EVALUATION OF AIRCRAFT PERFORMANCE VARIATION DURINGDAILY FLIGHT OPERATIONS

C. Deiler, DLR (German Aerospace Center),Institute of Flight Systems

Lilienthalplatz 7, 38108 Braunschweig, Germany

Abstract

A novel energy-based methodology to predict the flight performance within an entire aircraft fleet basedon flight data records is presented. It combines knowledge about the aircraft’s flight mechanics withstatistical methods and estimation techniques to solve the big data problem. Therefore, this methodprovides a new smart way to analyze the flight data of modern aircraft during daily flight operations(normal airline operation) to monitor the change of individual aircraft characteristics. The methodology isdescribed in detail first, validated with simulated flight data afterwards and finally applied to flight dataof more than 75 000 flights with a Boeing B737 fleet. The corresponding very promising results showthat this distinct knowledge-based methodology allows to reliably predict the aircraft flight performancevariation and can easily overcome several shortcomings such as poor data resolution or limited quality.

NOMENCLATURE

Symbols

(·) mean value

C(·) aerodynamic coefficient

CD0 zero-lift drag coefficient

∆CD

equivalent drag coefficient

D drag force N

∆D predicted drag variation

∆f additional model function to describe thethrust influence on power imbalance

δthrottle engine power lever angle rad

E energy J

E energy change in time respectively power,aircraft power imbalance W

EGT exhaust gas temperature K

EPR engine pressure ratio

F force N

g acceleration due to gravity m/s2

γ flight path angle rad

H altitude m

k variable

L lift force N

mAC aircraft mass kg

mfuel fuel flow kg/s

N number of data points

N1 engine fan speed

N2 engine shaft rotational speed %

V velocity, m/s

P model parameter

P percentile/ quantile

pstat static pressure N/m2

q dynamic pressure Pa

R2 coefficient of determination

σ residual

SW wing surface area m2

t time s

Tstat static air temperature K

z measured value

Subscripts

IAS indicated airspeed

LH left hand

max maximum

min minimum

opt optimal

ref reference

sim simulation

TAS true airspeed

tot total

Abbreviations

ATRA Advanced Technology Research Aircraft

QAR Quick Access Recorder

1 INTRODUCTION

For today’s cost-efficient daily flight operations airlineshave to reduce the direct operating costs of their fleet.Beside several other impact factors, the amount of fuelrequired for typical flight scenarios is one main driverof overall costs. The fuel consumption of a particularaircraft is directly linked to its flight performance whichnormally drives the airline’s decision to buy aircraft ofspecific type. But even within a fleet of a single aircrafttype the flight performance characteristics of each indi-vidual aircraft slightly differs. Some of the factors caus-ing the flight performance variations across airplanesfrom the same type are: production tolerances, aircraftskin repairs, aircraft skin contamination (e.g. dirt), en-gine aging causing reduced efficiency, or engine con-tamination (e.g. dirt). For example, an aircraft is nor-mally expected to show at least a drag increase up to2% in five years [1]. But depending on e.g. the factorsgiven above this increase can be significantly higher.Airbus provides in Ref. 1 some further drag-increasinginfluences and corresponding scales for different air-craft types in its portfolio. Therefore it is expectablethat for a given large flight data set the resulting perfor-mance variation becomes visible. This knowledge aboutthe detailed deterioration of individual aircraft perfor-mance further allows to e. g. plan necessary actions ofaircraft maintenance.

Figure 1 illustrates this expectable flight performancewith respect to the aircraft drag curve in the lift-drag-coefficient plane as an area of varying drag coefficientin the vicinity of the typical normal operation’s lift-to-drag ratio. In cruise flight, its optimal value (L/D)opt is

expectedperformancevariation

γmin

(L/D)opt

Drag Coefficient CD

Lift

Co

effi

cien

tCL

Figure 1: Expected flight performance variation withinan aircraft fleet illustrated as change of dragcoefficient

around 0.866 of the maximum lift-to-drag ratio1 result-ing in a minimal fuel consumption [2]. The fight dataanalysis of an entire aircraft fleet presented in this paperreveals very comparable results in terms of the locationof the expected variation.

There has been several noticeable previous works re-lated to the extraction of flight performance from flightdata recorder data sets, e.g. Ref. 3, or to estimate inreal-time, aboard the aircraft, the impact of aerodyna-mics deterioration on the flight safety and on the safeflight envelope [4–6]. However, these approaches arenot well suited for the considered case. For instance,the proper estimation of dynamic derivatives (for ex-ample roll and yaw damping coefficient) requires someamount of excitation of the aircraft, which is usuallynot present in data recorded on-board with the flightdata recorder (FDR) and even if some relatively aggres-sive maneuvers would have been flown, the samplingrate of FDR data is usually too low to permits this kindof modeling. Note that even for on-board real-timeperformance monitoring (for which the sampling rateis sufficient), the need for dynamic excitation is a strongdisadvantage for the application to civil airliners in regu-lar operations. Furthermore, there had been some workon the prediction and evaluation of aircraft fuel con-sumption based on flight data records [7–9], which isdirectly linked to the flight performance.

