Overview of Recent Flight Flutter Testing Research at … Technical Memorandum 4792 Overview of Recent Flight Flutter Testing Research at NASA Dryden April 1997 Martin J. Brenner,

NASA Technical Memorandum 4792

Overview of Recent Flight Flutter Testing Researchat NASA Dryden

April 1997

Martin J. Brenner, Richard C. Lind, and David F. Voracek

NASA Technical Memorandum 4792

National Aeronautics and Space Administration

Office of Management

Scientific and Technical Information Program

1997


Dryden Flight Research CenterEdwards, California

Overview of Recent FlightFlutter Testing Researchat NASA Dryden

OVERVIEW OF RECENT FLIGHT FLUTTERTESTING RESEARCH AT NASA DRYDEN

Martin J. Brenner,* Richard C. Lind,† David F. Voracek‡

NASA Dryden Flight Research CenterEdwards, California

Abstract

In response to the concerns of the aeroelasticcommunity, NASA Dryden Flight Research Center,Edwards, California, is conducting researchinto improving the flight flutter (includingaeroservoelasticity) test process with more accurate andautomated techniques for stability boundary prediction.The important elements of this effort so far include thefollowing: 1) excitation mechanisms for enhancedvibration data to reduce uncertainty levels in stabilityestimates; 2) investigation of a variety of frequency,time, and wavelet analysis techniques for signalprocessing, stability estimation, and nonlinearidentification; and 3) robust flutter boundary predictionto substantially reduce the test matrix for flutterclearance. These are critical research topics addressingthe concerns of a recent AGARD Specialists’ Meeting onAdvanced Aeroservoelastic Testing and Data Analysis.This paper addresses these items using flight test datafrom the F/A-18 Systems Research Aircraft and theF/A-18 High Alpha Research Vehicle.

Nomenclature

a wavelet scaling parameter

AGARD Advisory Group for Aerospace Research and Development

AOA angle of attack

*Research Engineer, NASA, Dryden Flight Research Center, MS4840D/RS, Edwards, CA 93523-0273, 805.258.3793, [email protected].

†NRC Post Doctoral Research Fellow, NASA, Dryden FlightResearch Center, MS 4840D/RS, Edwards, CA 93523-0273, 805.258.3075, [email protected], Member AIAA.

‡Research Engineer, NASA, Dryden Flight Research Center, MS4840D/RS, Edwards, CA 93523-0273, 805.258.2463, [email protected]. Senior Member AIAA.

Copyright 1997 by the American Institute of Aeronautics andAstronautics, Inc. No copyright is asserted in the United States underTitle 17, U.S. Code. The U.S. Government has a royalty-free license toexercise all rights under the copyright claimed herein for Governmentalpurposes. All other rights are reserved by the copyright owner.

1American Institute of Aero

AR autoregressive

ASE aeroservoelastic

CWT continuous wavelet coefficient

ERA eigensystem realization algorithm

FFT fast Fourier transform

FORSE Frequency domain Observability Range Space Extraction

G spectral estimate

h(t) wavelet basis function

transfer function estimates

HARV High Alpha Research Vehicle

norm supremum norm over finite magnitude transfer functions

ID identification

IV instrumental variable estimation

k summation index

norm induced norm over signals of finite magnitude

norm norm of signals that are square integrable

norm induced norm over signals of finite

magnitude impulse response

LS least squares

Mach, critical flight parameters

MEM maximum entropy method

MIMO multi-input–multi-output

MLE maximum likelihood estimation

N4SID numerical algorithms for subspace state- space system identification

OBES on-board excitation system

OKID Observer/Kalman filter identification

H1 H2 Hv, ,

H∞

l1

l2

l∞

q

nautics and Astronautics

ORSE Observability Range Space Extraction

PEM prediction error method

pk computational method for unsteady aerodynamics

PSD power spectral density

psf pounds per square foot

dynamic pressure

SISO single-input–single-output

sps samples per second

SRA Systems Research Aircraft

t time

T transform of x(t)

TVCS thrust vectoring control system

input uncertainty weighting

x(t) time domain data

X(t,ω) time-frequency domain data

Subscripts

x, y input and output data for spectral estimates

Symbols

parametric variation of dynamic pressure

input multiplicative uncertainty

real parametric modal uncertainty

µ structured singular value

τ wavelet time shift parameter

ω radian frequency

* complex conjugate transpose

summation

Introduction

Flight flutter testing continues to be a challengingresearch area because of the concerns with cost, time,and safety in expanding the envelope of new or modifiedaircraft. Testing is often done at stabilized test points togenerate numerous data sets while attempting toestimate aeroelastic stability in an accurate and efficientmanner. Parameter estimation methods generallyproduce inconsistent results because of poor excitation,closely spaced modes, noisy data, nonlinearities, andlow modal stability levels. Flutter test procedures are

desired which will dramatically reduce test time,increase reliability, and provide accurate andconservative results.

In response to the concerns of the aeroelasticcommunity and in-house requirements, NASA DrydenFlight Research Center, Edwards, California, isconducting research into improving the flight flutter testprocess (including aeroservoelasticity) with moreaccurate and automated techniques for stabilityboundary prediction. The important elements of thiseffort so far include the following research:

1. Excitation mechanisms are being studied forenhanced vibration data to reduce uncertaintylevels in stability estimates. A wingtipaerodynamic excitation system was used forimproved aeroelastic excitation, and signalsgenerated from a flight control system wereprogrammed to activate the control surfaces foraeroservoelastic excitation.

2. A variety of frequency, time, and wavelet analysistechniques are being investigated for signalprocessing, stability estimation, and systemidentification. Traditional Fourier methods forfrequency response are being augmented withautoregressive estimation methods. Numerousalgorithms to estimate stability parameters andsystem dynamic models are being compared forefficiency and reliability. Time-frequency signalprocessing techniques are used for filtering, systemidentification, and detection of nonlinearities.

3. Robust flutter boundary prediction methods arebeing developed to substantially reduce the testmatrix for flutter clearance. These methods rely onidentification consistent with the uncertaintystructure in an aeroelastic model, thereby providingan explicit measure of stability for robust modelvalidation. Accounting for the uncertainty structurein this manner guarantees that any system willremain stable within a confidence bound.

These are critical research topics addressing theconcerns of a recent AGARD Specialists’ Meeting onAdvanced Aeroservoelastic Testing and Data Analysis.This paper addresses these items using a wingtipaerodynamic structural excitation system on the F/A-18Systems Research Aircraft (SRA) and an oscillatingcontrol surface excitation system on the F/A-18 HighAlpha Research Vehicle (HARV).

A flight flutter research program was initiated on theF/A-18 SRA in late 1994. The purpose of the SRA

q

Win

δq

∆in

∆modes

∑

2American Institute of Aeronautics and Astronautics

structural dynamics research to date was to accomplishthe following:

• Study the integrity and effectiveness of theexcitation system in a wide variety of subsonic,transonic, and supersonic test conditions.

• Investigate data properties over a range of linear andlogarithmic sinusoidal inputs at different forcelevels in a flight flutter test environment. Compareanalysis algorithms in the frequency, time, andwavelet domains using the time-varying data sets.

