Research Article Inflight Parameter Identification and Icing ...downloads.hindawi.com/journals/jcse/2014/396532.pdfResearch Article Inflight Parameter Identification and Icing Location

Research ArticleInflight Parameter Identification and Icing Location Detectionof the Aircraft The Time-Varying Case

Yiqun Dong1 and Jianliang Ai2

1 Department of Mechanics and Engineering Science Fudan University Shanghai 200433 China2Department of Mechanics and Engineering Science Institute of Aeronautics and Astronautics Fudan UniversityShanghai 200433 China

Correspondence should be addressed to Yiqun Dong yiqundong10fudaneducn

Received 9 February 2014 Accepted 19 June 2014 Published 10 July 2014

Academic Editor Onur Toker

Copyright copy 2014 Y Dong and J Ai This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper considers inflight parameter identification and icing location detection of the aircraft in a more common time-varyingnature In particular ice accumulation is modeled as a continuous process and the effect of the ice upon aircraft dynamics is tobe accreted with time Time-varying case of the Hinf algorithm is implemented to provide inflight estimate of aircraft dynamicparameters and the estimated results are delivered to a probabilistic neural network to decide icing location of the aircraft anexcitation measure of the aircraft is also adopted in the network input layer A database corresponding to different icing cases andseverities was generated for the training and test of the detection network Based on the test results the icing detection frameworkpresented in this paper is believed to be with promising applicableness for our further studies

1 Introduction

Current aviation research and development has begun tofocus more on creating aircraft that are safe and reliableduring severe weather conditions Aircraft icing is of greatconcern due to the detrimental effect of accreted ice onaircraft performances Most of the accidents related withaircraft icing occur because the ice accumulation modifiesthe stability and controllability of the aircraft [1 2] otheraccidents include engine failure or critical probes (pitot tubeetc) malfunctioning [3 4] Currently there are two mainapproaches to deal with the ice accretion problem Firstpilots are provided with weather information prior to flightmissions in the pursuit of avoiding potential icing conditionsor aircraft are thoroughly deiced before takeoff while an icingprotection system (IPS) could be operated in flight to removedangerous ice accretions

Under all circumstances apparently ice avoidance is amore desirable goal For most of the commercial flightcourses however while revenues and schedules must bemaintained IPS still occupies an important part in theinsurance of safe flight Current IPS mainly consists of

devices that could bleed hot engine exhaust to counteractthe frigid icing conditions or inflatable boots are used tobreak off the accumulated ice Generally the IPS functionsin an either advisory or primary capacity The advisoryIPS relies upon pilots to activate icing protection devicesbased on any aircraft icing information which might beallocated from icingenvironmental sensors As for IPS thatfunctions in the primary capacity it utilizes the informationcollected from various sensors and the deiceanti-ice devicesare activated automatically Pilots are given instantaneousupdates concerning aircraft icing and IPS status they couldalso manually override the system if necessary

Recently sporadic aircraft accidents indicate that the IPSstrategy does not adequately provide safe and reliable flightduring icing conditions The accident of American EagleATR-72 near Roselawn Indiana killed 68 people in October1994 [2] The China Eastern Airlines Flight 5210 (CRJ-200)crashed after takeoff in Baotou City in November 2004killing 55 people And in the year of 2009 the Air FranceFlight 447 (A330) crashed over the Atlantic Ocean all thepassengers on board were lost [3 4] These fatal accidents arenotable examples of the IPS inadequateness where either the

Hindawi Publishing CorporationJournal of Control Science and EngineeringVolume 2014 Article ID 396532 11 pageshttpdxdoiorg1011552014396532

2 Journal of Control Science and Engineering

IPS was not activated timely or the IPS was activated but noteffective To ensure flight safety of the aircraft an overall sys-tematic inspection of the icing hazard needs to be conducted

Back to 1994 after the ATR-72 accidents NASA and FAAin United States cosponsored a four-year Tailplane Icing Pro-gram (TIP) whichwas expected to expand the understandingof the aircraft ice contaminated tailplane stall (ICTS) hazard[5] In 1998 after the closure of TIP Brag advanced an icingmanagement system (IMS) as an additional layer of defenseagainst the aircraft icing accidents [6] IMS adopts the coreeffect of ice accretion upon aircraftmdashthe modification ofaircraft stability and controllability while IMS provides acontinual monitoring of the aircraft icing status traditionalIPS devices could be activated automatically by the IMS anda reconfiguration of the inline flight control laws could beincluded so as to restrict the aircraft maneuver within aproper margin of safety

The Commercial Aircraft Corporation of China(COMAC) in Shanghai is en route to the production ofChinarsquos first generation of large civil aircraft Due to thehazardous effect upon aircraft performance and safety iceaccretion draws a strong concern from us According to theschedule the research work on aircraft icing mainly includesa CFD inspection of the ice accumulation and an icingwind-tunnel examination of aircraft and real flight testingmaneuvers are also necessary to either verify the wind tunnelresults or evaluate the effect of ice during critical stages ofthe aircraft mission (eg landingtakeoff cycle) Lastly aself-adaptive mechanism could be implemented in the inlineflight control laws design

The aircraft icing research in Fudan University is mainlyfocused on the dynamics and in future time the controlof iced aircraft Our current work is formulated to providean exploration for the inflight detectioncharacterization ofthe accretedaccreting ice upon the airframe after the overalltest procedure is completed a control aid for the pilots willbe developed In our work similar to IMS we adopt thecore effect of ice on aircraft performancemdashthe modificationof stability and controllability Parameter identification tech-nique is employed to provide inline estimates of the aircraftdynamic parameters after which the aircraft icing locationand severity could be decided In [7] we have discusseda work on inline icing location detection of the aircraftBaseline scenario of the work was selected as trimmed steadylevel flight it was assumed that the ice has completed theaccumulation on the airframe and the aircraft dynamicparameter remains time-invariant over the maneuver periodIdentification maneuver was induced by separated commandinput of the aircraft control surfaces in the hope that thecoupling motion along different axes of the aircraft was to besuppressed After the ID maneuver was finished ID resultswere delivered to the neural network to decide icing locationof the aircraft Due to current shortness of the aircraft icingdata only four scenarios of clean wing icing tail icing andwing-tail both icing cases were discussed A very high degreeof accuracy of icing location detection was accomplished inthe work

One problem of this work however is that it could onlyprovide indication of the aircraft icing over short period

Certainly the designed command input could be repeatedconstantly but through simulation it was found that overloadof the aircraft was relatively high and passenger-ride qualityof the aircraft shall not be guaranteed Also a constant inputof all the 3 control surfaces affects the aircraft state severelyit was hardly possible for the aircraft to maintain the initialsteady level flight In such senses while the work discussed in[7] could be employed for detection of aircraft icing over shortperiod a long-period continual monitoring of icing statuscould not depend upon it

And in this paper we try to fill this gap Specifically wetry to develop a framework that could continually monitorstatus of the aircraft and based on all the data availableinformation pertaining to aircraft icing could be estimatedIn Section 2 of this paper we build up a long-period icingmodel of the aircraft The icing severity was modeled toincrease with time based on which the effect of ice on aircraftdynamic parameters was to be accreted Section 3 introducesa Hinf parameter ID technique developed for the time-varying system This technique depends solely on exogenousdisturbance signals of the system and dynamic parametersof the system could be estimated As this ID techniquerequires no specific excitation from the system input andit adopts only the state vector of the aircraft it arises as aperfect tool for the long-period continual monitoring taskIn Section 4 based on the parameter estimation results fromHinf algorithm probabilistic neural network (PNN) wasemployed to decide location of the aircraft icing A databasefor the net training and test was generated in this section andtest result of the detection net was discussed Accuracy of theconstructed network is considered to be acceptable FinallySection 5 contains a general conclusion of this paper someissues that highlight our future direction are also discussed

2 Flight Dynamics Model

21 Ice Effect on Dynamics In [8] Bragg et al proposed arepresentative model of the ice effect on aircraft dynamics

119862(lowast)iced = 119862(lowast)clean (1 + 120578ice119896119862lowast) (1)

where 120578ice is an icing severity parameter 119896119862lowast is the coefficienticing weight which depends on the parameter being modi-fied 119862(lowast)clean is the clean (not iced) aircraft parameter and119862(lowast)iced indicates the iced parameter In our work dynamicmodel of the aircraft is established based on the NASA TwinOtter icing research airplane Both clean and iced parametersof this aircraft are detailed in Table 1 [8] The iced parametersin the table are representative of icing severity 120578ice = 02119896119862lowast could then be calculated as the associated slope fromparticular parameters under different icing locations In thispaper similar to [9] a long-period continuous accretion ofice is captured by setting 120578ice to increase with time Thedifferential equation

119889

119889119905120578ice = 1198731 (1 + 1198732120578ice) 119862120578 (2)

is used as the model of ice accumulating on airframe where119862120578 represents the conduciveness of the atmosphere to icing

Journal of Control Science and Engineering 3

Table 1 Dynamic parameters of Twin Otter in clean and iced configurations

(a)

