NASA/TM—2011–216421

Reduced Uncertainties in the Flutter Analysis 

of the Aerostructures Test Wing

Chan-gi Pak and Shun-fat Lung

Dryden Flight Research Center, Edwards, California

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January 2011
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NASA/TM—2011–216421

Reduced Uncertainties in the Flutter Analysis 

of the Aerostructures Test Wing

Chan-gi Pak and Shun-fat Lung

Dryden Flight Research Center, Edwards, California

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January 2011
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Abstract

Tuning the finite element model using measured data to minimize the model uncertainties is a 

challenging task in the area of structural dynamics. A test validated finite element model can provide a 

reliable flutter analysis to define the flutter placard speed to which the aircraft can be flown prior to flight 

flutter testing. Minimizing the difference between numerical and experimental results is a type of 

optimization problem. Through the use of the National Aeronautics and Space Administration Dryden 

Flight Research Center’s (Edwards, California) multidisciplinary design, analysis, and optimization tool 

to optimize the objective function and constraints; the mass properties, the natural frequencies, and the 

mode shapes are matched to the target data, and the mass matrix orthogonality is retained. The approach 

in this study has been applied to minimize the model uncertainties for the structural dynamic model of the 

aerostructures test wing, which was designed, built, and tested at the National Aeronautics and Space 

Administration Dryden Flight Research Center. A 25-percent change in flutter speed has been shown after 

reducing the uncertainties. 

Nomenclature

AR aspect ratio

ATW aerostructures test wing

ATW1 the first aerostructures test wing

ATW2 the second aerostructures test wing

CEM central executive module

CG center of gravity

DC gradient-based algorithm that is DOT, with continuous design variables

DFRC Dryden Flight Research Center

DOF degrees of freedom

DOTs design optimization tools

F original objective function

FE finite element

G subscript for target values (or measured quantities)

GA genetic algorithm

GCD genetic algorithm with continuous discrete or mixed (continuous/discrete) design 

variables

GD genetic algorithm with discrete design variables

GVT ground vibration test

gi inequality constraints

hj equality constraints

IXX computed x moment of inertia about the center of gravity

IXXG target x moment of inertia about the center of gravity

IXY computed xy moment of inertia about the center of gravity

IXYG target xy moment of inertia about the center of gravity

IYY computed y moment of inertia about the center of gravity

IYYG target y moment of inertia about the center of gravity

IYZ computed yz moment of inertia about the center of gravity

IYZG target yz moment of inertia about the center of gravity

IZX computed zx moment of inertia about the center of gravity
2

IZXG target zx moment of inertia about the center of gravity

IZZ computed z moment of inertia about the center of gravity

IZZG target z moment of inertia about the center of gravity

J performance index

Ji objective functions (optimization problem statement number i = 1, 2, ... , 13)

K stiffness matrix

K orthonormalized stiffness matrix

L new objective function

l number of modes

M mass matrix

M orthonormalized mass matrix

MAC modal assurance criterion

MDAO multidisciplinary design, analysis, and optimization 

m number of sensors (or number of measured degrees of freedom)

NASA National Aeronautics and Space Administration

n number of modes to be matched

q number of inequality constraints

r number of equality constraints

SEREP system equivalent reduction expansion process

T transformation matrix

W computed total mass 

WG target total mass 

X x-coordinate of computed center of gravity

X design variables vector

XG x-coordinate of target center of gravity

Y y-coordinate of computed center of gravity

YG y-coordinate of target center of gravity

Z z-coordinate of computed center of gravity

ZG z-coordinate of target center of gravity

ε small tolerance value for inequality constraints

λ Lagrange multiplier

λi scaling factors

Φ computed eigen-matrix ( m × n )

ΦG target eigen-matrix ( m × n )

Ωj j-th computed frequency

1. Introduction

A test article called the aerostructures test wing (ATW) was developed and flown at the National 

Aeronautics and Space Administration (NASA) Dryden Flight Research Center (DFRC) (Edwards, 

California) on the NF15B (McDonnell Douglas, now The Boeing Company, Chicago, Illinois) test bed 

aircraft, as shown in figure 1, for the purpose of demonstrating and validating flutter prediction methods 

during flight (ref. 1). The first aerostructures test wing (ATW1), flown in 2001, was originally developed 

to directly address requests for better flight flutter test techniques by providing a functional flight test 

platform. While the first series of tests was extremely successful, the minimum amount of instrumentation 

(structural accelerometers and strain gages) was chosen to satisfy the scope of the program. These sensors 
3

were limited in the capability to answer questions of aeroelastic interactions, sources of nonlinearity, 

physical mechanisms of aeroelastic coupling, and feedback dynamics between the structure and 

aerodynamics.