• Identify nonlinear behavior, such as that resultingfrom transonic dynamics.

• Create a comprehensive data base of transient flightflutter data for the aeroelasticity and systemidentification disciplines to support development ofadvanced flight flutter test and analysis methods.

This paper presents F/A-18 SRA flight test results andanalyses using the wingtip exciter. Preliminary resultsfrom the F/A-18 HARV aircraft using an on-boardexcitation system (OBES) for control surface excitationare also presented. Flight flutter test techniqueresearch was conducted on the F/A-18 HARV tostudy the effectiveness of Schroeder-pulsed and sinc-pulse waveforms as excitation signals. Present modalestimation methods are reviewed, followed by an outlineof the robust aeroelastic model development, with theultimate objective being model validation for robust

flutter boundary prediction. A novel procedure forcomputing the robust flutter boundary from flight-derived uncertainty models, using the structuredsingular value (µ), is introduced.

Aircraft Descriptions of theF/A-18 SRA and HARV

The F/A-18 SRA aircraft is being flight tested at theNASA Dryden Flight Research Center primarily forflight systems experiments such as optical sensing, newactuation concepts, smart structures, and advancedairdata and flight control systems. Generally, it is verymuch like a standard production F/A-18. A major leftwing structural modification was done, however, on theSRA aircraft to allow for testing of several hydraulic andelectromechanical advanced aileron actuator concepts.Because the test actuators may be larger than thestandard one, a fitting called a ‘hinge-half’ supportingthe aileron hinge, the actuator, and a fairing had to bereplaced by larger and heavier items. A total of about35 lb was added to the wing. Table 1 lists calculatedmodal frequencies for symmetric and antisymmetricmodes for the F/A-18 SRA aircraft with left wingmodifications.

Another F/A-18 aircraft (fig. 1) was modifiedat NASA Dryden to perform flight research at highangle-of-attack (AOA) using thrust vectoring andincorporating control law concepts for agility and


Table 1. F/A-18 SRA with left wing modifications and without wingtip exciter: calculatedelastic modal frequencies. Fuel loading is FULL.

Symmetric mode Hz Antisymmetric mode Hz

Wing first bending 5.59 Fuselage first bending 8.15

Fuselage first bending 9.30 Wing first bending 8.84

Stabilator first bending 13.21 Stabilator first bending 12.98

Wing first torsion 13.98 Wing first torsion 14.85

Vertical tail first bending 16.83 Vertical Tail first bending 15.61

Wing second bending 16.95 Wing second bending 16.79

Wing outboard torsion 17.22 Fuselage second bending 18.62

Fuselage second bending 19.81 Trailing edge flap rotation 23.47

Trailing edge flap rotation 23.70 Fuselage torsion 24.19

Stabilator fore and aft 28.31 Launcher rail lateral 24.35

Wing second torsion 29.88 Stabilator fore and aft 28.58

Fuselage third bend, aileron rotation 33.44 Wing second torsion 29.93

Aileron torsion 38.60 Aft fuselage torsion 37.80

Stabilator second bending, wing third bending

43.17 Wing pitch 39.18

Figure 1. F/A-18 HARV.

performance enhancement, as well as providing data forcorrelation with computational fluid dynamics solutions.This vehicle is called the High-Alpha Research Vehiclewith Thrust Vectoring Control System (HARV-TVCS),referred to simply as the HARV throughout this report.As opposed to the SRA, the HARV was structurally verydifferent from a standard F/A-18 aircraft, as can be seenby comparing the HARV modal data in table 2 with theSRA data in table 1.

Modifications include addition of Inconel® vanes ineach engine exhaust for thrust vectoring andcorresponding ballast in the forward fuselage tomaintain the aircraft center-of-gravity location. Alsoadded were a research flight control system for feedbackcontrol of aerodynamic surfaces and the vanes, aninertial navigation system for AOA and sideslip ratefeedbacks, wingtip AOA vanes and pressure probes(for airdata research purposes), and additional


Table 2. F/A-18 HARV-TVCS calculated elastic modal frequencies. Fuel loadingis FULL.

Symmetric mode Hz Antisymmetric mode Hz

Wing first bending 5.72 Fuselage first bending 6.81

Fuselage first bending 7.45 Wing first bending 8.91

Wing first torsion 11.64 Wing first torsion 11.91

Stabilator first bending 13.68 Stabilator first bending 13.65

Wing fore-aft 18.10 Wing fore-aft 15.07

Vertical tail first bending 15.93 Vertical tail first bending 15.63

Wing second bending 17.04 Fuselage first torsion 18.82

Fuselage second bending 15.32 Fuselage second bending 21.03

Exhaust vane rotation 22.10 Exhaust vane rotation 22.10

Inboard flap rotation 23.47 Inboard flap rotation 23.03

Stabilator fore-aft 27.33 Fore-fuselage torsion 23.97

®Inconel is a registered trademark of Huntington Alloy ProductsDiv., International Nickel Co., Huntington, West Virigina.

instrumentation for loads, vane temperatures, andstructural dynamics.1

Excitation Systems

This section describes the excitation systems used foraeroelastic response on the SRA and aeroservoelasticexcitation of the F/A-18 HARV aircraft. Systemdescriptions, test procedures, flight experience, and testresults are discussed for each aircraft.

Wingtip Aeroelastic Excitation

Aeroelastic excitation of the F/A-18 SRA is discussedin this section. Details of the system and flight testingexperience is supplemented with flight test results.

System Description

The structural modifications to the SRA prompted aflight flutter envelope expansion and follow-on extensiveaeroelastic excitation research program with a dualwingtip structural excitation system. Figure 2 shows thiswingtip excitation system is a modification of the singlewingtip version used on an F-16XL.2 Exciters were15 lb mounted on each wingtip. The difference in modalfrequencies with exciters and without exciters (table 1)averaged 0.15 Hz with a maximum of 0.72 Hz. Eachexciter has a small fixed aerodynamic vane forward of arotating slotted hollow cylinder (fig. 2). When the

cylinder rotates, the aerodynamic pressure distributionon the vane generates a force changing at twice thecylinder rotation frequency. The vane is controlled froma cockpit control box which activates an avionics boxmounted in the instrumentation bay. The avionics boxpowers a variable-speed motor in the vane exciterassembly. Two force levels are possible by adjusting theslot openings to 25 percent (low-force, inner cylinderclosed) or 75 percent (high-force, inner cylinder open).Three possible positions for the exciters were mid-wingtip, forward wingtip at the wingtip leading edge,and aft wingtip near the wingtip trailing edge (fig. 2).

Other flight programs3,4,5 have used this system withvarying degrees of success. In particular, the dual systemoperates either symmetrically or antisymmetrically byattempting to maintain a constant (0° or 180°,respectively) phase relationship between exciters. Athigher dynamic pressure, the exciters were known toexhibit erratic phase-gain behavior due to binding inboth the motor drive mechanism and rotating cylinders.5

Testing at Dryden exhibited the same type ofcharacteristics with the exciters on the F/A-18 SRA.Figure 3 shows an example of phase difference betweenright- and left-wing exciters for both low and highdynamic pressure. At low dynamic pressure, the phasebetween exciters is relatively constant near zerocompared with the high dynamic pressure condition,where the phase varies randomly. Most conditions tested


Figure 2. Wingtip exciter for F/A-18 SRA (right) and installed on the aircraft in the aft wingtip position (left).