This paper presents a novel energy-based methodo-logy to determine the typical and abnormal flight per-formance variation encountered during regular airlineoperations (due to a real performance variation or sen-sor errors) based on flight recorder data sets. For-tunately, the performance monitoring technique pre-sented in this paper does not require dynamic excita-tions but relies on the information already contained inthe achieved steady state conditions. The goal and theapproach of Ref. 3 is very similar to the FDR data analy-sis shown in this paper, but the analysis that is presentedherein focuses more on pure performance (no dynamic

1which corresponds to the best glide at γmin

derivatives) and is more general, for example a 1 g flightis not assumed whereas it is implicitly assumed in [3].Ref. 10 deals with a comparable problem of detectionof flight performance variation, but mainly focuses onthe detection simulated faults instead of flight perfor-mance variation itself.

In the presented case, the available flight data recordsare obtained from the aircraft’s quick access recorder(QAR), which records the same information as the wellknown flight data recorder (FDR) for accident investi-gation but can be accessed post-flight by the airline toanalyze the flight and monitor the aircraft characteris-tics. As this data have only limited quality (e.g. con-cerning sample rate) typical and common system iden-tification methods (see [11] for further information onthese techniques) to evaluate the aircraft aerodynamiccharacteristics cannot be applied for this analysis. Ingeneral, the determination of an aircraft flight perfor-mance variation based on numerous flight data recordsis a big data problem, which is nowadays often faced bythe application of machine learning or statistical meth-ods. For example, such problem based on flight datarecords was addressed in [12] to e.g. monitor the air-craft speeds during approach. But in the presentedcase, the big data problem should be solved by utiliz-ing as much general knowledge about flight mechanicsas possible. Therefore, the big data is transferred intosmart data2, which eases the subsequent analysis. Notethat no distinct knowledge about the individual systembut only the physics of flight is required.

In section 2 of this paper, the energy-based metho-dology used to evaluate the flight data set resultingfrom normal airline operations is described. Section 3presents a first feasibility study which was done with thepresented methodology on simulated flight data simi-lar to the real aircraft data sets. Finally, the evaluationresults of data3 recorded by the German airline TUIflyduring their regular operations are given in section 4.

2 METHODOLOGY

The aircraft flight performance can be seen as follows

A/C FlightPerformance

=

Nominal A/C Flight Performance+ Nominal Engine Influence+ Variation

whereby the

• “Nominal A/C Flight Performance” represents theaircraft’s expected performance4 at the given flightcondition (e.g. steady horizontal flight),

2subset of data extracted from big data with certain algorithmscontaining only the information desired for a distinct analysis

3these flight data records were completely anonymized and didonly contain flight parameters without any information on the distinctaircraft or crew.

4for a representative aircraft of given type

• “Nominal Engine Influence” is the additional influ-ence of thrust due to a different engine parametersetting than the nominal one required for the givenflight condition,

• “Variation” part gathers the effects mentionedpreviously and is here the part that need to be an-alyzed.

By having a deep knowledge about the aircraft to be in-vestigated, the analysis of flight performance is an easytask: if all the influencing factors – for example aircraftaerodynamics, engine thrust, atmospheric conditions –are perfectly known, the variation can be directly cal-culated by solving a corresponding set of equations,which describe the individual aircraft’s forces and mo-ments equilibrium, for the searched “Variation” as e.g.an additional part of the total drag force. But withoutsuch detailed individual system knowledge assumptionsand simplifications have to be made to allow a com-bined evaluation of the big data collected with an en-tire fleet of specific aircraft type. As the determinationof one individual aircraft’s distinct aerodynamic charac-teristics and engine status5 late after the actual flightis not possible by only analyzing flight data recordedwith the QAR during normal operations, another reli-able approach to reliably calculate the searched “Varia-tion” must be found.

The methodology proposed in this paper to allowcombined evaluation of the flight data from a fleet ofsame aircraft type is based on the variation of the air-craft’s total energy during quasi-steady flight. It con-nects knowledge about the fundamental flight me-chanics with statistical methods. A detailed descriptionof this analysis is given in section 2.1 hereafter includ-ing an approach to determine the “Nominal Engine In-fluence” by introducing a linear thrust-related powerimbalance model. A feasibility study on this modelingapproach to find a suitable representation for the un-known thrust influences is presented in section 2.2.

2.1 ANALYSIS OF AIRCRAFT POWER IM-BALANCE

The methodology used to derive the aircraft perfor-mance from the recorded data is based on the total en-ergy of the airplane or rather its time-derivative. As theflight performance of an aircraft is driven by its char-acteristics to move through the surrounding air, the in-fluence of large scale atmospheric disturbances such ashorizontal and vertical wind must be considered withinthis energy-based approach. The methodology to ac-count for such wind influences is depended on thechoice of the reference system which is used to make

5related to the engine’s ability to produce a certain amount thrustwith a given system state at a certain flight point

up the balance of the total energy6. Within the pre-sented approach the aerodynamic system is chosen tocalculate the total energy removing the need of a com-plex wind correction in the equation and giving directlyan information about the aircraft flight performance it-self. The total energy of the aircraft with respect to thesurrounding air is

Etot =1

2·mAC · V 2

TAS +mAC · g ·H (1)

and the time-derivative of the energy Etot describes theaircraft’s real power imbalance, e.g. whether the totalenergy level is increasing due to an excess of enginethrust for the current flight situation. The power im-balance further describes the actual deviation of theaircraft performance from its nominal expected perfor-mance, containing both of the previously given influ-ences on flight performance (“Nominal Engine Influ-ence” and the “Variation”) in one value. The difficulttask is to discriminate these influences from each other,especially when no distinct engine model is available.

