the aileron channel of the lateral PID controller respectively; k ψ and They are the yaw angle feedback control gain and yaw angle differential gain of the rudder channel respectively.

[0104] (3) Automatic throttle control law design

[0105]

[0106] In the formula, Δδ Tis the throttle lever input; ΔV and V c are the speed deviation and speed command value along the x-axis direction of the body coordinate system respectively; L T , L T / T T and are the speed feedback error control gain, speed error integral gain and speed differential gain of the speed PID controller respectively, T T is the time constant of the integral part, Indicates the rate of change of aircraft speed.

[0107] 6. Fuel economy index

[0108] Considering the fuel economy evaluation problem of civil aircraft under the flight control law designed in step 2, the following fuel economy evaluation index is further constructed:

[0109] (1) Fuel consumption index F c

[0110] Fuel consumption is the most direct expression of flight economy and can be used as one of the indicators for fuel economy evaluation. Fuel economy evaluation can be used to optimize flight control laws and improve the fuel economy of civil aircraft.

[0111] First, the fuel consumption rate sfc under unit thrust is

[0112] sfc=C SFC (C T ,Ma)·SFC (13)

[0113] Where SFC is the fuel efficiency benchmark value of the engine under standard sea level conditions, usually obtained through experiments; C SFC C is the fuel consumption rate correction value related to altitude and speed under actual flight conditions, which can be obtained by looking up the engine theoretical model, test data or flight manual. T is the throttle lever input δ T Thrust correction factor related to Mach number Ma.

[0114] By defining the fuel consumption rate C s =T·sfc, the fuel consumption can be obtained by integrating the fuel consumption rate over time t, specifically:

[0115] F c =∫C s dt=∫T·sfcdt (14)

[0116] Where T represents the engine thrust.

[0117] (2) Sideslip angle integral index I β

[0118] As an important flight parameter during the flight of an aircraft, the sideslip angle increases the contact area between the airflow and the aircraft surface, increases the friction resistance and the total flight resistance, and significantly affects the fuel economy of civil aircraft. Considering that the calculation of aerodynamic force and aerodynamic moment of civil aircraft is closely related to the flight speed V, angle of attack α and sideslip angle β, the force equation group (2) of civil aircraft can be expressed as:

[0119]

[0120] Where L, D and Y represent lift, drag and lateral force respectively, G xa , G ya and G za The gravity of the aircraft in the airflow coordinate system x is a ,y a and z a The component below the axis can be expressed as:

[0121]

[0122] When the aircraft is in a horizontal sideslip steady-state flight, the pitch angle, roll angle, angle of attack and airspeed change rate are all zero, that is, T = D / cosβ; combined with the engine model (5) established in step 1, the thrust relationship can be further obtained:

[0123]

[0124] Therefore, the fuel consumption rate sfc of the aircraft under sideslip conditions is expressed as follows:

[0125]

[0126] According to the above formula, under normal flight conditions, DC SFC SFC / C T F max It is always positive, so the fuel consumption rate increases with the increase of the sideslip angle, so the sideslip angle integral index is selected As one of the fuel economy evaluation indicators, t final Indicates the flight time of the aircraft.

[0127] On the basis of the above technical solution, the present invention provides a method for evaluating the fuel economy of a civil aircraft based on Monte Carlo simulation, comprising the following steps:

[0128] Step 1: Select the specific model of civil aircraft for which fuel economy evaluation is required, set the aircraft mass m, moment of inertia I x ,I y and I z, reference area S and other necessary civil aircraft parameters, set the engine time constant τ and the maximum static thrust F at sea level in combination with the engine model max , relative pressure ratio δ(h), thrust correction factor C T Parameter values, the nonlinear dynamic model of civil aircraft is constructed, including force and aerodynamic torque model (1), force equation group (2), torque equation group (3), and navigation equation (4); at the same time, the engine model (5), sensor model (6), (7), (8), and wind field model (9) are constructed and integrated with the nonlinear dynamic model to obtain a comprehensive simulation model for fuel economy evaluation; the state variables of the model are: [u, v, w, φ, θ, ψ, p, q, r, x g ,y g ,h], the input variables are: [δ e ,δ r ,δ a ,δ T ].