A second aerostructures test wing (ATW2), as shown in figure 2, has been built for the demonstration 

of state-of-the-art sensor technologies for simultaneous, distributed, and collocated measurement of shear 

stress (skin friction); steady and unsteady pressures; and structural strain and accelerations for mode 

shapes and other modal properties. This wing was flown on the NF15B airplane in December 2009.

A block diagram for a robust flutter analysis procedure used at NASA DFRC is given in figure 3. 

Using a finite element (FE) model for a structural dynamic analysis becomes increasingly important in the 

modern aircraft design and analysis processes. In general, the quality of an initial FE model of an aircraft 

is not guaranteed, so we need to perform the ground vibration test (GVT) to validate the FE model. In 

most cases, these newly built FE models need to be tuned to minimize uncertainties in the structural 

dynamic FE models and flutter boundary results. Robust flutter analyses performed at NASA DFRC are 

mainly based on these validated FE models as shown in figure 3.

Model tuning is a common method to improve the correlation between numerical and experimental 

modal data, and many techniques have been proposed (ref. 2). Literature reviews on finite element model 

tuning are summarized in reference 3. These techniques can be divided into two categories: direct 

methods (adjust the mass and stiffness matrices directly) and parametric methods (correct the models by 

changing the structural parameters). The direct methods correct mass and stiffness matrices without 

taking into account the physical characteristics of the structures and may not be appropriate for use in 

model tuning processes. In this paper, the tuning method used in the optimization process is the 

parametric method. In the optimization process, structural parameters are selected as design variables: 

structural sizing information (thickness, cross sectional area, area moment of inertia, torsional constant, 

et cetera), point properties (lumped mass, spring constants, et cetera), and materials properties (density, 

Young's modulus, et cetera). Objective function and constraint equations include mass properties, mass 

matrix orthogonality, frequencies, and mode shapes. The use of these equations minimizes the difference 

between numerical results and target data.

The primary objective of this study is to reduce uncertainties in the structural dynamic FE model of 

the ATW2 to increase the accuracy of flutter speed prediction. Discrepancies are common between the 

test data and numerical results. However, the FE model can be fine tuned through the use of GVT data. 

Accurate and reliable GVT results are important to this adjusting process.

The secondary objective of the current study is to add model-tuning capabilities (ref. 3) in NASA 

Dryden’s object-oriented multidisciplinary design, analysis and optimization (MDAO) tool (ref. 4). This 

model tuning technique (ref. 3) is essentially based on a non-linear optimization problem.

2. Object-Oriented MDAO Framework

The heart of the object-oriented MDAO tool is the central executive module (CEM) as shown in 

figure 4. In this module the user will choose an optimization methodology; provide side constraints for 

continuous as well as discrete design variables and external file names for performance indices, which 

communicate between the CEM and each analysis module; submit script commands to prepare input data 

for each analysis code; execute analyses codes; compute performance indices using post-processor codes; 

and compute an objective function and constraints values from performance indices. The CEM was 

written in FORTRAN, and script commands for each performance index were submitted through the use 

of the FORTRAN call system command.
4

The performance indices for structural optimization problems can include total weight, safety factors, 

natural frequencies, mode shapes, flutter speed, divergence speed, structural responses at sensor locations, 

et cetera. On the other hand, the performance indices for the FE model tuning problems can include offdiagonal terms of orthonormalized mass and stiffness matrices, the total error between the measured and 

computed mode shapes at given sensor points, errors between computed and measured frequencies, total 

weight, center of gravity (CG) locations, moment of inertia, et cetera.

Two optimization codes are included in the object-oriented MDAO tool: design optimization tools 

(DOTs) (ref. 5) based on a gradient-based algorithm (ref. 6) and a genetic algorithm (GA) (ref. 7). The 

MSC/NASTRAN (MSC Software Corporation, Santa Ana, California), for example, uses a gradientbased approach for optimization (ref. 8). A drawback to this approach is the necessity to compute finite 

difference or analytical sensitivity values to perform the search, which often requires prior experience 

based on input defining the problem and search directions. 

The DOT is a commercial optimization code that can be used to solve a wide variety of nonlinear 

optimization problems. When the DOT requires the values of the objective and constraint functions 

corresponding to a proposed design, it returns control to the CEM. The CEM calls the DOT again to 

obtain the next design point. This process is repeated until the DOT returns a parameter to indicate that 

the optimum objective function is reached. Gradient-based algorithms work well for continuous design 

variable problems, whereas, GAs can easily handle continuous as well as discrete design variable 

problems. When there are multiple local minima, GAs are able to find the global optimum results, 

whereas, gradient-based methods may converge to a locally minimum value. 

The GA is directly applicable only to unconstrained optimization, so it is necessary to use some 

additional methods to solve the constrained optimization problem. The most popular approach is to add 

penalty functions, in proportion to the magnitude of the constraint violation, to the objective function 

(ref. 9). 