But such engine model can be derived out of all thedata by searching the model structure and parametervalues that minimizes the error between the model-based computed power imbalance Etot,model(P ) (with Pbeing the parameters of the engine model) and the ac-tual power imbalance Etot. Basically, the problem canbe formulated as:

Popt = argminP

(∑data

(Etot,model(P ) − Etot

)2

)(2)

Later, the vector of optimal parameter values Popt

is estimated and the corresponding power imbalance(Etot,model(Popt)) will be compared to the actual powerimbalance Etot to obtain the searched variation.

In practice, before being able to find Popt by solvingthe problem of equation (2) the flight data need to bepreprocessed. This preprocessing includes the detectionand cleanup of erroneous data (which can for instancehappen at times when some of the onboard comput-ers are being reset) as well as bringing the individualchannels to the same constant sampling rate and timebase. Then, the data are searched for steady engine andquasi-steady flight conditions for which several engineand flight parameters only slightly vary within prede-fined boundaries. According to these conditions theflight data are segmented resulting in time slices ofsteady conditions with an individual length between60 s and 120 s. Note that such duration is requiredto guarantee that local small scale effects (e.g. shortgusts) do not falsify the resulting flight performance

6conventionally a body-fixed inertial system would be used to bal-ance the total energy which would require a determination and con-sideration of the current 3D wind vector

variation. For each time slice mean values of altitude,speed or Mach number, temperature, gross weight, en-gine fan speed, fuel flow and energy change are calcu-lated and used for further evaluation. Using only meanvalues over data segments with steady flight conditionsallows to reduce the data significantly although all nec-essary information is still available. Furthermore, theresulting segments are presorted in categories of simi-lar operating points (e.g. altitude, speed, gross weightand engine status). Eventually, Etot,model(Popt) (the ref-erence power imbalance corrected from some of theunknowns affecting the engine thrust) can be writtenas

Etot,model(Popt) = Etot,nominal

+ ∆f(N1, N2,EGT,EPR, mfuel,

Tstat, VTAS,Ma, . . .),

(3)

with ∆f being the optimal affine adjustment of the en-gine thrust model on the considered category. A moredetailed description about the modeling approach usedto define the thrust influence ∆f is given in section 2.2.The remaining deviations between the expected powerimbalance Etot,model(Popt) and the actual power imbal-ance Etot (rate of change of the aircraft total energy)are the variations of the flight performance within theconsidered aircraft fleet.

While the chosen energy-based approach encom-passes all aspects of the flight performance and es-pecially the couplings between the involved physi-cal parameters, the scaling of the power imbalanceEtot,model(Popt) − Etot into a nondimensional equivalentdrag coefficient variation ∆C

Deases the physical in-

terpretation (same order of magnitude for differentspeeds, current lift, or even aircraft type). This scaling isrealized as follows:

∆CD

=Etot,model(Popt) − Etot

VTAS · q · SW(4)

The equivalent drag coefficient ∆CD

computed usingequation (4) describes the aircraft flight performancevariation inside the fleet, mostly but not only resultingfrom variation of the aircraft aerodynamic performance(e.g. due to dirt, structural deformation and repairs,or ice accretion). Other possible causes for this vari-ation are sensor errors, unaccounted wind influences(e.g. downdrafts), and variations in the actual engineperformance.

2.2 LINEAR ENGINE THRUST MODEL

The thrust of modern jet engines is dependent on sev-eral internal states and external influences. Basically,calculating thrust is a difficult task even with com-plete system knowledge and detailed actual state infor-mation and almost impossible without both of them.

N1

Fth

rust

∆V -effect

q-effect

VTAS

Fth

rust

pstat

Fth

rust

Tstat

Fth

rust

Figure 2: Relative influence of different internal and ex-ternal parameters on engine thrust (adaptedfrom [13,14])

Hence, any approach to model the searched engine in-fluence in Etot,model(Popt) (see equation (3)) based on thelimited information available in QAR data is only an ap-proximation of the actual thrust conditions. Using alinear engine model for the herein presented analysisof flight performance variation is the best trade-off be-tween model accuracy, simplicity and available informa-tion. In general, the thrust Fthrust is a thermodynamicalprocess inside the engine depending e.g. the airspeedand the current atmospheric conditions. Figure 2 givesand overview on the several internal and external pa-rameters affecting engine thrust and the correspondingchange of thrust with their variation.

Due to the different nonlinear effects of several pa-rameters on thrust, local linear models at certain op-erating points are the best approach to reliably coverthe engine thrust influence on the flight performance.Nevertheless, the linear regressors must be well chosento prevent overfitting but ensure good data coverageat the same time. For example, as the power imbal-ance is directly dependent on the airspeed, VTAS couldnot be a regressor of the linear thrust model in thatcase: the true airspeed is able to mathematically ex-plain the power imbalance – as it is part of equation (1)and consequently directly related to the resulting Etot –and therefore the flight performance variation and con-sequently mask the actual thrust effects. Hence, theMach number will be used because it physically containsa similar information about the aircraft’s speed but isnot part of power imbalance calculation in equation (1).

To define a suitable set of regressors describing theinternal engine parameters, a first study was madebased on an existing engine model used for real timeaircraft simulation. An arbitrary data set of varying in-ternal engine parameters was defined and the corre-sponding time history of engine thrust was generated(see Fig. 3). These data were fitted with the linear re-gression model

Fthrust,model = ∆f (N1, N2,EGT,EPR, mfuel) , (5)

and provide a more realistic scenario for the evaluation.Measurement errors were added to the input data inform of white noise with corresponding maximum am-plitudes as given in table 1.

