NASA Technical Memorandum 4792

Overview of Recent Flight

Flutter Testing Research

at NASA Dryden

Martin J. Brenner, Richard C. Lind,

and David F. Voracek

Dryden Flight Research Center

Edwards, California

National Aeronautics and

Space Administration

Office of Management

Scientific and Technical

Information Program

1997

OVERVIEW OF RECENT FLIGHT FLUTTER

TESTING RESEARCH AT NASA DRYDEN

Martin J. Brenner,* Richard C. Lind, t David F. Voracek _

NASA Dryden Flight Research Center

Edwards, California

Abstract AR

ASE

In response to the concerns of the aeroelastic

community, NASA Dryden Flight Research Center, CWT

Edwards, California, is conducting research ERA

into improving the flight flutter (including

aeroservoelasticity) test process with more accurate and FFT

automated techniques for stability boundary prediction. FORSE

The important elements of this effort so far include the

following: 1) excitation mechanisms for enhanced

vibration data to reduce uncertainty levels in stability G

estimates; 2) investigation of a variety of frequency, h(t)

time, and wavelet analysis techniques for signal

processing, stability estimation, and nonlinear

identification; and 3) robust flutter boundary prediction

to substantially reduce the test matrix for flutter

clearance. These are critical research topics addressing

the concerns of a recent AGARD Specialists' Meeting on

Advanced Aeroservoelastic Testing and Data Analysis.

This paper addresses these items using flight test data

from the F/A-18 Systems Research Aircraft and the

F/A-18 High Alpha Research Vehicle.

Nomenclature

a

AGARD

AOA

wavelet scaling parameter

Advisory Group for Aerospace Research

and Development

angle of attack

autoregressive

aeroservoelastic

continuous wavelet coefficient

eigensystem realization algorithm

fast Fourier transform

Frequency domain Observability Range

Space Extraction

spectral estimate

wavelet basis function

H1, H2, H v transfer function estimates

HARV

H_ norm

ID

IV

k

l 1 norm

12 norm

l_ norm

LS

*Research Engineer, NASA, Dryden Flight Research Center, MS

4840D/RS, Edwards, CA 93523-0273, 805.258.3793, gonzo@xrd. Mach, ?/

dfrc.nasa.gov.

?NRC Post Doctoral Research Fellow, NASA, Dryden Flight MEM

Research Center, MS 4840D/RS, Edwards, CA 93523-0273, 805.

258.3075, lind@xrd.dfrc.nasa.gov, Member AIAA. MIMO

:_Research Engineer, NASA, Dryden Flight Research Center, MS MLE

4840D/RS, Edwards, CA 93523-0273, 805.258.2463, voracek@flutter.

dfrc.nasa.gov. Senior Member AIAA. N4SID

Copyright © 1997 by the American Institute of Aeronautics and

Astronautics, Inc. No copyright is asserted in the United States under

Title 17, U.S. Code. The U.S. Government has a royalty-free license to OBES

exercise all rights under the copyright claimed herein for Governmental

purposes. All other rights are reserved by the copyright owner. OKID

High Alpha Research Vehicle

supremum norm over finite magnitude

transfer functions

identification

instrumental variable estimation

summation index

induced norm over signals of finite

magnitude

norm of signals that are square integrable

induced norm over signals of finite

magnitude impulse response

least squares

critical flight parameters

maximum entropy method

multi-input-multi-output

maximum likelihood estimation

numerical algorithms for subspace statespace system identification

on-board excitation system

Observer/Kalman filter identification

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ORSE

PEM

pk

PSD

psf

Z7

SISO

sps

SRA

t

T

TVCS

Win

x(t)

x(t,o_)

Subscripts

x, y

5_

Ain

Amodes

g

01

Observability Range Space Extraction

prediction error method

computational method for unsteady

aerodynamics

power spectral density

pounds per square foot

dynamic pressure

single-input-single-output

samples per second

Systems Research Aircraft

time

transform of x(t)

thrust vectoring control system

input uncertainty weighting

time domain data

time-frequency domain data

input and output data for spectral estimates

parametric variation of dynamic pressure

input multiplicative uncertainty

real parametric modal uncertainty

structured singular value

wavelet time shift parameter

radian frequency

complex conjugate transpose

summation

Introduction

Flight flutter testing continues to be a challenging

research area because of the concerns with cost, time,

and safety in expanding the envelope of new or modified

aircraft. Testing is often done at stabilized test points to

generate numerous data sets while attempting to

estimate aeroelastic stability in an accurate and efficient

manner. Parameter estimation methods generally

produce inconsistent results because of poor excitation,

closely spaced modes, noisy data, nonlinearities, and

low modal stability levels. Flutter test procedures are

desired which will dramatically reduce test time,

increase reliability, and provide accurate and

conservative results.

In response to the concerns of the aeroelastic

community and in-house requirements, NASA Dryden

Flight Research Center, Edwards, California, is

conducting research into improving the flight flutter test

process (including aeroservoelasticity) with more

accurate and automated techniques for stability

boundary prediction. The important elements of this

effort so far include the following research:

1. Excitation mechanisms are being studied for

enhanced vibration data to reduce uncertainty

levels in stability estimates. A wingtip

aerodynamic excitation system was used for

improved aeroelastic excitation, and signals

generated from a flight control system were

programmed to activate the control surfaces for

aeroservoelastic excitation.

2. A variety of frequency, time, and wavelet analysis

techniques are being investigated for signal

processing, stability estimation, and system

identification. Traditional Fourier methods for

frequency response are being augmented with

autoregressive estimation methods. Numerous

algorithms to estimate stability parameters and

system dynamic models are being compared for

efficiency and •reliability. Time-frequency signal

processing techniques are used for filtering, system

identification, and detection of nonlinearities.

3. Robust flutter boundary prediction methods are

being developed to substantially reduce the test

matrix for flutter clearance. These methods rely on

identification consistent with the uncertainty

structure in an aeroelastic model, thereby providing

an explicit measure of stability for robust model

validation. Accounting for the uncertainty structure

in this manner guarantees that any system will

remain stable within a confidence bound.

These are critical research topics addressing the

concerns of a recent AGARD Specialists' Meeting on

Advanced Aeroservoelastic Testing and Data Analysis.

This paper addresses these items using a wingtip

aerodynamic structural excitation system on the F/A-18

Systems Research Aircraft (SRA) and an oscillating

control surface excitation system on the F/A-18 High

Alpha Research Vehicle (HARV).

A flight flutter research program was initiated on the

F/A-18 SRA in late 1994. The purpose of the SRA

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structural dynamics research to date was to accomplish

the following:

• Study the integrity and effectiveness of the

excitation system in a wide variety of subsonic,

transonic, and supersonic test conditions.

• Investigate data properties over a range of linear and

logarithmic sinusoidal inputs at different force

levels in a flight flutter test environment. Compare

analysis algorithms in the frequency, time, and

wavelet domains using the time-varying data sets.

• Identify nonlinear behavior, such as that resulting

from transonic dynamics.

• Create a comprehensive data base of transient flight

flutter data for the aeroelasticity and system

identification disciplines to support development of

advanced flight flutter test and analysis methods.