The general form of the exterior penalty function is shown in equation (1):

L(X) = F(X) + λigi(X) + λ j+qhj(X)

j=1

r

∑

i=1

q

∑ (1)

where L(X) indicates the new objective function to be optimized, F(X) is the original objective 

function, gi(X) is the inequality constraint, hj(X) is the equality constraint, λi are the scaling factors, 

X is the design variables vector, and q and r are the number of inequality and equality constraints, 

respectively.

Five optimization methodologies available in the CEM are described as follows: (1) Genetic 

algorithm with continuous, discrete or mixed (continuous/discrete) design variables (GCD); (2) Gradientbased algorithm, that is DOT, with continuous design variables (DC); (3) Start with GCD then continue 

with DC; (4) Start with GCD then continue with DC then continue with genetic algorithm with discrete 

design variables (GD); and (5) Start with DC then continue with GD.
5

3. Structural Dynamic Model Tuning Procedure 

Discrepancies in frequencies and mode shapes are minimized using a series of optimization 

procedures (refs. 3, 10, 11). The numerical mass properties, the mass matrix orthogonality, and the natural 

frequencies and mode shapes are matched to the target values based on the following three tuning steps.

3.1 Step 1: Tuning Mass Properties

The difference in the numerical and target values of the total mass, the CG location, and mass 

moment of inertias at the CG location are used as performance indices. The resulting 10 performance 

indices, as shown in equations (2) through (11), are defined to minimize the uncertainties in the rigid 

body dynamics.

J1 = (W − WG )

2 / WG2 (Total weight) (2)

J2 = (X − XG )

2 / XG

2 (X-CG) (3)

J3 = (Y − YG )

2 / YG

2 (Y-CG) (4)

J4 = (Z − ZG )

2 / ZG

2 (Z-CG) (5)

J5 = (IXX − IXXG )

2 / IXXG

2 (Ixx at CG location) (6)

J6 = (IYY − IYYG )

2 / IYYG

2 (Iyy at CG location) (7)

J7 = (IZZ − IZZG )

2 / IZZG

2 (Izz at CG location) (8)

J8 = (IXY − IXYG )

2 / IXYG

2 (Ixy at CG location) (9)

J9 = (IYZ − IYZG )

2 / IYZG

2 (Iyz at CG location) (10)

J10 = (IZX − IZXG )

2 / IZXG

2 (Izx at CG location) (11)

In the case of a DOT optimization, it is recommended to start an optimization procedure at a feasible 

domain. When the optimization procedure starts in an infeasible domain, there is no guarantee that the 

design will move to a feasible domain. To this end, these ten sub-optimization criteria are used (if test 

data is available) to make a feasible starting configuration for the second and the third optimization steps. 
6

The exterior penalty function approach given in equation (1) is used for the GA optimization. For 

example, the performance index J1 and performance indices J2 through J10 can be selected as an 

objective function and constraints, respectively. Therefore, the following objective function, J , can be 

used for the GA optimization as shown in equation (12):

J = J1 + λiJi

i=2

10

∑ (12)

where λi is the scaling factors and i = 2,..., 10.

3.2 Step 2: Tuning Mass Matrix

The off-diagonal terms of the orthonormalized mass matrix are reduced to improve the mass 

orthogonality as shown in equation (13):

J11 = (Mij)

2

i=1,j=1,i≠ j

n

∑ (13)

where n is the number of modes to be matched and M is defined as shown in equation (14).

M = ΦG

TTTMTΦG (14)

The performance index J11 is used as the objective function, and performance indices J1 through 

J10 are used as constraints in this step. In equation (14), the mass matrix M is calculated from the FE 

model, while the target eigen-matrix ΦG is measured from the GVT. The eigen-matrix ΦG remains 

constant during the optimization procedure. A transformation matrix T (ref. 3) in equation (14) is based 

on Guyan reduction, improved reduction system (ref. 12) or system equivalent reduction expansion 

process (SEREP) (ref. 13). This reduction is required due to the limited number of available sensor 

locations and difficulties in measuring the rotational degrees of freedom (DOF). 

3.3 Step 3: Tuning Frequencies and Mode Shapes 

Two options can be used for tuning the frequencies and mode shapes. In the first option, the objective 

function considered combines a performance index J12 (the normalized errors between GVT and 

computed frequencies) as shown in equation (15) with a performance index J13 (the total error associated 

with the off-diagonal terms of the orthonormalized stiffness matrix) as shown in equation (16).

J12 = Ωi − ΩiG

Ωi

⎛

⎝

⎜

⎞

⎠

⎟

2

i=1

n

∑ (15)

J13 = (Kij)

i=1,j=1,i≠ j

n

∑

2

 (option 1) (16)
7

The matrix K is obtained from the following matrix products as shown in equation (17):

K = ΦG

TTTKTΦG (17)

where the stiffness matrix, K , is calculated from the FE model.