[0129] Step 2: Use the wind field model to correct the force and aerodynamic torque model (1) to obtain a corrected comprehensive simulation model; the details are as follows:

[0130] As the main source of disturbance during the flight of civil airliners, wind fields will significantly affect the fuel economy of aircraft. The impact of wind fields must be fully considered during the Monte Carlo simulation process.

[0131] According to the wind field model (9), the wind field can bring additional speed u Wg , ν Wg and w Wg , so that the aircraft has an additional angle of attack α W and the additional sideslip angle β W , which in turn affects the aerodynamic force and aerodynamic moment described by equation (1).

[0132]

[0133] Where, the flight speed under the wind field is V represents the flight speed.

[0134] Therefore, the aerodynamic force and aerodynamic moment model under the action of wind field can be corrected as follows:

[0135]

[0136] In the formula, C L (α W ), C D (α W ), C Y (α W ,β W )、mz (α W ,β W )、m x (α W ,β W ) and m y (α W ) are the lift coefficient, drag coefficient, side force coefficient, yaw moment coefficient, roll moment coefficient and pitch moment coefficient brought by the additional angle of attack and sideslip angle, L t , D t , Y t is the corrected lift, drag and lateral force, M zt 、M xt 、M yt is the corrected three-axis moment.

[0137] Therefore, by replacing the original equation (1) with the aerodynamic force and aerodynamic torque correction model equation (21) under the action of the wind field, the dynamic system model of the civil aircraft under wind field disturbance can be obtained.

[0138] Step 3, applying the designed civil aircraft flight control law, including the longitudinal flight control law (10), the lateral flight control law (11) and the automatic throttle control law (12), to the revised integrated simulation model, thereby obtaining a closed-loop flight control system for the civil aircraft;

[0139] The input of the closed-loop flight control system is the flight control command, i.e., the pitch angle command θ in equations (10), (11) and (12): c , height command h c , speed command V c , yaw angle command ψ c , lateral displacement command y c ; By adjusting the various gains in equations (10), (11) and (12), the stability of the flight control system is ensured; wherein, the flight control instructions are given by the flight air traffic control system and the route planning module, and the present invention will no longer describe this part in detail.

[0140] Step 4: Construct a sensor error probability model and a wind field impact area probability model.

[0141] The fuel economy evaluation based on Monte Carlo simulation will select wind field and sensor as random deviation factors, and the sensor error and wind field distribution law can be adjusted according to the actual simulation requirements.

[0142] 4.1 Construction of sensor error probability model

[0143] Considering that the measurement values ​​of sensors such as accelerometers and gyroscopes in the comprehensive simulation of civil aircraft are uncertain and follow a zero-mean normal distribution, we further obtain the sampling values ​​under the probability model of the sensor model parameters. The sensor error probability model is constructed as follows:

[0144]

[0145] In the formula, y ri Represents the output value of each sensor model, y mi represents the corresponding measured value; η i Represents the measurement error of each sensor model, and the measurement error obeys the zero-mean normal distribution, σ i is the standard deviation of the normal distribution.

[0146] 4.2 Construction of probability model of wind farm impact area

[0147] Considering that the probability of the influence area of ​​various wind fields in the comprehensive simulation of civil aircraft obeys the binomial distribution probability model, the sampling values ​​under the wind field probability model are further obtained; the probability model of the wind field influence area is constructed as follows:

[0148]

[0149] Where W i Represents different wind field models such as quasi-steady wind and wind shear; P(W i = k) means that W appears exactly k times in the nth simulation i The probability of wind field action; c is W in each simulation i The probability of wind field action.

[0150] Step 5: Set the number of Monte Carlo simulations to N and the duration of the full flight simulation to t. a seconds, the simulation step is t s Based on this, the uncertainty sampling values ​​of the sensor model parameters and the uncertainty sampling values ​​of the wind field influence area are generated.