This paper presents F/A-18 SRA flight test results and

analyses using the wingtip exciter. Preliminary results

from the F/A-18 HARV aircraft using an on-board

excitation system (OBES) for control surface excitation

are also presented. Flight flutter test technique

research was conducted on the F/A-18 HARV to

study the effectiveness of Schroeder-pulsed and sincpulse waveforms as excitation signals. Present modal

estimation methods are reviewed, followed by an outline

of the robust aeroelastic model development, with the

ultimate objective being model validation for robust

flutter boundary prediction. A novel procedure for

computing the robust flutter boundary from flightderived uncertainty models, using the structured

singular value (Ix), is introduced.

Aircraft Descriptions of the

F/A- 18 SRA and HARV

The F/A-18 SRA aircraft is being flight tested at the

NASA Dryden Flight Research Center primarily for

flight systems experiments such as optical sensing, new

actuation concepts, smart structures, and advanced

airdata and flight control systems. Generally, it is very

much like a standard production F/A-18. A major left

wing structural modification was done, however, on the

SRA aircraft to allow for testing of several hydraulic and

electromechanical advanced aileron actuator concepts.

Because the test actuators may be larger than the

standard one, a fitting called a 'hinge-half' supporting

the aileron hinge, the actuator, and a fairing had to be

replaced by larger and heavier items. A total of about

35 lb was added to the wing. Table 1 lists calculated

modal frequencies for symmetric and antisymmetric

modes for the F/A-18 SRA aircraft with left wing

modifications.

Another F/A-18 aircraft (fig. 1) was modified

at NASA Dryden to perform flight research at high

angle-of-attack (AOA) using thrust vectoring and

incorporating control law concepts for agility and

Table 1. F/A-18 SRA with left wing modifications and without wingtip exciter: calculated

elastic modal frequencies. Fuel loading is FULL.

Symmetric mode Hz Antisymmetric mode Hz

Wing first bending 5.59

Fuselage first bending 9.30

Stabilator first bending 13.21

Wing first torsion 13.98

Vertical tail first bending 16.83

Wing second bending 16.95

Wing outboard torsion 17.22

Fuselage second bending 19.81

Trailing edge flap rotation 23.70

Stabilator fore and aft 28.31

Wing second torsion 29.88

Fuselage third bend, aileron rotation 33.44

Aileron torsion 38.60

Stabilator second bending, wing 43.17

third bending

Fuselage first bending 8.15

Wing first bending 8.84

Stabilator first bending 12.98

Wing first torsion 14.85

Vertical Tail first bending 15.61

Wing second bending 16.79

Fuselage second bending 18.62

Trailing edge flap rotation 23.47

Fuselage torsion 24.19

Launcher rail lateral 24.35

Stabilator fore and aft 28.58

Wing second torsion 29.93

Aft fuselage torsion 37.80

Wing pitch 39.18

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Figure1.F/A-18HARV.

performanceenhancement, aswellasprovidingdatafor

correlationwithcomputational fluiddynamicssolutions.

ThisvehicleiscalledtheHigh-AlphaResearchVehicle

withThrustVectoringControlSystem(HARV-TVCS),

referredtosimplyastheHARVthroughout thisreport.

AsopposedtotheSRA,theHARVwasstructurallyvery

differentfromastandardF/A-18aircraft,ascanbeseen

bycomparingtheHARVmodaldataintable2withthe

SRAdataintable1.

Modificationsincludeadditionof Inconel ® vanes in

each engine exhaust for thrust vectoring and

corresponding ballast in the forward fuselage to

maintain the aircraft center-of-gravity location. Also

added were a research flight control system for feedback

control of aerodynamic surfaces and the vanes, an

inertial navigation system for AOA and sideslip rate

feedbacks, wingtip A0A vanes and pressure probes

(for airdata research purposes), and additional

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

is 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 Products

Div., International Nickel Co., Huntington, West Virigina.

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• J

instrumentation for loads, vane temperatures, and

structural dynamics. 1

Excitation Systems

This section describes the excitation systems used for

aeroelastic response on the SRA and aeroservoelastic

excitation of the F/A-18 HARV aircraft. System

descriptions, test procedures, flight experience, and test

results are discussed for each aircraft.

Wingtip Aeroelastic Excitation

Aeroelastic excitation of the F/A-18 SRA is discussed

in this section. Details of the system and flight testing

experience is supplemented with flight test results.

System Description

The structural modifications to the SRA prompted a

flight flutter envelope expansion and follow-on extensive

aeroelastic excitation research program with a dual

wingtip structural excitation system. Figure 2 shows this

wingtip excitation system is a modification of the single

wingtip version used on an F-16XL. 2 Exciters were

15 lb mounted on each wingtip. The difference in modal

frequencies with exciters and without exciters (table 1)

averaged 0.15 Hz with a maximum of 0.72 Hz. Each

exciter has a small fixed aerodynamic vane forward of a

rotating slotted hollow cylinder (fig. 2). When the

cylinder rotates, the aerodynamic pressure distribution

on the vane generates a force changing at twice the

cylinder rotation frequency. The vane is controlled from

a cockpit control box which activates an avionics box

mounted in the instrumentation bay. The avionics box

powers a variable-speed motor in the vane exciter

assembly. Two force levels are possible by adjusting the

slot openings to 25 percent (low-force, inner cylinder

closed) or 75 percent (high-force, inner cylinder open).

Three possible positions for the exciters were midwingtip, forward wingtip at the wingtip leading edge,

and aft wingtip near the wingtip trailing edge (fig. 2).

Other flight programs 3'4'5 have used this system with

varying degrees of success. In particular, the dual system

operates either symmetrically or antisymmetrically by

attempting to maintain a constant (0 ° or 180 °,

respectively) phase relationship between exciters. At

higher dynamic pressure, the exciters were known to

exhibit erratic phase-gain behavior due to binding in

both the motor drive mechanism and rotating cylinders. 5

Testing at Dryden exhibited the same type of

characteristics with the exciters on the F/A-18 SRA.

Figure 3 shows an example of phase difference between

right- and left-wing exciters for both low and high

dynamic pressure. At low dynamic pressure, the phase

between exciters is relatively constant near zero

compared 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).

5

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Phase between symmetric exciters, _1= 175 _ Phase between symmetric exciters, q = 1123 200

150

100

50

Phase, 0

deg

-50

- 100

- 150

- 200

0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40

Frequency, Hz Frequency, Hz

970218

Figure 3. Phase between left and right wingtip exciter force inputs for symmetric excitation. Low dynamic pressure at

175 psf (left). High dynamic pressure at 1123 psf (right).

had some phase discrepancy of the measured force

which was caused by both the phase degradation in the

individual exciters and to asymmetries in the aeroelastic

dynamics of the aircraft. However, the phase

discrepancies did not detract from the effectiveness of

the structural excitation, and it was still possible to

extract the proper transfer functions from each exciter to

the individual accelerometer responses. 6 Furthermore,

both symmetric and antisymmetfic modes were excited

for a particular sweep, whether it was a symmetric or

antisymmetric sweep.