EC 95-42988-14 920765

Outer cylinder

Inner cylinder

Plug

Fairing

Strain guage

Figure 3. Phase between left and right wingtip exciter force inputs for symmetric excitation. Low dynamic pressure at175 psf (left). High dynamic pressure at 1123 psf (right).

0 5 10 15 20 25 30 35 40Frequency, Hz

Phase between symmetric exciters, q = 1123

0 5 10 15 20 25 30 35 40

200

150

100

50

0

– 50

– 100

– 150

– 200

Phase, deg

Frequency, Hz

Phase between symmetric exciters, q = 175

970218

had some phase discrepancy of the measured forcewhich was caused by both the phase degradation in theindividual exciters and to asymmetries in the aeroelasticdynamics of the aircraft. However, the phasediscrepancies did not detract from the effectiveness ofthe structural excitation, and it was still possible toextract the proper transfer functions from each exciter tothe individual accelerometer responses.6 Furthermore,both symmetric and antisymmetric modes were excitedfor a particular sweep, whether it was a symmetric orantisymmetric sweep.

Test Procedure

Linear and logarithmic sinusoidal sweeps up to 40 Hzwere used on the F/A-18 SRA, although the exciter iscapable of sweeping to 50 Hz. The exciters weremounted on the wingtip launcher rails in forward and aftposition, independently. They were operated in bothlow-force and high-force modes for 15-, 30-, or 60-sec

forward and reverse frequency sweeps. Some sweepswere actually multiples of two or four shorter durationsweeps with no interrupt. Generally sweeps wereperformed for symmetric and antisymmetric excitationin each configuration. A total of 260 test points wereflown with the exciters in one or more of these optionalconfigurations at the specified flight condition. The testparameters are summarized in table 3.

These test points were conducted to determine theexcitation system effectiveness in the subsonic,transonic, and supersonic regimes. Frequency rangeswere chosen to excite the primary modes used in theaeroelastic analysis, shown in table 1. A 3–12 Hz sweepattempted to distinguish the first wing and fuselagebending modes, and the 25–35 Hz sweep was done toexcite the aileron rotation mode for detection of anytransonic aileron buzz phenomena. Accelerationmeasurements were taken at 200 sps from the fore andaft wingtips, ailerons, and vertical and horizontal tails.


Table 3. F/A-18 SRA aeroelastic flight test matrix.

Exciter configuration Symmetric, antisymmetric, and independent

Exciter position Both forward, both aft, and left-aft/right-forward

Mach 0.54, 0.65, 0.70, 0.80, 0.85, 0.90, 0.95, 1.05, 1.2, 1.4, 1.6

Altitude, ft 10k, 30k, and 40k

Force Low and high

Sweep Linear and logarithmic

Duration, sec 15, 30, and 60

Range, Hz 3–12, 3–25, 25–35, 3–35, 35–3, and 3–40

Multiple Single, double, and quadruple contiguous sweeps per maneuver

Strain gage response, also sampled at 200 sps, wastaken at the exciter vane root to monitor the force input atthe aircraft wingtip. In reality, the force input isdistributed about the vane planform, but for simplicity’ssake a point force location was chosen to measure staticand dynamic force levels of the vane bending withrespect to the wingtip. Vane root strain is assumed to bedirectly proportional to the vane airloads caused byexcitation. It is important to note that this is ameasurement of vane strain and not normal force, so italso contains inertial effects from the vane itself as wellas modal response of the vane from the aircraftaeroelastic dynamics.

For the last two flights the excitation system softwarewas modified to excite each vane independently, onefollowed by the other, for each maneuver. Furthermore,lower gear ratios were installed to overcome thepreviously mentioned binding problem at high dynamicpressure. The new gears reduced the frequencybandwidth of the system from 50 to 25 Hz. Therefore,these last maneuvers were 3–25 Hz sweeps.

Test Results

Flutter clearance of the F/A-18 SRA wasaccomplished before structural dynamics research wasperformed. Unfortunately, the excitation system hadsome problems early in the flight clearance phase.Ground operation of the system before flight wassatisfactory, but in flight some of the followinganomalies occurred:

• Inconsistent rough starts and sweep motion in high-force mode

• Vane cylinders would not open in high-force mode

• Vane cylinders would not reset, or “home,” properlyafter sweep in either high- or low-force mode

These were thought to be environmentally related toambient temperature, dynamic pressure, or both. Failureswere duplicated in ground environmental test chambersat low temperatures, but difficult to reproduce. Someminor modifications in the vane electronics and homingsensors resolved the homing problems, but the problemsrelated to the high-force mode persisted in flight.Subsequently, after eighty maneuvers in six flights it wasdecided to test only in the low-force mode. This wasadequate for envelope clearance and tolerated forresearch flights.

Spectral information provided the most immediateindication of the quality of data in terms of exciter sweepparameters such as sweep direction, linear as comparedwith logarithmic and, high- as compared with low-forcelevels. Variations resulting from these test procedures areimportant in modal estimation and flutter boundaryprediction. For example, to estimate uncertainty sets forrobust flutter prediction, numerous data sets are analyzedat the same flight condition to discriminate betweendynamic and real model uncertainty, and differences dueto test procedure and nonrepeatability.7 Figures 4 and 5show differences that can occur in responses due only to


Figure 4. Transfer function of symmetric exciter force to wingtip accelerometer for 30-sec linearly increasingfrequency sweep at M = 0.8 and 30 k ft. Sweep range: 3–35 Hz.

Wing 1st bending

Fuselage 1st bending

Wing 2nd bending

Fuselage 2nd bending

0 205 10 15 25 30 35 40

.01

.02

.03

.04

.05

.06

.07

Magnitude

Frequency, Hz 970219

Figure 5. Transfer function of symmetric exciter force to wingtip accelerometer for 30-sec linearly decreasingfrequency sweep at M = 0.8 and 30 k ft. Sweep range: 35–3 Hz.

Wing 1st bending

Fuselage 1st bending

Wing torsion

0 205 10 15 25 30 35 40

.02

.04

.06

.08

.10

.12

.14

Magnitude


the direction of the sweep. Clearly, the decreasing sweep(fig. 5) generally provides much more response, but theincreasing sweep (fig. 4) improves modal excitationbetween 15–20 Hz relative to the other modes.

The responses in the following PSDs (power spectraldensities) were generated at Mach 0.9, an altitude of30,000 ft, and dynamic pressure of 360 psf from awingtip accelerometer. With the vanes in the aft wingtipposition, an antisymmetric reverse linear 30-secfrequency sweep is compared with a reverse logarithmic

sweep in the PSDs of figure 6. Logarithmic sweepsimpart more energy in the lower frequencies, illustratedby the first wing bending modes having more power near6 Hz and 8 Hz. Figure 7 indicates that there is nosignificant advantage in increasing the sweep durationfrom 30-sec to 60-sec. However, figure 8 shows possibleimprovement in response power by adding more sweepswithin the same period of time (30 sec). Antisymmetricwing first bending is much more responsive while theother modes are relatively unaffected by the sweep type.The exception is the significant decrease in modal


Figure 6. Wingtip accelerometer PSD from antisymmetric linear (left) and logarithmic (right) exciter sweeps. Sweeprange: 3–35 Hz.

