WO2015196259A1

WO2015196259A1 - Fuel estimation for an aircraft

Info

Publication number: WO2015196259A1
Application number: PCT/AU2015/050359
Authority: WO
Inventors: Salah Sukkarieh; Nicholas LAWRANCE; Bertrand MASSON
Original assignee: The University Of Sydney
Priority date: 2014-06-26
Filing date: 2015-06-26
Publication date: 2015-12-30

Abstract

A method (400) for predicting fuel consumption for a flight plan of an aircraft, the flight plan including multiple flight portions. The method (400) may be performed at a processing system and includes partitioning (406) flight data of at least one flight by the aircraft into flight data portions, each flight data portion corresponding to one of the flight portions. The method (400) also includes generating a plurality of flight portion models, wherein each flight portion model is generated using an optimisation process (422) based on a set of physical attributes of the aircraft and the respective flight data portion. The method (400) also includes applying (470) the plurality of flight portion models to a flight plan for the aircraft to generate (480) a predicted fuel consumption for the aircraft to travel the flight plan.

Description

FUEL ESTIMATION FOR AN AIRCRAFT

Technical Field

[0001] The present disclosure relates to a method, system, processing system, computer readable medium, and/or computer program for determining fuel estimation in relation to an aircraft.

Background

[0002] Airlines estimate fuel requirements for an aircraft during flight planning. In order to assist with estimating fuel consumption for the aircraft, aircraft manufacturers typically provide airlines with a baseline model for estimating fuel consumption associated with the particular make and configuration of aircraft. Such models are usually generated from data collected on a test aircraft of a particular make of aircraft with one or more engine configurations. The models are then applied to any instance of that aircraft and engine configuration. While these general models provide a reasonable estimate of fuel consumption for different types of aircraft, the general models do not account for variations between individual instances of a particular make and configuration of aircraft.

[0003] In order to compensate for variations between individual instances of a particular make and configuration of an aircraft, one particular approach includes the airline calculating a tail correction for the specific instance of aircraft, wherein the tail correction is the difference in fuel consumption for the individual aircraft from the baseline model for that type of aircraft, expressed as a percentage deviation value. To calculate the tail correction, a small number of data samples at discrete points in time during a stable cruise portion of a flight are captured by a data acquisition unit and later used to calculate the tail correction. In future flight planning procedures, the airline uses the baseline model and the relevant tail correction to obtain an estimate of fuel consumption for that particular aircraft.

[0004] However, a problem with this approach is that the tail correction is applied to all portions of the flight, such as the ascent and descent portions, despite the tail correction only being determined based on sampled data from stable cruise conditions during a single flight. Further, as conditions during the cruise portion of a flight vary from one flight to another, the application of the tail correction does not result in accurate fuel predictions.

[0005] The reference in this specification to any prior publication (or information derived from the prior publication), or to any matter which is known, is not, and should not be taken as an acknowledgment or admission or any form of suggestion that the prior publication (or information derived from the prior publication) or known matter forms part of the common general knowledge in the field of endeavour to which this specification relates.

Summary

[0006] In a first aspect, there is provided a method for predicting fuel consumption for a flight plan of an aircraft, the flight plan including multiple flight portions, the method including:

partitioning, at a processing system, flight data of at least one flight by the aircraft into flight data portions, each flight data portion corresponding to one of the flight portions;

generating, at a processing system, a plurality of flight portion models, wherein each flight portion model is generated using an optimisation process based on a set of physical attributes of the aircraft and the respective flight data portion; and

applying, at the processing system, the plurality of flight portion models to a flight plan for the aircraft to generate a predicted fuel consumption for the aircraft to travel the flight plan.

[0007] In certain embodiments, the data includes high-frequency flight data received from a flight data acquisition unit on the aircraft.

[0008] In certain embodiments, the plurality of flight portion models include:

a climb model configured to determine a fuel consumption for one or more climb portions of the flight plan;

a cruise model configured to determine a fuel consumption for one or more cruise portions of the flight plan; and

a descent model configured to determine a fuel consumption for one or more descent portions of the flight plan. [0009] In certain embodiments, the flight portion models include a plurality of model parameters, wherein optimising each flight portion model includes the computer iteratively refining one or more of the model parameters by attempting to minimise a discrepancy between a predicted fuel consumption and observed fuel consumption indicated by the flight data for the respective flight portion.

[0010] In certain embodiments, each flight portion model includes a plurality of model parameters which are refined during optimisation, wherein for each flight portion model the respective plurality of model parameters are optimised by the processing system according to the following steps:

(a) setting the respective model parameters according to an optimisation algorithm or initialisation values;

(b) determining a lift coefficient;

(c) determining a drag coefficient based upon a first subset of the model parameters;

(d) determining a thrust requirement, based on the lift coefficient, the drag coefficient and a second subset of the model parameters;

(e) determining a corrected fuel flow, based on the thrust requirement and a third subset of the model parameters;

(f) determining an actual fuel flow, based on the corrected fuel flow and a fourth subset of the model parameters;

(g) determining a discrepancy between the actual fuel flow and an observed fuel flow indicated by the flight data; and

(h) repeating steps (a) to (g) until said the model parameters converge according to the optimisation algorithm.

[0011] In certain embodiments, the method includes:

calculating, by the processing system, a weighting factor based on a discrepancy between the predicted fuel consumption and a manufacturer model for the aircraft; and

modifying the predicted fuel consumption according to the weighting factor. [0012] In a further aspect, there is also provided a method for fuelling an aircraft, wherein the method includes predicting fuel consumption for a flight plan according to any one of the methods described above and filling the aircraft with fuel based on the predicted fuel consumption.

[0013] In a further aspect there is provided a processing system for predicting fuel consumption for a flight plan of an aircraft, the flight plan including multiple flight portions, wherein the processing system is configured to:

partition flight data of at least one flight by the aircraft into flight data portions, each flight data portion corresponding to one of the flight portions;

generate a plurality of flight portion models, wherein each flight portion model is generated using an optimisation process based on a set of physical attributes of the aircraft of the aircraft and the respective flight data portion; and

apply the plurality of flight portion models to a flight plan for the aircraft to generate a predicted fuel consumption for the aircraft to travel the flight plan.