Test Procedure

Linear and logarithmic sinusoidal sweeps up to 40 Hz

were used on the F/A-18 SRA, although the exciter is

capable of sweeping to 50 Hz. The exciters were

mounted on the wingtip launcher rails in forward and aft

position, independently. They were operated in both

low-force and high-force modes for 15-, 30-, or 60-see

forward and reverse frequency sweeps. Some sweeps

were actually multiples of two or four shorter duration

sweeps with no interrupt. Generally sweeps were

performed for symmetric and antisymmetric excitation

in each configuration. A total of 260 test points were

flown with the exciters in one or more of these optional

configurations at the specified flight condition. The test

parameters are summarized in table 3.

These test points were conducted to determine the

excitation system effectiveness in the subsonic,

transonic, and supersonic regimes. Frequency ranges

were chosen to excite the primary modes used in the

aeroelastic analysis, shown in table 1. A 3-12 Hz sweep

attempted to distinguish the first wing and fuselage

bending modes, and the 25-35 Hz sweep was done to

excite the aileron rotation mode for detection of any

transonic aileron buzz phenomena. Acceleration

measurements were taken at 200 sps from the fore and

aft wingtips, ailerons, and vertical and horizontal tails.

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

Exciter configuration

Exciter position

Mach

Altitude, ft

Force

Sweep

Duration, sec

Range, Hz

Multiple

Symmetric, antisymmetric, and independent

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

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

10k, 30k, and 40k

Low and high

Linear and logarithmic

15, 30, and 60

3-12, 3-25, 25-35, 3-35, 35-3, and 3-40

Single, double, and quadruple contiguous sweeps per maneuver

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Strain gage response, also sampled at 200 sps, was

taken at the exciter vane root to monitor the force input at

the aircraft wingtip. In reality, the force input is

distributed about the vane planform, but for simplicity's

sake a point force location was chosen to measure static

and dynamic force levels of the vane bending with

respect to the wingtip. Vane root strain is assumed to be

directly proportional to the vane airloads caused by

excitation. It is important to note that this is a

measurement of vane strain and not normal force, so it

also contains inertial effects from the vane itself as well

as modal response of the vane from the aircraft

aeroelastic dynamics.

For the last two flights the excitation system software

was modified to excite each vane independently, one

followed by the other, for each maneuver. Furthermore,

lower gear ratios were installed to overcome the

previously mentioned binding problem at high dynamic

pressure. The new gears reduced the frequency

bandwidth 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 was

accomplished before structural dynamics research was

performed. Unfortunately, the excitation system had

some problems early in the flight clearance phase.

Ground operation of the system before flight was

satisfactory, but in flight some of the following

anomalies occurred:

• Inconsistent rough starts and sweep motion in highforce mode

• Vane cylinders would not open in high-force mode

• Vane cylinders would not reset, or "home," properly

after sweep in either high- or low-force mode

These were thought to be environmentally related to

ambient temperature, dynamic pressure, or both. Failures

were duplicated in ground environmental test chambers

at low temperatures, but difficult to reproduce. Some

minor modifications in the vane electronics and homing

sensors resolved the homing problems, but the problems

related to the high-force mode persisted in flight.

Subsequently, after eighty maneuvers in six flights it was

decided to test only in the low-force mode. This was

adequate for envelope clearance and tolerated for

research flights.

Spectral information provided the most immediate

indication of the quality of data in terms of exciter sweep

parameters such as sweep direction, linear as compared

with logarithmic and, high- as compared with low-force

levels. Variations resulting from these test procedures are

important in modal estimation and flutter boundary

prediction. For example, to estimate uncertainty sets for

robust flutter prediction, numerous data sets are analyzed

at the same flight condition to discriminate between

dynamic and real model uncertainty, and differences due

to test procedure and nonrepeatability. 7 Figures 4 and 5

show differences that can occur in responses due only to

Wing

.05 1st bending

.04

Magnitude

/- Fuselage

.03 / 1st bending

/ /- Wing 2nd bending

.02

.01

0 5 10 15 20 25 30 35 40

Frequency, Hz 970219

Figure 4. Transfer function of symmetric exciter force to wingtip accelerometer for 30-sec linearly increasing

frequency sweep at M = 0.8 and 30 k ft. Sweep range: 3-35 Hz.

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.14

/- Wing

i / 1st bending

.12

/- Fuselage

/ 1st bending

.10

.08

Magnitude F Wing torsion

.06 /

.04

.02

It

0 5 10 15 20 25 30 35 40

Frequency, Hz 970220

Figure 5. Transfer function of symmetric exciter force to wingtip accelerometer for 30-sec linearly decreasing

frequency sweep at M = 0.8 and 30 k ft. Sweep range: 35-3 Hz.

the direction of the sweep. Clearly, the decreasing sweep

(fig. 5) generally provides much more response, but the

increasing sweep (fig. 4) improves modal excitation

between 15-20 Hz relative to the other modes.

The responses in the following PSDs (power spectral

densities) were generated at Mach 0.9, an altitude of

30,000 ft, and dynamic pressure of 360 psf from a

wingtip accelerometer. With the vanes in the aft wingtip

position, an antisymmetric reverse linear 30-sec

frequency sweep is compared with a reverse logarithmic

sweep in the PSDs of figure 6. Logarithmic sweeps

impart more energy in the lower frequencies, illustrated

by the first wing bending modes having more power near

6 Hz and 8 Hz. Figure 7 indicates that there is no

significant advantage in increasing the sweep duration

from 30-sec to 60-sec. However, figure 8 shows possible

improvement in response power by adding more sweeps

within the same period of time (30 sec). Antisymmetric

wing first bending is much more responsive while the

other modes are relatively unaffected by the sweep type.

The exception is the significant decrease in modal

Magnitude

.050

.045

.040

.035

,030

.025

.020

.015

.010

.005

_ Antisymmetric linear sweep

5 10 15 20 25 30 0

Frequency, Hz

_ Antisymmetric logarithmic sweep

5 10 15 20 25 30

Frequency, Hz

970221

Figure 6. Wingtip accelerometer PSD from antisymmetric linear (left) and logarithmic (right) exciter sweeps. Sweep

range: 3-35 Hz.

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! ;

" i

.050

.045

.040

.035

.030

Magnitude .025

.020

.015

.010

.005

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

m

B

m

m

5 10 15 20 25 30

Frequency, Hz

D

n

_vb%,

0 5 10

Frequency, Hz

15 20 25 30

970222

Figure 7. Wingtip accelerometer PSD from symmetric 30-sec (left) and 60-sec (right) exciter sweeps. Sweep

range: 3-35 Hz.

.050

.045

.040

.035

.o3o

'_ .025

.o2o

:i .015

.010

.005

0

Antisymmetric single

linear sweep

p

5 10 15 20 25 30

Frequency, Hz

Antisymmetric double

linear sweep

E

0 5 10 15 20

Frequency, Hz

Antisymmetric quadruple

linear sweep

25 30 0 5 10 15 20 25 30

Frequency, Hz

970223

Figure 8.Wingtip accelerometer PSD from antisymmetric single (left), double (middle), and quadruple (right) linear

exciter sweeps. Sweep range: 3-35 Hz. Sweep duration: 30-sec total.

response in the symmetric fuselage mode near 10 Hz

from single to quadruple sweeps. This mode apparently

needs the longer dwell time in the single sweep to

respond appropriately to an antisymmetric excitation.