In the second option, the objective function considered combines the performance index J12 with a 

new performance index J13 (the total error between GVT and computed mode shapes at given sensor 

points) as shown in equation 18. 

J13 =

i=1

m

∑ (Φij − ΦijG )

2 (option 2)

j=1

n

∑ (18)

The performance index J13, in the second option, is much simpler than in the first option for this 

application. Any errors in both the modal frequencies and the mode shapes are minimized by including an 

index for each of these in the objective function. For the second option, a small number of sensor 

locations can be used at which errors between the GVT and computed mode shapes are obtained. 

Instead of using the summation in equations (13) and (15), each individual term can be a separate 

performance index. In this case, the total number of performance indices for steps 2 and 3 will increase, 

however, it is easier to apply the military standard requirements.

Any one or combinations of performance indices J1 through J13 can be used as the objective 

function with the other performance indices treated as constraints. This gives the flexibility to achieve the 

particular optimization goal while maintaining the other properties as close to the desired target value as 

possible. The optimization problem statement can be written as

Minimize Ji

Such that Jk ≤ εk , for k = 1 through 13 and k ≠ i

where εk is a small value that can be adjusted according to the tolerance of each constraint condition.

4. Test Article 

The ATW2 was used to demonstrate NASA Dryden’s object-oriented MDAO tool through the 

process of ground vibration testing and the model tuning technique. This test article was a small-scale 

airplane wing comprised of an airfoil and wing tip boom as shown in figure 5. The major structural 

component was the composite wing spar with a rectangular cross section. This wing had equally spaced 

four ribs and composite upper and lower cover skins. The empty space between the upper and the lower 

cover skins was filled with plastic foam. This wing was based on a NACA-65A004 airfoil shape with a 

3.28 aspect ratio. The wing had a half span of 18 in with a root chord length of 13.2 in and a tip chord 

length of 8.7 in. The total area of this wing was 197 in2. The wing tip boom was a 1-in diameter hollow 

tube with a length of 21.5 in. The total weight of the wing was 2.66 lb.

Since the ATW2 was attached to the NF15B flight test fixture, the construction of the wing was 

limited to lightweight materials with no metal for the safety of re-contact with the aircraft after a possible 

separation. The wing and spar were constructed from fiberglass cloth, the tip boom used carbon fiber 
8

composite, the wing core consisted of rigid foam, and the components were attached by epoxy. The wing 

skin was made of three plies of fiberglass cloth with a 0.01-in thickness. The internal spar located at the 

30-percent chord line was composed of 10 plies with a 0.05-in thickness of carbon at the root, and 

decreasing to 1 ply 0.005-in thickness at the tip. 

5. Test Setup

Ground vibration tests were performed to determine the dynamic modal characteristics of the ATW2. 

In the test set up, the ATW2 was clamped on to a circular aluminum plate, which was bolted to a 

mounting panel, and then installed into a small strong back called the ground test fixture in the NASA 

Dryden Flight Loads Laboratory. The PONTOS photogrammetry optical measuring system (Gesellschaft 

für Optische Messtechnik, Braunschweig, Germany) (ref. 14), as shown in figure 6, was used to measure 

output displacement at the sensor points, shown in figure 7. For the excitation method, an impulse 

hammer with an impedance head was used to excite the ATW2’s natural frequencies and mode shapes as 

well as to measure input forces.

PONTOS is a non-contact optical 3D measuring system. It analyzes, computes, and documents object 

deformations, rigid body movements, and the dynamic behavior of a measuring point (ref. 14). The 

PONTOS system provides an alternative for complex sensor technology like laser sensor, draw-wire 

sensors, or accelerometers, which are commonly used in the GVT for measuring responses of the 

structure. The features of the PONTOS system include:

• an unlimited number of sensors (The sensor markers are extremely lightweight so that a large 

number of sensors can be used at the same time without essentially altering the total weight or the 

mode shapes of the structure.), 

• non-contact acquisition of the precise 3D position of any number of measuring points,

• mobility and flexibility due to an easy and compact measuring system, and

• easy and quick adaptation to different measuring volumes and measuring tasks.

The limitations of the PONTOS system include: 

• measuring frame rate up to 500 Hz at 1280x1024 pixels,

• measuring volume up to 1700 by 1360 by 1360 mm3, and use on a plane or a slightly curved 

surface. 

6. Flutter Analysis Before Model Tuning

Natural frequencies obtained from the GVT and the MSC/NASTRAN modal analyses using FE

models before model tuning are compared in table 1. The starting configuration of the FE model was 

obtained from the ATW1 model. The GVT frequencies in this table were based on the time history 

responses data, as shown in figure 8, collected by the PONTOS system at each of the sensor points. The 

eigensystem realization algorithm routine, which was developed by Juang and Pappa (ref. 15) at NASA 

Langley Research Center (Hampton, Virginia), was then used to identify the frequencies and mode shapes 

of the system. The FE model for the MSC/NASTRAN (ref. 16) modal analysis is shown in figure 9. 