1198621198850 119862119885120572 119862119885119902 119862119885120575119890 1198621199090 119870 1198621198980 119862119898120572 119862119898119902 119862119898120575119890

Clean minus0380 minus5660 minus19970 minus0608 minus0041 0052 0008 minus1310 minus34200 minus1740Wing minus0380 minus5342 minus19700 minus0594 minus0050 0053 0008 minus1285 minus33000 minus1709Tail minus0380 minus5520 minus19700 minus0565 minus0046 0053 0008 minus1263 minus33000 minus1593Both minus0380 minus5094 minus19700 minus0550 minus0062 0057 0008 minus1180 minus33000 minus1566

(b)

119862119884120573 119862119884119901 119862119884119903 119862119884120575119903 119862119897120573 119862119897119901 119862119897119903 119862119897120575119886 119862119897120575119903 119862119899120573 119862119899119901 119862119899119903 119862119899120575119886 119862119899120575119903

Clean minus06 minus02 04 015 minus008 minus05 006 minus015 0015 01 minus006 minus018 minus012 minus0001Both minus048 minus02 04 0135 minus0072 minus045 006 minus0135 00138 008 minus006 minus0169 minus011 minus0001

In (2) the coefficients 1198731 and 1198732 are determined from anassumed icing severity profile characterized by the durationtime of icing encounter which is denoted by 119879cld and thefinal and middle values of the icing severity 120578ice(119879cld) and120578ice(119879cld2) respectively

In this paper the scenario discussed is assumed to bea period of steady level flight with disturbances through aldquocloudrdquo of potential icing conditions The icing encounter ischaracterized by the duration time 119879cld and the icing severityparameters at119879cld and119879cld2 For all the simulations discussedherein conduciveness of the atmosphere to icing is assumedto be a raised cosine as

119862120578 (119905) =1

2[1 minus cos(2120587119905

119879cld)] + 119889120578 (3)

Note that uncertaintybias of this conduciveness model isincluded in 119889120578 Substituting 119879cld 120578ice(119879cld) and 120578ice(119879cld2)into (2)-(3) and considering an ideal situation as the con-duciveness model uncertaintybias being 119889120578 = 0 1198731 and 1198732are determined as

1198732 =120578ice (119879cld) minus 2120578ice (119879cld2)

[120578ice(119879cld2)]2

1198731 =2

1198732119879cldln [1 + 1198732120578ice (119879cld)]

(4)

where ln(lowast) indicates the natural logarithm functionTwo icing encounter scenarios plus the clean aircraft case

will be investigated in this paper as depicted in Figure 1 Forthemoderate icing encounter119879cld = 600 120578ice(119879cld) = 02 and120578ice(119879cld2) = 012 For the severerapid icing encounter119879cld = 300 120578ice(119879cld) = 03 and 120578ice(119879cld2) = 02 To fullyunderstand performance of the aircraft undertaking icea total of 900-second simulation for all the investigatedscenarios will be discussed

22 Nonlinear Dynamics Motion equations adopted in thispaper borrow directly from the 6 degree-of-freedom qua-sistate nonlinear aircraft dynamics [10] Clean and icedparameters of icing severity 120578ice = 02 are detailed in Table 1For all cases thework in this paper is simulatedwith an initialcondition of steady level flight at altitude 3500m and velocity

0 100 200 300 400 500 600 700 800 900minus005

0

005

01

015

02

025

03 Severerapid icing

Moderate icing

Clean aircraft

120578ic

e

t (s)

Figure 1 Two icing scenarios and the aircraft clean case

70ms At the beginning of the simulation icing severity ofthe aircraft is 0 while during the simulation period the icingseverity takes the shape determined as in (2)ndash(4) or as inFigure 1

23 Disturbances and Measurement Noise Performance ofthe iced aircraft under different disturbances and measure-ment noise was discussed in [11] A further research workof the microbust and gravity wave effects on the aircraftwas presented in [12] In our work both disturbances andmeasurement noise are modeled based on [9 13] as samplepaths of zero-mean band limited white Gaussian noise withbandwidth 50Hz Linearized relation of aircraftmotion equa-tions yields 119881 asymp 119906 120572 asymp 119908119881 and 120573 asymp V119881 between aircraftwind and body axes Intensity of disturbances is modeled asperturbation to velocities along body axes namely 119908 V119908and 119908

119908 asymp 119908

119908 asymp119908

119881

120573119908 asympV119908119881

(5)


For all the simulations discussed herein a most severe levelof the disturbance is adopted as 119889119901 = 119908 = V119908 = 119908 = 040 gIntensities of measurement noise are chosen based on speci-fications of the simulated aircraft sensor resolutions detailedinformation on instruments of aircraft state and controlsurfaces is presented in [14]

3 Inflight Parameter Identification

31 Hinf ID Algorithm In [7] we have discussed the Hinfparameter ID framework for the time-invariant system astate-space system in the form of

= 119860 (119909 V) 120594 + 119887 (119909 V) + 119889119901

119910 = 119909 + 119889119898

(6)

was used In (6) 119909 isin 119877119899 is system state vector 119910 isin 119877

119899

is the measured state vector and V isin 119877119894 indicates input

of the system In (6) the state-space form is linear withthe parameter vector 120594 isin 119877

119903 while 119860 (119909 V) and 119887 (119909 V)could include nonlinear terms of 119909 and V Disturbance isrepresented by 119889119901 isin 119877

119899 in the model and 119889119898 isin 119877119899 is the

system measurement noiseTime-varying algorithm of the Hinf ID technique con-

siders an assumed linear differential model of the parameterevolution as

120594 = 119867120594 + 119870119889120594 1205941003816100381610038161003816119905=0 = 1205940 (7)

where119867 isin 119877119903times119903 and119870 isin 119877

119903times119904 are coefficient weights and 119889120594 isin119877119904 indicates any uncertaintybias between the linear terms in

(7) and the actual value of 120594 differentialTo obtain (7) to be used by time-varying Hinf algorithm

for the icing problem noting that 1205940 = 119862(lowast)clean and 120594 =

119862(lowast)iced we could have

120594 = 1205940 (1 + 119870119862lowast120578ice) (8)

Combining (2)-(3) the differential form of (8) is in the formof

120594 = 1205940119870119862lowast1198731 (1 + 1198732120578ice) times 1

2[1 minus cos(2120587119905

119879cld)] + 119889120578

(9)

At starting point of the icing encounter 119905 = 0 120578ice = 0 (9)yields

1205941003816100381610038161003816119905=0 = 1205940119870119862lowast1198731119889120578 (10)

From (7) and (10) we could have

1198671205940 + 119870119889120594 = 1205940119870119862lowast1198731119889120578 (11)

In (11) 1205940 indicates clean aircraft parameters and 119870119862lowast is thecoefficient weight corresponding to the parameter being dis-cussed both119889120594 and119889120578 represent (unknown) uncertaintybiaswithin the model Also considering (1)ndash(3) note that theaircraft icing model adopted in this paper is driftless which

means that ice accretion is induced by exogenous icingconditions only thus inherent dynamic parameter of thesystem does not enter the evolution differentials in (7) hence119867 ≐ 0 From (11) the uncertaintybias weight 119870 adoptedby time-varying Hinf algorithm for the icing problem hereinis dependent on the parameters being examined (althoughthe real relation might not be derived due to the existence ofunknown 119889120594 and 119889120578) In our study a value of 119870 = 1205940119870119862lowast1198731

will be used where1198731 corresponds to the value of moderateicing determined as in (4)

For the system described in the form of (6) and forthe aircraft icing problem discussed herein the time-varyingalgorithm of Hinf ID technique involves a disturbance atten-uation level 120574 between the target estimation result (120594) and theunknown certaintybias within the estimation model in theform of

1003817100381710038171003817120594 minus 1205941003817100381710038171003817

2

119876

le 1205742[(10038171003817100381710038171003817119889119901

10038171003817100381710038171003817119868)2+ (

10038171003817100381710038171198891198981003817100381710038171003817119868)2+ (

10038171003817100381710038171003817119889120594

10038171003817100381710038171003817119868)2+ (

10038171003817100381710038171003817119889120578

10038171003817100381710038171003817119868)2

+(10038161003816100381610038161199090 minus 1199090

10038161003816100381610038161198750

)2+ (

1003816100381610038161003816120594 minus 120594010038161003816100381610038161198760

)2]

(12)

where1205940 isin 119877119903 and1199090 isin 119877

119899 are priori estimates of120594 and initialaircraft state 1199090 In this paper1205940 is chosen as the clean aircraftparameters for all cases in the meantime 1199090 is the trimmedsteady state of the aircraft The form lowast 119876 is an 1198712 normwith a predefined semipositiveweighting function119876 ge 0 and| lowast |119876

0

is a generalized Euclidean norm1198831198791198760119883 with positive

weight 1198760 gt 0 In (12) both 1198750 isin 119877119899times119899 and 1198760 isin 119877