‖∆EPR‖ 0.001

‖∆mfuel‖ 0.0005 kg/s‖∆EGT‖ 5 K‖∆N1‖ 0.1 %‖∆N2‖ 0.1 %

Table 1: Amplitudes for signal noise

All possible combinations of regressors were used tofit the given thrust data with the corresponding lin-ear model. The results were then evaluated concerningtheir goodness of fit respectively the linear model’s ca-pability to accurately reproduce the thrust data. There-fore, the coefficient of determination R2 was calculatedin each case. It allows to define the goodness of fitin one single value between 0 (no correlation betweenused the regression model outputs y and given mea-surements z ) and 1 (perfect fit with completely linearcorrelation). It is defined as

R2 = 1−∑

k σ2k∑

k (zk − z)2 , (6)

where z denotes the mean value of given k measure-ments, zk the k-th measurement and σk the residual ofk-th simulation and measurement.

As an example, Fig. 4 contains the resulting coeffi-cients of determination for 5 different regression mod-els containing a different number of regressors. Theexample shows that even with two well chosen regres-sors (mfuel, N1) a good fit is possible. Taking additionalregressors into account and therefore adding more in-formation to the regression problem results in a slightlybetter fit for the given example. But this increases alsothe risk of overfitting when using real flight data lateron because the simple linear model structure is only arough approximation of the real engine/aircraft behav-ior and more regressors do not necessarily enhance theaccuracy in that case. This shows that a trade-off be-tween the accuracy of the model (data fitting) and themodel complexity is necessary. The analysis of all othercombinations revealed that the most of the regressorcombinations did not result in a satisfactory fit of themeasured data. Direct correlation between fan speedor engine pressure ratio and thrust – as it is commonlyknown – is clearly noticeable in the subset of combi-nations which contains the highest values of R2. Asthe fan speed and fuel flow are able to describe the

0 2 4 6 8 10 12 14

14 500

15 000

t [s]

Fthrust

[N]

Figure 3: Time history plots of engine thrust simulation: example case for determination of suitable regressorcombinations

mfuel N1mfuel

N1mfuelEPR

N1mfuelEPR

EGT

N1N2mfuelEPR

EGT

0

0.5

1

0.0874

0.8125 0.8871 0.8896 0.8907

R2

[-]

Figure 4: Results of engine thrust regression: coeffi-cient of determination R2 for regression mod-els with different combinations of regressors

thrust variation in general, N1, mfuel and Ma seem tobe a good choice for regressors of the linear model inEquation (3).

3 METHODOLOGY VERIFICATION

The herein presented approach for the determination ofthe flight performance variation within an aircraft fleetis independent of the aircraft type analyzed. Hence,simulated flight data of any arbitrary large transport air-craft can be used to verify the methodology prior tothe final flight data analysis. Therefore, simulated flightdata with a known variation was generated with a sim-ulation model of DLR’s research aircraft Airbus A 320ATRA (“Advanced Technology Research Aircraft”). Theoperation point for the following example was chosenas steady horizontal flight at an altitude of 15000 ft and320 kt indicated airspeed. Based on this condition, sev-eral small variations of altitude, airspeed and flight pathangle (see table 2) were introduced to obtained a database similar to the flight data records at the chosenaircraft operating point in the aircraft flight envelope.All data sets contain time histories of aircraft inputsand outputs necessary for the previously presented ap-proach of flight performance evaluation. With a mini-mum simulation time of 90 s it is possible to extract timeslices of steady conditions with a length of at least 60 sas described in section 2.1. For all these simulations noflight control system of the A 320 was activated.

Beside the slight variation of the aircraft trim condi-tions, a change of engine state was introduced to fur-

parameterstep maximumsize change

altitude (H) 50 ft ±100 ftvelocity (VIAS) 1 kt ±6 ktflight path angle (γ) 0.25◦ ±0.75◦

Table 2: Variation of trim points around one exampleoperating point to generate a wide range ofsimulated flight data for method validation:ranges and step sizes of altitude, airspeed andflight path angle variation

ther create a subset of simulated flight data with a dis-tinct power imbalance. Therefore, the engine throttleδthrottle was varied 3 % around the value obtained forthe trimmed horizontal flight conditions:

(δthrottle)sim = (δthrottle)tr im · k with k ∈ [0.97, 1, 1.03]

With the additional thrust variation most of the sourcesof an aircraft power imbalance during normal operationshould be covered. But the presented methodology isdeveloped to determine an aircraft’s flight performancewithin a fleet and consequently an additional data setwith changed aircraft flight performance characteristicsis needed to validate this approach. This change ofcharacteristics was done with a distinct variation of air-craft drag coefficient during the first 20 s of the aircraftflight simulation by constantly fading in an additionaldrag coefficient ∆CD (from zero to its maximum prede-fined value). Eight different cases of drag variation wereused, defined by

∆CD = ±k · CD0 with k ∈ [0.05, 0.1, 0.15, 0.2].

Consequently, the goal of the presented validation at-tempt to reliably predict this change of aircraft dragwith the proposed methodology.