[0014] In certain embodiments, the said flight data consists of high-frequency data received from a flight data acquisition unit on the aircraft.

[0015] In certain embodiments, the plurality of flight portion models include:

a descent model configured to determine a fuel consumption for one or more descent portions of the flight plan.

[0016] In certain embodiments, the flight portion models include a plurality of model parameters, wherein the processing system optimises each flight portion model by iteratively refining one or more of the model parameters to minimise a discrepancy between a predicted fuel consumption and observed fuel consumption indicated by the flight data for the respective flight portion. [0017] In certain embodiments, each flight portion model includes a plurality of model parameters which the processing system is configured to optimise, wherein the processing system is configured to optimise the respective model parameters for each flight portion model by performing the following steps:

(b) determining a lift coefficient;

[0018] In certain embodiments, the processing system is configured to:

calculate a weighting factor based on a discrepancy between the predicted fuel consumption and a manufacturer model for the aircraft; and

modify the predicted fuel consumption according to the weighting factor.

[0019] In another aspect, there is provided a system for filling an aircraft with fuel based on predicted fuel consumption for a flight plan of the aircraft, wherein the system includes:

a processing system configured according to the second aspect; and

a fuel supply device for filling the aircraft with fuel according to the predicted fuel consumption. [0020] In another aspect, there is provided a computer readable medium including executable instructions for configuring a processing system to predict fuel consumption for a flight plan of an aircraft, the flight plan including multiple flight portions, wherein the processing system is configured by the executable instructions to:

[0021] In certain embodiments, the said flight data consists of high-frequency data received from a flight data acquisition unit on the aircraft.

[0022] In certain embodiments, the plurality of flight portion models include:

[0023] In certain embodiments, the flight portion models include a plurality of model parameters, wherein the processing system optimises each flight portion model by iteratively refining one or more of the model parameters to minimise a discrepancy between a predicted fuel consumption and observed fuel consumption indicated by the flight data for the respective flight portion.

[0024] In certain embodiments, each flight portion model includes a plurality of model parameters which the processing system is configured to optimise, wherein the processing system is configured by the executable instructions to optimise the respective model parameters for each flight portion model by performing the following steps:

(b) determining a lift coefficient;

[0025] In certain embodiments, the processing system is configured by the computer executable instructions to:

modify the predicted fuel consumption according to the weighting factor.

Brief Description of the Drawings

[0026] Example embodiments should become apparent from the following description, which is given by way of example only, of at least one preferred but non-limiting embodiment, described in connection with the accompanying figures.

[0027] Figure 1 is a schematic representation illustrating forces on an aircraft during a steady climbing flight condition (ascent); [0028] Figure 2 is a schematic representation of a system flow for calculating thrust from a flight condition, using an aerodynamic thrust model;

[0029] Fig. 3 is a schematic representation of a system flow for an engine model to use the calculated thrust to generate a fuel flow estimate; and

[0030] Figure 4 A is a flowchart representing a method for determining set of model parameters for each flight portion for a particular instance of aircraft;

[0031] Figure 4B is example pseudocode representing the method of Figure 4 A;

[0032] Figure 4C is a flowchart representing a method for predicting fuel consumption for a flight path of the aircraft using the set of model parameters calculated by the method of Figure 4A; and

[0033] Figure 5 is a system that includes a processing system for implementing one or more embodiments.

Detailed Description

Overview

[0034] The following modes, given by way of example only, are described in order to provide a more precise understanding of the subject matter of a preferred embodiment or embodiments.

[0035] Method steps or features in the accompanying drawings that have the same reference numerals are to be considered to have the same function(s) or operation(s), unless the contrary intention is expressed or implied.

[0036] Disclosed herein is a method and system for use in predicting fuel consumption of a proposed flight path for an aircraft, based on data acquired throughout one or more previous flights by that aircraft. In one implementation, the data acquired can be Quick Access Recorder (QAR) data received from a flight data acquisition unit (FDAU) which is recorded on a commercial jet aircraft.

[0037] The system uses a physical model of performance equations. An initial performance estimate is generated using known physical parameters of the aircraft. The model is then adjusted using data derived from the QAR records to generate a refined set of parameters, which accurately predict the fuel use for the instance of the aircraft. The resulting output model is then available for use in estimating flight fuel in future flights.

[0038] Computer implementation of the predictive model results in obtaining an estimate of the fuel consumed by the engines of an aircraft at a particular flight condition. The flight condition is defined by a set of flight parameters that may include, for example, mass of the aircraft, the Mach number, the pressure altitude, total air temperature, an inertial vertical speed, and flight path acceleration. The predictive model can be used to predict the total amount of trip fuel consumed in a planned flight by summing fuel use estimates calculated for different flight portions of a proposed flight path.

[0039] The predictive model uses: (i) a physics-based parametric model to estimate the drag and required thrust; and (ii) an engine model to calculate the fuel consumption, given the required thrust and air conditions. The predictive model of the present disclosure generates unique models for an individual aircraft by making use of the QAR data that is recorded at high frequency in flight. The QAR data is collected, filtered, and then used as training data to determine the relevant parameters of the predictive model for a selected flight portion, in order to minimise error between a fuel use prediction by the predictive model and the observed fuel use.

[0040] The method and system acquire data for different portions of a flight (i.e. ascent, cruise, descent), which allows fuel consumption predictions to be more accurate than known approaches. The parameters of the predictive model are determined and fine-tuned by comparing a fuel estimate output by the model for a particular flight portion and comparing that fuel estimate to a set of real-life observations obtained by the high-frequency flight data recorder during a set of flights in a predetermined window of time. The predetermined window of time may be, for example, one week or two weeks. Further, the method and system apply a non-linear model to different portions of a flight, using a different set of parameters for each flight portion, to provide a fuel estimate for that flight.

[0041] The fuel prediction method and system can be used to estimate flight fuel during flight planning. The fuel prediction method and system allow for variation of the fuel use over the range of previously observed flight conditions for a particular aircraft, in contrast to existing systems, which provide a fixed offset from the manufacturer fuel estimates.

