Civil aircraft fuel economy evaluation method based on Monte Carlo simulation

Abstract

The application discloses a kind of civil aviation passenger plane fuel economy evaluation method based on Monte Carlo simulation, in which the comprehensive simulation model of civil aviation passenger plane is constructed for fuel economy evaluation, and the comprehensive simulation flight control law of civil aviation passenger plane is designed;Fuel economy evaluation index including fuel consumption and sideslip angle integral is established, and the uncertainty probability model of fuel influencing factor is established based on Monte Carlo method;Through multiple comprehensive simulation simulation, fuel economy evaluation statistical sample is established, combined with Monte Carlo statistical characteristics for analysis, to accurately evaluate the fuel economy of civil aviation passenger plane under different flight conditions;The method improves the credibility and effectiveness of civil aviation passenger plane fuel economy evaluation result.

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 a key market competition indicator, economic efficiency plays a crucial role in the commercial success of civil aircraft projects. Improving economic efficiency can significantly reduce the unit cost of an aircraft, thereby increasing airlines' willingness to purchase and further enhancing the market competitiveness of civil aircraft. During the design and development phase of civil aircraft, direct operating costs have always been a key factor in evaluating the economic efficiency of civil aircraft. Fuel, as a non-renewable energy source, plays a crucial role in measuring the economic efficiency of civil aircraft.

[0003] The actual flight environment of civil aircraft is complex and ever-changing, with diverse factors influencing fuel consumption. The impact of individual factors and their combination on fuel consumption is difficult to distinguish and define, making it difficult to accurately determine fuel loading. Two main research approaches are currently used to evaluate the fuel economy of civil aircraft. One utilizes Quick Access Recorder (QAR) data to analyze and model the factors influencing civil aircraft fuel consumption through regression analysis. The other utilizes QAR data to study the relationship between influencing factors and fuel consumption through neural networks and establish an aircraft fuel consumption model. However, both approaches require extensive real-world flight data, requiring large amounts of performance data and high cost. Furthermore, aircraft performance, atmospheric conditions, and flight plans may change during flight. Traditional QAR data analysis methods, based on single routes or single performance, rely on static model data and fail to fully account for 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 is designed to analyze and explore the key influencing factors of fuel consumption during flight, which is of great significance in guiding the design, manufacturing 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 a civil aircraft based on Monte Carlo simulation includes the following steps:

[0007] Step 1: Select the specific model of civil aircraft for which fuel economy evaluation is to be conducted and set the aircraft parameters. Also, set the engine parameters based on the engine model. Build a nonlinear dynamic model for the civil aircraft, including force and aerodynamic torque models, force equations, torque equations, and navigation equations. Simultaneously, build an engine model, sensor model, and 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, the force and aerodynamic torque model is modified to obtain a modified comprehensive simulation model;

[0009] Step 3: Apply the designed civil aircraft flight control laws, including the longitudinal flight control law, the lateral flight control law, and the autothrottle control law, to the revised integrated simulation model to obtain a closed-loop flight control system for the civil aircraft. The input of the closed-loop flight control system is the flight control command.

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

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

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

[0013] During the 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 sideslip angle integral 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 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 coefficient C T .

[0017] Furthermore, the wind field model is used to modify the force and aerodynamic torque model to obtain a modified 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 torque model under the action of wind field can be modified as follows:

[0021]

[0022] Where 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, respectively. 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] Where y ri Represents the output value of each sensor model, y mi represents the corresponding measurement 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 Indicates 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 generating of the sensor model parameter uncertainty sampling value and the wind field influence area uncertainty sampling value by using the sensor error probability model and the wind field influence area probability model 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, where m = 1, 2..., N, and n = 1, 2..., t a / t s ;

[0034] Set the wind farm impact duration to t w seconds, the total wind farm affected area is t a / t w Set the number of quasi-steady wind, wind shear, and gust occurrences 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, based on the probability model of the wind field impact area, the uncertainty sampling value of the impact area is generated. The sampling value is the specific time period in which 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, and 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 errors, 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 fuel economy evaluation results, thereby improving the economic benefits of civil aircraft in control law design. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 Schematic diagram of the principle of the method of the present invention;

[0046] Figure 2 Schematic diagram of the overall framework of the method of the present invention;

[0047] Figure 3 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 graph showing the aircraft control surface in an embodiment of the present invention;

[0050] Figure 6 This is a graph showing changes in engine parameters in an embodiment of the present invention;

[0051] Figure 7 Schematic diagram of the wind field influence area in an 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] Figure 9 This is a wind speed sampling simulation histogram according to an embodiment of the present invention;

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

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

[0056] Figure 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 civil aircraft based on Monte Carlo simulation. First, 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 statistical sample for fuel economy evaluation is established through multiple comprehensive simulations, and the sample is analyzed in combination with Monte Carlo statistical characteristics to accurately evaluate the fuel economy of the civil aircraft under different flight conditions.