119903times119903 aredetermined by the user Generally (12) provides a guaranteedworst-case performance of the ID algorithm bounded by 120574

for any real 120594 and 1199090 (practically could never be obtainedwithout measuring bias) and the uncertaintybias within themodels 119889119901 119889119898 119889120594 and 119889120578 as long as 120574 is larger than theminimum achievable disturbance attenuation level 120574lowast

Time-varying algorithm of the Hinf ID technique is

[

119909

120594] = [

0 119860 (119910 V)0 119867

][119909

120594] + [

119887 (119910 V)0

] + Σminus1[119868

0] (119910 minus 119909)

(13)

where Σ = Σ(119905) isin 119877(119899+119903)times(119899+119903) is defined as

Σ = minus Σ [0 119860 (119910 V)0 119867

] minus [0 0

119860(119910 V)119879 119867119879]Σ

+ [119868 0

0 minus120574minus2119876] minus Σ[

119868 0

0 119870119870119879]Σ

(14)

With initial condition Σ(0) = diag(1198750 1198760) Note that in (13)-(14) the dependence of119860(119910 V) and 119887(119910 V) differs from (6) inthis paper measurement noise is included in the model both119860(119910 V) and 119887(119910 V) adopt noise-perturbed measuring of thesystem state vector

One critical issue of the Hinf ID algorithm is to deter-mine the minimum disturbance attenuation level 120574lowast Thetime-invariant case has been discussed in [13 15] and in [9]


a general result was obtained for the time-varying case Herewe adopt the conclusion directly as by using the partition

Σ = [

[

Σ1 Σ2

Σ1198792 Σ3

]

]

(15)

with Σ1 isin 119877119899times119899 120574lowast equiv 1could be achieved by specifying 1198750 = 119868

and 119876 = Σ1198792Σminus21 Σ2 for any 1198760 gt 0

32 Hinf ID Simulation Results Simulation of the proposedHinf algorithm is conducted in order to evaluate the time-liness and accuracy of the parameter estimates Baselinescenarios of all the cases presented are the trimmed steadylevel flight at given altitude (3500m) and speed (70ms) Forall scenarios excitation is provided only by exogenous distur-bances Both clean and iced simulationswill be included Twoicing encounters depicted in Figure 1 are considered and theclean-aircraft simulation is included to investigate the falsealarm or a positive icing indication for the clean case

As in [7] it was determined that moment derivativesalong different axes of the aircraft provide useful informationfor the ice indicated (119862119898120572 119862119898120575119890 119862119897119901 119862119897120575119886 119862119899120573 and 119862119899120575119886)Generally the force parameters along body 119911-axis convergetoo slowly and the 119909-axis force parameters are too sensitive tonoise For all cases discussed in this paper baseline scenarioof the simulation is trimmed at a steady level flight and theID technique is expected to provide a continualmonitoring ofthe aircraft icing status It adopts disturbance as sole excita-tion for the system As no control surface input is involvedit is not possible to identify the controllability parameters(119862119898120575119890 119862119897120575119886 and 119862119899120575119886) additionally through simulation workit was determined that 119862119897119901 is too sensitive to disturbancesHence only the stability parameters along longitudinal (119862119898120572)and lateraldirectional (119862119899120573) axes will be used in our study

One issue that needs to be addressed prior to the IDsimulation is the choosing of an appropriate1198760 gt 0 as in (14)In this paper 1198760 = (1 times 10

minus4)119868 is used for the longitudinal

parameters and 1198760 = (1 times 10minus2)119868 for lateraldirectional

estimates Also a value of 120574 gt 120574lowast

equiv 1 is used asthrough simulation we found that 120574 = 120574

lowastequiv 1 could result

in a numerically unstable computation For longitudinalestimates 120574 = 2 and for lateraldirectional estimates 120574 = 4Generally there is not a universal standard for choosing either1198760 or 120574 the results presented herein are based on a trial-and-error work of the authors While a future modificationcould be included current performance of the proposed IDframework is presented and discussed as follows

For all scenarios discussed in this paper the simulationlasts 900 seconds In [7] to examine flight safety andpassenger-ride quality of the aircraft a time history of the air-craft response under the designed control input was includedIn this paper safety and comfortableness of the aircraft withan increasing ice effect and a most severe disturbance arealso of our concern Figure 2 represents an example of theaircraft response history up to 900 seconds In the interestof brevity only clean and the severerapid case of wing-tailboth icing was presented (which by intuition is decided astheworst case of icing) Given that no external control input is

included most of the state variables remain stable around thetrimmed value Based on aircraft pitchrolling angle and theoverload along body 119911119910-axis passenger-ride quality of theaircraft is considered to be acceptable Altitude of the aircraftundertakes a severe change in the simulation which descendsup to 3000m in the 900-second simulation While in realitypilots could take actions to deal with the altitude loss in thiswork a descending of 3000m in 15min is considered to bewith redeemable margin of safety No pilot action is includedand the overall system adopts exogenous disturbance signalas input only

Parameter ID results of the Hinf algorithm is shown inFigures 3ndash5 Clean aircraft ID result is shown in Figure 3while moderatesevere case for wing-tail both icing is inFigures 4 and 5 respectively Note that in all the figures theestimated parameters have been normalized with the cleanaircraft value take 119862119898120572 as an example 119862119898120572 = 119862119898120572(iced)

119862119898120572(clean) wherein 119862119898120572 is the result presentedFor all the figures in Figures 3ndash5 25 runs of the

simulation were included to realize different disturb-ancemeasurement noise paths An average performanceof the 25 runs is represented as dashed line in the figurethick solid line indicates real value of normalized parameterFor clean aircraft as in Figure 3 both longitudinal andlateraldirectional estimates vary significantly which iscaused in part by the random disturbancenoise effect andin part by the numerical sensitiveness of the Hinf algorithmGenerally the estimate for the clean aircraft case does notexceed the icing severity of 120578ice = 01 as indicated by thedotted line in Figure 3 This is considered to be sufficient inthe fact that in [7] 5 levels of icing severity 02 04 0608 10 were discussed and the parameter ID for clean casepresented herein does not trespass between different levels

Simulation results for the iced aircraft are given in Figures4 and 5 Moderate icing case is shown in Figure 4 andsevere icing in Figure 5 Average performance of the 25 IDsimulation runs is depicted by dashed lines in the figures Forlateraldirectional identification the estimate is very accurateand the estimated parameter corresponds to the real valuevery well For longitudinal parameter a certain delay wasencountered for various icing levels denoted by dotted linesGenerally as in [7] 5 levels of the aircraft icing were adoptedand we hope to decide the icing status before the next level isactually reached For moderate icing in Figure 4 the estimateis considered to be sufficient in the fashion of time as adeeper probe indicates that the average performance yieldsa delay time of no longer than 415 s For the severe icing inFigure 5 delay time of the longitudinal estimates is relativelylarge a maximum delay of about 100 s was encountered forthe highest level of 120578ice = 03 (indicated by the dotted lineat bottom) However note that although the delay was highestimated parameter and the real value generally belong to thesame level of icing in such sense the ID algorithm discussedherein is still considered to be applicable

One issue which the authors would like to mention is theldquodriftrdquo of Hinf estimated parameters As in Figure 3 a certain(constant) bias exists between the average performanceand real value Also in Figures 4 and 5 particularly for


IcedClean

IcedClean

0 100 200 300 400 500 600 700 800 90050

60

70

80Ve

loci

ty (m

s)

t (s)

0 100 200 300 400 500 600 700 800 9000

1

2

3

Ang

le o

f atta

ck (d

eg)

t (s)0 100 200 300 400 500 600 700 800 900

minus2

minus1

0

1

2

Rolli

ng an

gle (

deg)

t (s)

0 100 200 300 400 500 600 700 800 900minus01

minus005

0

005

01

gy (g

)

t (s)

0 100 200 300 400 500 600 700 800 9000

1000

2000

3000

4000

Alti

tude

(m)

t (s)0 100 200 300 400 500 600 700 800 900

minus14

minus12

minus1

minus08

minus06

gz (g

)

t (s)

0 100 200 300 400 500 600 700 800 900minus10

minus5

0

5

10

Pitc

h an

gle (

deg)

t (s)

0 100 200 300 400 500 600 700 800 900minus2

minus1

0

1

2

Side

slip

angl

e (de

g)

t (s)

Figure 2 Aircraft response clean and wing-tail severe icing

the longitudinal estimates as can be seen from the averageperformance an ldquoadvanced indicationrdquo of the icing levelwas encountered This does not correspond to theoreticalcharacteristics of the Hinf algorithm in the fact that for theclean case the estimated value should be twined aroundthe real parameter and for the iced case a delay shouldbe encountered as the Hinf algorithm functions basedon a historical examination of the system What addsto the complicatedness of this issue is that although thelateraldirectional identification takes exactly the same formas longitudinal estimates the above-mentioned phenomenawere never found Although the authors are still not withascertained conclusions upon this issue this could be causeddue to nonlinear terms within longitudinal equations of theaircraft For all scenarios in this paper the aircraft is trimmedas steady level flight lateraldirectional state variables are setto 0 while the longitudinal velocity angle of attack and soforth are not certain nonlinearity could therefore be induced

in the equations The ldquodriftrdquo issue belongs to the algorithmstability analysis and the ldquoadvanced indicationrdquo problemcould be examined based on a frequency-domain analysisWhile this part of the work might be forwarded in the futurecurrently the authors aremainly focused on application of theHinf algorithm towards aircraft icing in this paper instabilityor isochronism of the algorithm is expected to be toleratedby the neural networks as described in the following section