Fuel Consumption Predictive Model

[0042] The fuel consumption model is a parametric model based on aerodynamic and performance equations used to predict the rate of fuel burn as a function of the flight condition and a learned set of parameters for a particular aircraft and date range (set of high- frequency flight data). A learning process is performed by a computer using a set of training data and identifying a set of parameters, K, which produce a model that most accurately predicts the training data.

[0043] The training data includes a set of input and corresponding output points. The first set, X, comprises of n input points. In this case each point is defined as:

where:

GW is mass

M is Mach number

h is the pressure altitude

TAT is total air temperature

TVS is inertial vertical speed

V_fl is the flight path acceleration.

[0044] Each point includes measured or estimated values for the altitude, Mach number, gross weight, total air temperature, inertial vertical speed and rate of airspeed acceleration. The second set, ^m ₀bs,i , is the corresponding observed total fuel flow to all engines of the aircraft. The goal of the fuel consumption model, /, is to provide predictions based on the input set X which minimises a metric distance to the measured output m_abs . In the current implementation, the sum of squared error is used as the metric, such that the problem can be formulated as:

where / is the fuel consumption predictive model. That is, the computer generates the function / which predicts the fuel flow in such a way as to minimise the sum squared error between the predictions and the observations. In the current system, the model / is a mathematical model based on a set of equations to model the lift, drag, thrust and engine performance. These equations are parameterised by the set of model parameters K (herein referred to as "free parameters"). With fixed equations and variable parameters, the computer can apply an optimisation algorithm to identify the set of K values that minimise the squared error, as defined by Equation 3 below.

[0045] The fuel model / used to generate fuel predictions is a two stage model. The first stage attempts to estimate the thrust required to maintain the specified flight condition, and the second stage attempts to estimate the fuel flow required to provide the specified thrust at that condition. Initial estimates of the parameter vector K are generated based on known aircraft parameters as will be discussed below.

Required thrust

[0046] The first stage of the model uses the air properties and mass of the aircraft to estimate the required thrust in the current flight condition. As shown in Fig 1, thrust is the force required to overcome the forces due to drag, a component of weight (when climbing) and any forward acceleration of the aircraft 100. Drag is dependent on lift, so firstly the required lift must be found. To solve for lift, a number of air properties must be calculated. Firstly, the altitude is specified as a pressure altitude, such that the altitude uniquely identifies the air pressure p rather than physical height above ground, as specified in the International Standard Atmosphere (ISA). The outside static air temperate T_s is calculated from the total measured air temperature T_t and Mach number M as shown in Equation 4 where γ is the ratio of specific heats in air, γ = 1 :4. Note that temperatures are assumed to be in units of Kelvin.

[0047] From the static temperature, pressure and the specific gas constant of air (R, 287.05 J kg^"1 K^"1) the air density p can be calculated.

P

R air T s

[0048] The speed of sound a at these conditions is:

[0049] Thus, given the current Mach number M the true airspeed V_a is:

V_a = Ma. ... Eq. 7

[0050] With the current flight condition and aircraft mass it is possible to determine the lift force required to maintain flight. Firstly, the inertial vertical speed IVS and true airspeed V_a are used to determine the flight path climb angle Γ .

Γ = 8ΐη-¹ ^ ... Eq. 8 v..

[0051] The required lift L is estimated by assuming that there is negligible acceleration in the lift direction, such that the lift force is the value required to overcome the component of gross weight in the lift direction (perpendicular to the airspeed vector). Note that common notation which refers to gross weight GW is usually specifying the total vehicle mass rather than the weight force.

L = GWg cos Γ ... Eq. 9 where g is gravitational acceleration.

[0052] From the lift force, the corresponding dimensionless lift coefficient C_L calculated from the current air density p, airspeed V_a and reference wing area S.

[0053] For most aircraft, there is a relatively stable relationship between the drag and lift coefficients that persists over a wide range of flight conditions. A common approximation (for low-speed aircraft) for estimating drag coefficient is the sum of a parasitic drag component and a lift-induced drag component. Parasitic drag is the drag due to the resistance of a fluid to an object moving through it and is a combination of the form drag due to the shape of the object and skin friction. The parasitic drag coefficient can be approximated as a constant value denoted C_D._O- Lift induced drag is the drag caused by an object which produces lift. This drag is due to the vortices produced between the high and low pressure regions of a lifting surface. Lifting line theory for an ideal (elliptical) lift distribution gives the induced drag coefficient equation in terms of the wing aspect ratio, AR. For a wing area b²

of S and span b the aspect ratio AT? =— . For non-ideal conditions, the equation is modified s

using Oswald's efficiency factor, e, which represents the deviation of the real design from the ideal elliptical case. The total drag coefficient is the sum of the parasitic and induced drag coefficients.

[0054] However, this does not account for drag variability in the Mach number due to compressibility. Mach drag is difficult to determine theoretically, but in general, at subsonic and transonic speeds drag increases with Mach number. This is accounted for by adding a quadratic Mach correction, and the resulting drag equation is:

C_D,Base = K_{l +} K₂C_L ² + K₃M\ ... Eq. 12 where the K_1: K₂, R values are scalar model parameters.

[0055] The reference altitude h_ref is calculated based on a threshold quadratic function of the aircraft gross mass GW divided by the pressure ratio δ .

GW² GW -_e GW -K₅

Κ_Λ + K_< + K„ if—— < ⁵

δ 2K,

h r.e_f Eq. 13

K, A - K₅

δ

where K4, K5, K6 are scalar model parameters.

[0056] Once the reference altitude is obtained the drag correction must be calculated. This is done by calculating the (proportional) specific Reynolds number to Mach ratio at the current atmospheric conditions and the reference conditions. The reference ratio f -^- \ ref value

{Ml J obtained using the reference altitude temperature ratio Θ and pressure ratio δ . Note that the reference Reynolds ratio is marginalised over the length scale / which is an arbitrary length independent of atmospheric conditions.

[0057] The difference is calculated by taking logs to determine the resulting drag correction, and the difference is added to the total drag coefficient.