[0151] 5.1 Sensor model parameter uncertainty sampling values

[0152] The sensor model includes the accelerometer model, the gyroscope model and the pressure measurement sensor model. The uncertainty of the model parameters involved in the sensor model is mainly the random error of various sensors, which generally obeys the zero-mean normal distribution, that is, there is Considering that all sensors have measurement errors at the time of the full flight simulation, and the measurement errors generated at each time step obey the zero-mean normal distribution, corresponding to the sensor models described in equations (6), (7), and (8), for a single measurement state, the size of N×t can be obtained by sampling the sensor error probability model equation (22). a / ts The sampling matrix M of the pressure measurement sensor model is as follows: a The element in the mth row and nth column represents the measurement error of the pressure measurement sensor model at the nth time step in the mth Monte Carlo simulation, m=1,2...,N, n=1,2...t a / t s .

[0153] 5.2 Uncertainty sampling values ​​of wind farm impact areas

[0154] Set the wind farm impact duration to t w seconds, the total area affected by the wind farm is t a / t w Set the number of quasi-steady wind, wind shear, and gusts to n1, n2, and n3, respectively, and n1+n2+n3=t a / t w ; Considering that the occurrence probability of various wind field types is given, taking quasi-steady wind as an example, if its occurrence probability is p1, it is necessary to generate an N×n1 probability distribution matrix, the distribution characteristics of each row of the matrix are binomial distribution, and the distribution law is B(n1,p1); finally, according to the probability model of the wind field influence area given in formula (23), the uncertainty sampling value of the influence area is generated, and the sampling value is the specific time period when the set wind field model appears.

[0155] Step 6, based on the revised comprehensive simulation model and the closed-loop flight control system of the civil aircraft, Monte Carlo simulation of the civil aircraft is performed; when performing the simulation, the uncertainty sampling value of the wind field influence area is used to set the specific time period in which different wind field models appear, and the sampling matrix M is used to obtain the measurement error of each sensor model at the nth time step in the mth Monte Carlo simulation, and the measurement error is used as the zero-mean Gaussian noise of the three axes in the sensor model equations (6), (7), and (8), so that the output value of each sensor model under the mth Monte Carlo simulation can be obtained as the measurement output of the system, so that the simulation process can simulate the real situation more objectively and accurately; finally, after the mth simulation is completed, the fuel consumption F described by equation (14) is calculated c and the sideslip angle integral I β , we can get the mth statistical sample x m =[F c,m ,I β,m ] T .

[0156] By repeating the above steps until the Nth Monte Carlo simulation is completed, a 2×N statistical sample set Π={x1,x2,...,x m}, m=1,2,...,N.

[0157] In order to more directly characterize the fuel economy of civil aircraft, its fuel economy can be further evaluated through Monte Carlo statistical eigenvalues. The main statistical eigenvalues ​​include mean, variance, skewness and kurtosis, as follows:

[0158] (1) Mean It can reflect the concentration trend of fuel consumption and sideslip angle integral during the flight of civil aviation passenger aircraft. The lower mean value indicates that under the simulated flight conditions, the overall fuel efficiency of the aircraft is higher and the average fuel consumption is lower; k represents the index, that is, the fuel consumption F c Or the sideslip angle integral; x k,m Represents the kth indicator in the mth statistical sample.

[0159] (2) Variance Can be used to measure fuel consumption, sideslip angle integral and their corresponding mean The degree of deviation between k is the standard deviation of the corresponding index. Smaller variance indicates that the fuel consumption and sideslip angle integral values ​​are more stable, and the aircraft economy changes less under different flight conditions.

[0160] (3) Skewness It can be used to measure the asymmetry of the distribution of fuel consumption and sideslip angle integral during the flight of civil aircraft. Positive skewness indicates that there are extremely high fuel consumption and high sideslip angle integral, and the economic risk is higher. Negative skewness indicates that there are more cases of low fuel consumption and small sideslip angle integral, and the economy is better. Close skewness indicates that the distribution of fuel economy and sideslip angle integral values ​​is more balanced, and there is no extremely uneconomical working condition.