As an example, the results of several of these differ-ent aircraft simulations (at given speed and altitude) arepresented in Fig. 5 as time history plots of flight pathangle, altitude, speed, engine fan speed and power im-balance. The direct comparison of the different casesshows the individual influence of each case (changeof flight path angle, throttle command and additionaldrag coefficient) on the resulting power imbalance as

0 20 40 60 80

−0.5

0

0.5

t [s]

Etot

[MW

]

4 500

4 600

4 700

H[m

]

201

202

203

VTAS

[m/s

] 59

60

61

62

N1,LH

[%]

−0.5

0

0.5

γ[◦

]γ = 0.25◦ γ = −0.25◦

0.97 · (δthrottle)ref 1.03 · (δthrottle)ref∆CD = −0.1 · CD0 ∆CD = 0.1 · CD0reference trim

Figure 5: Example of (simulated) flight data from differ-ent cases: baseline simulation (reference trimpoint), change of flight path angle, enginethrust variation (throttle change) and changeof aircraft drag coefficient; time history plotsof flight path angle, left hand engine fanspeed, true airspeed, altitude and total powerimbalance for different dynamic aircraft simu-lations starting from a reference trim point

well as comparable magnitude of the power imbalancein all cases. Within this example it gets clear that com-pletely different sources have similar effects on Etot andthe challenge of the analysis is to reliably split the influ-ences.

The results of the 1950 different simulations werepre-processed for the flight performance evaluation:data segments with (nearly) steady conditions were ex-tracted and corresponding mean values of observationcalculated. Figure 6 shows the time histories of severalsimulation outputs for one example (additional drag in-fluence) in Fig. 5 and in addition the extracted data in-dicated through horizontal lines of mean values in thetime histories.

Application of the method described in section 2 withthe regression model of nominal thrust influence de-fined in section 2.2 allows to split the total measuredpower imbalance Etot into the thrust related influence

0 20 40 60 80−1−0.50

t [s]

Etot

[MW

] 4 450

4 500

4 550

H[m

]

200

201

202

VTAS

[m/s

]

6060.56161.5

N1,LH

[%]

Figure 6: Example of selected (simulated) flight datasegment with steady flight conditions: timehistory plots of left engine fan speed, true air-speed altitude and total power imbalance fora simulation with variation of drag coefficient(∆CD = 0.1 · CD0); illustration of mean valuesas horizontal lines for the selected data seg-ment

EEngine and the remaining variation E∆D

. The latter con-tains the applied drag variation as well as a combinationof all errors introduced through the simplifications andapproximations with the proposed methodology. Forexample, the assumption of a linear thrust model is agood approximation but does not fully cover the com-plexity of the engine model used during simulation onthe one hand, and the regressors used for the predic-tion of EEngine cannot complete describe the thrust be-havior on the other. Also the approach of using themean values of the observed aircraft parameters doesfurther introduce some errors in the analysis.

Figure 7 shows the split of the power imbalance of all1950 analyzed segments and the energy change is plot-ted against the combined engine fan speed7. The leftplot shows that for Etot a linear dependency of somedata is clearly visible, but also contains some data with-out any visible correlation (which results from the dragchange). This dependency is fully covered by the pre-dicted thrust related power imbalance EEngine in thecenter plot. The remaining (not predictable) variationE

∆Din the right plot is related to the drag change which

was introduced to several of the aircraft flight simula-

7mean value of both engine within one segment; due to the sym-metric thrust and similar engine states of left and right engines, thiscombination of information does not affect the results, but simplifiesthe data evaluation

55 60 65−2

−1

0

1

2

N1 [%]

Eto

t[M

W]

55 60 65−2

−1

0

1

2

N1 [%]

EEngine

55 60 65−2

−1

0

1

2

N1 [%]

E∆D

totalpower imbalance

thrust relatedpower imbalance

remainingvariation

= +

Figure 7: Power imbalance variation for simulated flight data segments: fan speed N1 versus total power imbalanceEtot as well as separation into estimated thrust-related power imbalance EEngine and the remaining not-assignable variation (in this particular example related to the introduced drag change ∆CD)

−0.01 0 0.01−2

−1

0

1

2

∆CD [-]

E∆D

[MW

]

−0.01 0 0.01

−0.01

0

0.01

∆CD [-]

∆CD

[-]

Figure 8: Comparison of predicted drag-change relatedaircraft power imbalance E

∆Dand drag co-

efficient ∆CD

with actual drag change (∆CD)in simulation: measure for flight performancevariation around a certain example trim point

tions and also contains the above described additionaleffects and errors. Similar plots result for the remainingtwo regressors (mfuel and Ma) used in the linear modelfor EEngine.

The illustration of the drag change ∆CD versus theremaining variation E

∆Din the left plot of Fig. 8 shows

the searched dependency with the drag change. Theright plot in Fig. 8 further compares the predicted equiv-alent drag coefficient ∆C

Dwith the actual drag change

in the simulation. The direct correlation validates theproposed methodology to determine the flight perfor-mance variation within a large flight data set with onlysome small remaining variation caused by the used ap-proximations and simplifications.

4 FLIGHT DATA EVALUATION

In order to determine the real typical flight perfor-mance variation encountered during daily flight opera-tions, data of 75, 689 flights with Boeing B 737-700 and

Figure 9: TUIfly Boeing 737-800 during final approach8

B 737-800 aircraft operated by TUIfly (see Fig. 98) areanalyzed. The data of each flight was recorded with thequick access recorder (QAR), which receives the samesignals as the flight data recorder, and downloaded bythe airline after the flight. The data time resolution ofthe individual signals ranges from 8 Hz (e.g. accelera-tions) to 1/64 Hz (e.g. gross weight).

No direct information about the aircraft thrust wasrecorded in the data and no engine simulation modelpermitting the calculation of these values out of mea-sured engine parameters was available. This would nor-mally posed some difficulties for the intended flight per-formance analysis due to the major role played by theengines. But this problem could be overcome accept-ably well thanks to the proposed methodology with es-timation of engine influence from fight data and thehuge quantity of data available itself.