AC_D>& ... Eq. 15

where K₇ is a scalar model parameter.

[0058] The resulting drag coefficient is:

c = c D,Base + AC D,Re ... Eq. 16

[0059] Once the drag coefficient has been estimated, the drag force can be calculated.

D = C - pv_a ²s ... Eq. 17

[0060] With the lift and drag forces in Figure 1 resolved, it is possible to calculate the thrust force T required to accelerate at a specified rateV_fl . The thrust required is the force to overcome the sum of the total drag D, the weight force in the thrust direction GW g sin Γ , and the force required to accelerate the gross weight at the specified rate of acceleration GWV_a .

T = D + GW g sin Γ + G WV_a ... Eq. 18

Engine Model

[0061] The fuel flow m_f is estimated based on the atmospheric conditions and required thrust. For this model we use a common approximation that the effective pressure ratio is related to the altitude-corrected thrust. Let the total temperature ratio and total pressure ratio at the current conditions respectively. The total pressure corrected thrust is:

T

τ -— ... Eq. 19 δ ^'

[0062] We assume a quadratic relationship between corrected thrust and corrected fuel flow:

= ^Κ _% ¹ + K₉T + K_l0 , ... Eq. 20 where K₈, K_9: and K₁₀ are scalar model parameters. [0063] The corrected fuel flow is converted back into the actual fuel flow using the temperature and pressure ratios, and applying a lower bound threshold as a free parameter (K₁₂) representing the engine idle condition: m_f = max i ^f'^corr ' ' ... Eq. 21

^Kn

where K_n< and K_n are scalar model parameters.

[0064] The model is trained by the computer using an optimisation algorithm to minimise the sum of squares error between observed data m_obs and the parametric model prediction with parameter vector K = [Κ^ Κ, , . , Κ^ evaluated at the training points. This is performed using a non-linear least squares solver with initial parameters estimated as will be discussed further below.

System Example

[0065] Figure 2 is a schematic representation of a system flow 200 for calculating thrust from a flight condition 205, using an aerodynamic thrust model. The flight condition 205 is defined by a set of flight parameters 210. The flight parameters 210 may include one or more of the mass of the aircraft GW, the Mach number M, the pressure altitude h, total air temperature T_t, an inertial vertical speed IVS, and flight path acceleration^ . The flight parameters 210 of the flight condition 205 are input by the computer into an aerodynamic thrust model 220, which calculates the lift 230 required to maintain that flight condition. The lift 230 is presented as an input to a theoretical drag model, which estimates the resulting drag from a parametric equation over the required lift coefficient and Mach number. Performing a force balance with adjustment for the airspeed acceleration and rate of climb yields the required thrust 250 as an output of the aerodynamic thrust model 220.

[0066] Figure 3 is a schematic representation of a system flow 300 for an engine model 710 to use the calculated thrust 250 to generate a fuel flow estimate. The engine model 310 also receives the flight parameters 210 of the flight condition 205. The thrust 250 is presented as an input to the engine model 310, which uses the thrust 250 to estimate a total pressure corrected thrust 320. The engine model 310 coverts the total pressure corrected fuel flow 320 into actual fuel flow 330 using temperature and pressure ratios.

[0067] To train the parametric model, a set of initial model parameters is estimated from known aircraft data. A set of fuel estimates is generated based on the input training data and model. A gradient-descent optimiser is then used to successively adjust the model parameters for each flight portion to minimise the sum squared error between the model predictions and observed fuel flow. Once a suitable convergence tolerance is reached, the final set of model parameters K for the flight portion is returned and the resulting model can be used to generate fuel flow predictions for the respective flight portion.

[0068] The fuel prediction method and system of the present disclosure use data collected from the high-frequency flight data recorder of a data acquisition system on a commercial jet aircraft. The data is processed by the computer to develop a model for estimating how much fuel is being consumed by the aircraft during a future flight.

[0069] The high-frequency flight data recorder is located on board an aircraft which collects and records a comprehensive set of sensor data recorded at high frequency (up to 1 Hz) across different portions of an entire flight. Further, the fuel prediction method and system of the present disclosure provide a set of performance deviation models which take into account the variability of fuel use with changes in gross weight, Mach number, altitude and total air temperature. The set of performance deviation models enable fuel flow corrections to be determined across all portions of a flight envelope. In one implementation, high-frequency flight data is provided or stored in a portable file form, such as Comma-Separated Values (CSV) or Extensible Markup Language (XML).

Example Method for determining fuel estimate

[0070] Figure 4A is a flow diagram illustrating a method 400 for determining a fuel estimate of a particular aircraft, based on flight data records acquired from one or more preceding flights. The method 400 begins at an initial step 401 where the computer retrieves aircraft data from a database, wherein the database stores aircraft data for a plurality of instances of aircraft. In particular, a user of the computer may input a registration number of the instance of the aircraft via the input device of the computer, wherein the registration number is used to retrieve the aircraft data. The aircraft data includes a set of parameters that may include, for example, but are not limited, reference wing span S (m²), wing span b (m), Minimum Flight Weight MFW (Kg), Maximum Take Off Weight MTOW (Kg), the number of engines, and the reference altitude h_ref (generally selected as a rough estimate of the typical cruise altitude in kft). Other parameters that may be retrieved include the Centre of Gravity (CG) position, engine performance variables, such as engine pressure ratio (EPR), fan speed (Nl), exhaust gas temperature (EGT), and fuel consumption for each engine.

[0071] At step 402, the method includes the computer initialising the model parameters Ki. 1₂ for the aircraft. Some of the model parameters have a default value and some of the model parameters are calculated based on known aircraft parameters. Examples default values or equations used by the computer to calculate the respective model parameters is shown in Table 1.

Table 1: Fuel model initial parameter estimates. Each initial parameter estimate either has a default value or is calculated using known aircraft parameters. Note that A_min and A_max are defined as the gross weight to pressure ratio limits such that, A_min = MFW x 1CT⁶ and is an estimate of the corrected thrust

required at 40000ft assuming a glide ratio of 17. m_{f idU} and m_{f cruise} are corrected idle and cruise fuel estimates respectively.