4 Icing Characterization

The objective of icing characterization work is to detect andclassify the ice accretion based on sensor data and parameterID results In this paper we adopt a conservative stancethat sensor data is not included and only the icing locationdetectionwill be discussedThe ldquodetectionrdquo introduced hereinis slightly different with what has been used in IMS in the


0 100 200 300 400 500 600 700 800 90008

085

09

095

1

105

25 ID runsAverage ID valueReal value


0 100 200 300 400 500 600 700 800 90006

065

07

075

08

085

09

095

1

105

11

t (s) t (s)

Nor

mal

ized

Cm120572

estim

ate

Nor

mal

ized

Cn120573

estim

ate

Figure 3 ID results for clean aircraft

0 100 200 300 400 500 600 700 800 90008

085

09

095

1

105


t (s)


t (s)

Nor

mal

ized

Cm120572

estim

ate

Nor

mal

ized

Cn120573

estim

ate

0 100 200 300 400 500 600 700 800 90006

065

07

075

08

085

09

095

1

105

11

Figure 4 ID results for moderate icing scenario

fact that in IMS ldquodetectionrdquo only refers to a determination onwhether the aircraft has encountered ice accumulation whilein our study however icing detection work is additionallyexpected to provide timely information about the locationwhere the ice has accumulated Due to the shortness ofaircraft iced data currently only 4 scenarios of the icing casesare included in our work clean wing icing tail icing andwing-tail both icing

Previous work by authors reported in [7] is focusedon icing location detection in a short period Dynamicparameters of the aircraft were assumed to be time-invariantduring the parameter ID maneuver which was induced

by a specifically designed control surface input momentderivatives along different axes of the aircraft were deliveredto the icing detection network and icing location detectioncould be accomplished with a very high degree of accuracy

In this study we mainly address the icing location detec-tion for a more common steady level flight where the iceis accreting gradually on the aircraft and hence dynamicparameters of the aircraft are varying in the fashion of timeIdentically the icing detection work reported herein adoptsestimated parameters from the Hinf ID algorithm For allscenarios discussed in this study however it is assumed thatpilot input is not included and exogenous disturbance signal


0 100 200 300 400 500 600 700 800 90008

085

09

095

1

105

0 100 200 300 400 500 600 700 800 90006

065

07

075

08

085

09

095

1

105

11



t (s) t (s)

Nor

mal

ized

Cm120572

estim

ate

Nor

mal

ized

Cn120573

estim

ate

Figure 5 ID results for severerapid icing scenario

serves as the sole input for the system Due to the absence ofexcitation input effectiveness of the parameter ID techniquemight be limited as some controllability parameters couldnot be estimated Another source of information thereforeis expected to be included to bridge this potential gap Alsoin [7] an overall detection error of only 030 was achievedwhile in this study generally a larger error is acceptable in thefact that the ice accretion is assumed to take place over a longperiod (up to 5ndash10 minutes) with a broader margin of safetyand precipitation of icing accidents is less likely in the absenceof pilot action

As in [6 9 13] IMSwas restricted to longitudinal dynam-ics of the aircraft In the authorsrsquo work lateraldirectionalanalysis is included in the model which therefore adds tothe complicatedness of our study Also for IMS work icingseverity classification was discussed in our work currentlythe authors decide not to spend much time upon this issueThis decision was made mainly based on twofold First weare currently focused on detection of the aircraft icing andalthough icing severity could be adopted as a quantificationalindication of ice effect it provides very limited informationfor the notification of pilot as the pilot generally is not clear(or concerned) about the meaning of a numerical data 120578ice =10 This actually represents a dilemma of our icing detectionwork in the fact that although a quantitative description ofice accretion is necessary eventually we still need to estimateour work from a qualitative aspect which might be modeledbased on a large-volume data of the pilot assessment Addi-tionally through preliminary CFD inspection of the aircraftdynamics we do have certain suspicion upon accuracy of theicing model in (1) While a general detection work based on(1) using neural networks is believed to be with sufficientrobustness for further study a specified classification of icingseverity might not Due to these two reasons while in futurestudies we will report the classification work of icing severity

(probably based on our own iced aircraft model) currentlythis part of the work is not presented

Icing detection in this paper is established by using PNN[16 17] As the detection network is expected to decidelocation of the aircraft icing the net output layer contains4 knots each of which corresponding to certain pattern ofthe aircraft icing (clean wing icing tail icing and wing-tail both icing) The activation of a certain knot is usedfor the indication of location deciding Input layer of thePNN includes parameter estimate results from the Hinf IDtechnique Also as no excitation input from the pilot isincluded in the system effectiveness of Hinf technique mightbe limited To fill this gap this paper adopts the concept ofldquoexcitation measurerdquo of aircraft as in [18] the bias from initialstate of the aircraft is defined as 119875120579 = 120579minus1205790 and119875119867 = 119867minus1198670where 1205790 and1198670 indicate initial state of the aircraft Both 119875120579and 119875119867 will be adopted in the input layer of the network

The PNN input data including parameter estimate (119862119898120572119862119899120573) and excitationmeasure (119875120579 119875119867) are sampled and storedat a 10-second intervalThe detection network uses 30 s of thestored data Instant value of the input data is also adopted bythe detection netTherefore input layer uses a total of 16 data4 samples of each term for the icing location estimationworkThis batching of the passed 30-second parameter estimatesand excitation measures were used to take advantage ofany consistent trends within the data However a delaytime of 30 s will be caused In previous paragraphs we havediscussed the tolerance of possible network detection errorAs the ice is modeled to accumulate over a long period andgenerally handling events will not take place in the absenceof pilot action this detection delay of 30 s is considered to beacceptable in our study

Once structure of the PNN detection net is decided adatabase for the training and test of the network needs to begenerated Basically this database is expected to envelope all


certain situations that might occur when the net is practicallydeployed In the current stage of our study four scenariosof the icing cases including clean wing tail and wing-tailboth icing are discussed For each icing case two shapesof the icing severity accretion model depicted in Figure 1will be included Moreover as discussed in the previoussection certain bias and an ldquoadvanced indicationrdquo might beencountered when the parameter ID technique is used Thenetwork is expected to tolerate such potential deficienciesA large volume of the parameter ID simulation needs to beincluded in order to capture the trends of the Hinf algorithmaverage performance

After a proper database is generated another issue whichwe need to consider is selecting from this database forthe net training and test data Typically data used for thenet training and test must be separated strictly also testdata generally should exceed about 25 of the entire datavolume with the intention that this could help to suppressthe ldquoathlete-refereerdquo problemmdashif the network is trained andtested based on a very same database (serving as both athleteand referee) although accuracy of the net could be achievedwith sufficient training efforts this network is still useless forthe practical deployment in the fact that this net has beenshaped particularly and exclusively for the training data [19]

In summary we have run simulations corresponding todifferent icing cases and icing severities as follows

(i) pattern 0 clean aircraft(ii) pattern 1 wing icing case moderate and severerapid

icing(iii) pattern 2 tail icing case moderate and severerapid

icing(iv) pattern 3 wing-tail both icing case moderate and

severerapid icing

Also in order to capture the richness of unknowndisturbancenoise impact on the system different samplepaths were repeated for each of the 4 patterns Totally 60simulations were performed for pattern 0 (clean aircraft) ofwhich 40 runs were used for training and the remaining 20for test In the 3 icing patterns for each icing severity shape20 simulations were performed for training and another 10for the test Eventually a database of 240 simulation runswas obtained wherein 160 were used for training and theremaining 80 for test For each sample run in the databasea simulation of 900 seconds was investigated As the networkis designed to decide icing location at an interval of 30 s 30decision points are induced by each sample run and totallythis database contains 7200 points of network employmentwherein 4800 are used for training and the remaining 2400for test Note that test data occupies 13 of the entire datavolume the ldquoathlete-refereerdquo problem could be avoided

In training stage of the PNNdetection net two parameterestimates (119862119898120572 119862119899120573) and the excitation measures of aircraft(119875120579 119875119867) are delivered to the input layer The input nodesadopt sampled data at 30 s 20 s and 10 s prior to thedecision time instantaneous value at the decision time isalso included Nodes within output layer of the detectionnet are assigned with corresponding patterns During the

Table 2 Detected result for each (actual) icing case

Network detected case (percent)Clean Wing Tail Both

Clean 9467 133 367 033Wing iced 383 9251 283 083Tail iced 417 150 9283 150Both iced 233 100 167 9500

