Abstract

This work illustrates application of the minimum model error system identification method to obtain the nonlinear state space models of a fluttering panel. Identification using position and velocity data from forced response of the panel is presented here. The response was numerically simulated using two different discretization approaches: through finite differences and using the Galerkin’s method. Data from two different parts of response time history were considered. First, data where transients due to initial conditions and the forcing were present were used for identification. Then, data when only transients due to forcing were present were used for identification. The models obtained using the forced response of the panel were able to capture the behavior of the true system relatively accurately. Identification of models of different sizes is also discussed. Reduced size models can be successfully created from the forced response data using the minimum model error method. It is demonstrated that the number of degrees of freedom in the model attempted to be identified should be consistent with the number modes observed in the measurements. The response surface method was successfully applied to generate models for various flow regimes.

1.
Juang
,
J.-N.
, 1994,
Applied System Identification
,
Prentice Hall PTR
,
Englewood Cliffs, NJ
.
2.
Maia
,
N. M. M.
, and
e Silva
,
J. M. M.
, 1998,
Theoretical and Experimental Modal Analysis
,
Research Studies Press
,
Philadelphia
.
3.
Ewins
,
D. J.
, 1992,
Modal Testing: Theory and Practice
,
Research Studies Press
,
New York
.
4.
Baldelli
,
D. H.
,
Chen
,
P. C.
,
Liu
,
D. D.
,
Lind
,
R.
, and
Brenner
,
M.
, 2004, “
Nonlinear Aeroelastic Modeling by Block-Oriented Identification
,”
45th AIAA/ASME/ASCE/ASC/AHS Structures, Structural Dynamics & Materials Conference
,
Palm Springs, California
, April 19–22, AIAA Paper No. 2004-1938.
5.
Marzocca
,
P.
,
Lazzaro
,
R.
, and
Librescu
,
L.
, 2004, “
Flutter/Aeroelastic Response of Panels Via a Combined Galerkin-Volterra Series Approach
,”
45th AIAA/ASME/ASCE/ASC/AHS Structures, Structural Dynamics & Materials Conference
,
Palm Springs, California
, April 19–22, AIAA Paper No. 2004-1855.
6.
Epurenau
,
B. I.
, and
Dowell
,
E. H.
, 2003, “
Compact Methodology of Computing Limit-Cycle Oscillations in Aeroelasticity
,”
J. Aircr.
0021-8669,
40
(
5
), pp.
955
963
.
7.
Prazenica
,
R. J.
,
Reisentel
,
P. H.
,
Kurdila
,
A. J.
, and
Brenner
,
M. J.
, 2004, “
Volterra Kernel Identification and Extrapolation for the f/a-18 Active Aeroelastic Wing
,”
45th AIAA/ASME/ASCE/ASC/AHS Structures, Structural Dynamics & Materials Conference
,
Palm Springs, California
, April 19–22, AIAA Paper No. 2004-1939.
8.
Mook
,
D.
, and
Junkins
,
J.
, 1988, “
Minimum Model Error Estimation for Poorly Modeled Dynamic Systems
,”
J. Guid. Control Dyn.
0731-5090,
11
(
3
), pp.
256
261
.
9.
Stry
,
G.
, 1991, “
MME Nonlinear Dynamic System Identification
,” Ph.D thesis, University of New York at Buffalo.
10.
Geering
,
H.
, 1976, “
Continuous Time Optimal Control Theory for Cost Functionals Including Discrete State Penalty Terms
,”
IEEE Trans. Autom. Control
0018-9286,
AC-21
(
6
), pp.
866
869
.
11.
Mook
,
D.
, and
Lew
,
J.-S.
, 1991, “
Multiple Shooting Algorithms for Jump-Discontinuous Problems in Optimal Control and Estimation
,”
IEEE Trans. Autom. Control
0018-9286,
36
(
8
), pp.
979
983
.
12.
Shiryayev
,
O. V.
, and
Slater
,
J. C.
, 2004, “
Panel Flutter Model Identification Using the Minimum Model Error Method on the Free Response Measurements
,” AIAA J. Guidance, Control and Dynamics (accepted for publication).
13.
Dowell
,
E.
, 1966, “
Nonlinear Oscillations of a Fluttering Plate
,”
AIAA J.
0001-1452,
4
(
7
), pp.
1267
1275
.
14.
Mortara
,
S.
, 2002, “
Advanced Computational Aeroelastic Methods
,” Master’s thesis, Wright State University, Dayton, Ohio.
15.
Holmes
,
P.
,
Lumley
,
J.
, and
Berkooz
,
G.
, 1996,
Turbulence, Coherent Structures, Dynamical Systems and Symmetry
,
Cambridge University Press
,
Cambridge
.
16.
Slater
,
J. C.
, and
Inman
,
D. J.
, 1997, “
On the Effects of Weak Non-Linearities on Linear Controllability and Observability Norms, an Invariant Manifold Approach
,”
J. Sound Vib.
0022-460X,
199
(
3
), pp.
417
429
.
17.
The Math Works Inc.
, 2002, Using MATLAB, 3 Apple Hill Dr., Natick, MA 01760.
18.
Gopinathan
,
A.
, 1999, “
Robust Nonlinear System Identification Using Correlation Techniques
,” Master’s thesis, Wright State University, Dayton, Ohio.
19.
Welch
,
P.
, 1967, “
The Use of Fast Fourier Transform for the Estimation of Power Spectra: A Method Based on Time Averaging Over Short, Modified Periodograms
,”
IEEE Trans. Audio Electroacoust.
0018-9278,
AU-15
(
2
), pp.
70
73
.
You do not currently have access to this content.