[0072] At step 403, flight data in the form of the high-frequency flight data for the particular instance of aircraft is retrieved by the computer from a data store. The particular aircraft is a single airframe with a given engine configuration. The high-frequency flight data is generally recorded at high frequency (1Hz) from a range of sensed and calculated values. The high- frequency flight data is collected during flight, stored on-board and transferred from the aircraft to a ground monitoring station on the ground at the end of each flight. The data is recorded in a proprietary secure binary file, which is decrypted into a binary format by the airline. This decrypted data is then converted into a newly-defined plain text format, such that only relevant parameters are retained, and there exists only one high-frequency flight data record per flight. The flight data can include flight data records for measurements such as gross weight (GW), Mach number (M), altitude h, total air temperature (TAT), inertial vertical speed (IVS) for the aircraft. In some instances, the high-frequency flight data may also include flight path acceleration (V_a ) although in other instances this may not be included in which case it is derived by the computer as discussed in step 405. The high-frequency flight data is uploaded to a central storage medium. The central storage medium is adapted to store multiple sets of flight data, each set of flight data corresponding to a separate flight by the aircraft. Each set of flight data corresponds to one or more flight portions of a total flight path. In one particular form, only a subset of the high-frequency flight data is retrieved that was recorded within a predefined time period to train the model. In one example, the predefined time period is one week, wherein the sets of flight data acquired during flights by the aircraft during the defined week are used to train the model. In particular implementations, the user can input a first and second date (Dateo and Datei respectively) to define the predefined time period. [0073] Control then passes to step 404, wherein the computer filters the sets of flight data to remove erroneous data points. The high-frequency flight data file delivered to the fuel prediction program may contain incorrect sensor readings and corrupt records. In order to use the data to train the fuel prediction model, the data is filtered and checked for bad records. A record is a single time-instance of recorded data, wherein all sensor readings are recorded with the same time stamp. The computer applies a number of rules to define 'bad' or erroneous data. In each case, if any data record is considered bad from any of the included sensor sources, the entire record is removed.

[0074] First, each record contains a date timestamp as a string and a Coordinated Universal Time (UTC) timestamp which is the number of (whole) seconds since midnight. These two values are combined in SQL to give a Unix time stamp, which is an integer representing the total number of seconds since midnight UTC, 1 January 1970. It is assumed that no records should contain legitimate data from before this date, so any record which defines a time before this is considered invalid. Due to recording limitations, the smallest time increment is one second. In some cases, two records may be generated with the same timestamp, due to rounding to the nearest second. In this case, one of the records is removed. For some aircraft systems the data acquisition unit records a particular value in one field (such as the flight number) to note that the record was incorrectly or incompletely recorded. These records are removed.

[0075] In some cases, some sensors record erroneous data. To remove these instances, a number of data filter rules are implemented. These are defined as allowable data ranges. The filter rules applied to all aircraft implemented in the current system are:

• Gross weight must lie between predefined minimum and maximum gross weight limits (typically minimum flight weight (MFW) and maximum take-off weight (MTOW) respectively);

• Total air temperature must be lie between -150°C and 150°C;

• Mach number must be greater than zero and less than Mach 1.0; and

• Pressure altitude must be greater than -100 ft. [0076] The resulting data is checked for anomalous data by removing records that contain sensor data which lie outside a 5σ deviation from the mean recorded value (where at least 1000 valid data records above 1500ft are present). These filter rules typically remove between 0% and 2% of the total data records. Given that the available data is significantly larger than the amount of data which can be processed by the current system, this is considered acceptable.

[0077] Control passes to step 405, wherein the computer may derives estimates of the airspeed acceleration using the set of selected flight data if not recorded in the high-frequency flight data. The airspeed acceleration can be estimated by the computer by calculating the rate of change of measured airspeed. However, due to noise on the airspeed sensor, a direct single-step derivative yields very noisy flight path acceleration estimates. Thus, the computer applies some smoothing to estimate the actual airspeed acceleration. This is achieved by the computer in the current framework by examining a window of data around the target point and calculating a time-weighted least-squares linear fit to the true airspeed measurements, with the resulting gradient representing a smooth estimate of the airspeed acceleration.

[0078] The same method can be used to obtain a smoothed estimate of the inertial vertical speed. However, as this is a direct observation, the goal is to smooth out sensor noise rather than determine the derivative. Thus, a smaller window is used by the computer and the value of the linear fit at the target point is used rather than the gradient. The computer stores the derived estimates of the airspeed acceleration and the inertial vertical speed in memory.

[0079] At step 406, the computer partitions the selected flight data for each flight portion. As each flight portion has different characteristics in relation to fuel consumption, one arrangement divides a flight path into constituent flight portions and determines a set of model parameters for each respective flight portion. In one example, the flight portions are climb, cruise, and descent. An estimate of the total specific power is used to isolate the flight portions. Total s ecific power is calculated by the computer using Equation 22:

where: P is Pressure (Pa)

m is mass (kg)

g is gravitational acceleration (ms^"2)

V_IVS is Inertial Vertical Speed

M is the Mach Number

R_ai_r is specific gas constant of dry air (287.05 J kg¹ K¹)

T_s Absolute temperature (K)

V is airspeed (knots or m/s)

Records where the specific power is below a threshold of -6W/kg are labelled as descent, above a threshold of 6W/kg are labelled as climb and the remainder are labelled as cruise records if the altitude is above a threshold of 24000ft.

[0080] At step 407, the computer samples a subset of the selected flight data as training data. In particular, the computer samples a subset of the resulting data set as it is computationally infeasible to attempt to process the entire set. To attempt to remove any local data biases the data is uniformly subsampled from the complete set of data (covering all flight records within the current search window) down to a fixed training data set size.

[0081] Control passes from step 407 to step 408, wherein the computer selects the next flight portion. If the computer is performing the first iteration of optimisation, the computer selects the first flight portion which is a climbing portion. In this example, the computer selects a flight portion corresponding to a climbing flight portion.