0 1 2 30

1

2

3

4

5

6

7

8

Icing pattern

Erro

r of e

ach

patte

rn (

)

Wrong locationFalse clean

Figure 6 Network test error for each icing pattern

net training stage one parameter that we need to decideis spread or smoothing factor of the PNN decision-surfaceshape Generally a smaller spread yields a stricter standardfor pattern classifying of the training data Although higherpattern-recognition accuracy could be achieved for the train-ing data via a smaller spread choosing the decision surfaceconstructed might be too sharp for the test data and a largebias of the net test could be encounteredThe choice of spreadtherefore requires a balance between a ldquocauserdquo of training dataand ldquoeffectrdquo of the test data In our study the authors decidethat spread = 30 yields a balance between test accuracy andthe net complicatedness

Net test result is shown in Figures 6 and 7 detailedresults are characterized in Table 2 Note that in Figure 6and Table 2 detection error was discussed for each of thepatterns separately while Figure 7 investigates an overall testerror distribution versus the actual aircraft icing severityFrom Figure 6 and Table 2 false-alarm rate of the detectionnetwork or a positive icing indicating the clean case is533 In our study this false-alarm rate is considered to beacceptable For icing patterns of the aircraft possible erro-neous icing location decision was encountered as depictedby the deep-color line segments in Figure 6 A detailed resultis presented in Table 2 363 of wing icing 300 of tailicing and 267 of both icing test output yields a wronglocation although positive icing was decided Moreover we


0 005 01 015 02 025 030

1

2

3

4

5

6

7

8

Icing severity

Det

ectio

n er

ror d

istrib

utio

n (

)

Figure 7 Overall detection error versus aircraft (actual) icingseverity

are very concerned about ldquodanger raterdquo of icing detectionwhich in our study is defined as a false-clean indication foriced aircraft This sort of error is presented by light linesegments in Figure 6 and based on Table 2 it was decidedthat the danger rate of net test was 383 417 and 233for each icing pattern respectively In summary for all the2400 test samples of the detection net an overall error rate(including false alarm wrong-location decision and dangerrate) of 625 was achieved Distribution of the detectionerror versus local icing severity of the aircraft is depicted inFigure 7 The whole detection error was encountered in theicing severity threshold below 120578ice = 010 which is consideredto be accurate enough in the fact that as in [7] 5 levels ofthe icing severity 020 040 060 080 100 were adopted120578ice = 010 still belongs to the first level and even if a detectionerror was encountered the relatively low icing severity wouldexert very limited impact upon the aircraft especially as theice accretion takes place in a long period and handling eventgenerally will not happen as pilot action is not included

5 Concluding Remarks

This paper introduced a research work on the inflight param-eter identification and icing location detection for the icedaircraft As opposed to the previously reported work fora short period where the parameters were assumed to betime-invariant and a system excitation input was specificallydesigned this study considers the time-varying nature ofthe problem Ice accumulation is modeled as a continuousprocess where the effect of the ice upon aircraft dynamicsis assumed to be accreted over a long period Time-varyingalgorithm of the Hinf parameter identification techniquewas employed to provide inflight parameter estimates of theaircraftThis technique adopts exogenous disturbances as thesystem excitation only and no pilot action is included in theID framework Two stability parameters along longitudinaland lateraldirectional axis were particularly presented and

discussed Although certain delay of the ID algorithm doesexist it was considered to be acceptable The icing locationdetection work in this paper is constructed by using theprobabilistic neural network While different cases of theicing location are classified as different patterns in the netoutput layer input layer of the network adopts the Hinfparameter estimate results and also excitation measure of theaircraft All the input of the detection networkwas sampled atan interval of 10 s and the data were windowed at a period of30 s to take advantage of any potential consistent trendwithinthe data A database corresponding to different icing casesice accumulation processes and disturbancenoise paths wasgenerated for the net training and test Test result of theclean aircraft yields a false alarm rate of 533 also overalldetection error of the network is 625 A deeper probe intothe error distribution indicates that all the test errors wereencountered at the icing severity no more than 010 Whilethe aircraft with such low icing severity is believed to be withsufficient safety margin the detection network developed inthis paper is believed to be applicable for further studies

As explained in the paper direction of authorsrsquo work hasshifted slightly In our future works we will not spend muchof the time upon icing severity classification of the aircraftThe authors plan to further the detection work for moreicing cases (aircraft nose airspeed probe engine inlet etc)and more scenarios of the aircraft flight mission (landingtake-off etc) will be investigated Additionally although thelinearized model advanced by Brag has been used for manyyears accuracy of this model does warrant our close interestWe do hope to extract a more accurate as well as applicablemodel for the aircraft icing problem

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work is supported by Chinarsquos Aerospace Fund and alsoby Fudanrsquos Graduate Innovation Fund The authors are alsoindebted to Qin Lu and Lin Li from the Flight Test Sectionin Commercial Aircraft Corporation of China (COMAC) inShanghai China

References

[1] M Bragg ldquoAircraft aerodynamic effects due to large droplet iceaccretionsrdquo in Proceedings of the 34th AIAA Aerospace SciencesMeeting and Exhibit AIAA-96-0932 Reno Nev USA 1996

[2] ldquoAircraft accident report inflight icing encounter and loss ofcontrol ATR model 72-212 Roselawn Indiana October 311994rdquo Tech Rep NTSBAAR-9601 National TransportationSafety Board 1996

[3] InterimReport on theAccident on 1 June 2009 to theAirbusA330-203 Registered F-GZCP Operated by Air France Flight AF 447Rio de Janeiro-Paris Bureau dEnquetes et dAnalyses pour laSecurite de lAviation Civile (BEA) Paris France 2009


[4] ldquoSafety Investigation Following the Accident on 1st June 2009to the Airbus A330-203 Flight AF 447-Summaryrdquo (Englishedition) Paris Bureau drsquoEnquetes et drsquoAnalyses pour la securitede lrsquoAviation civile (BEA) 2012

[5] T P Ratvasky J F van Zante and J T Riley ldquoNASAFAATail-plane Icing Program Overviewrdquo Number AIAA-99-0370NASATM-1999-208901 1999

[6] M Brag W Perkins N Aarter et al ldquoAn interdisciplinaryapproach to inflight aircraft icing safetyrdquo in Proceedings of the36th AIAA Aerospace Sciences Meeting and Exhibit AIAA-98-0095 Reno Nevada 1998

[7] YDong and J Ai ldquoResearch on inflight parameter identificationand icing location detection of the aircraftrdquo Aerospace Scienceand Technology vol 29 no 1 pp 305ndash312 2013

[8] MBragg THutchison JMerret ROltman andD PokhariyalldquoEffects of ice accretion on aircraft flight dynamicsrdquo in Proceed-ings of the 38 th AIAA Aerospace Sciences Meeting and ExhibitAIAA-2000-0360 Reno Nev USA 2000

[9] J W Melody T Hillbrand T Basar and W R Perkins ldquoHinfinparameter identification for inflight detection of aircraft icingthe time-varying caserdquo Control Engineering Practice vol 9 no12 pp 1327ndash1335 2001

[10] Z P Fang W C Chen and S G Zhang Aerospace VehicleDynamics Beihang University Press Beijing China 1st edition2005

[11] M Bragg THutchison JMerret ROltman andD PokhariyalldquoEffects of ice accretion on aircraft flight dynamicsrdquo in Proceed-ings with the 38th AIAAAerospace SciencesMeeting and Exhibitnumber AIAA-2000-0360 Reno Nev USA 2000

[12] D Pokhariyal M Bragg T Hutchison and J Merret ldquoAircraftflight dynamics with simulated ice accretionrdquo in Proceedings ofthe 39th AIAA Aerospace Sciences Meeting and Exhibit AIAA-2001-0541 pp 2001ndash0541 Reno Nev USA 2001

[13] J W Melody T Basar W R Perkins and P G VoulgarisldquoParameter identification for inflight detection and character-ization of aircraft icingrdquo Control Engineering Practice vol 8 no9 pp 985ndash1001 2000

[14] T P Ratvasky and R J Ranaudo ldquoIcing effects on aircraft sta-bility and control determined from flight datardquo in Proceedingsof the 31st Aerospace Sciences Meeting and Exhibit Reno NevUSA 1993 number AIAA-93-0398

[15] G Didinsky Z Pan and T Basar ldquoParameter identification ofuncertain plants using119867infin methodrdquo Automatica vol 31 no 9pp 1227ndash1250 1995

[16] D F Specht ldquoProbabilistic neural networksrdquo Neural Networksvol 3 no 1 pp 109ndash118 1990

[17] D F Specht and P D Shapiro ldquoGeneralization accuracy ofprobabilistic neural networks compared with back-propagationnetworksrdquo Internal report of Lockheed Palo Alto ResearchLaboratory Lockheed Palo Alto Research Laboratory 1991