Unfortunately the data used for this analysis wereanonymized such that the correspondence between aparticular airplane and a recorded flight data was notavailable. As a consequence, all available informationof each fleet (B 737-700 and the B 737-800 separately)is used together to estimate a global engine influenceand predict the flight performance variation. Note that

8 c©TUIfly, with permission for publication;https://www.tuifly.com/downloads/Boeing_737_-_800_bereit_zur_Landung_gr.JPG (download: October 11th, 2016)

validation,segmentation,categorization,

calculation

analysis andprediction

of variation

1st step 2nd stepsegment #1segment #2segment #3segment #4segment #5segment #6

segment #m

flight #1

flight #2

flight #3

flight #4

flight #n

performancevariation

Figure 10: Flight data analysis: two step approachto predict the flight performance variationwithin a fleet

for this analysis it is crucial to consider the data from allthe aircraft of the same type since the aim is to com-pensate the missing engine data / information but notto adjust the performance for each individual aircraft.The unavailability of the correspondence informationprevented the detection of outliers in the data, whichfor instance happens if one of the airplanes has a sig-nificantly better or worse performance than the others.Eventually, this process enabled to obtain an acceptableestimate of the missing information on the engines, buta real engine model would probably have been signifi-cantly more precise.

The herein presented flight data evaluation containsof two different steps: first the a-priori data analysis andsegmentation and second the prediction of the aircraftflight performance variation. As illustrated in Fig. 10,the data was first checked and validated to remove er-roneous data sets from the subsequent analysis con-taining unreliable sensor measurements, unexplainabledata jumps or missing time segments. The data wasautomatically segmented in relatively short time-slicesduring which the aircraft was flying in a quasi-steadystate (see section 2): stabilized flight path (cruise, butalso climb or descend) and possibly steady turns. Onekey requirement for each segment was a well compa-rable engine state, which is required by the evaluationmethod applied afterwards. Data segments with verydynamical maneuvers (e.g. high roll rate or rapid vari-ation of load factor) were ignored in this first analysisbut could be considered in future evaluations as well.Later on, the segments were categorized according totheir average speed, altitude, fan speed, gross weightand outside air temperature. Each category describesan engine operating point allowing the estimation ofthe linear model describing the engine influence on theflight performance similar to the validation example insection 3. Calculation of the necessary values for eachsegments completed the first evaluation step. In a sec-ond step, the data segments of each evaluated categorywere analyzed and the flight performance variation rep-resented by the equivalent drag coefficient ∆C

Dwas

predicted. This procedure is very similar to the method-ology validation presented in section 3.

3 650 3 700 3 750 3 800

−1012

t [s]Etot

[MW

]

54 200

54 300

mAC

[kg

]

225

226

227

VTAS

[m/s

]

7 2407 2607 2807 3007 320

H[m

]

78

80

82

84

N1

[%]

Figure 11: Example of automatically selected flight datasegments with nearly steady flight condition

An example of such extracted flight data segmentsis given in the time histories of several aircraft observa-tion variables in Fig. 11. In the case shown in this fig-ure, segments during cruise flight right after the aircraftclimbed to 24 000 ft (7 315 m) are selected. With stabi-lized engine conditions the aircraft speed only containssmall variations and the quasi-steady flight assumptionis valid. This applies also to the resulting power imbal-ance, which shows only small oscillations around zero,indicating no significant change of the flight condition.

With this method 202 797 segments were extractedfrom the B 737-700 data set and 5 161 814 segmentsfrom the B 737-800 data set. These segments containmainly parts of the en-route flight but climb to and de-scend from the cruise flight levels are also representedwithin the extracted data sets. The estimation of the lo-cal engine influence on the recorded aircraft flight per-formance in each category of the above mentioned five-dimensional domain (V ,H,Tstat,N1,mAC) is performedusing a regression technique on a subset of the data.It is possible to reliably estimate the engine model pa-rameter values within a category only if each evaluatedcategory contains enough segments. In the B 737-700data set the 340 categories with the highest number ofsegments were selected, which resulted in the abovegiven number of extracted segments. Similarly, in theB 737-800 data set the 750 categories with the highestnumber of segments were selected. The lowest num-ber of segments in these categories were respectively

0.4 0.6 0.8

6 000

8 000

10 000

12 000

Ma [-]

H[m

]B 737-700B 737-800

Figure 12: Quasi-steady flight points of evaluated flightdata segments in altitude-Mach diagramwithin the limits of the B 737 flight envelope

271 in the the B 737-700 case and 572 in the B 737-800case. In both cases, an affine adjustment of the perfor-mance based on only three engine parameters (the fanspeed N1, the fuel flow mfuel, and the Mach numberMa) was found sufficient for the presented case, butmust be eventually extended in future applications e.g.considering data of different points of the flight enve-lope. Note that when an affine adjustment with only 3

linear terms (one per parameter) on data sets contain-ing several hundreds of data points is applied, there isno real risk of overfit.

In Fig. 12, all quasi-steady flight points of the ex-tracted data segments are plotted together with thelimits of the B 737 flight envelope in the altitude-Machdiagram. Most of selected data is related to cruiseflight points which is logical as the en-route flight phasemainly contains quasi-steady flight conditions with therequired duration of more than 60 s. Note that due tothe large number of flights available for the B 737-800the corresponding segments are all located in the up-per right corner of the flight envelope after limitationto 750 categories as the presented analysis was not en-titled to cover all data available or the complete flightenvelope.