[0082] Control passes to step 409, wherein the computer calculates the lift coefficient. In one arrangement, the method 400 uses computer executable instructions stored in memory which represent Equations 1 to 10 to determine the lift coefficient which is stored in the computer's memory. [0083] In a following step 410, the computer estimates the drag coefficient using computer executable instructions stored in memory which represent Equations 1 1 and 12, wherein the drag coefficient is stored in the computer's memory.

[0084] In a following step 412, the computer estimates the required thrust which is determined using computer executable instructions stored in memory which represent Equations 13 to 18, wherein the required thrust is stored in the computer's memory.

[0085] In a following step 414, the computer estimates the total pressure corrected thrust using computer executable instructions stored in memory which represent Equation 19, wherein the total pressure corrected thrust is stored in the computer's memory.

[0086] Control passes to step 416, which estimates the corrected fuel flow using computer executable instructions stored in memory which represent Equation 20, wherein the corrected fuel flow is stored in the computer's memory.

[0087] At step 418, the computer then estimates the actual fuel flow using computer executable instructions stored in memory which represent using Equation 21, wherein the actual fuel flow is stored in the computer's memory.

[0088] At step 420, the computer determines a Root Mean Square (RMS) error using Equation 23, based on the high-frequency flight data captured during real flights and the estimate calculated in step 418.

[0089] The method runs until the parameters converge, minimising RMSE at each iteration using an optimisation algorithm such as gradient descent optimisation. At each iteration, the method returns new parameters K].₁₂. At step 421, the computer determines whether the parameters have converged sufficiently. If the parameters have not yet converged, the computer performs step 422 by refining the parameter values and then returns to step 409 to begin a further iteration of the training of the model to determine the set of parameters for the selected flight portion. If the parameters have converged, control passes from decision step 421 to step 424, which returns the model parameters for the selected flight portion.

[0090] Control passes to decision step 426, which determines whether parameters are to be calculated for a new flight portion. If parameters are to be determined for a new flight portion, control returns to step 408 to select the next flight portion. However, if at step 427 parameters are not to be determined for a new flight portion, control passes to an End step 428 and the method 400 terminates. The output of the method 400 is the set of model parameters for each calculated flight portion. As will be discussed in more detail below, the sets of model parameters can be used by the computer in conjunction with the model to provide a fuel estimate for the particular aircraft for each flight portion for a future flight. Summing fuel estimates for the flight portions can be used to provide a total fuel estimate for a flight comprising one or more flight portions.

[0091] Example pseudocode for performing the computer-implemented method 400 is provided in Figure 4B. As can be seen, the model generation function can be initiated upon user input of the registration and the dates of the predefined window. At line 2, aircraft parameters are retrieved based on the registration and dates. At line 3, the model parameters are initialised. At line 4, the full set of high-frequency flight data for the particular aircraft is retrieved. At line 5, the full set of high-frequency flight data is filtered. At line 6, the airspeed acceleration is estimated. At line 7, the full set of high-frequency flight data is partitioned into flight portions. At line 8, the full set of high-frequency flight data is sub sampled to obtain the training flight data. The fuel model function defined between lines 9 and 34 is executed to determine the estimated fuel flow. The fuel model function is iteratively executed at lines 34 and 35 until the error between the estimated fuel flow and the observed fuel flow in minimised via an optimisation algorithm to thereby return the model parameter vector K at line 36.

[0092] Once the model parameter vector K is determined, the computer can perform a validation step by comparing the generated model against the manufacturer data. In particular, this step is performed to ensure that the model is not being used beyond its predictive capability. For example, there may be flight conditions which are not in the observed data but for which a planner may request performance data. In this case, the model may not behave correctly and the system should revert to manufacturer data. In this instance, there is a blending between model predictions and manufacturer predictions. This is also to ensure that the system meets regulator requirements, where it can be shown that the system will not make predictions which vary more than a certain amount from the OEM predictions. To implement this feature, the computer is configured to use a distance-based filter which calculates the difference between the model prediction and the manufacturer prediction and weights the result accordingly. Let f_0EM be the manufacturer model, f_m be the leaned model, f_fllt be the filtered result and be the proportional difference ε (in the current model this is set at 7.5% to represent a balance between providing the model sufficient flexibility and preventing excessi deviation from the manufacturer prediction).

where ω is the weighting factor.

[0093] Figure 4C is a flow diagram of a method 450 for estimating fuel consumption for an aircraft, based on the parameters calculated in the method 400 of Figure 4A. The method 450 begins at a Start step 455 and proceeds to step 460, in which a user indicates a proposed flight path to the computer in the software application. The proposed flight path includes one or more flight portions, such as climb, cruise, and descent. Each flight portion is associated with a set of attributes, such as time, altitude, rate of climb, rate of descent, total air temperature (TAT), and gross weight.

[0094] Control passes to step 465, wherein the computer identifies the respective flight portions of the proposed flight path. In a next step 470, the model is applied to each flight portion of the proposed flight path. For each flight portion, the respective model is applied using the respective model parameters corresponding to the respective flight portion, as calculated in method 400 of Figure 4A, in order to determine a fuel estimate for each flight portion of the proposed flight path. Step 470 produces a fuel estimate for each identified flight portion. It will be appreciated that the fuel estimates for each flight portion are generally calculated by the computer sequentially (i.e. a fuel estimate for a first flight portion is calculated, then a fuel estimate for the second flight portion is calculated, etc) due to factors such as the gross weight of the aircraft changing over time which are dependent upon estimations of earlier flight portions.

[0095] Step 475 sums the fuel estimates for each flight portion to produce a total fuel estimate for the proposed flight path, which is output via an output device of the computer at step 480. Control passes to an End step 485 and the method 450 terminates. The aircraft can then be filled with fuel based on the output fuel estimate.

[0096] In certain implementations, the user can interact with the software application, via the input device of the computer, to request the computer to generate one or more fuel tables including integrated climb tables, instantaneous cruise fuel flow tables, and descent tables. The fuel model is used to build integrated climb trajectories. To obtain integrated tables, the complete trajectory is simulated from the ground to the target altitude. Cruise tables are generated using instantaneous fuel estimates covering the flight envelope. This includes a range of Mach numbers, altitudes, ISA deviations and gross weights over which the flight planner may query the fuel use. Since the model generates these estimates directly, the computer queries the model with the calculated parameters at each target point and the result is written to file.