[18] J Melody D Pokhariyal J Merret et al ldquoSensor integrationfor inflight icing characterization using neural networksrdquo inProceedings of the 39th AIAA Aerospace Sciences Meeting andExhibit AIAA-2001-0542 Reno Nev USA 2001

[19] D F Zhang Application in the Design of Neural Networks UsingMATLAB China Machine Press Beijing China 2009

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



IPS was not activated timely or the IPS was activated but noteffective To ensure flight safety of the aircraft an overall sys-tematic inspection of the icing hazard needs to be conducted

Back to 1994 after the ATR-72 accidents NASA and FAAin United States cosponsored a four-year Tailplane Icing Pro-gram (TIP) whichwas expected to expand the understandingof the aircraft ice contaminated tailplane stall (ICTS) hazard[5] In 1998 after the closure of TIP Brag advanced an icingmanagement system (IMS) as an additional layer of defenseagainst the aircraft icing accidents [6] IMS adopts the coreeffect of ice accretion upon aircraftmdashthe modification ofaircraft stability and controllability while IMS provides acontinual monitoring of the aircraft icing status traditionalIPS devices could be activated automatically by the IMS anda reconfiguration of the inline flight control laws could beincluded so as to restrict the aircraft maneuver within aproper margin of safety

The Commercial Aircraft Corporation of China(COMAC) in Shanghai is en route to the production ofChinarsquos first generation of large civil aircraft Due to thehazardous effect upon aircraft performance and safety iceaccretion draws a strong concern from us According to theschedule the research work on aircraft icing mainly includesa CFD inspection of the ice accumulation and an icingwind-tunnel examination of aircraft and real flight testingmaneuvers are also necessary to either verify the wind tunnelresults or evaluate the effect of ice during critical stages ofthe aircraft mission (eg landingtakeoff cycle) Lastly aself-adaptive mechanism could be implemented in the inlineflight control laws design

The aircraft icing research in Fudan University is mainlyfocused on the dynamics and in future time the controlof iced aircraft Our current work is formulated to providean exploration for the inflight detectioncharacterization ofthe accretedaccreting ice upon the airframe after the overalltest procedure is completed a control aid for the pilots willbe developed In our work similar to IMS we adopt thecore effect of ice on aircraft performancemdashthe modificationof stability and controllability Parameter identification tech-nique is employed to provide inline estimates of the aircraftdynamic parameters after which the aircraft icing locationand severity could be decided In [7] we have discusseda work on inline icing location detection of the aircraftBaseline scenario of the work was selected as trimmed steadylevel flight it was assumed that the ice has completed theaccumulation on the airframe and the aircraft dynamicparameter remains time-invariant over the maneuver periodIdentification maneuver was induced by separated commandinput of the aircraft control surfaces in the hope that thecoupling motion along different axes of the aircraft was to besuppressed After the ID maneuver was finished ID resultswere delivered to the neural network to decide icing locationof the aircraft Due to current shortness of the aircraft icingdata only four scenarios of clean wing icing tail icing andwing-tail both icing cases were discussed A very high degreeof accuracy of icing location detection was accomplished inthe work

One problem of this work however is that it could onlyprovide indication of the aircraft icing over short period

Certainly the designed command input could be repeatedconstantly but through simulation it was found that overloadof the aircraft was relatively high and passenger-ride qualityof the aircraft shall not be guaranteed Also a constant inputof all the 3 control surfaces affects the aircraft state severelyit was hardly possible for the aircraft to maintain the initialsteady level flight In such senses while the work discussed in[7] could be employed for detection of aircraft icing over shortperiod a long-period continual monitoring of icing statuscould not depend upon it

And in this paper we try to fill this gap Specifically wetry to develop a framework that could continually monitorstatus of the aircraft and based on all the data availableinformation pertaining to aircraft icing could be estimatedIn Section 2 of this paper we build up a long-period icingmodel of the aircraft The icing severity was modeled toincrease with time based on which the effect of ice on aircraftdynamic parameters was to be accreted Section 3 introducesa Hinf parameter ID technique developed for the time-varying system This technique depends solely on exogenousdisturbance signals of the system and dynamic parametersof the system could be estimated As this ID techniquerequires no specific excitation from the system input andit adopts only the state vector of the aircraft it arises as aperfect tool for the long-period continual monitoring taskIn Section 4 based on the parameter estimation results fromHinf algorithm probabilistic neural network (PNN) wasemployed to decide location of the aircraft icing A databasefor the net training and test was generated in this section andtest result of the detection net was discussed Accuracy of theconstructed network is considered to be acceptable FinallySection 5 contains a general conclusion of this paper someissues that highlight our future direction are also discussed

2 Flight Dynamics Model

21 Ice Effect on Dynamics In [8] Bragg et al proposed arepresentative model of the ice effect on aircraft dynamics

119862(lowast)iced = 119862(lowast)clean (1 + 120578ice119896119862lowast) (1)

where 120578ice is an icing severity parameter 119896119862lowast is the coefficienticing weight which depends on the parameter being modi-fied 119862(lowast)clean is the clean (not iced) aircraft parameter and119862(lowast)iced indicates the iced parameter In our work dynamicmodel of the aircraft is established based on the NASA TwinOtter icing research airplane Both clean and iced parametersof this aircraft are detailed in Table 1 [8] The iced parametersin the table are representative of icing severity 120578ice = 02119896119862lowast could then be calculated as the associated slope fromparticular parameters under different icing locations In thispaper similar to [9] a long-period continuous accretion ofice is captured by setting 120578ice to increase with time Thedifferential equation

119889

119889119905120578ice = 1198731 (1 + 1198732120578ice) 119862120578 (2)

is used as the model of ice accumulating on airframe where119862120578 represents the conduciveness of the atmosphere to icing



(a)

1198621198850 119862119885120572 119862119885119902 119862119885120575119890 1198621199090 119870 1198621198980 119862119898120572 119862119898119902 119862119898120575119890


(b)

119862119884120573 119862119884119901 119862119884119903 119862119884120575119903 119862119897120573 119862119897119901 119862119897119903 119862119897120575119886 119862119897120575119903 119862119899120573 119862119899119901 119862119899119903 119862119899120575119886 119862119899120575119903




119862120578 (119905) =1

2[1 minus cos(2120587119905

119879cld)] + 119889120578 (3)



[120578ice(119879cld2)]2

1198731 =2

1198732119879cldln [1 + 1198732120578ice (119879cld)]

(4)




0 100 200 300 400 500 600 700 800 900minus005

0

005

01

015

02

025


Moderate icing

Clean aircraft

120578ic

e

t (s)




119908 asymp 119908

119908 asymp119908

119881

120573119908 asympV119908119881

(5)





= 119860 (119909 V) 120594 + 119887 (119909 V) + 119889119901

119910 = 119909 + 119889119898

(6)


119899







120594 = 119867120594 + 119870119889120594 1205941003816100381610038161003816119905=0 = 1205940 (7)






120594 = 1205940 (1 + 119870119862lowast120578ice) (8)


120594 = 1205940119870119862lowast1198731 (1 + 1198732120578ice) times 1

2[1 minus cos(2120587119905

119879cld)] + 119889120578

(9)


1205941003816100381610038161003816119905=0 = 1205940119870119862lowast1198731119889120578 (10)


1198671205940 + 119870119889120594 = 1205940119870119862lowast1198731119889120578 (11)





1003817100381710038171003817120594 minus 1205941003817100381710038171003817

2

119876

le 1205742[(10038171003817100381710038171003817119889119901

10038171003817100381710038171003817119868)2+ (

10038171003817100381710038171198891198981003817100381710038171003817119868)2+ (

10038171003817100381710038171003817119889120594

10038171003817100381710038171003817119868)2+ (

10038171003817100381710038171003817119889120578

10038171003817100381710038171003817119868)2

+(10038161003816100381610038161199090 minus 1199090

10038161003816100381610038161198750

)2+ (

1003816100381610038161003816120594 minus 120594010038161003816100381610038161198760

)2]

(12)



0






[

119909

120594] = [

0 119860 (119910 V)0 119867

][119909

120594] + [

119887 (119910 V)0

] + Σminus1[119868

0] (119910 minus 119909)

(13)


Σ = minus Σ [0 119860 (119910 V)0 119867

] minus [0 0

119860(119910 V)119879 119867119879]Σ

+ [119868 0


119868 0

0 119870119870119879]Σ

(14)





Σ = [

[

Σ1 Σ2

Σ1198792 Σ3

]

]

(15)




















IcedClean

IcedClean

0 100 200 300 400 500 600 700 800 90050

60

70

80Ve

loci

ty (m

s)

t (s)

0 100 200 300 400 500 600 700 800 9000

1

2

3

Ang

le o

f atta

ck (d

eg)

t (s)0 100 200 300 400 500 600 700 800 900

minus2

minus1

0

1

2

Rolli

ng an

gle (

deg)

t (s)

0 100 200 300 400 500 600 700 800 900minus01

minus005

0

005

01

gy (g

)

t (s)