[0058] 1. Nonlinear dynamic model of civil aircraft

[0059] Classical equations for aircraft modeling are used to describe the dynamics and kinematics of civil aircraft. The origin of the body coordinate system is defined as the center of mass of the aircraft. The x-axis lies within the plane of symmetry, parallel to the theoretical longitudinal axis of the aircraft, and points toward the nose. The y-axis lies perpendicular to the plane of symmetry, pointing to the right of the fuselage. The z-axis lies within the plane of symmetry, perpendicular to the x-axis, and points downward.

[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 aviation passenger 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 airliner is as follows:

[0062]

[0063] Where Q, S and c are dynamic pressure, reference area and mean aerodynamic chord length respectively; L, D and Y are 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 superscript dot on the parameter represents its first-order derivative, the same below; F x 、F y and F z They represent the xyz three-axis forces acting on the aircraft in the body coordinate system.

[0067] The moment equations for civil airliners are:

[0068]

[0069] Where, 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 They 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 transient 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 stick 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] Where y accel,x 、y accel,y and y accel,z are the three-axis numerical output values ​​of the accelerometer; 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] Where y gyro,x 、y gyro,y and y gyro,z are the gyroscope output values; 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 y 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 are pressure measurement bias drift and three-axis zero-mean Gaussian noise, respectively.

[0086] 4. Wind field model

[0087] As the main source of disturbance during the flight of civil aircraft, 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 wind, wind shear, atmospheric turbulence, gusts, and random wind, we have:

[0088]

[0089] Where 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 in the ground coordinate system can be described 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 other 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 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), and (4), as well as the engine model equation (5), sensor model equations (6), (7), and (8), and wind field model equation (9), are integrated to obtain a comprehensive simulation model for fuel economy evaluation.

[0095] 5. Civil Aircraft Flight Control Laws

[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 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] Where, δ a , δ r are the aileron and rudder inputs respectively; ψ c and y c They are heading instruction and lateral displacement instruction respectively, y represents the lateral displacement of the passenger 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] Where Δδ Tis the throttle stick 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, as the most direct indicator of flight economy, can be used as one of the indicators for fuel economy assessment. Fuel economy assessment can be used to optimize flight control laws and improve the fuel economy of civil aircraft.

[0111] First, the fuel consumption rate sfc per 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 stick 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 frictional resistance and the total flight resistance, and significantly affects the fuel economy of civil aircraft. Considering that the calculation of aerodynamic forces and aerodynamic moments of civil aircraft are closely related to the flight speed V, the angle of attack α, and the sideslip angle β, the force equations (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] Based on 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, combined with the engine model to set the engine time constant τ, the maximum static thrust F at sea level max , relative pressure ratio δ(h), thrust correction coefficient C T The nonlinear dynamic model of civil aircraft is constructed by using the parameter values, including the force and aerodynamic torque model (1), the force equation group (2), the torque equation group (3), and the navigation equation (4). At the same time, the engine model (5), the sensor model (6), (7), (8), and the 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 modify the force and aerodynamic torque model (1) to obtain a modified comprehensive simulation model; the details are as follows:

[0130] Wind fields are the main source of disturbance during the flight of civil airliners and will significantly affect the fuel economy of the 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 torque model under the action of wind field can be modified as follows:

[0135]

[0136] Where 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, respectively. 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 (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 auto-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 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] Where y ri Represents the output value of each sensor model, y mi represents the corresponding measurement 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 follows 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 Indicates 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 Uncertainty sampling values ​​of sensor model parameters

[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 by 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; taking the pressure measurement sensor model as an example, 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, where m = 1, 2..., N, and 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 wind farm affected area is t a / t w Set the number of quasi-steady wind, wind shear, and gust occurrences 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, a Monte Carlo simulation of the civil aircraft is performed. During 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. 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 formulas (6), (7), and (8). 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 formula (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, the 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 indicator. A 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 This measure measures the degree of asymmetry in the distribution of fuel consumption and sideslip angle integral during flight for civil aircraft. Positive skewness indicates extreme high fuel consumption and high sideslip angle integrals, indicating a high economy risk. Negative skewness indicates a higher incidence of low fuel consumption and low sideslip angle integrals, indicating better economy. Close skewness indicates a more balanced distribution of fuel economy and sideslip angle integral values, with no extreme uneconomical operating conditions.

[0161] (4) Kurtosis This measure measures the kurtosis of the probability distribution of fuel consumption and sideslip angle integrals. A higher kurtosis indicates that the aircraft's fuel consumption and sideslip angle integrals are concentrated within a certain range, indicating more stable flight economy. A lower kurtosis indicates greater volatility in fuel consumption and sideslip angle integrals, indicating a high incidence of uneconomic conditions.