[0161] (4) Kurtosis It can be used to measure the peak state of the probability distribution of fuel consumption and sideslip angle integral. A higher kurtosis indicates that the aircraft's fuel consumption value and sideslip angle integral are concentrated in a certain range, and the flight economy is more stable. A lower kurtosis indicates that the fuel consumption and sideslip angle integral are highly volatile, and there are a large number of non-economic states.

[0162] By calculating the above statistical eigenvalues, the fuel economy of civil aircraft can be comprehensively evaluated. The mean and variance mainly reflect the overall level and volatility of fuel economy, while the skewness and kurtosis can reveal the symmetry and centralization trend of fuel economy distribution, capture possible extreme fuel consumption conditions, and provide a reference for the design optimization and operation strategy of civil aircraft.

[0163] Example:

[0164] The embodiment of the present invention uses the Boeing-747 model as the research object for simulation, and its basic properties are as follows:

[0165] Table 1B 747 aircraft basic attributes

[0166]

[0167] First, a comprehensive simulation of the entire process was performed without adding wind field effects and sensor errors. Some simulation result curves are shown in Figure 2. Figures 4 to 6 shown.

[0168] Figure 5 and Figure 6 It reflects the changes in control surfaces and engine parameters during the full flight simulation of a civil aircraft. Figure 6 In the figure, N1 represents the engine low-pressure rotor speed, FQ represents the engine fuel consumption rate, Thrust represents the engine thrust, and FuelFlow represents the fuel consumption.

[0169] The fuel economy evaluation based on Monte Carlo simulation will select wind field and sensor as random deviation factors, as follows:

[0170] As the main manifestation of the atmospheric environment, the wind field has an impact on the performance of civil aircraft that cannot be ignored. However, the impact of the wind field on the flight process is intermittent, and its impact area, number of occurrences, and type of occurrence are all random. The distribution law of the uncertainty parameters of the wind field impact area is given in Table 2.

[0171] Table 2 Distribution law of uncertainty parameters in wind farm impact area

[0172]

[0173] There are many types of wind fields in the simulation study, and the parameters of various wind field models are different. Among them, the uncertainty parameters of the quasi-steady wind model include wind speed and wind direction, and the uncertainty parameters of the wind shear model include wind speed and wind direction. The uncertainty parameters involved in atmospheric turbulence are relatively more, including wind speed, wind direction, exceedance probability, and noise seed. In general, there are many random variables involved in wind field factors, including four parameters: wind speed, wind direction, exceedance probability, and noise seed.

[0174] Table 3 Distribution law of model uncertainty parameters

[0175]

[0176] The distribution law of model uncertainty parameters can be adjusted according to actual simulation requirements. GJB366.2-87 (Atmospheric Wind Field) in the table provides spatial distribution data of wind characteristics in my country from 0 to 25 km, which is used to estimate the performance of aircraft in the design stage and in use. Other model uncertainty parameters are set based on engineering experiments, as shown in Table 3. Among them, normal distribution is represented by the letter N, and uniform distribution is represented by the letter U.

[0177] The number of Monte Carlo simulations is set to 100 times, and the uncertainty sampling values ​​of the impact area are generated according to the distribution law of the uncertainty parameters of the wind field impact area in Table 2. Considering that the simulation time of the full-process flight simulation generally does not exceed 7000s, since the impact time of each type of wind field in Table 2 is set to 200s, 200s is taken as a unit impact area, so there are 35 impact areas in total; then, since the occurrence areas of various types of wind fields obey uniform distribution, taking quasi-steady wind as an example, its maximum number of occurrences is 6, it is necessary to generate a 100×6 regional distribution matrix, and the distribution law of each row of the matrix is ​​U(1,35); secondly, since the occurrence probability of each type of wind field is given, taking quasi-steady wind as an example, its occurrence probability is 0.5, it is necessary to generate a 100×6 probability distribution matrix, the distribution characteristics of each row of the matrix are binomial distribution, and the distribution law is B(6,0.5), where 0 represents the absence of wind field and 1 represents the presence of wind field; finally, the regional distribution matrix and the probability distribution matrix are point multiplied to obtain the sampling value of the uncertainty of the impact area.