Figure 9 shows a symmetric sweep from 3-35 Hz

as compared with a 3-12 Hz sweep response, both over

a 30-sec time period. Here there is noticeable

improvement in the wing bending modal responses

below 12 Hz from the 3 to 12 Hz sweep, as expected.

Notice the similarity between responses in figures 9

and 6, even though one is a symmetric and the other an

antisymmetric exciter sweep. This is a consequence of

the phase disparity between exciters mentioned earlier.

Finally, a comparison of responses with the exciters

moved from their aft position to forward positions on the

wingtips is seen in figure 10. The accelerometer

measurement is from the left aft wingtip. Symmetric first

wing bending shows an order of magnitude power

density increase near 6 Hz, but there is a dramatic

decrease in the wing second bending modal responses

near 16-17 Hz. These results are indicative of the

differences to expect in placement of the exciters relative

to output measurements, and how the effective mode

shape may influence the results.

To summarize the wingtip excitation test results,

despite the erratic performance of the exciters in

particularly the high force mode, a voluminous amount

of high quality data was accumulated for investigation of

differences resulting from exciter test configuration. Test

procedure is shown to be a significant parameter in test

results, except for sweep duration which did not improve

response seriously beyond 30-sec. Including multiple

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American Institute of Aeronautics and Astronautics
.050

.045

.004

.035

.030

Magnitude .025

.020

.015

.010

.005

Symmetric 3-35 Hz linear sweep

m

m

n

5 10 15 20 25 30

Frequency, Hz

Symmetric 3-12 Hz linear sweep

m

n

m

m

0 5 10 15 20 25 30

Frequency, Hz 970224

Figure 9. Wingtip accelerometer PSD from symmetric 3-35 Hz (left) and 3-12 Hz (right) exciter sweeps. Sweep

duration: 30-sec.

10-1

Magnitude 10 -2

10-3

100 Wingtip exciter vanes AFT

5 10 15 20 25 30

Frequency, Hz

10-4

0 0 5

Wingtip exciter vanes FWD

I I I I I

I 0 15 20 25 30

Frequency, Hz

970225

Figure 10. Wingtip aft accelerometer PSD from antisymmetric aft wingtip exciter (left) and forward exciter (right)

sweeps. Sweep range: 3-35 Hz, antisymmetric sweep.

sweeps within the same time window offers advantages

when including increasing and decreasing data in the

same test, as long as sufficient time is allowed for

adequate modal response. Exciter placement plays a

major role in swapping modal response between the

modes because of mode shape. Test repeatability is a

problem as long as exciter phase discrepancies exist.

Control Surface Aeroservoelastic Excitation

System Description

An important element of the F/A-18 HARV flight

system was the on-board excitation system (OBES).

This system was implemented to add programmed

digital signals to the control system actuator commands

for structural excitation. Inputs up to 25 Hz were added

to the stabilator, aileron, rudder, and pitch and yaw

vectored thrust commands. Data was generated with

80 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 the

aircraft center-of-gravity as 80 sps feedbacks to the

control system. The feedback measurements are more

critical than other structural measurements when

using excitation for aeroservoelastic considerations.

Verification of closed-loop stability is the primary

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American Institute of Aeronautics and Astronautics
objective.Measurement of signalsat the input

summingjunction(actuatorcommands) andfeedback

measurements allowcomputationofopen-andclosedlooptransferfunctions,loopgains,andmultivariable

stabilitymargins.

Test Results

Schroeder-phased harmonic signals which produce

approximately fiat spectral characteristics 8'9 were

compared to sinc sinx (..__) pulses, which theoretically

have fiat power spectra across a defined frequency range.

Contrarily, linear and logarithmic sweeps are known

to be deficient at lower and higher frequencies,

respectively. Figure 11 displays examples of sinc-pulse

and Schroeder-phased inputs from OBES into the

surface commands. These signals are stored in flight

computer memory. The Schroeder-phased signal is

calculated as

x(t)= A_cos((ot + _)

k

(1)

where N is the number of data and A is a specified

amplitude to acquire maximum power under the

saturation limits.

Note from the PSDs in figure 12 that the frequency

range for the sinc-pulse is 0-25 Hz, whereas the

Schroeder-phased signal was programmed for 5-25 Hz.

1.2

1.0

.8

•u .6

m .4 -

• 2 --

0

--.2

5.0

_ Sinc-pulse input

O

"O

._=

eo_

o=

:E

_ Schroeder-phasedinput 1.0

.8

.6

.4

.2

0

--.2

--.4

--.6

--.8

-1.0 I I I I I t I i I t I I I I

5.5 6.0 6.5 7.0 7.5 3 4 5 6 7 8 9 10 11 12

Time, sec Time, sec

970226

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

input (fight).

2.5

O.

t-

"; 2.0

-i

?- 1.5

O

C

1.0

3.5 X 10 -5 Maximum entropy PSD

3.0 --__vv1j_v_ _% _

.5

4.5 X 10 -3 Maximum entropy PSD

4.0 -

3.5 -

.E 3.0 --

_ 2.s -

rL 2.O -

"0

ID

2 1.5 -

,,C

_ 1.0 --

• 5 --

0 5

I 1 I I _ I I I

0 5 10 15 20 25 30 10 15 20

Frequency, Hz Frequency, Hz

25 30

970227

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

11

American Institute of Aeronautics and Astronautics
More importantly,for inputscloseto unity,the

Schroeder-phased PSDis two ordersof magnitude

greaterthanthe sinc-pulse,therebyverifyingthe

propertyoflowpeakfactorforagivenpowerspectrum

(fig.11).1° Peakor crestfactoris definedas the

differencebetweensignalmaximumandminimum

valuesdividedbytheroot-mean-square valueofasignal.

It is ameasureof theflatnessof thepowerspectrum.

Lowpeakfactorsignalsaregenerallydesirableinsystem

testingto avoidlargesystemperturbations. Thisisan

obviousbenefitfor preventinginputsaturationwhile

maximizingsignal-to-noise ratio.

PSDsof normalandlateralaccelerationfeedback

responsesareshownin figure13for sinc-pulseand

Schroeder-phased OBESinputs.Disregardingtheorder

ofmagnitudedifference, theresponsesarequitesimilar

intermsof modalresponse. Differencesareseeninthe

largerelativeresponsebelow10Hzfromthesinc-pulse

lateralaccelerationcomparedwithhigherfrequency

modes,andsomeactivityaround20Hzfromnormal

accelerationfortheSchroeder-phased responsethatthe

sinc-pulsedoesnotexcite.

Figures14and15comparetransferfunctionsbetween

sinc-pulsedand Schroeder-phased OBES inputs,

,. 5x10 -5

.2__ 4_ iIMaximumentr°pyPSD

°

0

g

ell

z OL /_

,. 5 x 10 -4

,'-°__ 4ou 32IMaxlmumentr°pyP__ ° A z 0 t . If'_-_

c 2.5 x 10 -6

2.0

1.5

O

,_ 1.0

_ .5

0

_ 0

.,J 5 10 15 20

Frequency, Hz

_L...