5 10 15 20 25 300

.005

.010

.015

.020

.025

.030

.035

.040

.045

.050

Magnitude

Frequency, Hz5 10 15 20 25 300

Frequency, Hz

Antisymmetric linear sweep Antisymmetric logarithmic sweep

970221

Figure 7. Wingtip accelerometer PSD from symmetric 30-sec (left) and 60-sec (right) exciter sweeps. Sweeprange: 3–35 Hz.

Figure 8.Wingtip accelerometer PSD from antisymmetric single (left), double (middle), and quadruple (right) linearexciter sweeps. Sweep range: 3–35 Hz. Sweep duration: 30-sec total.

5 10 15 20 25 300

.005

.010

.015

.020

.025

.030

.035

.040

.045

.050

Magnitude

Frequency, Hz5 10 15 20 25 300

Frequency, Hz

Symmetric 30-sec linear sweep Symmetric 60-sec linear sweep

970222

15105 20 25 30

.035

.040

.045

.050

.025

.030

.015

.020

.005

0

.010

Mag

nit

ud

e

Frequency, Hz151050 20 25 30

Frequency, Hz151050 20 25 30

Frequency, Hz

Antisymmetric quadruple linear sweep

Antisymmetric double linear sweep

Antisymmetric single linear sweep

970223

response in the symmetric fuselage mode near 10 Hzfrom single to quadruple sweeps. This mode apparentlyneeds the longer dwell time in the single sweep torespond appropriately to an antisymmetric excitation.

Figure 9 shows a symmetric sweep from 3–35 Hzas compared with a 3–12 Hz sweep response, both overa 30-sec time period. Here there is noticeableimprovement in the wing bending modal responsesbelow 12 Hz from the 3 to 12 Hz sweep, as expected.Notice the similarity between responses in figures 9and 6, even though one is a symmetric and the other anantisymmetric exciter sweep. This is a consequence ofthe phase disparity between exciters mentioned earlier.Finally, a comparison of responses with the excitersmoved from their aft position to forward positions on thewingtips is seen in figure 10. The accelerometer

measurement is from the left aft wingtip. Symmetric firstwing bending shows an order of magnitude powerdensity increase near 6 Hz, but there is a dramaticdecrease in the wing second bending modal responsesnear 16–17 Hz. These results are indicative of thedifferences to expect in placement of the exciters relativeto output measurements, and how the effective modeshape may influence the results.

To summarize the wingtip excitation test results,despite the erratic performance of the exciters inparticularly the high force mode, a voluminous amountof high quality data was accumulated for investigation ofdifferences resulting from exciter test configuration. Testprocedure is shown to be a significant parameter in testresults, except for sweep duration which did not improveresponse seriously beyond 30-sec. Including multiple


Figure 9. Wingtip accelerometer PSD from symmetric 3–35 Hz (left) and 3–12 Hz (right) exciter sweeps. Sweepduration: 30-sec.

Figure 10. Wingtip aft accelerometer PSD from antisymmetric aft wingtip exciter (left) and forward exciter (right)sweeps. Sweep range: 3–35 Hz, antisymmetric sweep.

.050

.045

.004

.035

.030

.025

.020

.015

.010

.005

Magnitude

Frequency, Hz

Symmetric 3-35 Hz linear sweep

0 5 10 15 20 25 30Frequency, Hz

50 10 15 20 25 30

Symmetric 3-12 Hz linear sweep

970224

5 10 15 20 25 300

100

10–1

10– 2

10–3

10–4

Magnitude

Frequency, Hz

Wingtip exciter vanes AFT

5 10 15 20 25 300Frequency, Hz

Wingtip exciter vanes FWD

970225

sweeps within the same time window offers advantageswhen including increasing and decreasing data in thesame test, as long as sufficient time is allowed foradequate modal response. Exciter placement plays amajor role in swapping modal response between themodes because of mode shape. Test repeatability is aproblem as long as exciter phase discrepancies exist.

Control Surface Aeroservoelastic Excitation

System Description

An important element of the F/A-18 HARV flightsystem was the on-board excitation system (OBES).

This system was implemented to add programmeddigital signals to the control system actuator commandsfor structural excitation. Inputs up to 25 Hz were addedto the stabilator, aileron, rudder, and pitch and yawvectored thrust commands. Data was generated with80 sps OBES commands at from 5° to 70° AOA at 1 g.Accelerometers were located in the aircraft nose,vertical and horizontal tails, wingtips, and near theaircraft center-of-gravity as 80 sps feedbacks to thecontrol system. The feedback measurements are morecritical than other structural measurements whenusing excitation for aeroservoelastic considerations.Verification of closed-loop stability is the primary


objective. Measurement of signals at the inputsumming junction (actuator commands) and feedbackmeasurements allow computation of open- and closed-loop transfer functions, loop gains, and multivariablestability margins.

Test Results

Schroeder-phased harmonic signals which produceapproximately flat spectral characteristics8,9 werecompared to sinc ( ) pulses, which theoreticallyhave flat power spectra across a defined frequency range.Contrarily, linear and logarithmic sweeps are knownto be deficient at lower and higher frequencies,respectively. Figure 11 displays examples of sinc-pulse

and Schroeder-phased inputs from OBES into thesurface commands. These signals are stored in flightcomputer memory. The Schroeder-phased signal iscalculated as

(1)

where N is the number of data and A is a specifiedamplitude to acquire maximum power under thesaturation limits.

Note from the PSDs in figure 12 that the frequencyrange for the sinc-pulse is 0–25 Hz, whereas theSchroeder-phased signal was programmed for 5–25 Hz.

xsinx----------

x t( ) A ωtπk

2

N---------+

cosk∑=


Figure 11. F/A-18 HARV sinc-pulse and Schroeder-phased OBES inputs. Sinc-pulse input (left). Schroeder-phasedinput (right).

Figure 12. PSDs of sinc-pulse and Schroeder-phased input (note scale difference). Sinc-pulse input (left). Schroeder-phased input (right).

5.5 6.0 6.5 7.0 7.55.0

1.2

1.0

.8

.6

.4

.2

0

–.2

Mag

nit

ud

e

1.0

.8

.6

.4

.2

0

–.2

–.4

–.6

–.8

– 1.0

Mag

nit

ud

e

Time, sec43 5 6 7 8 9 10 11 12

Time, sec

Sinc-pulse input Schroeder-phased input

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970227

5 10 15 20 25 30

3.5 X 10–5

3.0

4.5 X 10– 3

4.0

3.5

3.0

2.5

2.0

1.5

1.0

.5

0

2.5

2.0

1.5

1.0

.5

0

Sin

c-p

uls

e in

pu

t

Frequency, Hz5 10 15 20 25 30

Frequency, Hz

Maximum entropy PSD Maximum entropy PSD

Sch

roed

er-p

has

ed in

pu

t

More importantly, for inputs close to unity, theSchroeder-phased PSD is two orders of magnitudegreater than the sinc-pulse, thereby verifying theproperty of low peak factor for a given power spectrum(fig. 11).10 Peak or crest factor is defined as thedifference between signal maximum and minimumvalues divided by the root-mean-square value of a signal.It is a measure of the flatness of the power spectrum.Low peak factor signals are generally desirable in systemtesting to avoid large system perturbations. This is anobvious benefit for preventing input saturation whilemaximizing signal-to-noise ratio.