[0178] The uncertainty sampling values ​​generated are represented by a schematic diagram of the affected area, such as Figure 7 As shown in the figure, the red area represents the constant wind field, and the other areas are not disturbed by the constant wind field.

[0179] Sensor types include accelerometers, gyroscopes, pressure sensors, and airflow angle sensors. The uncertainty of the model parameters involved in the sensors is mainly the random errors of various sensors, which generally obey the zero-mean normal distribution. The error of the sensor measurement value from the true value changes with time. Taking the sideslip angle sensor as an example, its error obeys the normal distribution of N(0, 0.0001). The error sampling value of the sideslip angle sensor is as follows: Figure 8 shown.

[0180] According to the distribution law of the model uncertainty parameters in Table 3, taking the cruise phase wind speed as an example, its 100 random sampling values ​​are obtained, as follows: Fig. 9 The wind speed follows a distribution law with a mean of 21.5 m / s and a standard deviation of 21.3 m / s. Fig. 9 It can be seen that the generated random sampling values ​​are mostly distributed between 0m / s and 60m / s, and the maximum wind speed is about 58m / s.

[0181] The Monte Carlo simulation model was used to conduct 100 flight simulation experiments and analyze the fuel economy of the B747 aircraft. The specific process is as follows: Fig.10 shown.

[0182] according to Fig.10The process shown in the figure is used to conduct 100 flight simulation experiments, adding random wind disturbances and sensor error disturbances, and obtaining the fuel consumption data of 100 flight simulation experiments. Due to the large number of flight experiments, only the first 20 flight simulation experiment data are listed here, as shown in Table 4. For the sake of comparison, in the comprehensive simulation results of the civil aircraft without adding wind disturbances and sensor error disturbances, the fuel consumption is 51.658710×kg and the sideslip angle integral is 1.3138rad.

[0183] Table 4 Flight simulation data (first 20 times)

[0184]

[0185] Based on the data of 100 flight simulation experiments, the fuel consumption histogram and scatter distribution diagram are drawn as follows: Fig.11 and Fig.12 As shown. Fig.11 In the figure, the interval range of the horizontal axis is [1.63×10 5 ,1.69×10 5 ] and is divided into 20 equal parts. It can be seen that the fuel consumption in the 100 flight simulation experiments is mostly distributed in [1.654×10 5 ,1.666×10 5 ] interval, and the minimum fuel consumption is distributed in [1.639×10 5 ,1.642×10 5 ] interval, the maximum fuel consumption is distributed in [1.684×10 5 ,1.687×10 5 ] interval. Fig.12 It can be seen that the fuel consumption of the 100 flight simulation experiments mostly fluctuates around the fuel consumption of flight without wind disturbance. The fuel consumption of about 9 flight simulation experiments differs from that of flight without wind disturbance by more than 800 kg.

[0186] In addition to histograms and scatter plots, Monte Carlo statistical eigenvalues ​​can more directly evaluate the fuel economy of civil aircraft. The main statistical eigenvalues ​​include mean, variance, skewness and kurtosis. Among them, mean is the most commonly used statistic in statistics. As an indicator reflecting the concentration trend of fuel consumption, variance measures the degree of deviation between the fuel consumption variable and the mean. Skewness is a digital feature used to measure the degree of asymmetry of the fuel consumption distribution. Kurtosis measures the peak state of the probability distribution of fuel consumption. The Monte Carlo statistical eigenvalues ​​of 100 flight simulation experiments are shown in Table 5.

