In this work, linear matrix inequality (LMI) methods are proposed for computationally efficient solution of damage detection problems in structures. The structural damage detection problem that is considered consists of estimating the existence, location, and extent of stiffness reduction in structures using experimental modal data. This problem is formulated as a convex optimization problem involving LMI constraints on the unknown structural stiffness parameters. LMI optimization problems have low computational complexity and can be solved efficiently using recently developed interior-point methods. Both a matrix update and a parameter update formulation of the damage detection is provided in terms of LMIs. The presence of noise in the experimental data is taken explicitly into account in these formulations. The proposed techniques are applied to detect damage in simulation examples and in a cantilevered beam test-bed using experimental data obtained from modal tests. [S0739-3717(00)00104-5]
Issue Section:
Technical Papers
1.
Pandey
, A.
, Biswas
, M.
, and Samman
, M.
, 1991
, “Damage Detection from Changes in Mode Shapes
,” J. Sound Vib.
, 145
, pp. 321
–332
.2.
Hajela
, P.
, and Soeiro
, F.
, 1991
, “Structural Damage Detection Based on Static and Modal Analysis
,” AIAA J.
, 28
, pp. 1110
–1116
.3.
Agbabian
, M.
, Masri
, S.
, Miller
, R.
, and Caughey
, T.
, 1991
, “System Identification Approach to Detection of Structural Changes
,” ASCE J. Eng. Mech.
, 117
, pp. 370
–390
.4.
Yuen
, M.
, 1985
, “A Numerical Study of the Eigen-parameters of a Damaged Catilevered Beam
,” J. Sound Vib.
, 103
, pp. 301
–310
.5.
Cawley
, P.
, and Ray
, R.
, 1988
, “A Comparison of the Natural Frequency Changes Produced by Cracks and Slots
,” ASME J. Vib., Acoust., Stress, Reliab. Des.
, 110
, pp. 366
–370
.6.
Ismail
, F.
, Ibrahim
, A.
, and Martin
, H.
, 1990
, “Identification of Fatigue Cracks from Vibration Testing
,” J. Sound Vib.
, 140
, pp. 305
–317
.7.
Chondros
, T.
, and Dimarongonas
, A.
, 1989
, “Dynamic Sensitivity of Structures to Cracks
,” ASME J. Vib., Acoust., Stress, Reliab. Des.
, 111
, pp. 251
–256
.8.
Baruch
, M.
, and Bar Itzhack
, I. Y.
, 1978
, “Optimum Weighted Orthogonalization of Measured Modes.
” AIAA J.
, 16
, No. 4
, pp. 346
–351
.9.
Zimmerman, D., and Smith, S. W., 1992, “Model Refinement and Damage Location for Intelligent Structures,” Intelligent Structural Systems, Tzou, H. S., and Anderson, G. L., eds., Kluwer Academic, Dordrecht, pp. 403–452.
10.
Doeblin, S. W., Farrar, C. R., Prime, M. B., and Sheritz, D. W., “Damage Identification and Health Monitoring of Structural and Mechanical Systems from Changes in their Vibration Characteristics: A Literature Review,” Los Alamos Report LA-13070-MS, NM, 1996.
11.
Mottershead
, J. E.
, and Friswell
, M. I.
, 1993
, “Model Updating in Structural Dynamics: A Survey
,” J. Sound Vib.
, 167
, No. 2
, pp. 347
–375
.12.
Kabe
, A.
, 1985
, “Stiffness Matrix Adjustment Using Mode Data
,” AIAA J.
, 23
, No. 9
, pp. 1431
–1436
.13.
Kammer
, D.
, 1988
, “Optimum Approximation for Residual Stiffness in Linear Systems Identification
,” AIAA J.
, 26
, No. 1
, pp. 104
–112
.14.
Smith, S., and Beattie, C., 1993, “Simultaneous Expansion and Orthogonalization of Measured Modes for Structural Identification,” Proc. of the AIAA Dynamic Specialist Conference, Long Beach, CA, pp. 261–270.
15.
Smith, S., 1992, “Iterative Use of Direct Matrix Updates: Connectivity and Convergence,” Proc. of the 33rd AIAA Structures, Structural Dynamics and Materials Conference, pp. 1797–1806.
16.
Abdalla
, M.
, Grigoriadis
, K. M.
, and Zimmerman
, D.
, 1998
, “Enhanced Damage Detection Using Alternating Projections
,” AIAA J.
, 36
, No. 2
, pp. 1305
–1311
.17.
Zimmerman, D., and Santos, J., 1996, “Structural Damage Detection Using Minimum Rank Update Theory and Parameter Estimation,” AIAA/ASME/AHS Adaptive Structures Forum, pp. 168–175.
18.
Hemez
, F.
, and Farhat
, C.
, 1993
, “Locating and Identifying Structural Damage Using a Sensitivity-Based Model Updating Methodology
,” AIAA J.
, 31
, No. 12
, pp. 2648
–2653
.19.
Zimmerman, D., Yap, K., and Hasselman, T., 1997, “Evolutionary Approach for Model Refinement,” Proc. 15th International Modal Analysis Conference, Orlando, FL, pp. 551–557.
20.
Zimmerman
, D.
, and Kaouk
, M.
, 1992
, “Eigenstructure Assignment Approach for Structural Damage Detection
,” AIAA J.
, 30
, No. 7
, pp. 1848
–1855
.21.
Kaouk
, M.
, and Zimmerman
, D.
, 1994
, “Structural Damage Assessment Using a Generalized Minimum Rank Perturbation Theory
,” AIAA J.
, 32
, No. 4
, pp. 836
–842
.22.
Zimmerman
, D.
, and Kaouk
, M.
, 1994
, “Structural Damage Detection Using a Minimum Rank Update Theory
,” ASME J. Vibr. Acoust.
, 116
, pp. 222
–231
.23.
Zimmerman
, D.
, Kaouk
, M.
, and Simmermacher
, T.
, 1995
, “Structural Health Monitoring Using Vibration Measurements and Engineering Insight
,” Trans. ASME
, Special 50th Anniversary Issue, 117
, pp. 214
–221
.24.
Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V., 1994, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia.
25.
Grigoriadis
, K.
, and Skelton
, R.
, 1996
, “Low-order Control Design for LMI Problems Using Alternating Projection Methods
,” Automatica
, 32
, No. 8
, pp. 1117
–1125
.26.
Gahinet, P., Nemirovski, A., Laub, A., and Chilali, M., 1995, LMI Control Toolbox, The MATHWORKS Inc.
27.
Pappa
, R. S.
, James
III, G. H.
, and Zimmerman
, D. C.
, 1998
, “Autonomous Modal Identification of the Space Shuttle Tail Rudder
,” AIAA J. Spacecraft Rockets
, 35
, No. 2
, pp. 163
–169
.28.
Imregun, M., and Ewins, D. J., “An Investigation into Mode Shape Expansion Techniques,” Proc. 11th International Modal Analysis Conference, Kissimmee, FL, pp. 168–175.
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