PSDs of normal and lateral acceleration feedbackresponses are shown in figure 13 for sinc-pulse andSchroeder-phased OBES inputs. Disregarding the orderof magnitude difference, the responses are quite similarin terms of modal response. Differences are seen in thelarge relative response below 10 Hz from the sinc-pulselateral acceleration compared with higher frequencymodes, and some activity around 20 Hz from normalacceleration for the Schroeder-phased response that thesinc-pulse does not excite.

Figures 14 and 15 compare transfer functions betweensinc-pulsed and Schroeder-phased OBES inputs,


Figure 13. F/A-18 HARV feedback accelerometer responses to sinc-pulse and Schroeder-phased inputs (note scaledifference): normal acceleration (top) and lateral acceleration (bottom). Sinc-pulse accelerometer response (left).Schroeder-phased accelerometer response (right).

Figure 14. Sinc-pulse transfer functions from OBES input to accelerometer feedbacks.

2.5 x 10–6

5 x 10–5

1.5

2.0

4

3

2

1

0

1.0

.50

15105 20 25 30

Lat

eral

acc

eler

atio

nN

orm

al a

ccel

erat

ion

Frequency, Hz

Maximum entropy PSD

15105 20 25 30

970228Frequency, Hz

2.5 x 10–5

5 x 10–4

1.5

2.0

4

3

2

1

0

1.0

.50L

ater

al a

ccel

erat

ion

No

rmal

acc

eler

atio

n

Maximum entropy PSD

Magnitude, dB

Magnitude, dB

0 5 10 15 20 25 30 35

970229

40

– 40

– 50

– 30

– 20

– 10

0

10

– 30

– 20

– 10

0

Frequency, Hz

Sinc-pulse transfer functions OBES input to normal acceleration

OBES input to lateral acceleration

Figure 15. Schroeder-phased transfer functions from OBES input to accelerometer feedbacks.

Magnitude, dB

Magnitude, dB

0 5 10 15 20 25 30 35

970230

40

– 40

– 50

– 30

– 20

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Scroeder-phased transfer functions OBES input to normal acceleration

OBES input to lateral acceleration

respectively. OBES inputs are to all the surfacessequentially, and outputs are normal and lateralacceleration feedbacks. Sinc-pulse transfer functionslack the detail and definition of the Schroeder-phasedresponses. Magnitudes differ by as much as 20 dB near15 Hz. Schroeder-phased responses tend to highlight thesignal from the noise and discriminate dominant modaldynamics more readily than sinc-pulse responses. Animportant aspect of this comparison is the extent towhich responses can differ depending on the input. Thisdifference is a critical factor if stability analyses dependon these results. These results are preliminary and moreextensive analyses can be found in reference.11

Signal Analysis of Aeroelastic Data

In this section, some signal processing properties ofthe input signals and accelerometer responses arestudied for model validation and flight flutter boundaryprediction. Wavelet analyses are highlighted to detecttime-varying and nonlinear dynamics. Also, time-frequency applications for enhanced signal processing ofvibration data are presented.

Spectral Analysis

Analysis of transient data violates the assumptions ofany FFT-based spectral estimation technique. Thistechnique assumes time-invariance, stationariness, and asignal composed of a sum of infinite sinusoids.Windowing and averaging can help remove somedistortion but also add bias errors. For these reasons,autoregressive (AR) spectral estimation is preferred for

transient data. In the class of AR spectral estimationmethods are the reflection coefficient estimationalgorithms. In particular, the maximum entropymethod12 (MEM) is one method being adopted byNASA Dryden for frequency domain transient signalanalysis. MEMs estimate the correlation sequencesassuming finite correlation extrapolation to infinity ismost random, or has maximum entropy, thereby assuringa positive definite power spectral density function.

Autoregressive coefficients of an all-pole filterrepresentation of the signal are estimated directly fromthe data without using autocorrelations. Akaikeinformation criteria12 are used to determine theautoregressive order of the process (which can also bemultichannel, or MIMO) for PSD and transfer functionestimation. Model order selection for the AR model ofthe signal represents the classic tradeoff between higherresolution and decreased variance.

Examples of classical FFT-based PSD estimatescompared to MEM estimates are represented in figure 16with F/A-18 SRA wingtip accelerometer data. Thesedata were acquired at Mach 1.2, an altitude of 30,000 ft,and 630 psf dynamic pressure with symmetricexcitation. Top plots are left wingtip accelerometers andthe bottom plots are right wingtip accelerometers.Comparing the classical (left) with MEM (right)estimates, both methods estimate activity nearsymmetric wing first bending (6 Hz), but then the MEMestimates of modal response between 7–10 Hz isdramatically different from the relatively suppressed


Figure 16. Classical FFT-based PSDs compared to maximum entropy estimates: Left wingtip accelerometer (top) andright wingtip accelerometer (bottom) responses. Classical (left). Maximum entropy (right).

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classical response estimates. Symmetric fuselage firstbending or antisymmetric wing first bending near 9 Hzare not even visible in the classical estimates.Alternatively, near 15 Hz the classical estimates arenearly double the maximum entropy estimates. Between13–18 Hz the classical estimates include contributionsfrom wing torsion, second bending, and wing outboardtorsion, whereas the MEM estimates are not significantin this range.

These comparisons are intended to highlight thestrengths and weaknesses of the two estimates. Areasonable conclusion is that the standard practice ofdepending on classical estimates is suspect. Otherspectral analysis techniques should be supplemented

with the standard ones for a thorough complementaryanalysis.

Frequency domain modal system identification andstability estimation rely on high quality frequencyresponses to get reliable results. Some estimationtechniques attempt to curve fit the data with a parametricrepresentation of the response, and use the parameters todetermine stability. Others incorporate frequencyresponse data into a state space identification algorithmand stability is derived from this realization.

To compare the MEM to classical methods in a systemidentification procedure, a symmetric linear sweepresponse is used in a transfer function fit procedure formodal frequency and damping estimation. Figure 17


Figure 17. Left forward wingtip accelerometer responses from a symmetric linear sweep using classical (left) andMEM methods (right). Classical response (dashed) and 20th-order fit (solid). MEM response (dashed) and 20th-orderfit (solid).

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Classical response and 20th-order curve fit MEM response and 20th-order curve fit

(left) is a left forward wingtip accelerometer magnituderesponse from symmetric F/A-18 SRA excitationcomputed using a classical method and fit with a 20th-order parameterized stable minimum phase transferfunction.13 In figure 17 (right) the correspondingresponses are plotted using a MEM method. Theclassical response is noisier than the MEM, and does notexhibit the wing first bending modal response of theMEM method near 6 Hz or symmetric wing first torsionnear 15 Hz. However, MEM does not distinguish wingsecond bending near 17 Hz as well as the classicalmethod. Figure 18 shows the same comparisons aremade with the left aft wingtip accelerometer. Again, theMEM method estimates more modal response near 6 Hz,yet elsewhere the responses are similar.