[0162] By calculating these statistical eigenvalues, we can comprehensively assess the fuel economy of civil aircraft. The mean and variance primarily reflect the overall level and volatility of fuel economy, while the skewness and kurtosis reveal the symmetry and central tendency of the fuel economy distribution, capturing possible extreme fuel consumption conditions and providing a reference for civil aircraft design optimization and operational strategies.

[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 conducted without adding wind field effects and sensor errors. Some simulation result curves are shown in the figure below. Figures 4 to 6 shown.

[0168] Figure 5 and Figure 6 It reflects the changes in control surface and engine parameters during the full flight process simulation of 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 uses wind field and sensor as random deviation factors, as follows:

[0170] As a primary manifestation of the atmospheric environment, wind fields have a significant impact on the performance of civil aircraft. However, their impact on flight is intermittent, with random influences on the affected area, frequency, and type of occurrence. Table 2 shows the distribution of uncertainty parameters for the wind field's impact area.

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

[0172]

[0173] Simulation studies involve a wide variety of wind field types, and the parameters of each wind field model vary. The uncertainty parameters of the quasi-steady wind model include wind speed and direction, while the uncertainty parameters of the wind shear model also include wind speed and direction. Atmospheric turbulence involves relatively more uncertainty parameters, specifically wind speed, wind direction, exceedance probability, and noise seed. In general, wind field factors involve numerous random variables, including four parameters: wind speed, wind direction, exceedance probability, and noise seed.

[0174] Table 3 Distribution of model uncertainty parameters

[0175]

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

[0177] The Monte Carlo simulations were set to 100 times, and the uncertainty sampling values ​​for the impact areas were generated based on the distribution of the uncertainty parameters for the wind field impact areas in Table 2. Considering that the full flight simulation time generally does not exceed 7000 seconds, and since the impact duration of each wind field type in Table 2 is set to 200 seconds, 200 seconds is used as a unit impact area, resulting in a total of 35 impact areas. Furthermore, since the occurrence areas of each wind field type follow a uniform distribution, taking quasi-steady wind as an example, its maximum occurrence number is 6. Therefore, a 100×6 regional distribution matrix is ​​generated, with the distribution pattern of each row being U(1, 35). Secondly, since the occurrence probability of each wind field type is given, taking quasi-steady wind as an example, its occurrence probability is 0.5, a 100×6 probability distribution matrix is ​​generated, with the distribution characteristics of each row being binomial distribution and the distribution pattern being B(6, 0.5), where 0 represents the absence of a wind field and 1 represents the presence of a wind field. Finally, the regional distribution matrix and the probability distribution matrix are dot-multiplied to obtain the uncertainty sampling values ​​for the impact areas.

[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 area with 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 error of each type of sensor, which generally obeys a 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 a normal distribution of N(0, 0.0001). The sampling value of the sideslip angle sensor error is as follows: Figure 8 shown.

[0180] According to the distribution law of the uncertainty parameters of the model in Table 3, taking the cruise phase wind speed as an example, its 100 random sampling values ​​are obtained, as shown in Figure 9 The wind speed follows a distribution law with a mean of 21.5m / s and a standard deviation of 21.3m / s. Figure 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 to analyze the fuel economy of the B747 aircraft. The specific process is as follows: Figure 10 shown.

[0182] according to Figure 10The process shown here was followed by 100 flight simulations, incorporating random wind disturbances and sensor error perturbations. Fuel consumption data for these 100 flight simulations was obtained. Due to the large number of flight experiments, only the first 20 flight simulations are listed here, as shown in Table 4. For comparison, the full-process comprehensive simulation results for a civil aircraft, without wind disturbances and sensor error perturbations, show fuel consumption of 51.658710 kg and an integrated sideslip angle of 1.3138 rad.

[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 plot are drawn as follows: Figure 11 and Figure 12 As shown. Figure 11 In the figure, the 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. Figure 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 assess the fuel economy of civil aircraft. Key statistical eigenvalues ​​include mean, variance, skewness, and kurtosis. The mean is the most commonly used statistic in statistics, reflecting the central tendency of fuel consumption. Variance measures the deviation of the fuel consumption variable from the mean. Skewness is a numerical characteristic used to measure the degree of asymmetry in the fuel consumption distribution. Kurtosis measures the peaked state of the fuel consumption probability distribution. The Monte Carlo statistical eigenvalues ​​for 100 flight simulations are shown in Table 5.