The second step of the evaluation was the segmentdata analysis and prediction of the flight performancevariation within the fleet of same aircraft type. The esti-mation of engine influence and calculation of remainingpower imbalance was conducted similar to the examplein section 3 and Fig. 13 contains the combined enginefan speed versus the power imbalance for one examplecategory (B 737-700). Comparison of the left and rightplot reveals that considering the thrust related powerimbalance allows to explain several outliers and a gen-eral linear trend and can reduce some of the variation.It gets visible again that without the estimation and re-moval of the engine thrust influence the resulting pre-

dicted flight performance variation would be deficient.The removal of engine thrust influence turns the scat-tered distribution of power imbalance points (compari-son of left and right plot) which reduces the predictedvariation except for the fact that some outliers cannotbe explained with this method at all. The remainingpower imbalance E

∆Dwas then used to calculate the

equivalent drag coefficient ∆CD

per category as definedin Equation (4).

In order to represent the complete data (millionsof data points) in an intelligible way, convex hulls (inthe (CD,CL)-plane, nominal drag polar extracted from“Base of Aircraft Data” Family 3 [15]) corresponding toseveral quantiles of the data were computed and rep-resented graphically in Fig. 14 for the B 737-700 (left)and B 737-800 (right). On these individual figures

• the black line represents the nominal drag polar ofthe aircraft,

• the dot-dashed gray lines are defined as by shiftingthe nominal drag polar by steps of 25 % CD0 andserve as grid in this figure,

• the gray area represents schematically the accu-racy that the author expects to be able to reachwith better resolution of flight data and moredetailed knowledge about the individual aircraft,which could be used to track a single aircraft’s per-formance degradation in operational service,

• the areas defined by the dashed dark, dot-dasheddark, dotted gray and solid light gray polygon linesare the convex hulls of the selected data quantiles(95 %, 99 %, 99.9 % and 100 %).

Most of the variation is found around the optimalcruise flight point (L/D)opt, where most of the data isavailable. The distribution of the different convex hullsshow that less than 0.1 % of data contains the majorityof predicted variation. The P99-line indicates that 99 %

of the flight performance variation lies below 10 % ofzero lift drag. Moreover, the predicted P95-variation of∆C

Dis even lower and similar to the values of normal

drag increase for in-service airplanes given in [1].There are several sources of errors affecting this anal-

ysis and presumably causing the large predicted varia-tion of the small subset of data: a limited knowledgeon the engine power characteristics of these two air-craft types, a low resolution (sampling-time and quanti-zation) of the recorded data, a missing vertical wind in-formation (which can hardly be recovered from the dataavailable). In addition, the B 737-800 data include air-craft equipped with different types of winglets. More-over, the results are further affected by missing infor-mation about e.g. large scale atmospheric effects, sen-sor miscalibration, engine deficiencies or aircraft icing.After considering the knowledge gained from the data

85 90 95−2

−1

0

1

2

N1 [%]

Eto

t[M

W]

85 90 95−2

−1

0

1

2

N1 [%]

EEngine

85 90 95−2

−1

0

1

2

N1 [%]

E∆D

totalpower imbalance

thrust relatedpower imbalance

remainingvariation

= +

Figure 13: Power imbalance variation for different analyzed data segments in one example category (B 737-700):fan speed N1 versus total power imbalance Etot as well as separation into estimated thrust-relatedpower imbalance EEngine and the remaining not-assignable variation

0.02 0.040

0.2

0.4

0.6

0.8

175%CD0

150%CD0

75%CD0

200%CD0

225%CD0

50%CD0

125%CD0

B 737-700

CD [-]

CL

[-]

0.02 0.040

0.2

0.4

0.6

0.8

175%CD0

150%CD0

75%CD0

200%CD0

225%CD0

50%CD0

125%CD0

B 737-800

CD [-]

CL

[-]

nominal polar (P0)(L/D)opt

estimated method

accuracy

P95P99P99.9P100

Figure 14: Obtained equivalent drag coefficient (convex hulls of P95, P99,P99.9 & P100) within the two differentfleets of B 737-700 and B 737-800 aircraft; resulting flight performance variation during normal airlineoperations with respect to nominal aircraft drag polar (P0) and optimal cruise flight point for minimalfuel consumption (L/D)opt; estimated methodology accuracy for better data resolution and withoutanonymization

and the sensitivity of the results to the different sourcesof errors, an educated guess was made for the perfor-mance estimation uncertainty that can be reached inpractice by using the methodology and the standardaircraft instrumentation (air data and inertial referencesystems) but with higher sampling rate and more de-tailed knowledge about the individual aircraft history.This estimate on the achievable precision is representedby the gray areas in Fig. 14.

The results of this QAR data analysis support the ini-tial guess that it is possible to monitor the aircraft per-formance of all aircraft from a complete fleet using theregular sensors and with a level of precision that per-mits to detect a flight performance variation and con-sequently degradation. The way the QAR data wasprocessed in the analysis presented in this section wasstrongly tailored to a long term big data analysis, buta slightly adapted version of the methodology might

be used for post-flight or even on-board flight perfor-mance monitoring.