[0097] In one form, the system and method map be implemented as a secure website hosted by a server processing system. The server processing system receives from a client processing system a particular date range and registration via user interaction with the website. The server processing system executes a computer program, such as a Perl script, upon receiving the input data to determine the vehicle type and the set of aircraft parameters used for the initial parameter estimation as discussed in relation to Table 1. The computer program then collects the relevant high-frequency flight data files from a data store and runs the fuel prediction algorithm as discussed above. The algorithm returns the set of parameters K which best predicts the input training points (based on the sum of squares error between the recorded data and the model predicted data). These parameters, along with the fuel prediction function, can then be used to query fuel flow at any flight condition to estimate fuel flow directly for a flight planning system or to generate fuel flow tables.

Example Computer

[0098] The fuel estimation system of the present disclosure may be practised using a computing device, such as a general purpose computer or computer server. Fig. 5 is a schematic block diagram of a system 500 that includes a general purpose computer 510. The general purpose computer 510 includes a plurality of components, including: a processor 512, a memory 514, a storage medium 516, input/output (I/O) interfaces 520, and input/output (I/O) ports 522. Components of the general purpose computer 510 generally communicate using a bus 548.

[0099] The memory 514 may include Random Access Memory (RAM), Read Only Memory (ROM), or a combination thereof. The storage medium 516 may be implemented as one or more of a hard disk drive, a solid state "flash" drive, an optical disk drive, or other storage means. The storage medium 516 may be utilised to store one or more computer programs, including an operating system, software applications, and data. The software applications may include, for example, an airline performance package for fuel estimation, such as The Boeing Company's INFLT program or Airbus SAS's PEP program. In one mode of operation, instructions from one or more computer programs stored in the storage medium 516 are loaded into the memory 514 via the bus 548. Instructions loaded into the memory 514 are then made available via the bus 548 or other means for execution by the processor 512 to effect a mode of operation in accordance with the executed instructions.

[00100] One or more peripheral devices may be coupled to the general purpose computer 510 via the I/O ports 522. In the example of Fig. 5, the general purpose computer 510 is coupled to each of a speaker 524, a camera 526, a display device 530, an input device 532, a printer 534, and an external storage medium 536. The speaker 524 may include one or more speakers, such as in a stereo or surround sound system. [00101] The camera 526 may be a webcam, or other still or video digital camera, and may download and upload information to and from the general purpose computer 510 via the I/O ports 522, dependent upon the particular implementation. For example, images recorded by the camera 526 may be uploaded to the storage medium 516 of the general purpose computer 510. Similarly, images stored on the storage medium 516 may be downloaded to a memory or storage medium of the camera 526. The camera 526 may include a lens system, a sensor unit, and a recording medium.

[00102] The display device 530 may be a computer monitor, such as a cathode ray tube screen, plasma screen, or liquid crystal display (LCD) screen. The display 530 may receive information from the computer 510 in a conventional manner, wherein the information is presented on the display device 530 for viewing by a user. The display device 530 may optionally be implemented using a touch screen, such as a capacitive touch screen, to enable a user to provide input to the general purpose computer 510.

[00103] The input device 532 may be a keyboard, a mouse, or both, for receiving input from a user. The external storage medium 536 may be an external hard disk drive (HDD), an optical drive, a floppy disk drive, or a flash drive.

[00104] The I/O interfaces 520 facilitate the exchange of information between the general purpose computing device 510 and other computing devices. The I/O interfaces may be implemented using an internal or external modem, an Ethernet connection, or the like, to enable coupling to a transmission medium. In the example of Fig. 5, the I/O interfaces 522 are coupled to a communications network 538 and directly to a computing device 542. The computing device 542 is shown as a personal computer, but may be equally be practised using a smartphone, laptop, or a tablet device. Direct communication between the general purpose computer 510 and the computing device 542 may be effected using a wireless or wired transmission link.

[00105] The communications network 538 may be implemented using one or more wired or wireless transmission links and may include, for example, a dedicated communications link, a local area network (LAN), a wide area network (WAN), the Internet, a telecommunications network, or any combination thereof. A telecommunications network may include, but is not limited to, a telephony network, such as a Public Switch Telephony Network (PSTN), a mobile telephone cellular network, a short message service (SMS) network, or any combination thereof. The general purpose computer 510 is able to communicate via the communications network 538 to other computing devices connected to the communications network 538, such as the mobile telephone handset 544, the touchscreen smartphone 546, the personal computer 540, and the computing device 542.

[00106] The general purpose computer 510 may be utilised to implement a computing device running a fuel estimation software application to effect a system for fuel estimation in accordance with the present disclosure. In such an implementation, the memory 514 and storage 516 are utilised to store data relating to configuration files for aircrafts and engine configurations and baseline models provided by aircraft manufacturers.

[00107] Software for implementing the fuel estimation system is stored in one or both of the memory 514 and storage 516 for execution on the processor 512. The software includes computer program code for effecting method steps in accordance with the method of predicting fuel consumption described herein. In particular, computer program code stored in one or both of the memory 514 and storage 516 execute on the processor 512 to implement the methods 400, 450 of Fig.4a and Fig. 4b to determine a set of parameters for a model for each flight portion and for use in determining a fuel estimate for a proposed flight path, based on the determined sets of parameters.

[00108] The arrangements described are applicable to the airline industries.

[00109] The foregoing describes only some embodiments of the present invention, and modifications and/or changes can be made thereto without departing from the scope and spirit of the invention, the embodiments being illustrative and not restrictive.

[00110] In the context of this specification, the word "comprising" and its associated grammatical constructions mean "including principally but not necessarily solely" or "having" or "including", and not "consisting only of. Variations of the word "comprising", such as "comprise" and "comprises" have correspondingly varied meanings.