[0187] The Monte Carlo method can cover all random sampling requirements and reflect the range and impact of parameter changes, so its evaluation results are more reliable. The Monte Carlo statistical eigenvalue can more directly characterize the fuel economy of civil aircraft. Therefore, in the actual flight control law economy evaluation and even the fuel economy of civil aircraft, the economy can be evaluated by comparing the Monte Carlo statistical eigenvalue. Taking the mean and variance as an example, generally speaking, the smaller the mean and variance, the better the fuel economy of the designed flight control law and civil aircraft.

[0188] Table 5 Monte Carlo statistical eigenvalues

[0189]

[0190] The present invention does not focus on the design of flight control laws. Therefore, in the actual fuel economy evaluation process of civil aircraft, the fuel economy evaluation results of multiple flight control laws can be obtained by replacing the control law or control parameters and performing Monte Carlo simulation according to the method proposed by the present invention, so as to complete the comparison of the economic advantages and disadvantages of the flight control laws. At the same time, the present invention can also evaluate the fuel economy of aircraft of similar models. The evaluation results vary due to the basic properties of the specific aircraft model (mass, moment of inertia, aerodynamic parameters, etc.). The present invention can be used to guide the design, manufacture, improvement and optimization of civil aircraft control laws.

[0191] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A method for evaluating the fuel economy of civil aircraft based on Monte Carlo simulation, characterized in that: The following steps are involved: Step 1: Select the specific model of civil aircraft for which fuel economy evaluation is required to set the parameters of the civil aircraft, and set the engine parameters in combination with the engine model; construct a nonlinear dynamic model of the civil aircraft, including force and aerodynamic torque model, force equation group, torque equation group, and navigation equation; At the same time, the engine model, sensor model, and wind field model are constructed and integrated with the nonlinear dynamics model to obtain a comprehensive simulation model for fuel economy evaluation; Step 2, using the wind field model to correct the force and aerodynamic torque model formula to obtain a corrected comprehensive simulation model; Step 3, applying the designed civil aircraft flight control law, including the longitudinal flight control law, the lateral flight control law and the automatic throttle control law, to the revised integrated simulation model, thereby obtaining a closed-loop flight control system for the civil aircraft, the input of which is the flight control command; Step 4, constructing a sensor error probability model and a wind field impact area probability model; Step 5, setting the number of Monte Carlo simulations, the duration of the full-process flight simulation, and the simulation step size, and using the sensor error probability model and the wind field influence area probability model to generate the sensor model parameter uncertainty sampling value and the wind field influence area uncertainty sampling value; Step 6, performing a Monte Carlo simulation of the civil aircraft based on the revised comprehensive simulation model and the closed-loop flight control system of the civil aircraft; When performing simulation, the uncertainty sampling value of the wind field impact area is used to set the specific time period in which different wind field models appear. The sampling matrix is ​​used to obtain the measurement error of each sensor model at each time step in each Monte Carlo simulation, and the measurement error is used as the zero-mean Gaussian noise of the three axes in the sensor model. After each simulation is completed, the fuel consumption and the integral of the sideslip angle are calculated as the statistical samples obtained in this simulation; After all simulations are completed, the fuel economy is evaluated by statistical characteristics of the statistical samples.

2. The method for evaluating fuel economy of civil aircraft based on Monte Carlo simulation according to claim 1, characterized in that: The civil aircraft parameters include the aircraft mass m, the moment of inertia I x ,I y and I z , reference area S, engine parameters including time constant τ, maximum static thrust at sea level F max , relative pressure ratio δ(h), thrust correction factor C T .