0 100 200 300 400 500 600 700 800 9000

1000

2000

3000

4000

Alti

tude

(m)

t (s)0 100 200 300 400 500 600 700 800 900

minus14

minus12

minus1

minus08

minus06

gz (g

)

t (s)

0 100 200 300 400 500 600 700 800 900minus10

minus5

0

5

10

Pitc

h an

gle (

deg)

t (s)

0 100 200 300 400 500 600 700 800 900minus2

minus1

0

1

2

Side

slip

angl

e (de

g)

t (s)







0 100 200 300 400 500 600 700 800 90008

085

09

095

1

105



0 100 200 300 400 500 600 700 800 90006

065

07

075

08

085

09

095

1

105

11

t (s) t (s)

Nor

mal

ized

Cm120572

estim

ate

Nor

mal

ized

Cn120573

estim

ate


0 100 200 300 400 500 600 700 800 90008

085

09

095

1

105


t (s)


t (s)

Nor

mal

ized

Cm120572

estim

ate

Nor

mal

ized

Cn120573

estim

ate

0 100 200 300 400 500 600 700 800 90006

065

07

075

08

085

09

095

1

105

11







0 100 200 300 400 500 600 700 800 90008

085

09

095

1

105

0 100 200 300 400 500 600 700 800 90006

065

07

075

08

085

09

095

1

105

11



t (s) t (s)

Nor

mal

ized

Cm120572

estim

ate

Nor

mal

ized

Cn120573

estim

ate















severerapid icing






0 1 2 30

1

2

3

4

5

6

7

8

Icing pattern

Erro

r of e

ach

patte

rn (

)






0 005 01 015 02 025 030

1

2

3

4

5

6

7

8

Icing severity

Det

ectio

n er

ror d

istrib

utio

n (

)









Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











(a)

1198621198850 119862119885120572 119862119885119902 119862119885120575119890 1198621199090 119870 1198621198980 119862119898120572 119862119898119902 119862119898120575119890


(b)

119862119884120573 119862119884119901 119862119884119903 119862119884120575119903 119862119897120573 119862119897119901 119862119897119903 119862119897120575119886 119862119897120575119903 119862119899120573 119862119899119901 119862119899119903 119862119899120575119886 119862119899120575119903




119862120578 (119905) =1

2[1 minus cos(2120587119905

119879cld)] + 119889120578 (3)



[120578ice(119879cld2)]2

1198731 =2

1198732119879cldln [1 + 1198732120578ice (119879cld)]

(4)




0 100 200 300 400 500 600 700 800 900minus005

0

005

01

015

02

025


Moderate icing

Clean aircraft

120578ic

e

t (s)




119908 asymp 119908

119908 asymp119908

119881

120573119908 asympV119908119881

(5)





= 119860 (119909 V) 120594 + 119887 (119909 V) + 119889119901

119910 = 119909 + 119889119898

(6)


119899







120594 = 119867120594 + 119870119889120594 1205941003816100381610038161003816119905=0 = 1205940 (7)






120594 = 1205940 (1 + 119870119862lowast120578ice) (8)


120594 = 1205940119870119862lowast1198731 (1 + 1198732120578ice) times 1

2[1 minus cos(2120587119905

119879cld)] + 119889120578

(9)


1205941003816100381610038161003816119905=0 = 1205940119870119862lowast1198731119889120578 (10)


1198671205940 + 119870119889120594 = 1205940119870119862lowast1198731119889120578 (11)





1003817100381710038171003817120594 minus 1205941003817100381710038171003817

2

119876

le 1205742[(10038171003817100381710038171003817119889119901

10038171003817100381710038171003817119868)2+ (

10038171003817100381710038171198891198981003817100381710038171003817119868)2+ (

10038171003817100381710038171003817119889120594

10038171003817100381710038171003817119868)2+ (

10038171003817100381710038171003817119889120578

10038171003817100381710038171003817119868)2

+(10038161003816100381610038161199090 minus 1199090

10038161003816100381610038161198750

)2+ (

1003816100381610038161003816120594 minus 120594010038161003816100381610038161198760

)2]

(12)



0






[

119909

120594] = [

0 119860 (119910 V)0 119867

][119909

120594] + [

119887 (119910 V)0

] + Σminus1[119868

0] (119910 minus 119909)

(13)


Σ = minus Σ [0 119860 (119910 V)0 119867

] minus [0 0

119860(119910 V)119879 119867119879]Σ

+ [119868 0


119868 0

0 119870119870119879]Σ

(14)





Σ = [

[

Σ1 Σ2

Σ1198792 Σ3

]

]

(15)




















IcedClean

IcedClean

0 100 200 300 400 500 600 700 800 90050

60

70

80Ve

loci

ty (m

s)

t (s)

0 100 200 300 400 500 600 700 800 9000

1

2

3

Ang

le o

f atta

ck (d

eg)

t (s)0 100 200 300 400 500 600 700 800 900

minus2

minus1

0

1

2

Rolli

ng an

gle (

deg)

t (s)

0 100 200 300 400 500 600 700 800 900minus01

minus005

0

005

01

gy (g

)

t (s)

0 100 200 300 400 500 600 700 800 9000

1000

2000

3000

4000

Alti

tude

(m)

t (s)0 100 200 300 400 500 600 700 800 900

minus14

minus12

minus1

minus08

minus06

gz (g

)

t (s)

0 100 200 300 400 500 600 700 800 900minus10

minus5

0

5

10

Pitc

h an

gle (

deg)

t (s)

0 100 200 300 400 500 600 700 800 900minus2

minus1

0

1

2

Side

slip

angl

e (de

g)

t (s)







0 100 200 300 400 500 600 700 800 90008

085

09

095

1

105



0 100 200 300 400 500 600 700 800 90006

065

07

075

08

085

09

095

1

105

11

t (s) t (s)

Nor

mal

ized

Cm120572

estim

ate

Nor

mal

ized

Cn120573

estim

ate


0 100 200 300 400 500 600 700 800 90008

085

09

095

1

105


t (s)


t (s)

Nor

mal

ized

Cm120572

estim

ate

Nor

mal

ized

Cn120573

estim

ate

0 100 200 300 400 500 600 700 800 90006

065

07

075

08

085

09

095

1

105

11







0 100 200 300 400 500 600 700 800 90008

085

09

095

1

105

0 100 200 300 400 500 600 700 800 90006

065

07

075

08

085

09

095

1

105

11



t (s) t (s)

Nor

mal

ized

Cm120572

estim

ate

Nor

mal

ized

Cn120573

estim

ate















severerapid icing






0 1 2 30

1

2

3

4

5

6

7

8

Icing pattern

Erro

r of e

ach

patte

rn (

)






0 005 01 015 02 025 030

1

2

3

4

5

6

7

8

Icing severity

Det

ectio

n er

ror d

istrib

utio

n (

)









Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













= 119860 (119909 V) 120594 + 119887 (119909 V) + 119889119901

119910 = 119909 + 119889119898

(6)


119899







120594 = 119867120594 + 119870119889120594 1205941003816100381610038161003816119905=0 = 1205940 (7)






120594 = 1205940 (1 + 119870119862lowast120578ice) (8)


120594 = 1205940119870119862lowast1198731 (1 + 1198732120578ice) times 1

2[1 minus cos(2120587119905

119879cld)] + 119889120578

(9)


1205941003816100381610038161003816119905=0 = 1205940119870119862lowast1198731119889120578 (10)


1198671205940 + 119870119889120594 = 1205940119870119862lowast1198731119889120578 (11)





1003817100381710038171003817120594 minus 1205941003817100381710038171003817

2

119876

le 1205742[(10038171003817100381710038171003817119889119901

10038171003817100381710038171003817119868)2+ (

10038171003817100381710038171198891198981003817100381710038171003817119868)2+ (

10038171003817100381710038171003817119889120594

10038171003817100381710038171003817119868)2+ (

10038171003817100381710038171003817119889120578

10038171003817100381710038171003817119868)2

+(10038161003816100381610038161199090 minus 1199090

10038161003816100381610038161198750

)2+ (

1003816100381610038161003816120594 minus 120594010038161003816100381610038161198760

)2]

(12)



0






[

119909

120594] = [

0 119860 (119910 V)0 119867

][119909

120594] + [

119887 (119910 V)0

] + Σminus1[119868

0] (119910 minus 119909)

(13)


Σ = minus Σ [0 119860 (119910 V)0 119867

] minus [0 0

119860(119910 V)119879 119867119879]Σ

+ [119868 0


119868 0

0 119870119870119879]Σ

(14)





Σ = [

[

Σ1 Σ2

Σ1198792 Σ3

]

]

(15)




















IcedClean

IcedClean

0 100 200 300 400 500 600 700 800 90050

60

70

80Ve

loci

ty (m

s)

t (s)

0 100 200 300 400 500 600 700 800 9000

1

2

3

Ang

le o

f atta

ck (d

eg)

t (s)0 100 200 300 400 500 600 700 800 900

minus2

minus1

0

1

2

Rolli

ng an

gle (

deg)

t (s)