Frequency and damping ratios computed by fitting theresponses with a parameterized transfer function forthese respective wingtip accelerometers are displayed intable 4. Note that the table only addresses symmetricmodes even though antisymmetric modes are also beingexcited (figs. 17 and 18). Since there are some significantdifferences between classical and MEM estimates,without a truth model an argument can again be madethat FFT-based methods need to be complemented withother types of analyses.

Transfer Functions

Traditional transfer function estimation generally useswhat is called the estimate, yet it is well known tobe biased with input measurement noise. Another

H1


Figure 18. Left aft wingtip accelerometer responses from a symmetric linear sweep using classical (left) and MEMmethods (right). Classical response (dashed) and 20th-order fit (solid). MEM response (dashed) and 20th-order fit(solid).

Table 4. Modal frequencies and damping ratios from F/A-18 SRA wingtip accelerometer data from asymmetric wingtip exciter sweep.

Symmetricmode

Wingfirst bending

Fuselagefirst bending

Wingfirst torsion

Wingsecond bending

Wingoutboard torsion

Method FFT MEM FFT MEM FFT MEM FFT MEM FFT MEM

Frequency, Hz

Wingtip fwd 6.0 6.0 11.0 11.5 13.5 13.9 16.5 15.2 17.6 18.1

Wingtip aft 5.8 6.0 11.0 10.0 12.5 13.7 16.6 16.4 17.6 18.3

Damping ratio

Wingtip fwd 0.06 0.10 0.12 0.17 0.06 0.04 0.03 0.12 0.08 0.06

Wingtip aft 0.04 0.06 0.18 0.10 0.03 0.02 0.05 0.10 0.04 0.03

10–3

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970233

Classical response and 20th-order curve fit MEM response and 20th-order curve fit

estimate, , is less common since it is biased underoutput measurement noise and unmeasured externaldisturbances. is the geometric mean of and ,where ( , , , and are spectral densities),

• = / , minimizes error due to noise atoutput y, sensitive to input noise

• = / , minimizes error due to noise atinput x, sensitive to output noise

Therefore, for a single input,

(2)

where < < , and the true noise-free transferfunction also satisfies < < . is theso-called robust transfer function estimate14 because itis uniformly less biased than either or .

Data generated from the wingtip excitation system isnot ideal at either accelerometer outputs or excitationinput. Some data corruption results from using straingauge measurements for the inputs. The response in thiscase feeds back to the excitation force applied since thestrain gage is measuring strain between the respondingwingtip and forced vane root. Ideally, the spectralestimates should be referenced to an excitation drive

signal (like torque), but this is not available as ameasurement. Therefore, for systems in which the inputexcitation force is unavailable, provides optimaltransfer function estimation. can be degraded byunmeasured external disturbances, but the force inputfrom the exciter is believed to dominate thesephenomena.

Frequency responses using the three estimates areplotted in figure 19 using the traditional FFT-basedspectral estimates, and in figure 20 using the maximumentropy AR method at the same resolution. These areresponses from the left force exciter to a left wingtipaccelerometer. They are comparable but differ in somedetails. Typically, the gap between the lower boundand upper bound is wider in the MEM response. TheMEM response is smoother while distinguishingessential features. Modes near 6 Hz, 8–9 Hz, 14 Hz, inthe 15–20 Hz range, and even 22 Hz and 24 Hz aredistinguishable in both classical and MEM responses.Calculating both types of responses gives more credenceto the analysis. Otherwise, some of the modes may bemisinterpreted. Also notice the dramatic differences thatcan result between or , and .

Admittedly, there are different techniques foranalyzing specific types of excitation data, (random,periodic or transient) with classical methods. But the ARmethods are not subject to restrictions depending on

H2

Hv H1 H2Gxy Gyx Gxx Gyy

H1 Gyx Gxx

H2 Gyy Gxy

Hv

Gyx

Gyx------------

Gyy

Gxx---------

H1

H2-------= =

H1 Hv H2H0 H1 H0 H2 Hv

H1 H2

HvHv

H1H2

H1 H2 Hv


Figure 19. Classical FFT-based transfer functions , , and .

0 5 10 15 20 25

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Magnitude,dB

Hv, H1, and H2 transfer functions HvH1H2


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Figure 20. Maximum entropy transfer functions , , and .

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Hv, H1, and H2 transfer functions HvH1H2


Hv H1 H2

the type of data, so alterations from averaging andwindowing are unnecessary.

Time-Frequency Analysis

Analysis of the frequency content of a signal x(t)traditionally uses the Fourier transform which projectsthe signal onto sinewave basis functions of infiniteduration for stationary signals. This transform is notlocalized in time. For time-varying signals a transform ofthe form

(3)

is needed to locate instantaneous frequencies in x(t).Such a transform is limited in resolution bythe Hiesenberg uncertainty principle ≥ 2.Resolution problems resulting from the uncertaintyprinciple can be minimized by a time-frequencydecomposition called the wavelet decomposition.15

The wavelet decomposition performs an orthonormalprojection of the signal onto functions that are adapted tothe frequency resolution needed. A continuous wavelettransform (CWT) is defined as

(4)

where is the wavelet basis function, *

is its complex conjugate transpose, τ is the local time,and a is a scale or dilation parameter set to match thelevel of resolution desired. With the CWT the timeresolution is arbitrarily good at high frequencies and thefrequency resolution becomes arbitrarily good at lowfrequencies, within the limits of the uncertaintyprinciple. Time-frequency analyses attempt to minimizethe effects of this resolution problem by using a prioriknowledge of the signal properties, or adapting theresolution to the signal.16,17

A procedure has been developed6 to filter unwanteddistortions and extract desired features from the inputexcitation and output structural response data of theF/A-18 SRA and HARV aircraft. These feature filtereddata are then used to compute cleaned signals fortransfer functions and system identification algorithms.

An example of filtering the undesirable features ofmore complicated input-output signals using a time-frequency representation will be a double logarithmicsweep from the F/A-18 SRA excitation system. Ascalogram of the original input signal is shown infigure 21 (top). Harmonics from the strain gage inputmeasurement can be readily detected in the time-frequency map as the darker portions of the image.

T x t( )( ) X t ω,( )=

∆ω ∆t⋅

CWT τ a,( ) 1

a------- x t( )∞–

∞∫= h∗ t τ–a

---------- dt

ha τ, t( ) ht τ–

a---------- =


These areas in the map represent large amplitude CWTcoefficients. The harmonics indicate nonlinear excitervane response from the rotating slotted cylinders at thewingtips, which is deemed undesirable for subsequentlinear state-space identification methods. Therefore, theinput signal is modified by extracting the desired time-frequency map from the scalogram to retain thecommanded input signal from the main harmonic(fig. 21 (bottom)).

Figure 21. Scalogram of original double logarithmicexciter input and feature filtered input. Scalogram oforiginal exciter input signal (top). Scalogram of featurefiltered exciter input signal (bottom).