Detailed GVT sensor locations and GVT mode shapes are provided in reference 17. Corresponding 

natural frequencies and mode shapes computed using the MSC/NASTRAN code are shown in figure 10. 

In table 1 and figure 10, the mode numbers 1, 2, and 3 are the first bending, first torsion, and second 

bending modes, respectively.
9

Table 1. Natural frequencies of the ATW2 before and after model tuning.

Before tuning After tuning

Mode GVT 

(Hz) MSC/NASTRAN 

(Guyan/full; Hz) Error (%) MSC/NASTRAN (SEREP/full; Hz) Error (%)

1 17.24 17.61/17.60 2.15/2.09 17.79/17.79 3.19/3.19

2 44.10 23.27/23.26 -47.20/-47.30 44.71/44.71 1.38/1.38

3 84.00 99.02/93.99 17.90/11.90 84.33/84.33 0.39/0.39

A matched flutter analysis of the ATW2 using the ZAERO code (ref. 18) is presented in this section. 

The first 10 natural modes were used for the flutter analysis. The aerodynamic model has 200 surface 

elements on the wing and 216 body elements on the boom. Forty-four splining points were used between 

the structural dynamic and aerodynamic models. The aerodynamic model of the ATW2 and the first three 

splined mode shapes on the aerodynamic model are shown in figures 11 and 12, respectively. The 

matched flutter analyses were performed at Mach 0.60, 0.75, 0.82 and 0.95. The aerodynamic influence 

coefficient matrices at each Mach number were generated at 16 reduced frequencies and the g-method 

(ref. 18) was used in the matched flutter analysis.

The speed versus damping, V-g, and speed versus frequency, V-w, curves from the matched flutter 

analysis at Mach 0.82 (the ATW1 flutter Mach number) (ref. 1) before model tuning are given in figure 

13. The structural damping used for the flutter speed computation was 3 percent. The flutter speed was 

407.4 KEAS, flutter frequency was 22.86 Hz, and the corresponding altitude was 15,010 ft, as shown in 

table 2. 

Table 2. Flutter boundaries before and after model tuning.

Mach = 0.60 Mach = 0.75 Mach= 0.82 Mach = 0.95

Speed, KEAS 453.0 421.5 407.4 377.9

Before tuning Frequency, Hz 23.18 22.97 22.86 22.53

Altitude, ft -7,501 8,751 15,010 25,590

Speed, KEAS 361.3 364.6 365.3 367.0

After tuning Frequency, Hz 38.47 37.73 37.32 36.20

Altitude, ft 5,101 16,080 20,310 26,920

Speed difference,

percent 25.4 15.6 11.5 3.0

Modal participation factors for the first flutter mode are given in table 3. Modal participation of the 

first three natural frequencies was more than 96 percent before model tuning. In-plane modes, mode 

numbers 4, 6, and 8, did not contribute to the first flutter mode. In table 3, we can conclude that the 

primary structural dynamic modes for the first flutter mode were modes 1, 2 and 3 and the secondary 

modes for the first flutter mode were modes 5, 7, 9 and 10. The first mode is the dominant mode for the 

primary flutter mode.
10

Table 3. Modal participation factors at Mach 0.82 before model tuning.

Mode Frequency, Hz Modal participation factor, percent

1 17.60 75.0

2 23.26 16.8

3 93.99 4.8

96.6*

4 135.40 0.0

5 163.10 2.6

6 174.50 0.0

7 257.50 0.5

8 391.60 0.0

9 394.30 0.1

10 445.60 0.3

3.4**

 *: The total of the first three modes

**: The total of modes 5, 7, 9 and 10

7. Model Tuning 

Based on military standards (ref. 19, 20), the frequency error should be less than 3 percent for the 

primary modes and 10 percent for the secondary modes. Using a norm of frequency differences as an 

objective function with mass properties, mass orthogonality, and mode shapes as constraint equations, the 

frequencies after model tuning are presented in table 1. Before model tuning the frequency error for the 

second mode was 47.3 percent and the frequency error for the third mode was 11.9 percent. These 

frequency errors violate the 3-percent frequency error requirements in military standards. After model 

tuning the 2.09-percent error becomes 3.19 percent, the 47.3-percent error becomes 1.38 percent, and the 

11.9-percent error becomes 0.39 percent. After model tuning, 3 percent frequency error requirements for 

the primary modes were satisfied for modes 2 and 3, and close to being satisfied for mode 1. 

Since Guyan reduction is a static condensation, it is only accurate for lower modes. For higher modes, 

the errors become too large as shown in table 1. Unlike Guyan reduction, the SEREP preserves the 

dynamic character of the original full system model for selected modes of interest. The dynamic 

characteristics of the reduced model were virtually the same as the full model as shown in table 1. 