3. The method for evaluating fuel economy of civil aircraft based on Monte Carlo simulation according to claim 1, characterized in that: The wind field model is used to correct the force and aerodynamic torque model to obtain a corrected comprehensive simulation model; the details are as follows: The wind field can bring additional speed u Wg , ν Wg and w Wg , so that the aircraft has an additional angle of attack α W and the additional sideslip angle β W , which in turn affects the aerodynamic force and aerodynamic moment; Among them, the flight speed under the action of wind field V represents the flight speed; Therefore, the aerodynamic force and aerodynamic moment model under the action of wind field can be modified as follows: In the formula, C L (α W ), C D (α W ), C Y (α W ,β W )、m z (α W ,β W )、m x (α W ,β W ) and m y (α W ) are the lift coefficient, drag coefficient, side force coefficient, yaw moment coefficient, roll moment coefficient and pitch moment coefficient brought by the additional angle of attack and sideslip angle, L t , D t , Y t is the corrected lift, drag and lateral force, M zt 、M xt 、M yt is the corrected three-axis moment.

4. The method for evaluating fuel economy of civil aircraft based on Monte Carlo simulation according to claim 1, characterized in that: The flight control instructions include a pitch angle instruction θ c , height command h c , speed command V c , yaw angle command ψ c , lateral displacement command y c .

5. The method for evaluating fuel economy of civil aircraft based on Monte Carlo simulation according to claim 1, characterized in that: The construction of the sensor error probability model and the wind field impact area probability model includes: The sensor error probability model is constructed as follows: In the formula, y ri Represents the output value of each sensor model, y mi represents the corresponding measured value; η i Represents the measurement error of each sensor model, and the measurement error obeys the zero-mean normal distribution, σ i is the standard deviation of the normal distribution; The probability model of wind farm impact area is constructed as follows: Where W i Represents different wind field models such as quasi-steady wind and wind shear; P(W i = k) means that W appears exactly k times in the nth simulation i The probability of wind field action; c is W in each simulation i The probability of wind field action.

6. The method for evaluating fuel economy of civil aircraft based on Monte Carlo simulation according to claim 1, characterized in that: The method of using the sensor error probability model and the wind field influence area probability model to generate the sensor model parameter uncertainty sampling value and the wind field influence area uncertainty sampling value includes: The sensor model includes the accelerometer model, the gyroscope model and the pressure measurement sensor model; the size of N×t can be obtained by sampling the sensor error probability model a / t s The sampling matrix M of the Monte Carlo simulation is N times, and the duration of the full-process flight simulation is t. a seconds, the simulation step is t s ; For the pressure measurement sensor model, the corresponding sampling matrix M a The element in the mth row and nth column represents the measurement error of the pressure measurement sensor model at the nth time step in the mth Monte Carlo simulation, m=1,2...,N, n=1,2...t a / t s ; Set the wind farm impact duration to t w seconds, the total area affected by the wind farm is t a / t w Set the number of quasi-steady wind, wind shear, and gusts to n1, n2, and n3 respectively, and n1+n2+n3=t a / t w ; For quasi-steady wind, if the probability of its occurrence is p1, it is necessary to generate an N×n1 probability distribution matrix. The distribution characteristics of each row of the matrix are binomial distribution, and the distribution law is B(n1,p1); finally, according to the probability model of the wind field impact area, the uncertainty sampling value of the impact area is generated, and the sampling value is the specific time period when the set wind field model appears.

7. The method for evaluating fuel economy of civil aircraft based on Monte Carlo simulation according to claim 1, characterized in that: The fuel consumption F c The calculation of is as follows: sfc=C SFC (C T ,Ma)·SFC Where sfc is the fuel consumption rate under unit thrust, SFC is the fuel efficiency benchmark value of the engine under standard sea level conditions, C SFC It is the fuel consumption rate correction value related to altitude and speed under actual flight conditions; By defining the fuel consumption rate C s =T·sfc, the fuel consumption can be obtained by integrating the fuel consumption rate over time t, specifically: F c =∫C s dt=∫T·sfcdt Where T represents the engine thrust.

8. The method for evaluating fuel economy of civil aircraft based on Monte Carlo simulation according to claim 1, characterized in that: The sideslip angle integral β is the sideslip angle, t final Indicates flight duration.

9. The method for evaluating fuel economy of civil aircraft based on Monte Carlo simulation according to claim 1, characterized in that: The statistical characteristics include mean, variance, skewness and kurtosis.

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