These CWT coefficients are then used to reconstructthe time domain input signal by inverse transforming ateach frequency ω back to the time domain. Figure 22shows the original signal in the top plot, including

harmonics. Reconstruction from the scalogram offigure 21 (top) is shown in the middle plot. Notice thereconstruction is not exact since there is some distortionin the wavelet processing procedure. Finally, the featurefiltered signal from figure 22 (middle) is reconstructedwith only the main harmonic, as shown in the bottomplot of figure 22.

Similar procedures are performed on theaccelerometer measurements and transfer functions arecomputed using the feature filtered data sets from theF/A-18 SRA. Transfer functions from both exciter inputs(left and right columns, respectively) to an accelerometeroutput are plotted in figure 23. The top four plots resultfrom classical Fourier methods, and the correspondingbottom plots are results of using the feature filtered time-frequency method. As shown, very general maps in thetime-frequency plane can be effectively filtered in thismanner. More details concerning the development andapplication of wavelet filters to analysis of F/A-18 SRAaeroelastic data can be found in references.6

Flight Flutter Prediction

Several modal estimation algorithms have beenapplied to flight flutter testing in both frequency and timedomain18,19 for extracting stability estimates anddetecting time-varying and/or nonlinear dynamics. Noalgorithm has been unanimously accepted in theaeroelastic community because of 1) problems withestimation of closely spaced modes or assuring stableestimates for stable systems, 2) assumption of timeinvariance, linearity, or stationariness, 3) sensitivity totype of input or noise levels, 4) lack of technique forestimating error bounds, and, 5) computationalcomplexity. In an attempt to qualify the relative merit ofthe methods with actual flight data, a non-exhaustive listof algorithms in table 5 is being considered forevaluation at NASA Dryden for usefulness in fluttertesting. The frequency domain subspace identificationmethods combined with time-frequency multiscalewavelet techniques are the most promisingalgorithms.6,20,21

Modal damping is unfortunately the most popularparameter to track for determining proximity to theflutter boundary. It can be a very poor indicator ofimpending instability as it depends on critical flightparameters (Mach, ) in a highly nonlinear fashion.Tests performed with different input signals, and the verycommon occurrence of nonrepeatability at identical testconditions, can change damping estimates dramaticallyusing state-of-the-art identification schemes.

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Figure 22. Original F/A-18 SRA exciter input signal (top), reconstruction of original signal (middle), andreconstruction of feature filtered input signal (bottom).

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Reconstructed signal in time domain


Figure 23. Transfer functions computed with classical Fourier technique and feature-filtered time-frequency method:Left F/A-18 SRA exciter input to wingtip accelerometer output (left). Right F/A-18 SRA exciter input to wingtipaccelerometer output (right). Classical Fourier transfer functions (top). Time-frequency generated transfer functions(bottom).

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Robust Flutter Boundary Prediction

A µ-based measure of flutter boundary prediction isproposed which has the following important desirablefeatures:

1. Robust (reliable) identification in the presence ofestimation model uncertainty

2. Quantification of the error bounds because ofunmodeled dynamics, uncertain parameters andnoise

3. Well-behaved stability measured as a function ofcritical flight parameters (Mach, )

4. Incorporation of model structure into theidentification procedure (prior knowledge)

5. Dependence on a minimum amount of test pointsfor extrapolation to the flutter boundary

6. Algorithmic simplicity for on-line implementations

7. Realistic assumptions

This µ-based flutter prediction method with theseseven advantages to compute flutter instabilityboundaries is of obvious benefit to the aeroelasticcommunity. In this method, flight data is incorporatedinto the model validation process to account for any

differences between the model and the aircraft. Robustworst-case flutter margins are computed to directlyaccount for variations in the data (non-repeatability) andmodel parameter uncertainty. These robust fluttermargins are generated by forming realistic uncertaintyoperators that ensure that a family of models includes theactual aircraft dynamics. The procedure can greatlyimprove the efficiency and safety of an envelopeexpansion with accurate and confident identification.Data from safe and benign flight conditions are used topredict flutter boundaries.

Critical elements for this technique are modelvalidation and robust stability measures. System-induced norms are used for model error descriptions tomeasure the ‘closeness’ of systems in the context ofrobust control.38,52 The key question for modelvalidation is this:

Given the available data and model, does thereexist a perturbation within the range of allowednorm-bounded uncertainty such that the modeldescribes the data?

A nonconservative approach to this issue is to find thesmallest perturbation such that the data fits the model.Robust flutter prediction poses this additional question:

Table 5. Survey of modal estimation algorithms for aeroelastic applications.

Frequency domain Time domain

Spectral analysis Time series analysis

FFT/correlation methods22 Correlation/null-space methods23,24,25

Maximum entropy/maximum likelihood12,26 Linear prediction (LS, MLE, IV, PEM)27

and curve fitting28,29,30,31 Total least squares (TLS)32

Orthogonal polynomials33,34 Total least norm (TLN)35

Robust identification36

Norm-bounded ID37 Worst-case input-output ID38

Subspace identification39,40

Realization-based methods

Transfer Function Fitting (TFF)41 ERA/OKID42

Auto-Cross-Spectra Fitting (ACSF)41 Q-markov cover43

State-Space Frequency Domain (SSFD)44 Stochastic Realization (SRA)45

Direct subspace identification

FORSE,20,46,47 McKelvey21 ORSE,48 N4SID39

High order spectral analysis49

Frequency-time multiscale wavelets15,50,51

l2 l∞

H∞ l1

q


Given the available data and models, what is thesmallest norm-bounded perturbation of the currentflight condition that can drive the system tobecome unstable?

This is the robust stability aspect of the problem. Inthis context, structuring the error in the aeroelasticmodel and applying model validation concepts usingflight-derived uncertainty models avoids relying ondamping estimates as a measure of modal stability.53,54

Here the structure of the aeroelastic model is preserved,and uncertainty enters the system in a prescribedmanner. Damping estimates are replaced by the stabilitymargin µ.

These robust stability concepts are used toparameterize an aeroelastic model with dynamicpressure at specific Mach numbers, and introduceuncertainty structure to account for model inaccuracy.Figure 24 represents a robust stability parameterizationover of the state-space aeroelastic system. Thenominal flutter margin is that value of which results inaeroelastic instability.

Figure 24. Robust stability parameterization over fornominal flutter margin.

For the F/A-18 SRA, numerous data sets from 40k,30k, and 10k ft altitude for each Mach number (table 3)

are analyzed to determine whether the data is accountedfor by the model. If not, the model is adjusted byincreasing the real parameter uncertainty in modalfrequency and damping. After this procedure, otherunmodeled dynamic uncertainty is adjusted to includemultiple data sets at a particular flight condition(Mach, ).

An uncertainty description consisting of modaluncertainty, , and input multiplicativeuncertainty, , is used to account for errors andunmodeled dynamics resulting in the system depicted infigure 25. This model is created for each flight condition,from all the available flight data responses. Now themodel envelopes all the aeroelastic dynamics of theaircraft at a particular Mach number. Since the model isnow validated by the flight data, realistic robust fluttermargins can be computed.