25

tO

30

2.5 x 10 -5

1.5

1.

5 10 15 20 25 30

Frequency, Hz

970228

Figure 13. F/A-18 HARV feedback accelerometer responses to sinc-pulse and Schroeder-phased inputs (note scale

difference): normal acceleration (top) and lateral acceleration (bottom). Sinc-pulse accelerometer response (left).

Schroeder-phased accelerometer response (right).

Magnitude,

dB

0

-10

- 20

- 30

Sinc-pulse transfer functions

_ OBES input to normal acceleration

I I I I t t I I

Magnitude,

dB

10 I-- OBES input to lateral acceleration

L

0

-10

-20

- 30

- 40

- 50

0 5 10 15 20 25 30 35 40

Frequency, Hz

970229

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

12

American Institute of Aeronautics and Astronautics
v I _

Magnitude,

dB

0

-10

- 20

-30

-- Scroeder-phased transfer functions

- I I

Magnitude,

dB

10 -- OBES input to lateral acceleration

0

-10

- 20

- 30

- 40

-5o I I I I I I I I

0 5 10 15 20 25 30 35 40

Frequency, Hz

970230

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

respectively. OBES inputs are to all the surfaces

sequentially, and outputs are normal and lateral

acceleration feedbacks. Sinc-pulse transfer functions

lack the detail and definition of the Schroeder-phased

responses. Magnitudes differ by as much as 20 dB near

15 Hz. Schroeder-phased responses tend to highlight the

signal from the noise and discriminate dominant modal

dynamics more readily than sinc-pulse responses. An

important aspect of this comparison is the extent to

which responses can differ depending on the input. This

difference is a critical factor if stability analyses depend

on these results. These results are preliminary and more

extensive analyses can be found in reference. 11

Signal Analysis of Aeroelastic Data

In this section, some signal processing properties of

the input signals and accelerometer responses are

studied for model validation and flight flutter boundary

prediction. Wavelet analyses are highlighted to detect

time-varying and nonlinear dynamics. Also, timefrequency applications for enhanced signal processing of

vibration data are presented.

Spectral Analysis

Analysis of transient data violates the assumptions of

any FFT-based spectral estimation technique. This

technique assumes time-invariance, stationariness, and a

signal composed of a sum of infinite sinusoids.

Windowing and averaging can help remove some

distortion but also add bias errors. For these reasons,

autoregressive (AR) spectral estimation is preferred for

transient data. In the class of AR spectral estimation

methods are the reflection coefficient estimation

algorithms. In particular, the maximum entropy

method 12 (MEM) is one method being adopted by

NASA Dryden for frequency domain transient signal

analysis. MEMs estimate the correlation sequences

assuming finite correlation extrapolation to infinity is

most random, or has maximum entropy, thereby assuring

a positive definite power spectral density function.

Autoregressive coefficients of an all-pole filter

representation of the signal are estimated directly from

the data without using autocorrelations. Akaike

information criteria 12 are used to determine the

autoregressive order of the process (which can also be

multichannel, or MIMO) for PSD and transfer function

estimation. Model order selection for the AR model of

the signal represents the classic tradeoff between higher

resolution and decreased variance.

Examples of classical FF-T-based PSD estimates

compared to MEM estimates are represented in figure 16

with F/A-18 SRA wingtip accelerometer data. These

data were acquired at Mach 1.2, an altitude of 30,000 ft,

and 630 psf dynamic pressure with symmetric

excitation. Top plots are left wingtip accelerometers and

the bottom plots are right wingtip accelerometers.

Comparing the classical (left) with MEM (right)

estimates, both methods estimate activity near

symmetric wing first bending (6 Hz), but then the MEM

estimates of modal response between 7-10 Hz is

dramatically different from the relatively suppressed

13

American Institute of Aeronautics and Astronautics
.04

•_ .03

"_ .02

01

m

:S .01

Classical PSD Maximum entropy PSD

I I

.04

.02

:s .01

I

0 5 10 15 20

Frequency, Hz

25 30 0 5 10 15 20 25 30

Frequency, Hz

970231

Figure 16. Classical FFT-based PSDs compared to maximum entropy estimates: Left wingtip accelerometer (top) and

right wingtip accelerometer (bottom) responses. Classical (left). Maximum entropy (right).

classical response estimates. Symmetric fuselage first

bending or antisymmetric wing first bending near 9 Hz

are not even visible in the classical estimates.

Alternatively, near 15 Hz the classical estimates are

nearly double the maximum entropy estimates. Between

13-18 Hz the classical estimates include contributions

from wing torsion, second bending, and wing outboard

torsion, whereas the MEM estimates are not significant

in this range.

These comparisons are intended to highlight the

strengths and weaknesses of the two estimates. A

reasonable conclusion is that the standard practice of

depending on classical estimates is suspect. Other

spectral analysis techniques should be supplemented

with the standard ones for a thorough complementary

analysis.

Frequency domain modal system identification and

stability estimation rely on high quality frequency

responses to get reliable results. Some estimation

techniques attempt to curve fit the data with a parametric

representation of the response, and use the parameters to

determine stability. Others incorporate frequency

response data into a state space identification algorithm

and stability is derived from this realization.

To compare the MEM to classical methods in a system

identification procedure, a symmetric linear sweep

response is used in a transfer function fit procedure for

modal frequency and damping estimation. Figure 17

10-1

Magnitude 10-2

10-3

Classical response and 20th-order curve fit

I I I

5 10 15 20 25

Frequency, Hz

MEM response and 20th-order curve fit

^ _

" _, _^

I I F f

5 10 15 20 25

Frequency, Hz

970232

Figure 17. Left forward wingtip accelerometer responses from a symmetric linear sweep using classical (left) and

MEM methods (right). Classical response (dashed) and 20th-order fit (solid). MEM response (dashed) and 20th-order

fit (solid).

14

American Institute of Aeronautics and Astronautics
(left) is a left forward wingtip accelerometer magnitude

response from symmetric F/A-18 SRA excitation

computed using a classical method and fit with a 20 thorder parameterized stable minimum phase transfer

function. 13 In figure 17 (right) the corresponding

responses are plotted using a MEM method. The

classical response is noisier than the MEM, and does not

exhibit the wing first bending modal response of the

MEM method near 6 Hz or symmetric wing first torsion

near 15 Hz. However, MEM does not distinguish wing

second bending near 17 Hz as well as the classical

method. Figure 18 shows the same comparisons are

made with the left aft wingtip accelerometer. Again, the

MEM method estimates more modal response near 6 Hz,

yet elsewhere the responses are similar.

Frequency and damping ratios computed by fitting the

responses with a parameterized transfer function for

these respective wingtip accelerometers are displayed in

table 4. Note that the table only addresses symmetric

modes even though antisymmetric modes are also being

excited (figs. 17 and 18). Since there are some significant

differences between classical and MEM estimates,

without a truth model an argument can again be made

that FFT-based methods need to be complemented with

other types of analyses.

