In this work, a general approach is formulated for updating the parameters of systems governed by multiphysics equations. The optimization technique is based on Genetic Algorithms (GAs). GAs represent a class of probabilistic optimization strategies loosely patterned after a simplified evolutionary scheme and Darwin’s “survival of the fittest” concepts. The GA is coupled to a commercially available multiphysics finite element program. In the context of this, issues of mode tracking, eigenvector comparisons, and approximate function evaluations are discussed. The approach is demonstrated on a micro-electro-mechanical (MEMS) micromirror which is governed by both structural and electrostatic physics. The MEMS mirror is characterized dynamically using a laser vibrometer. These experimental measurements are then used in the model updating of the finite element structural model and the electrostatic model. Several interesting observations that were encountered in this development will also be discussed.

1.
Clarke
,
D. W.
, 1967, “
Generalized Least-Squares Estimation of the Parameters of a Dynamic Model
,”
Proceedings of the IFAC Symposium on Identification of Automatic Control Systems
, paper No. 3.17.
2.
Collins
,
J. D.
,
Hart
,
G. C.
,
Hasselman
,
K. T.
, and
Kennedy
,
B.
, 1974, “
Statistical Identification of Structures
,”
AIAA J.
0001-1452,
12
(
2
), pp.
185
190
.
3.
Chen
,
M. Y.
, and
Lin
,
Y.
, 1983, “
An Iterative Algorithm for Solving Inverse Problems in Structural Dynamics
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
19
, pp.
825
829
.
4.
Berger
,
H.
,
Chaquin
,
J. P.
, and
Ohayon
,
R.
, 1984, “
Finite Element Model Adjustment Using Experimental Data
,”
Proceedings of the 2nd International Modal Analysis Conference
,
Orlando, FL
.
5.
Hoff
,
C. J.
,
Bernitsas
,
M. M.
,
Sandstrom
,
R. E.
, and
Anderson
,
W. J.
, 1984, “
Inverse Perturbation Method for Structural Redesign with Frequency and Mode Shape Constraints
,”
AIAA J.
0001-1452,
22
(
9
), pp.
1304
1309
.
6.
Soeiro
,
F. J.
, and
Hajela
,
P.
, 1990, “
Damage Detection in Composite Materials Using Identification Techniques
,”
Proceedings of the 31st AI/AA SDM Conference
, Paper No. AIAA-90–0917-CP, pp.
950
960
.
7.
Hemez
,
F. M.
, and
Farhat
,
C.
, 1993, “
Correlating Finite Element Models to Modal Tests for Large Flexible Space Structures
,”
Proceedings of the 1993 CSMA/GAMNI/INRIA National Conference in Structural Design
,
Giens, France
.
8.
Maben
,
E.
, and
Zimmerman
,
D. C.
, 1992, “
Advances in Parameter Estimation Techniques Applied to Flexible Structures
,” NASA Workshop on Distributed Parameter Modelling and Control of Flexible Aerospace Systems, Williamsburg, VA, June 8–10, pp.
215
239
(published as NASA Conference Publication 3242, June 1994).
9.
Larson
,
C.
, and
Zimmerman
,
D. C.
, 1993, “
On the Use of Genetic Algorithms in Structural Damage Detection
,” in
Proceedings of the 11th International Modal Analysis Conference
,
Orlando, FL
, pp.
1095
1101
.
10.
Fulcher
,
C. W.
,
Marek
,
E. L.
, and
Mayes
,
R. L.
, 1993, “
Test/Analysis Correlation and Model Updating of the STARS I & II Missile Systems
,” in
Structural Dynamic Modelling Test, Analysis and Correlation, Dynamic Testing Agency and NAFEMS
,
Bell
and
Bain
, eds.,
Glasgow
,
Scotland
.
11.
Carlin
,
R. A.
, and
Garcia
,
E.
, 1996, “
Parameter Optimization of a Genetic Algorithm for Structural Damage Detection
,”
Proceedings of the 14th International Modal Analysis Conference
,
Dearborn, MI
, pp.
1292
1298
.
12.
Zimmerman
,
D. C.
,
Yap
,
C. K.
, and
Hasselman
,
T.
, 1999, “
Evolutionary Approach for Model Correlation
,”
Mech. Syst. Signal Process.
0888-3270,
13
(
4
), pp.
609
625
.
13.
Ruotolo
,
R.
,
Surace
,
C.
, and
Mares
,
C.
, 1997, “
Damage Identification Using Simulated Annealing
,” in
Proceedings of the 15th International Modal Analysis Conference
,
FL
, pp.
954
960
.
14.
Teughels
,
A.
, and
De
,
Roeck G.
, 2004, “
Structural Damage Identification of the Highway Bridge Z24 by F. E. Model Updating
,”
J. Sound Vib.
0022-460X,
278
(
3
), pp.
589
611
.
15.
Lauwagie
,
T.
,
Sol
,
H.
,
Heylen
,
W.
, and
Roebben
,
G.
, 2004, “
Determination of the In-Plane Elastic Properties of the Different Layers of Laminated Plates by Means of Vibration Testing and Model Updating
,”
J. Sound Vib.
0022-460X,
274
(
3–5
), pp.
529
546
.
16.
Ladeveze
,
P.
,
Nedjar
,
D.
, and
Reynier
,
M.
, 1994, “
Updating of Finite Element Models Using Vibration Tests
,”
AIAA J.
0001-1452,
32
(
7
), pp.
1485
1491
.
17.
Friswell
,
M. I.
, and
Mottershead
,
J. E.
, 1995,
Finite Element Model Updating in Structural Dynamics
,
Kluwer Academic
,
Norwell, MA
.
18.
M’Closkey
,
Robert T.
,
Gibson
,
Steve
, and
Hui
,
Jason
, 2000, “
Modal Parameter Identification of a MEMs Gyroscope
,” in
Proceedings of the American Control Conference
, Vol.
3
, pp.
1699
1704
.
19.
Furlong
,
C.
,
Kok
,
R.
, and
Ferguson
,
C. F.
, 2005, “
Dynamic Analysis and Characterization of MEMs Accelerometers by Computational and Opto-Electromechanical Methodologies
,” in
Proceedings of the 43rd Annual IEEE International Reliability Physics Symposium (IEEE Catalog No. 05CH37616)
, pp.
325
329
.
20.
Chipperfield
,
A.
, 1997, “
Introduction to Genetic Algorithms
,” in
Genetic Algorithms in Engineering Systems
,
A. M. S.
Zalzala
, and
P. J.
Fleming
, eds.
The Institution of Electrical Engineers
,
London, UK
.
21.
Goldberg
,
David E.
, 1989,
Genetic Algorithms in Search, Optimization and Machine Learning
,
Addison-Wesley Longman
,
Berkeley, CA
.
22.
23.
FEMLAB 3: User’s Guide, COMSOL AB, 2004.
25.
Zimmerman
,
David C.
,
Yap
,
Keng
, and
Hasselman
,
Timothy
, 1999, “
Evolutionary Approach for Model Refinement
,”
Mech. Syst. Signal Process.
0888-3270,
13
(
4
), pp.
609
625
.
26.
Golub
,
Gene H.
, and
Van Loan
,
Charles F.
, 1983,
Matrix Computations
,
Johns Hopkins University Press
,
Baltimore, MA
.
27.
Meirovitch
,
Leonard
, 1980,
Computational Methods in Structural Dynamics
,
Sijthoff and Noordhoff
,
Rockville, MD
, pp.
201
221
.
You do not currently have access to this content.