Flutter points are derived with respect to dynamicpressure and the system uncertainty model derived fromthe data, using the structured singular value,13 µ. Thisworst-case stability boundary guarantees stability withinthe range of system uncertainty deduced from themismatch between model and data.

Advantages of this µ-based robust flutter boundaryprediction method are as follows:

• Model validation can be cast in the frequency ortime domain52,55

• Parameter identification uncertainty can beincorporated into the model

• Identification error estimates are not essential

• Generalized uncertainty descriptions are admissible(real, complex, time-varying, nonlinear)

• Stability norms generally behave smoothly atinstability boundaries

qq

F-18

δq

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e d

q

q

∆modes∆in


Figure 25. F/A-18 uncertainty block diagram for robust flutter margin.

F-18

δq

∆ modes

∆ in Win

970238

Noise

de

• Some conservatism for flight safety will alwaysexist (nominal vs. robust flutter boundary)

• Aeroservoelastic stability is analyzed in the sameframework

• Procedure can be tuned for on-line analyses

• Naturally extends to robust control synthesis forflutter suppression

If the uncertainty model is invalidated at some flightcondition, either the identification procedure mustbe revisited, the uncertainty description modifiedaccordingly, or both. While the model is not invalidated,it remains a robust stability measure. A companionpaper53 details the procedure for using F/A-18 SRAaeroelastic data in prediction of the aeroelastic stabilityboundary.

Robust Stability Results

Flutter prediction computation uses the finite elementand unsteady aerodynamic pk solutions computed fromthe STARS56 code. Figures 26 and 27 represent thisflutter boundary with solid lines for symmetric andantisymmetric modes, respectively. These are the so-called ‘matched point’ flutter solutions which accountfor actual atmospheric conditions in the solutionprocess.

Circled points in the figures are solutions of theminimum destabilizing perturbation of dynamicpressure from a nominal condition using µ (fig. 26and 27). These points are nominal flutter solutions usingthe parameterization of figure 24 for each Machnumber with no uncertainty operators in the stabilitymargin computation. A good match with the solid linesindicates that using the generalized aerodynamic forcesat a nominal condition will extrapolate to the properanalytical result from the parameterization. The onlyexception where matches are not optimal occurs aroundthe transonic area where the aeroelastic pk solutions aremost sensitive.

Finally, the analytical flutter points are compared withthe robust structured singular value solutions computedwith respect to the uncertainty description , of figure 25. Using all available flight data, modelvalidation and robust stability computations result in thedashed lines of these figures (figs. 26 and 27). Robustresults are more conservative, as expected, due to theuncertainty model updates from incorporation of thedata.

Conclusions

Improvements in aeroelastic and aeroservoelasticflight testing have been addressed. F/A-18 SRA andHARV aircraft provide valuable data for analysis of

q

q

∆modes ∆in


Figure 26. Nominal and robust flutter points–symmetric modes.

0 .2 .6 1.0 1.2 1.8.4 .8 1.4 1.6

– 40,000

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20,000

40,000

60,000

Altitude, ft

Flight envelope

15 percent flutter margin

Mach 970239

Solid: nominal flutter using pk Circle: nominal flutter using µ Dashed: robust flutter using µ

pk

Figure 27. Nominal and robust flutter points–antisymmetric modes.

0 .2 .6 1.0 1.2 1.8.4 .8 1.4 1.6

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Solid: nominal flutter using pk Circle: nominal flutter using µ Dashed: robust flutter using µ

pk

excitation mechanisms, model estimation algorithms,and stability boundary prediction. External excitation foraeroelastic research was conducted on the F/A-18 SRAand on-board signal generation was used on the F/A-18HARV for aeroservoelastic investigation. However, datafrom excitation systems is only as reliable as the systemperformance, so excitation system anomalies need to beaccounted for when using estimation algorithms forstability estimates. Classical spectral estimates aresuspect in a time-varying or nonstationary environment,so parametric maximum entropy spectral estimates aresuggested as an alternative to supplement classicalanalyses. Furthermore, advanced procedures in time-frequency methods have been presented which will assistin detecting and compensating for data distortion, suchas nonlinearity, before modal analysis. Time-frequencywavelet analyses have also been exploited for detectingdepartures from time-invariance, stationariness, andnoise assumptions. Such applicable data processingtechniques, tuned for the particular test environment, aredesired for enhanced on-line analyses.

Modal identification must account for divergencefrom algorithmic assumptions in the form of errorbounds. A method which accounts for such uncertaintiesin the data and analysis results has been introduced.Modal damping as an unreliable stability predicter isreplaced by a robust µ-based stability margin for moreconfident and efficient stability boundary prediction.Identification consistent with the uncertainty structure in

an aeroelastic model provides an explicit measure ofstability in a modern robust control framework. Robustmodel validation accounts for the uncertainty structure,guaranteeing that any system will remain stable within aconfidence bound. Therefore, model validationtechniques are exploited to develop structureduncertainty models consistent with the data. Stability isguaranteed within the uncertainty deduced from the data.F/A-18 SRA data is used to demonstrate worst-caseflutter boundary prediction using this method. Thisprocedure can be tuned for robust aeroelastic andaeroservoelastic on-line stability prediction.

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NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)Prescribed by ANSI Std. Z39-18298-102

Overview of Recent Flight Flutter Testing Research at NASA Dryden

WU 522-32-34


NASA Dryden Flight Research CenterP.O. Box 273Edwards, California 93523-0273

H-2165

National Aeronautics and Space AdministrationWashington, DC 20546-0001 NASA TM-4792

In response to the concerns of the aeroelastic community, NASA Dryden Flight Research Center, Edwards,California, is conducting research into improving the flight flutter (including aeroservoelasticity) test processwith more accurate and automated techniques for stability boundary prediction. The important elements of thiseffort so far include the following: 1) excitation mechanisms for enhanced vibration data to reduce uncertaintylevels in stability estimates; 2) investigation of a variety of frequency, time, and wavelet analysis techniquesfor signal processing, stability estimation, and nonlinear identification; and 3) robust flutter boundaryprediction to substantially reduce the test matrix for flutter clearance. These are critical research topicsaddressing the concerns of a recent AGARD Specialists’ Meeting on Advanced Aeroservoelastic Testing andData Analysis. This paper addresses these items using flight test data from the F/A-18 Systems ResearchAircraft and the F/A-18 High Alpha Research Vehicle.

Aeroelasticity, Aeroservoelasticity, Flutter, Model validation, Robust stability,Stability prediction, Structural dynamics, System identification, Wavelet analysis

AO3

31

Unclassified Unclassified Unclassified Unlimited

April 1997 Technical Memorandum

Available from the NASA Center for AeroSpace Information, 800 Elkridge Landing Road, Linthicum Heights, MD 21090; (301)621-0390

Presented as AIAA 97-1023 at the 38th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, andMaterials Conference and Exhibit, Kissimmee, Florida, April 7–10, 1997.

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Overview of Recent Flight Flutter Testing Research at … Technical Memorandum 4792 Overview of Recent Flight Flutter Testing Research at NASA Dryden April 1997 Martin J. Brenner,