Transfer Functions

Traditional transfer function estimation generally uses

what is called the H 1 estimate, yet it is well known to

be biased with input measurement noise. Another

10-1

Magnitude 10 -2

10-3

5

Classical response and 2Orb-order curve fit MEM response and 20th-order curve fit

E

I

B

M

m

I I I I

10 15 20 25 15 20 25

Frequency, Hz Frequency, Hz 970233

t I I I

lO

Figure 18. Left aft wingtip accelerometer responses from a symmetric linear sweep using classical (left) and MEM

methods (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 a

symmetric wingtip exciter sweep.

Symmetric Wing Fuselage Wing Wing Wing

mode first bending first bending first torsion second bending outboard 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

15

American Institute of Aeronautics and Astronautics
estimate, H 2 , is less common since it is biased under

output measurement noise and unmeasured external

disturbances. H v is the geometric mean of H 1 and H 2 ,

where (Gxy, Gy x , Gxx, and Gyy are spectral densities),

• H 1 = Gyx/Gxx, minimizes error due to noise at

output y, sensitive to input noise

• H^ = G IG , minimizes error due to noise at

• z yy . xy

input x, sensxtlve to output no_se

Therefore, for a single input,

=Orgy= iayxl axx

(2)

where H 1 < H v < H2, and the true noise-free transfer

function H 0 also satisfies H 1 < H 0 < H 2 . H v is the

so-called robust transfer function estimate 14 because it

is uniformly less biased than either H 1 or H 2 .

Data generated from the wingtip excitation system is

not ideal at either accelerometer outputs or excitation

input• Some data corruption results from using strain

gauge measurements for the inputs• The response in this

case feeds back to the excitation force applied since the

strain gage is measuring strain between the responding

wingtip and forced vane root. Ideally, the spectral

estimates should be referenced to an excitation drive

signal (like torque), but this is not available as a

measurement. Therefore, for systems in which the input

excitation force is unavailable, H v provides optimal

transfer function estimation. H v can be degraded by

unmeasured external disturbances, but the force input

from the exciter is believed to dominate these

phenomena.

Frequency responses using the three estimates are

plotted in figure 19 using the traditional FFT-based

spectral estimates, and in figure 20 using the maximum

entropy AR method at the same resolution. These are

responses from the left force exciter to a left wingtip

accelerometer. They are comparable but differ in some

details. Typically, the gap between the H 1 lower bound

and H 2 upper bound is wider in the MEM response. The

MEM response is smoother while distinguishing

essential features. Modes near 6 Hz, 8-9 Hz, 14 Hz, in

the 15-20 Hz range, and even 22 Hz and 24 Hz are

distinguishable in both classical and MEM responses.

Calculating both types of responses gives more credence

to the analysis. Otherwise, some of the modes may be

misinterpreted. Also notice the dramatic differences that

can result between H 1 or H 2 , and H v .

Admittedly, there are different techniques for

analyzing specific types of excitation data, (random,

periodic or transient) with classical methods. But the AR

methods are not subject to restrictions depending on

Magnitude,

dB

-10

.'..,, ,, •

-20 .. ,

-30 f_

-50 I

- 60

- 70

0

Hv, H1, and H2 transfer functions -- Hv

---- H1

.... H2

i .... i i:i: 

•;, - _ • . :

V

I I I I I

5 10 15 20 25

Frequency, Hz 970234

Figure 19. Classical FFT-based transfer functions H v, H l, and H 2 .

16

American Institute of Aeronautics and Astronautics
Magnitude,

dB

-10

- 20

-3O

- 4O

- 5O

-6O

- 7O

f Hv, H1, and H2 transfer functions _ Hv

. __ H1 ,-

•: !- .... H2

•: :..

.",. :: - :. :i i/. i /

• "°'°" °' " "" I

'"'

" ii ".: "'." ." "",.""'"

\\/J la I

Ij

I I I I I

0 5 10 15 20 25

Frequency, Hz 970235

Figure 20. Maximum entropy transfer functions H v , H l, and H 2 .

the type of data, so alterations from averaging and

windowing are unnecessary.

Time-Frequency Analysis

Analysis of the frequency content of a signal x(t)

traditionally uses the Fourier transform which projects

the signal onto sinewave basis functions of infinite

duration for stationary signals. This transform is not

localized in time. For time-varying signals a transform of

the form

T(x(t)) = X(t, to)

is needed to locate instantaneous frequencies in x(t).

Such a transform is limited in resolution by

the Hiesenberg uncertainty principle Ato. At > 2.

Resolution problems resulting from the uncertainty

principle can be minimized by a time-frequency

decomposition called the wavelet decomposition. 15

The wavelet decomposition performs an orthonormal

projection of the signal onto functions that are adapted to

the frequency resolution needed. A continuous wavelet

transform (CWT) is defined as

IS_, ( t-'_ _ CWT('c,a) = "7 x(t)h*, _ jdt__ ,4a ",

where ha, x(t) = h t"--if-" - '_1 is the wavelet basis function, *

is its complex conjugate transpose, x is the local time,

and a is a scale or dilation parameter set to match the

level of resolution desired. With the CWT the time

resolution is arbitrarily good at high frequencies and the

frequency resolution becomes arbitrarily good at low

frequencies, within the limits of the uncertainty

principle. Time-frequency analyses attempt to minimize

the effects of this resolution problem by using a priori

knowledge of the signal properties, or adapting the

(3) resolution to the signal. 16,17

A procedure has been developed 6 to filter unwanted

distortions and extract desired features from the input

excitation and output structural response data of the

F/A- 18 SRA and HARV aircraft. These feature filtered

data are then used to compute cleaned signals for

transfer functions and system identification algorithms.

An example of filtering the undesirable features of

more complicated input-output signals using a timefrequency representation will be a double logarithmic

sweep from the F/A-18 SRA excitation system. A

scalogram of the original input signal is shown in

figure 21 (top). Harmonics from the strain gage input

(4) measurement can be readily detected in the timefrequency map as the darker portions of the image.

17

American Institute of Aeronautics and Astronautics
Theseareasinthemaprepresent largeamplitudeCWT

coefficients. The harmonics indicate nonlinear exciter

vane response from the rotating slotted cylinders at the

wingtips, which is deemed undesirable for subsequent

linear state-space identification methods. Therefore, the

input signal is modified by extracting the desired timefrequency map from the scalogram to retain the

commanded input signal from the main harmonic

(fig. 21 (bottom)).

o

5

1o

15

Frequency, 20

Hz

25

3O

35

40

0

Signalintime/frequencydomain

5 10 15 20 25 30

Time,sec

970017

SignalIntime/frequencydomain

0

5

10

15

Frequency, 20

Hz

25

30

35

40

0 5 10 15 20 25 30

Time,sec

970018

Figure 21. Scalogram of original double logarithmic

exciter input and feature filtered input. Scalogram of

original exciter input signal (top). Scalogram of feature

filtered exciter input signal (bottom).

These CWT coefficients are then used to reconstruct

the time domain input signal by inverse transforming at

each frequency (o back to the time domain. Figure 22

shows the original signal in the top plot, including

harmonics. Reconstruction from the scalogram of

figure 21 (top) is shown in the middle plot. Notice the

reconstruction is not exact since there is some distortion

in the wavelet processing procedure. Finally, the feature

filtered signal from figure 22 (middle) is reconstructed

with only the main harmonic, as shown in the bottom

plot of figure 22.