Therefore, the SEREP model reduction process was chosen for this ATW2 model update application.

Table 4 shows the total weight, orthonormalized mass matrix, and modal assurance criterion (MAC) 

(ref. 3) values of the ATW2 before and after model tuning. Based on military standards, the off-diagonal 

terms of the orthonormalized mass matrix should be less than 10 percent (ref. 19, 20). The off-diagonal 

terms of the orthonormalized mass matrix, with a maximum of 38 percent before model tuning, are 

minimized in the second tuning step. The maximum off-diagonal term of 7.43 percent after model tuning 

is observed in table 4 and satisfies the 10-percent limitation in military standards. Model correlation with 

test data prior to model tuning was poor and unacceptable to proceed to flight. The MAC values of 0.70 

and 0.75 for modes 2 and 3 before model tuning become 0.97 and 0.95, respectively. Therefore, we can 

conclude that excellent model correlation with the test data was achieved after model tuning, which leads 

to a more reliable flutter speed prediction.
11

Table 4. Summary of total weight, orthonormalized mass matrix, and MAC values for the ATW2 before 

and after model tuning.

Measured Before tuning After tuning

Total weight 2.66 lb 1.76 lb (error 34%) 2.72 lb (error 2.3%)

1 2 3 1 2 3

1 1.0000 -0.2490 0.3800 1.0000 0.0395 -0.0565

2 -0.2490 1.0000 -0.6610 0.0395 1.0000 -0.0743

Orthonormalized 

mass matrix

3 0.3800 -0.6610 1.0000 -0.0565 -0.0743 1.0000

Mode 1 0.97 0.99

Mode 2 0.70 0.97

Modal 

assurance 

criteria Mode 3 0.75 0.95

8. Flutter Analysis After Model Tuning 

Typical V-g and V-w curves from the matched flutter analysis at Mach 0.82 after model tuning are 

given in figure 14. The same 3-percent structural-damping value is used for flutter speed computation. In 

figure 14 we can observe a steeper merging behavior for the first bending and torsion modes after model 

tuning. It is important for the safety of flight that the model tuning results predict a more sudden, rather 

than a more gradual, flutter onset.

The results of the matched flutter analysis before and after model tuning are summarized in tables 2 

and 5. The modal participation factors in table 5 indicate that the first three modes have more than a 

95-percent contribution to the first flutter mode before model tuning and more than a 98-percent 

contribution after model tuning. The second mode, which has the maximum frequency difference before 

model tuning as shown in table 1, becomes more than 91 percent of the modal participation after model 

tuning at Mach 0.60. Therefore, the second mode after tuning becomes the dominant mode for the 

primary flutter mode. The resulting flutter speed difference due to model uncertainty was also a maximum 

at Mach 0.60, as shown in table 2. Table 2 shows that the flutter speed difference varies from 25.4 percent 

at Mach 0.60 to 3.0 percent at Mach 0.95. As shown in tables 2 and 5 after model tuning, the modal 

participation of the second mode, which is the dominant mode, decreased when Mach number increased; 

the differences in flutter speed due to uncertainty also decreased when Mach number increased.

Table 5. Modal participation factors before and after model tuning.

Modal participation factors before model tuning, percent Mode Frequency, Hz

Mach = 0.60 Mach = 0.75 Mach = 0.82 Mach= 0.95

1 17.60 68.1 72.9 75.0 79.7

2 23.26 22.2 18.3 16.8 13.6

3 93.99 5.2

95.5*

5.0

96.2*

4.8

96.6*

4.3

97.6*

Modal participation factors after model tuning, percent Mode Frequency, Hz Mach = 0.60 Mach = 0.75 Mach = 0.82 Mach = 0.95

1 17.79 6.7 9.8 12.3 24.3

2 44.71 91.9 88.4 85.6 72.4

3 84.33 0.6

99.2*

0.9

99.1*

1.1

99.0*

1.6

98.3*

*: These are the sum of modes 1, 2 and 3 for each Mach number.

Finally, flutter boundaries of the ATW2, before and after model tuning, are compared with the flight 

envelopes as shown in figure 15. The solid and long dash dotted lines are the flight envelope of the 
12

mother ship and its 15-percent margin, respectively. The dashed line represents the ATW 2 test envelope 

that is planned for flight, and the long dash double dot line is the 15-percent margin of the ATW2 test 

envelope. The solid line with the square marker is the flutter boundary before model tuning, and the solid 

line with the diamond marker represents flutter boundary after model tuning. It should be noted that 

flutter boundary after model tuning is more conservative than before model tuning.

9. Concluding Remarks 

This paper describes the reduced uncertainty procedures for the ATW2, which was developed at the 

NASA Dryden Flight Research Center for demonstrating flutter and advanced aeroelastic test techniques. 

It has been shown that model uncertainties can be reduced through the tuning of the finite element model 

using the NASA DFRC’s object-oriented MDAO tool. 