[0187] The Monte Carlo method can cover all random sampling requirements and reflect the range and impact of parameter variations, making its evaluation results more reliable. Monte Carlo statistical eigenvalues ​​can more directly represent the fuel economy of civil aircraft. Therefore, in actual flight control law economy evaluations, and even in the fuel economy of civil aircraft, the fuel economy can be assessed by comparing Monte Carlo statistical eigenvalues. 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] This 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 laws or control parameters and performing Monte Carlo simulations according to the proposed method, thereby completing the comparison of the economic performance of flight control laws. Furthermore, this invention can also evaluate the fuel economy of similar aircraft models. The evaluation results vary depending on the basic properties of the specific aircraft model (mass, moment of inertia, aerodynamic parameters, etc.). This 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 various embodiments of the present application, and should all be included in the scope of protection of the present application.

Claims

1. A method for evaluating 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 to be conducted and set the civil aircraft parameters. Also, set the engine parameters based on the engine model. Construct a nonlinear dynamic model of the civil aircraft, including force and aerodynamic torque models, force equations, torque equations, and navigation equations. Simultaneously, 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, the force and aerodynamic torque model is modified to obtain a modified comprehensive simulation model; Step 3: Apply the designed civil aircraft flight control laws, including the longitudinal flight control law, the lateral flight control law, and the autothrottle control law, to the revised integrated simulation model to obtain a closed-loop flight control system for the civil aircraft. The input of the closed-loop flight control system is the flight control command. Step 4: Construct a sensor error probability model and a wind field impact area probability model; Step 5: Set the number of Monte Carlo simulations, the duration of the full-process flight simulation, and the simulation step size, and use the sensor error probability model and the wind field influence area probability model to generate sensor model parameter uncertainty sampling values ​​and wind field influence area uncertainty sampling values; Step 6: Performing a Monte Carlo simulation of the civil aircraft based on the revised integrated simulation model and the closed-loop flight control system of the civil aircraft; During the 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 sideslip angle integral 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 aircraft mass m , in the body coordinate system xyz Moment of inertia of the three axes 、 and , reference area S , engine parameters include time constant , maximum static thrust at sea level , relative pressure ratio , thrust correction factor .

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 modify the force and aerodynamic torque model to obtain a modified comprehensive simulation model; the details are as follows: Wind field effects can bring additional speed 、 and , which gives the aircraft an additional angle of attack and additional sideslip angle , which in turn affects the aerodynamic force and aerodynamic moment; , ; Among them, the flight speed under the action of wind field , Indicates flight speed; Therefore, the aerodynamic force and aerodynamic torque model under the action of wind field is modified as follows: Where, 、 and represent lift, drag and lateral force respectively, 、 and are dynamic pressure, reference area and mean aerodynamic chord length, respectively. 、 and They are the three-axis moments of the civil aircraft in the body coordinate system, 、 、 、 、 and They 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, 、 、 are the corrected lift, drag and side force, 、 、 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 pitch angle instructions , altitude command , speed command , yaw angle command , lateral displacement command .

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: Where, Represents the output values ​​of various sensor models, Indicates the corresponding measurement value; Represents the measurement error of each sensor model, and the measurement error obeys the zero-mean normal distribution. is the standard deviation of the normal distribution; The probability model of wind farm impact area is constructed as follows: Where, Represents the wind field model, including quasi-steady wind and wind shear; Indicates in The simulation happened to Second-rate Probability of wind field action; For each simulation 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 generating the sensor model parameter uncertainty sampling value and the wind field influence area uncertainty sampling value by using the sensor error probability model and the wind field influence area probability model includes: The sensor model includes the accelerometer model, the gyroscope model and the pressure measurement sensor model; the size of The sampling matrix ; Among them, the number of Monte Carlo simulations is times, the full-process flight simulation duration is seconds, the simulation step size is ; For the pressure measurement sensor model, the corresponding sampling matrix Middle Rank Column elements represent In the Monte Carlo simulation, The pressure measurement sensor model measurement error under time steps is: , ; Set the wind farm impact duration to seconds, the total wind farm affected area is Set the number of quasi-steady wind, wind shear, and gust occurrences to 、 and ,and ; For quasi-steady wind, if the probability of its occurrence is , you need to generate a The probability distribution matrix of the matrix has the binomial distribution as its distribution characteristic, and the distribution law is Finally, based on the probability model of the wind field impact area, an uncertainty sampling value of the impact area is generated. The sampling value is the specific time period in which 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 The calculation of is as follows: Where, is the fuel consumption rate per unit thrust, is the fuel efficiency benchmark value of the engine under standard sea level conditions. It is the fuel consumption rate correction value related to altitude and speed under actual flight conditions; By defining the fuel consumption rate , the fuel consumption can be calculated by the fuel consumption rate over time. The points above are: in, T Indicates 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 , represents the sideslip angle, 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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