Similar procedures are performed on the

accelerometer measurements and transfer functions are

computed using the feature filtered data sets from the

F/A-18 SRA. Transfer functions from both exciter inputs

(left and right columns, respectively) to an acceler0meter

output are plotted in figure 23. The top four plots result

from classical Fourier methods, and the corresponding

bottom plots are results of using the feature filtered timefrequency method. As shown, very general maps in the

time-frequency plane can be effectively filtered in this

manner. More details concerning the development and

application of wavelet filters to analysis of F/A- 18 SRA

aeroelastic data can be found in references. 6

Flight Flutter Prediction

Several modal estimation algorithms have been

applied to flight flutter testing in both frequency and time

domain 18'19 for extracting stability estimates and

detecting time-varying and/or nonlinear dynamics. No

algorithm has been unanimously accepted in the

aeroelastic community because of 1) problems with

estimation of closely spaced modes or assuring stable

estimates for stable systems, 2) assumption of time

invariance, linearity, or stationariness, 3) sensitivity to

type of input or noise levels, 4) lack of technique for

estimating error bounds, and, 5) computational

complexity. In an attempt to qualify the relative merit of

the methods with actual flight data, a non-exhaustive list

of algorithms in table 5 is being considered for

evaluation at NASA Dryden for usefulness in flutter

testing. The frequency domain subspace identification

methods combined with time-frequency multiscale

wavelet techniques are the most promising

algorithms. 6,20,21

Modal damping is unfortunately the most popular

parameter to track for determining proximity to the

flutter boundary. It can be a very poor indicator of

impending instability as it depends on critical flight

parameters (Mach, ?_) in a highly nonlinear fashion.

Tests performed with different input signals, and the very

common occurrence of nourepeatability at identical test

conditions, can change damping estimates dramatically

using state-of-the-art identification schemes.

18

American Institute of Aeronautics and Astronautics
r

Amplitude

20

15

10

5

0

-5

-10

-15

-20

Original signal in time domain

'I

,i ,I JL.LIii

liilliIlilW

15

Reconstructed signal in time domain

Amplitude

10 -

5

o_

-10

-15

,Ill .111 i I_ II , I,IIII _

Amplitude

Reconstructed signal in time domain

8 1 IA i_,

6 '

4

2

0

-2

-4

[ t" t

i

0 5 10 15 20 25 30

Time, sec

970236

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

reconstruction of feature filtered input signal (bottom).

19

American Institute of Aeronautics and Astronautics
Magnitude

Phase,

deg

.20

.15

.10

.05

0

200

100

0

- 100

- 200

t

6 8 10

Frequency, Hz

12

i

.......................... i................................. : ........ i ............................

i

6 8 10 12

Frequency, Hz

970005

Magnitude

.20

.15

.10

.05

0

Phase,

deg

200

100

0

- 100

- 200

6 8 10 12 6 8 10 12

Frequency, Hz Frequency, Hz

970006

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 wingtip

accelerometer output (right). Classical Fourier transfer functions (top). Time-frequency generated transfer functions

(bottom).

20

American Institute of Aeronautics and Astronautics
Table 5. Survey of modal estimation algorithms for aeroelastic applications.

Frequency domain Time domain

Spectral analysis

FFT/correlation methods 22

Maximum entropy/maximum likelihood 12'26

l2 and l,, curve fitting 28'29'30'31

Orthogonal polynomials 33'34

Time series analysis

Correlation/null-space methods 23'24'25

Linear prediction (LS, MLE, IV, PEM) 27

Total least squares (TLS) 32

Total least norm (TLN) 35

Robust identification 36

H,, Norm-bounded ID 37 Worst-case input-output l 1 ID 38

Subspace identification 39'40

Realization-based methods

Transfer Function Fitting (TEE) 41 ERA/OKID 42

Auto-Cross-Spectra Fitting (ACSF) 41 Q-markov cover 43

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

Direct subspace identification

FORSE, 20,46,47 McKelvey 21 ORSE, 48 N4SID 39

High order spectral analysis 49

Frequency-time multiscale wavelets 15,50,51

Robust Flutter Boundary_ Prediction

A kt-based measure of flutter boundary prediction is

proposed which has the following important desirable

features:

1. Robust (reliable) identification in the presence of

estimation model uncertainty

2. Quantification of the error bounds because of

unmodeled dynamics, uncertain parameters and

noise

3. Well-behaved stability measured as a function of

critical flight parameters (Mach, 7/)

4. Incorporation of model structure into the

identification procedure (prior knowledge)

5. Dependence on a minimum amount of test points

for extrapolation to the flutter boundary

6. Algorithmic simplicity for on-line implementations

7. Realistic assumptions

This kt-based flutter prediction method with" these

seven advantages to compute flutter instability

boundaries is of obvious benefit to the aeroelastic

community. In this method, flight data is incorporated

into the model validation process to account for any

differences between the model and the aircraft. Robust

worst-case flutter margins are computed to directly

account for variations in the data (non-repeatability) and

model parameter uncertainty. These robust flutter

margins are generated by forming realistic uncertainty

operators that ensure that a family of models includes the

actual aircraft dynamics. The procedure can greatly

improve the efficiency and safety of an envelope

expansion with accurate and confident identification.

Data from safe and benign flight conditions are used to

predict flutter boundaries.

Critical elements for this technique are model

validation and robust stability measures. Systeminduced norms are used for model error descriptions to

measure the 'closeness' of systems in the context of

robust control. 38'52 The key question for model

validation is this:

Given the available data and model, does there

exist a perturbation within the range of allowed

norm-bounded uncertainty such that the model

describes the data?

A nonconservative approach to this issue is to find the

smallest perturbation such that the data fits the model.

Robust flutter prediction poses this additional question:

21

American Institute of Aeronautics and Astronautics
Given the available data and models, what is the

smallest norm-bounded perturbation of the current

flight condition that can drive the system to

become unstable?

This is the robust stability aspect of the problem. In

this context, structuring the error in the aeroelastic

model and applying model validation concepts using

flight-derived uncertainty models avoids relying on

damping 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 prescribed

manner. Damping estimates are replaced by the stability

margin g.

These robust stability concepts are used to

parameterize an aeroelastic model with dynamic

pressure at specific Mach numbers, and introduce

uncertainty structure to account for model inaccuracy.

Figure 24 represents a robust stability parameterization

over g/ of the state-space aeroelastic system. The

nominal flutter margin is that value of ?/ which results in

aeroelastic instability.

e-_------

F-18

970237

Figure 24. Robust stability parameterization over ?/ for

nominal 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 accounted

for by the model. If not, the model is adjusted by

increasing the real parameter uncertainty in modal

frequency and damping. After this procedure, other

unmodeled dynamic uncertainty is adjusted to include

multiple data sets at a particular flight condition

(Mach, ?:/).

An uncertainty description consisting of modal

uncertainty, Amodes, and input multiplicative

uncertainty, Ain, is used to account for errors and

unmodeled dynamics resulting in the system depicted in

figure 25. This model is created for each flight condition,

from all the available flight data responses. Now the

model envelopes all the aeroelastic dynamics of the

aircraft at a particular Mach number. Since the model is

now validated by the flight data, realistic robust flutter

margins can be computed.