After tuning the FE model, the frequency differences between GVT and analytical results are mostly 

within 3 percent and the off-diagonal terms of the orthonormalized mass matrix are within 10 percent 

satisfying the military standards. Excellent mode shape correlations were also achieved through the high 

MAC value (greater than 95 percent). With the updated FE model, the flutter speed prediction can be 

reduced as much as 25 percent at Mach 0.60. 
13

References

1. Lind, Rick, David Voracek, Roger Truax, Tim Doyle, Starr Potter, and Marty Brenner, “A Flight 

Test to Demonstrate Flutter and Evaluate Flutterometer,” The Aeronautical Journal, 

Vol. 107, No. 1076, pp 577 – 588, October 2003.

2. Friswell, M. I., and J. E. Mottershead, Finite Element Model Updating in Structural Dynamics, 

Kluwer Academic Publishers, Dordrecht, 1995.

3. Pak, Chan-gi, “Finite Element Model Tuning Using Measured Mass Properties and Ground 

Vibration Test Data,” ASME Journal of Vibration and Acoustics, Vol. 131, No. 1, February 2009.

4. Pak, Chan-gi, and Wesley Li, “Multidisciplinary Design, Analysis and Optimization Tool 

Development Using a Genetic Algorithm,” Proceedings of the 26th Congress of International 

Council of the Aeronautical Science, Anchorage, 2008.

5. DOT Design Optimization Tools User’s Manual Version 5.0, Vanderplaats Research & 

Development, Inc., Colorado Springs, 2001.

6. Vanderplaats, Garret N., Numerical Optimization Techniques for Engineering Design, 3rd ed., 

Vanderplaats Research & Development, Inc., Colorado Springs, 2001.

7. Charbonneau, Paul, and Barry Knapp, A User’s Guide to PIKAIA 1.0, National Center for 

Atmospheric Research, Boulder, CO, 1995.

8. EI-Borgi, S, M. Neifar, F. Cherif, S. Choura, and H. Smaoui, “Modal Identification, Model 

Updating and Nonlinear Analysis of a Reinforced Concrete Bridge,” Journal of Vibration and 

Control, Vol. 14, No. 4, pp. 511-530, 2008.

9. Yeniay, Özgür, “Penalty Function Methods for Constrained Optimization Using Genetic 

Algorithms,” Mathematical and Computational Applications, Vol. 10, No. 1, pp. 45-56, 2005.

10. Lung, Shun-fat, and Chan-gi Pak, “Structural Model Tuning Capability in an Object-Oriented 

Multidisciplinary Design, Analysis and Optimization Tool,” Proceedings of the 26th Congress of 

International Council of the Aeronautical Sciences, Anchorage, 2008.

11. Herrera, Claudia, and Chan-gi Pak, “Build-up Approach to Updating the Mock Quiet Spike Beam 

Model,” AIAA-2007-1776, Proceedings of the 48th AIAA/ASME/ASCE/AHS/ASC Structures, 

Structural Dynamics, and Materials Conference, Honolulu, Hawaii, April 23-26, 2007.

12. O’Callahan, John, “A Procedure for an Improved Reduced System (IRS) Model,” Proceedings of 

the 7th International Modal Analysis Conference, Vol. 1, pp. 17-21, Las Vegas, 1989.

13. O’Callahan, J., P. Avitabile, and R. Riemer, “System Equivalent Reduction Expansion Process,” 

Proceedings of the 7th International Modal Analysis Conference, Vol. 1, pp. 29-37, Las Vegas, 

1989.

14. Pontos User Manual Version 6.0, Gesellschaft für Optische Messtechnik, Braunschweig, 

Germany, 2007.
14

15. Juang, Jer-Nan, and Richard S. Pappa, “An Eigensystem Realization Algorithm for Modal 

Parameter Identification and Modal Reduction,” AIAA Journal of Guidance, Control, and 

Dynamics, Vol. 8, No. 5, pp. 620-627, 1984.

16. MSC/NASTRAN Quick Reference Guide Version 69, The MacNeal Schwendler Corporation, 

2005.

17. Lung, Shun-fat, and Chan-gi Pak, “Updating the Finite Element Model of the Aerostructures Test 

Wing Using Ground Vibration Test Data,” NASA TM-2009-214646, April 2009.

18. ZAERO User’s Manual Version 8.2, ZONA Technology, Inc., Scottsdale, AZ, October 2008. 

19. Military Standard. “Test Requirements for Launch, Upper-Stage, and Space Vehicles,” MILSTD-1540C Section 6.2.10, September 15, 1994.

20. Norton, William, J., Structures Flight Test Handbook, AFFTC-TIH-90-001, November 1990.
15

Figures

Figure 1. The aerostructures test wing mounted on the NF-15B airplane for flight flutter testing.