0 100 200 300 400 500 600 700 800 900minus01

minus005

0

005

01

gy (g

)

t (s)

0 100 200 300 400 500 600 700 800 9000

1000

2000

3000

4000

Alti

tude

(m)

t (s)0 100 200 300 400 500 600 700 800 900

minus14

minus12

minus1

minus08

minus06

gz (g

)

t (s)

0 100 200 300 400 500 600 700 800 900minus10

minus5

0

5

10

Pitc

h an

gle (

deg)

t (s)

0 100 200 300 400 500 600 700 800 900minus2

minus1

0

1

2

Side

slip

angl

e (de

g)

t (s)







0 100 200 300 400 500 600 700 800 90008

085

09

095

1

105



0 100 200 300 400 500 600 700 800 90006

065

07

075

08

085

09

095

1

105

11

t (s) t (s)

Nor

mal

ized

Cm120572

estim

ate

Nor

mal

ized

Cn120573

estim

ate


0 100 200 300 400 500 600 700 800 90008

085

09

095

1

105


t (s)


t (s)

Nor

mal

ized

Cm120572

estim

ate

Nor

mal

ized

Cn120573

estim

ate

0 100 200 300 400 500 600 700 800 90006

065

07

075

08

085

09

095

1

105

11







0 100 200 300 400 500 600 700 800 90008

085

09

095

1

105

0 100 200 300 400 500 600 700 800 90006

065

07

075

08

085

09

095

1

105

11



t (s) t (s)

Nor

mal

ized

Cm120572

estim

ate

Nor

mal

ized

Cn120573

estim

ate















severerapid icing






0 1 2 30

1

2

3

4

5

6

7

8

Icing pattern

Erro

r of e

ach

patte

rn (

)






0 005 01 015 02 025 030

1

2

3

4

5

6

7

8

Icing severity

Det

ectio

n er

ror d

istrib

utio

n (

)









Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Σ = [

[

Σ1 Σ2

Σ1198792 Σ3

]

]

(15)




















IcedClean

IcedClean

0 100 200 300 400 500 600 700 800 90050

60

70

80Ve

loci

ty (m

s)

t (s)

0 100 200 300 400 500 600 700 800 9000

1

2

3

Ang

le o

f atta

ck (d

eg)

t (s)0 100 200 300 400 500 600 700 800 900

minus2

minus1

0

1

2

Rolli

ng an

gle (

deg)

t (s)

0 100 200 300 400 500 600 700 800 900minus01

minus005

0

005

01

gy (g

)

t (s)

0 100 200 300 400 500 600 700 800 9000

1000

2000

3000

4000

Alti

tude

(m)

t (s)0 100 200 300 400 500 600 700 800 900

minus14

minus12

minus1

minus08

minus06

gz (g

)

t (s)

0 100 200 300 400 500 600 700 800 900minus10

minus5

0

5

10

Pitc

h an

gle (

deg)

t (s)

0 100 200 300 400 500 600 700 800 900minus2

minus1

0

1

2

Side

slip

angl

e (de

g)

t (s)







0 100 200 300 400 500 600 700 800 90008

085

09

095

1

105



0 100 200 300 400 500 600 700 800 90006

065

07

075

08

085

09

095

1

105

11

t (s) t (s)

Nor

mal

ized

Cm120572

estim

ate

Nor

mal

ized

Cn120573

estim

ate


0 100 200 300 400 500 600 700 800 90008

085

09

095

1

105


t (s)


t (s)

Nor

mal

ized

Cm120572

estim

ate

Nor

mal

ized

Cn120573

estim

ate

0 100 200 300 400 500 600 700 800 90006

065

07

075

08

085

09

095

1

105

11







0 100 200 300 400 500 600 700 800 90008

085

09

095

1

105

0 100 200 300 400 500 600 700 800 90006

065

07

075

08

085

09

095

1

105

11



t (s) t (s)

Nor

mal

ized

Cm120572

estim

ate

Nor

mal

ized

Cn120573

estim

ate















severerapid icing






0 1 2 30

1

2

3

4

5

6

7

8

Icing pattern

Erro

r of e

ach

patte

rn (

)






0 005 01 015 02 025 030

1

2

3

4

5

6

7

8

Icing severity

Det

ectio

n er

ror d

istrib

utio

n (

)









Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










IcedClean

IcedClean

0 100 200 300 400 500 600 700 800 90050

60

70

80Ve

loci

ty (m

s)

t (s)

0 100 200 300 400 500 600 700 800 9000

1

2

3

Ang

le o

f atta

ck (d

eg)

t (s)0 100 200 300 400 500 600 700 800 900

minus2

minus1

0

1

2

Rolli

ng an

gle (

deg)

t (s)

0 100 200 300 400 500 600 700 800 900minus01

minus005

0

005

01

gy (g

)

t (s)

0 100 200 300 400 500 600 700 800 9000

1000

2000

3000

4000

Alti

tude

(m)

t (s)0 100 200 300 400 500 600 700 800 900

minus14

minus12

minus1

minus08

minus06

gz (g

)

t (s)

0 100 200 300 400 500 600 700 800 900minus10

minus5

0

5

10

Pitc

h an

gle (

deg)

t (s)

0 100 200 300 400 500 600 700 800 900minus2

minus1

0

1

2

Side

slip

angl

e (de

g)

t (s)







0 100 200 300 400 500 600 700 800 90008

085

09

095

1

105



0 100 200 300 400 500 600 700 800 90006

065

07

075

08

085

09

095

1

105

11

t (s) t (s)

Nor

mal

ized

Cm120572

estim

ate

Nor

mal

ized

Cn120573

estim

ate


0 100 200 300 400 500 600 700 800 90008

085

09

095

1

105


t (s)


t (s)

Nor

mal

ized

Cm120572

estim

ate

Nor

mal

ized

Cn120573

estim

ate

0 100 200 300 400 500 600 700 800 90006

065

07

075

08

085

09

095

1

105

11







0 100 200 300 400 500 600 700 800 90008

085

09

095

1

105

0 100 200 300 400 500 600 700 800 90006

065

07

075

08

085

09

095

1

105

11



t (s) t (s)

Nor

mal

ized

Cm120572

estim

ate

Nor

mal

ized

Cn120573

estim

ate















severerapid icing






0 1 2 30

1

2

3

4

5

6

7

8

Icing pattern

Erro

r of e

ach

patte

rn (

)






0 005 01 015 02 025 030

1

2

3

4

5

6

7

8

Icing severity

Det

ectio

n er

ror d

istrib

utio

n (

)









Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 100 200 300 400 500 600 700 800 90008

085

09

095

1

105



0 100 200 300 400 500 600 700 800 90006

065

07

075

08

085

09

095

1

105

11

t (s) t (s)

Nor

mal

ized

Cm120572

estim

ate

Nor

mal

ized

Cn120573

estim

ate


0 100 200 300 400 500 600 700 800 90008

085

09

095

1

105


t (s)


t (s)

Nor

mal

ized

Cm120572

estim

ate

Nor

mal

ized

Cn120573

estim

ate

0 100 200 300 400 500 600 700 800 90006

065

07

075

08

085

09

095

1

105

11







0 100 200 300 400 500 600 700 800 90008

085

09

095

1

105

0 100 200 300 400 500 600 700 800 90006

065

07

075

08

085

09

095

1

105

11



t (s) t (s)

Nor

mal

ized

Cm120572

estim

ate

Nor

mal

ized

Cn120573

estim

ate















severerapid icing






0 1 2 30

1

2

3

4

5

6

7

8

Icing pattern

Erro

r of e

ach

patte

rn (

)






0 005 01 015 02 025 030

1

2

3

4

5

6

7

8

Icing severity

Det

ectio

n er

ror d

istrib

utio

n (

)









Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 100 200 300 400 500 600 700 800 90008

085

09

095

1

105

0 100 200 300 400 500 600 700 800 90006

065

07

075

08

085

09

095

1

105

11



t (s) t (s)

Nor

mal

ized

Cm120572

estim

ate

Nor

mal

ized

Cn120573

estim

ate















severerapid icing






0 1 2 30

1

2

3

4

5

6

7

8

Icing pattern

Erro

r of e

ach

patte

rn (

)






0 005 01 015 02 025 030

1

2

3

4

5

6

7

8

Icing severity

Det

ectio

n er

ror d

istrib

utio

n (

)









Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















severerapid icing






0 1 2 30

1

2

3

4

5

6

7

8

Icing pattern

Erro

r of e

ach

patte

rn (

)






0 005 01 015 02 025 030

1

2

3

4

5

6

7

8

Icing severity

Det

ectio

n er

ror d

istrib

utio

n (

)









Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 005 01 015 02 025 030

1

2

3

4

5

6

7

8

Icing severity

Det

ectio

n er

ror d

istrib

utio

n (

)









Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Research Article Inflight Parameter Identification and Icing ...downloads.hindawi.com/journals/jcse/2014/396532.pdfResearch Article Inflight Parameter Identification and Icing Location