[00111] As used throughout this specification, unless otherwise specified, the use of ordinal adjectives "first", "second", "third", "fourth", etc., to describe common or related objects, indicates that reference is being made to different instances of those common or related objects, and is not intended to imply that the objects so described must be provided or positioned in a given order or sequence, either temporally, spatially, in ranking, or in any other manner.

[00112] Although the invention has been described with reference to specific examples, it will be appreciated by those skilled in the art that the invention may be embodied in many other forms.

Nomenclature

Acronyms

CAS Calibrated Airspeed - IAS corrected for instrument and position error EAS Equivalent Airspeed - Sea level equivalent of TAS (density corrected) IAS Indicated Airspeed - Airspeed at standard conditions (15°C, 101.3kPa, 0% humidty)

ISA International Standard Atmosphere

MFW Minimum Flight Weight, kg

MTOW Maximum Take-Off Weight, kg

PALT Pressure Altitude

QAR Quick Access Recorder

RMSE Root-mean- square error

TAS True Airspeed

Greek Symbols

Γ Flight path angle

γ Adiabatic index of dry air, 1.4 δ Pressure ratio,—

pO

δ Pressure ratio

Θ Model parameter vector

T

Θ Temperature ratio— μ Dynamic viscosity, Pa.s

v Kinematic viscosity, m² /s

p Air density, kg/ m³

σ Density ratio

Θ Temperature ratio Roman Symbols a Speed of sound, m/s

AR Wing aspect ratio

b Wing span, m

C Sutherland's constant (120 for air), K

Drag coefficient

c Parasitic drag coefficient c_L Lift coefficient

D Drag, N

E Radius of the Earth (ISA), m

8 Gravitational acceleration, ms² h Geopotential altitude, m

h Pressure altitude, ft

L Lapse rate, K/km

L Lift, N

I Length scale, m

M Mach number

m_f Fuel flow, kghr ¹

P Pressure, Pa

Impact pressure, Pa

R Gas consultant (8.3144621 standard, 8.31432 ISA), J/mol.K

Kir Specific gas constant of dry air, 287.05 J kg¹ K¹

Re Reynolds number

S Reference wing area, m

T Absolute temperature, K

V Airspeed, (knots or m/s)

w Weight, N

z Geographic altitude, m

Subscripts

0 Sea level standard condition (ISA sea level 15°C) a Air-relative

b Base value (at the layer base in ISA)

s Static

t Total or stagnation

Claims

The claims defining the invention are as follows:

1. A method for predicting fuel consumption for a flight plan of an aircraft, the flight plan including multiple flight portions, the method including:

2. The method according to claim 1, wherein the said flight data is high-frequency flight data received from a flight data acquisition unit on the aircraft.

3. The method according to claim 1 or 2, wherein the plurality of flight portion models include:

4. The method according to any one of claims 1 to 3, wherein the flight portion models include a plurality of model parameters, wherein optimising each flight portion model includes the computer iteratively refining one or more of the model parameters by attempting to minimise a discrepancy between a predicted fuel consumption and observed fuel consumption indicated by the flight data for the respective flight portion.

5. The method according to any one of claims 1 to 3, wherein each flight portion model includes a plurality of model parameters which are refined during optimisation, wherein for each flight portion model the respective plurality of model parameters are optimised by the processing system according to the following steps:

(b) determining a lift coefficient;

6. The method according to any one of claims 1 to 5, wherein the method includes:

modifying the predicted fuel consumption according to the weighting factor.

7. A method for fuelling an aircraft, wherein the method includes:

predicting fuel consumption for a flight plan according to any one of claims 1 to 6; and

filling the aircraft with fuel based on the predicted fuel consumption.

8. A processing system for predicting fuel consumption for a flight plan of an aircraft, the flight plan including multiple flight portions, wherein the processing system is configured to:

9. The processing system according to claim 8, wherein the said flight data is high- frequency flight data received from a flight data acquisition unit on the aircraft.

10. The processing system according to claim 8 or 9, wherein the plurality of flight portion models include:

11. The processing system according to any one of claims 8 to 10, wherein the flight portion models include a plurality of model parameters, wherein the processing system optimises each flight portion model by iteratively refining one or more of the model parameters to minimise a discrepancy between a predicted fuel consumption and observed fuel consumption indicated by the flight data for the respective flight portion.

12. The processing system according to any one of claims 8 to 10, wherein each flight portion model includes a plurality of model parameters which the processing system is configured to optimise, wherein the processing system is configured to optimise the respective model parameters for each flight portion model by performing the following steps:

(b) determining a lift coefficient;

13. The processing system according to any one of claims 8 to 12, wherein the processing system is configured to:

modify the predicted fuel consumption according to the weighting factor.

14. A system for filling an aircraft with fuel based on predicted fuel consumption for a flight plan of the aircraft, wherein the system includes:

a processing system configured according to any one of claims 8 to 13; and

a fuel supply device for filling the aircraft with fuel according to the predicted fuel consumption.

15. A computer readable medium including executable instructions for configuring a processing system to predict fuel consumption for a flight plan of an aircraft, the flight plan including multiple flight portions, wherein the processing system is configured by the executable instructions to:

16. The computer readable medium according to claim 15, wherein the said flight data is high-frequency flight data received from a flight data acquisition unit on the aircraft.

17. The computer readable medium according to claim 15 or 16, wherein the plurality of flight portion models include:

18. The computer readable medium according to any one of claims 15 to 17, wherein the flight portion models include a plurality of model parameters, wherein the processing system optimises each flight portion model by iteratively refining one or more of the model parameters to minimise a discrepancy between a predicted fuel consumption and observed fuel consumption indicated by the flight data for the respective flight portion.

19. The computer readable medium according to any one of claims 15 to 17, wherein each flight portion model includes a plurality of model parameters which the processing system is configured to optimise, wherein the processing system is configured by the executable instructions to optimise the respective model parameters for each flight portion model by performing the following steps:

(b) determining a lift coefficient;

20. The computer readable medium according to any one of claims 15 to 19, wherein the processing system is configured by the computer executable instructions to:

calculate a weighting factor based a discrepancy between the predicted fuel consumption and a manufacturer model for the aircraft; and

modify the predicted fuel consumption according to the weighting factor.