Figure 2. The aerostructures test wing 2.
16

Figure 3. Robust flutter analysis procedure at NASA DFRC.
17

Need to develop;

depends on

analysis code

100290

Analysis code;

commercial

and/or inhouse codes

Need to develop;

depends on

analysis code

Preprocessor

#i

Design

variables

Optimizer

Preprocessor

#k

Postprocessor

#k

Preprocessor

#j

Postprocessor

#j

Discipline

#j

Discipline

#i

Central

executive

module

(FORTRAN)

Discipline

#k

Postprocessor

#i Objective

function J 

and

constraints

G(x)

Script

commands

Performance

indices

Figure 4. Central executive module.

A-A cross

section

AR = 3.28

18 in

φ1 in

100291

A A

21.5 in

6.375 in 8.7 in

13.2 in

Figure 5. Exploded view of the ATW2.
18

Figure 6. The PONTOS photogrammetry optical measuring system.

Excitation point

24 25

23

1 2

20 21 18

16

14

12

10

8

7

5

3

19

17

15

13

11

9

22

6

4

100293

Figure 7. GVT sensor and excitation locations.
19

Figure 8. Typical time history and frequency response GVT results for the ATW2.

100295

Figure 9. MSC/NASTRAN finite element model.
20

100296

Figure 10a. Mode 1 (1st bending): 17.60 Hz.

100297

Figure 10b. Mode 2 (1st torsion): 23.26 Hz.

Figure 10. Full model mode shapes before tuning.
21

100298

Figure 10c. Mode 3(2nd bending): 93.99 Hz.

Figure 10. Concluded.

100299

Figure 11. ZAERO unsteady aerodynamic model.
22

100300

Figure 12a. Splined mode 1.

100301

Figure 12b. Splined mode 2.

100302

Figure 12c. Splined mode 3.

Figure 12. Splined mode shapes on unsteady aerodynamic model.
23

Speed, KEAS

Damping, percent

100303

–0.5

–0.4

–0.3

–0.2

–0.1

0

0.1

200 300 400 500 600 700

Figure 13a. V-g plots.

Speed, KEAS

Frequency, Hz

100304

0

50

100

150

200 300 400 500 600 700

Figure 13b. V-w plots.

Figure 13. V-g and V-w plots for the ATW2 at Mach 0.82 before model tuning (plot the first 5 modes).
24

Speed, KEAS

Damping, percent

100305

–0.5

–0.4

–0.3

–0.2

–0.1

0

0.1

200 300 400 500 600 700

Figure 14a. V-g plots.

Speed, KEAS

Frequency, Hz

100306

150

100

50

0

200 300 400 500 600 700

Figure 14b. V-w plots.

Figure 14. V-g and V-w plots for the ATW2 at Mach 0.82 after model tuning (plot the first 5 modes).
25

Mach

Mother ship envelope

Mother ship envelope x 1.15

ATW2 test envelope

ATW2 test envelope x 1.15

Flutter boundary before model tuning

Flutter boundary after model tuning

Altitude, ft

100307

50000

40000

30000

20000

10000

0

–10000

–20000

0 0.5 1.0 1.5 2.0

Figure 15. Flutter boundary before and after model tuning.
REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

1. REPORT DATE (DD-MM-YYYY)

01-01-2011

2. REPORT TYPE 

Technical Memorandum

 4. TITLE AND SUBTITLE

Reduced Uncertainties in the Flutter Analysis of the Aerostructures Test Wing

5a. CONTRACT NUMBER

 6. AUTHOR(S)

Pak, Chan-gi and Lung, Shun-fat

 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)

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13. SUPPLEMENTARY NOTES

Pak and Lung, NASA Dryden Flight Research Center. Also presented as meeting paper 072 at the 27th Congress of the International

Council of the Aeronautical Sciences, Nice, France, September 19-24, 2010. 

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14. ABSTRACT

Tuning the finite element model using measured data to minimize the model uncertainties is a challenging task in the area of structural dynamics. 

A test validated finite element model can provide a reliable flutter analysis to define the flutter placard speed to which the aircraft can be flown 

prior to flight flutter testing. Minimizing the difference between numerical and experimental results is a type of optimization problem. 

Through the use of the National Aeronautics and Space Administration Dryden Flight Research Center's (Edwards, California) multidisciplinary 

design, analysis, and optimization tool to optimize the objective function and constraints; the mass properties, the natural frequencies, and the 

mode shapes are matched to the target data, and the mass matrix orthogonality is retained. The approach in this study has been applied to 

minimize the model uncertainties for the structural dynamic model of the aerostructures test wing, which was designed, built, and tested at the 

National Aeronautics and Space Administration Dryden Flight Research Center. A 25 percent change in flutter speed has been shown after

 reducing the uncertainties. 

15. SUBJECT TERMS

Aerostructures test wing, Flutter margin, Structural dynamic model tuning, Test validated structural dynamic model, Uncertainties

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