Flutter points are derived with respect to dynamic

pressure and the system uncertainty model derived from

the data, using the structured singular value, 13 g. This

worst-case stability boundary guarantees stability within

the range of system uncertainty deduced from the

mismatch between model and data.

Advantages of this g-based robust flutter boundary

prediction method are as follows:

• Model validation can be cast in the frequency or

time domain 52'55

• Parameter identification uncertainty can be

incorporated into the model

• Identification error estimates are not essential

• Generalized uncertainty descriptions are admissible

(real, complex, time-varying, nonlinear)

• Stability norms generally behave smoothly at

instability boundaries

Nise I 8_ __ A in H Win

e_l F.18 i_<{ _d

970238

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

22

American Instituteof Aeronautics and Astronautics
• Someconservatismfor flight safetywill always

exist(nominal vs.robustflutterboundary)

• Aeroservoelastic stabilityis analyzedinthesame

framework

• Procedurecanbetunedforon-lineanalyses

• Naturallyextendsto robustcontrolsynthesisfor

fluttersuppression

If theuncertaintymodelisinvalidatedatsomeflight

condition,eitherthe identificationproceduremust

berevisited,the uncertaintydescriptionmodified

accordingly, orboth.Whilethemodelisnotinvalidated,

it remainsa robuststabilitymeasure. A companion

paper53detailstheprocedurefor usingF/A-18SRA

aeroelasticdatainpredictionoftheaeroelasticstability

boundary.

Robust Stability Results

Flutter prediction computation uses the finite element

and unsteady aerodynamic pk solutions computed from

the STARS 56 code. Figures 26 and 27 represent this

flutter boundary with solid lines for symmetric and

antisymmetric modes, respectively. These are the socalled 'matched point' flutter solutions which account

for actual atmospheric conditions in the solution

process.

Circled points in the figures are solutions of the

minimum destabilizing perturbation of dynamic

pressure from a nominal condition using Ix (fig. 26

and 27). These points are nominal flutter solutions using

the 7/ parameterization of figure 24 for each Mach

number with no uncertainty operators in the stability

margin computation. A good match with the solid lines

indicates that using the generalized aerodynamic forces

at a nominal condition will extrapolate to the proper

analytical result from the rt parameterization. The only

exception where matches are not optimal occurs around

the transonic area where the aeroelastic pk solutions are

most sensitive.

Finally, the analytical flutter points are compared with

the robust structured singular value solutions computed

with respect to the uncertainty description Amodes, Ain

of figure 25. Using all available flight data, model

validation and robust stability computations result in the

dashed lines of these figures (figs. 26 and 27). Robust

results are more conservative, as expected, due to the

uncertainty model updates from incorporation of the

data.

Conclusions

Improvements in aeroelastic and aeroservoelastic

flight testing have been addressed. F/A-18 SRA and

HARV aircraft provide valuable data for analysis of

60,000

40,000

20,000

Altitude, 0

ft

- 20,000

- 40,000

- 60,000

I

15 percent flutter margin

Solid: nominal flutter

using pk

Circle: nominalflutter

using

Dashed: robust flutter

using

I I I

.2 .4 .6

/

\ /

\'_/ o

I I I I

.8 1.0 1.2 1.4 1.6 1.8

Mach 970239

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

23

American Institute of Aeronautics and Astronautics
Altitude,

ft

60,000

B

40,000

20,000

0

DClr!_eja ilid::r_!iaP_ nusingg ri /

/ ___,_u_

I I I I I 1 I I I

0 .2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8

Mach

970240

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

- 20,000

- 40,000

- 60,000

excitation mechanisms, model estimation algorithms,

and stability boundary prediction. External excitation for

aeroelastic research was conducted on the F/A-18 SRA

and on-board signal generation was used on the F/A-18

HARV for aeroservoelastic investigation. However, data

from excitation systems is only as reliable as the system

performance, so excitation system anomalies need to be

accounted for when using estimation algorithms for

stability estimates. Classical spectral estimates are

suspect in a time-varying or nonstationary environment,

so parametric maximum entropy spectral estimates are

suggested as an alternative to supplement classical

analyses. Furthermore, advanced procedures in timefrequency methods have been presented which will assist

in detecting and compensating for data distortion, such

as nonlinearity, before modal analysis. Time-frequency

wavelet analyses have also been exploited for detecting

departures from time-invariance, stationariness, and

noise assumptions. Such applicable data processing

techniques, tuned for the particular test environment, are

desired for enhanced on-line analyses.

Modal identification must account for divergence

from algorithmic assumptions in the form of error

bounds. A method which accounts for such uncertainties

in the data and analysis results has been introduced.

Modal damping as an unreliable stability predicter is

replaced by a robust It-based stability margin for more

confident and efficient stability boundary prediction.

Identification consistent with the uncertainty structure in

an aeroelastic model provides an explicit measure of

stability in a modern robust control framework. Robust

model validation accounts for the uncertainty structure,

guaranteeing that any system will remain stable within a

confidence bound. Therefore, model validation

techniques are exploited to develop structured

uncertainty models consistent with the data. Stability is

guaranteed within the uncertainty deduced from the data.

F/A-18 SRA data is used to demonstrate worst-case

flutter boundary prediction using this method. This

procedure can be tuned for robust aeroelastic and

aeroservoelastic on-line stability prediction.

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27

American Institute of Aeronautics and Astronautics
REPORT DOCUMENTATION PAGE FormApproved OMB No. 0704-0188

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April 1997 Technical Memorandum

4.TITLE AND SUBTITLE 5. FUNDING NUMBERS

Overview of Recent Flight Flutter Testing Research at NASA Dryden

6. AUTHOR(S)

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

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Dryden Flight Research Center

P.O. Box 273

Edwards, California 93523-0273

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

WU 522-32-34

8. PERFORMING ORGANIZATION

REPORT NUMBER

H-2165

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA TM-4792

11. SUPPLEMENTARY NOTES

Presented as AIAA 97-1023 at the 38th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and

Materials Conference and Exhibit, Kissimmee, Florida, April 7-10, 1997.

12a. DISTRIBUTION/AVAILABILITY STATEMENT

Unclas sified--Unlimited

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12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

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 process

with more accurate and automated techniques for stability boundary prediction. The important elements of this

effort so far include the following: 1) excitation mechanisms for enhanced vibration data to reduce uncertainty

levels in stability estimates; 2) investigation of a variety of frequency, time, and wavelet analysis techniques

for signal processing, stability estimation, and nonlinear identification; and 3) robust flutter boundary

prediction to substantially reduce the test matrix for flutter clearance. These are critical research topics

addressing the concerns of a recent AGARD Specialists' Meeting on Advanced Aeroservoelastic Testing and

Data Analysis. This paper addresses these items using flight test data from the F/A-18 Systems Research

Aircraft and the F/A-18 High Alpha Research Vehicle.

14. SUBJECTTERMS

Aeroelasticity, Aeroservoelasticity, Flutter, Model validation, Robust stability,

Stability prediction, Structural dynamics, System identification, Wavelet analysis

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION

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