5 CONCLUSION

A novel methodology to determine and monitor theaircraft flight performance during regular airline opera-tions within a fleet of same aircraft type was presented.The validity and applicability of the approach is sup-ported by two separated analysis. First, the method-ology was tested and validated with simulated flightdata of DLR’s Airbus A 320 research aircraft ATRA. It wasproven that an artificially introduced flight performancevariation could be reliably and accurately predicted bythe evaluation of the large flight data set. Second, theanalysis of a very large real flight data set indicated thatthe searched flight performance variation could be pre-dicted with the presented methodology and that it is

feasible to extract the flight performance informationwith very limited system knowledge. The overall resultsare very promising and in the methodology will be fur-ther developed in future projects to consider more datawithin all flight phases and aircraft configurations oralso track the individual flight performance change ofa single aircraft within the fleet.

ACKNOWLEDGEMENT

The author wants to specially thank TUIfly, in personFriedrich Lämmle and Moritz Horejschi, for providingthe herein evaluated flight data, and his DLR colleaguesDr. Fethi Abdelmoula, who converted the binary QARflight records into MATLAB-files for easier use with DLRin house tools, and Dr. Nicolas Fezans, who supportedthe development of the evaluation methodology withfruitful discussions.

References

[1] Airbus Industries, Getting Hands-On Experiencewith Aerodynamic Deterioration. Airbus Flight Op-erations Support & Line Assistance, Oktober, 2001,Blagnac Cedex, Frankreich.

[2] Raymer, Daniel P: Aircraft Design: A Conceptual Ap-proach. AIAA Education Series. American Institute ofAeronautics and Astronautics, Inc., Reston, Virginia,USA, 5 edition, 2012.

[3] Krajek, Karolina; Nikolic, Dario and Domitrovic,Anita: Aircraft performance monitoring from flightdata. Technical Gazette, Vol. 22, No. 5, pp. 1337–1344, Oktober, 2015.

[4] Lombaerts, Thomas; Schuet, Stefan; Wheeler,Kevin; Acosta, Diana and Kaneshige, John: Safe ma-neuvering envelope estimation based on a physicalapproach. Number AIAA 2013-4618 in AIAA Guid-ance, Navigation, and Control (GNC) Conference,Boston, Massachusetts, USA, August 19th - 22nd,2013. American Institute of Aeronautics and Astro-nautics, Inc. (AIAA).

[5] Lombaerts, Thomas; Schuet, Stefan; Acosta, Diana;Kaneshige, John and Martin, Lynne: Piloted Simu-lator Evaluation of Maneuvering Envelope Informa-tion for Flight Crew Awareness. Number AIAA 2015-1546 in AIAA SciTech - AIAA Guidance, Navigation,and Control Conference, Kissimmee, Florida, USA,January 5th - 9th, 2015. American Institute of Aero-nautics and Astronautics, Inc. (AIAA).

[6] Lombaerts, Thomas; Schuet, Stefan; Acosta, Dianaand Kaneshige, John: On-Line Safe Flight Envelope

Determination for Impaired Aircraft. Advances inAerospace Guidance, Navigation and Control, 2015.

[7] Collins, Bela P.: Estimation of Aircraft Fuel Con-sumption. Journal of Aircraft, Vol. 19, No. 11, pp.969–975, November, 1982.

[8] Turgut, Enis T.: Estimating Aircraft Fuel Flow for aThree-Degree Flight-Path-Angle Descent. Journal ofAircraft, Vol. 48, No. 3, pp. 1099–1106, May-June,2011.

[9] Lawrance, Nicholas R. J.; Sukkarieh, Salah and Mas-son, Bertrand: Using High-Frequency Data for Pre-dicting Fuel Use of Jet Transport Aircraft. Journal ofAircraft, Vol. 54, No. 6„ November-December, 2017.

[10] Chou, Eric; Gorinevsky, Dimitry and Boyd,Stephen P.: Detecting Aircraft PerformanceAnomalies from Cruise Flight Data. AIAA In-fotech@Aerospace, Atlanta, Georgia, USA, 20. - 22.April, 2010. American Institute of Aeronautics andAstronautics, Inc. (AIAA).

[11] Jategaonkar, Ravindra V.: Flight Vehicle SystemIdentification - A Time Domain Methodology, vol-ume 245 of Progress in Astronautics and Aeronau-tics. American Institute of Aeronautics and Astronau-tics, Inc., 1801 Alexander Bell Drive, Reston, Virginia20191, USA, 2 edition, 2015.

[12] Höhndorf, Lukas; Czado, Claudia; Bian, Huan-glei; Kneer, Jennifer and Holzapfel, Florian: Statis-tical Modeling of Dependence Structures of Oper-ational Flight Data Measurements not Fulfilling theI.I.D. Condition. Number AIAA 2017-3395 in AIAAAVIATION Forum - AIAA Atmospheric Flight Mechan-ics Conference, Denver, Colorado, USA, June 5th -9th, 2017. American Institute of Aeronautics and As-tronautics, Inc. (AIAA).

[13] Traeger, Irwin E.: Aircraft Gas Turbine Engine Tech-nology. Glencoe/McGraw-Hill, Westerville, Ohio,USA, 3 edition, 1996.

[14] Nicolai, Leland M. and Carichner, Grant E.: Fun-damentals of Aircraft and Airship Design, volume 1- Aircraft Design. American Institute of Aeronauticsand Astronautics, Inc. (AIAA), Reston, Virginia, USA,2010.

[15] Eurocontrol Experimental Centre, User Mamual forthe Base of Aircraft Data (BADA) Revision 3.12. Eu-ropean Organisation for the Safety of Air Naviga-tion (Eurocontrol), August, 2014, Brétigny-sur-OrgeCedex, Frankreich.