Active excitation is an emerging area of study within the field of structural health monitoring whereby prescribed inputs are used to excite the structure so that damage-sensitive features may be extracted from the structural response. This work demonstrates that the parameters of a system of ordinary differential equations may be adjusted via an evolutionary algorithm to produce excitations that improve the sensitivity and robustness to extraneous noise of state-space based damage detection features extracted from the structural response to such excitations. A simple computational model is used to show that significant gains in damage detection and quantification may be obtained from the response of a spring-mass system to improved excitations generated by three separate representative ordinary differential equation systems. Observed differences in performance between the excitations produced by the three systems cannot be explained solely by considering the frequency characteristics of the excitations. This work demonstrates that the particular dynamic evolution of the excitation applied to the structure can be as important as the frequency characteristics of said excitation if improved damage detection is desired. In addition, the implied existence of a globally optimum excitation (in the sense of improved damage assessment) for the model system is explored.
Issue Section:
Technical Papers
Keywords:
condition monitoring,
evolutionary computation,
differential equations,
springs (mechanical),
vibrations,
fault diagnosis,
structural health monitoring,
damage identification,
nonlinear dynamics,
attractor analysis,
differential evolution,
excitation optimization,
prediction error,
evolutionary algorithms
1.
Hunt
, D. L.
, Weiss
, S. P.
, West
, W. M.
, Dunlap
, T. A.
, and Freesmeyer
, S. R.
, 1990, “Development and Implementation of a Shuttle Modal Inspection System
,” Sound Vib.
0038-1810, 24
(9
), pp. 34
–42
.2.
Sohn
, H.
, and Farrar
, C. R.
, 2001, “Damage Diagnosis Using Time Series Analysis of Vibration Signals
,” Smart Mater. Struct.
0964-1726, 10
(3
), pp. 446
–451
.3.
Sohn
, H.
, Farrar
, C. R.
, Hunter
, N. F.
, and Worden
, K.
, 2001, “Structural Health Monitoring Using Statistical Pattern Recognition
,” J. Dyn. Syst., Meas., Control
0022-0434, 123
, pp. 706
–711
.4.
Hou
, Z.
, Noori
, M.
, and Amand
, R. S.
, 2000, “Wavelet-Based Approach for Structural Damage Detection
,” J. Eng. Mech.
0733-9399, 126
, pp. 677
–683
.5.
Doebling
, S. W.
, Farrar
, C. R.
, and Prime
, M. B.
, 1998, “A Summary Review of Vibration-Based Damage Identification Methods
,” Shock Vib. Dig.
0583-1024, 205
, pp. 631
–645
.6.
Sohn
, H.
, Farrar
, C. R.
, Hemez
, F. M.
, Czarnecki
, J. J.
, Shunk
, D. D.
, Stinemates
, D. W.
, and Nadler
, B. R.
, 2004, “A Review of Structural Health Monitoring Literature: 1996–2001
,” Technical Report No. LA-13976-MS, Los Alamos National Laboratory
, Los Alamos, NM.7.
Takens
, F.
, 1981, “Detecting Strange Attractors in Turbulence
,” Dynamical Systems and Turbulence (Springer Lecture Notes in Mathematics)
D.
Rand
and L. S.
Young
, eds., Springer
, New York
, Vol. 898
, pp. 366
–381
.8.
9.
Sauer
, T.
, and Yorke
, J. A.
, 1993, “How Many Delay Coordinates Do You Need?
,” Int. J. Bifurcation Chaos Appl. Sci. Eng.
0218-1274, 3
(3
), pp. 737
–744
.10.
Grassberger
, P.
, and Procaccia
, I.
, 1983, “Characterization of Strange Attractors
,” Phys. Rev. Lett.
0031-9007, 50
(5
), pp. 346
–349
.11.
Wolf
, A.
, Swift
, J. B.
, Swinney
, H. L.
, and Vastano
, J. A.
, 1985, “Determining Lyapunov Exponents from a Time Series
,” Physica D
0167-2789, 16
, pp. 285
–317
.12.
Wang
, W. J.
, Wu
, Z. T.
, and Chen
, J.
, 2000, “Fault Identification in Rotating Machinery Using the Correlation Dimension and Bispectra
,” Nonlinear Dyn.
0924-090X, 25
, pp. 383
–393
.13.
Trendafilova
, I.
, and Van Brussel
, H.
, 2001, “Non-Linear Dynamics Tools for the Motion Analysis and Condition Monitoring of Robot Joints
,” Mech. Syst. Signal Process.
0888-3270, 15
(6
), pp. 1141
–1164
.14.
Chelidze
, D.
, and Cusumano
, J. P.
, 2006, “Phase Space Warping: Nonlinear Time-Series Analysis for Slowly Drifting Systems
,” Philos. Trans. R. Soc. London, Ser. A
0962-8428, 364
, pp. 2495
–2513
.15.
Moniz
, L.
, Pecora
, L.
, Nichols
, J.
, Todd
, M. D.
, and Wait
, J. R.
, 2004, “Dynamical Assessment of Structural Damage Using the Continuity Statistic
,” Struct. Health Monit.
1475-9217, 3
(3
), pp. 199
–212
.16.
Nichols
, J. M.
, Nichols
, C. J.
, Todd
, M. D.
, Seaver
, M.
, Trickey
, S. T.
, and Virgin
, L. N.
, 2004, “Use of Data Driven Phase Space Models in Assessing the Strength of a Bolted Connection in a Composite Beam
,” Smart Mater. Struct.
0964-1726, 13
(2
), pp. 241
–250
.17.
Todd
, M. D.
, Nichols
, J. M.
, Pecora
, L. M.
, and Virgin
, L. N.
, 2001, “Vibration-Based Damage Assessment Utilizing State Space Geometry Changes: Local Attractor Variance Ratio
,” Smart Mater. Struct.
0964-1726, 10
(5
), pp. 1000
–1008
.18.
Nichols
, J. M.
, Todd
, M. D.
, and Wait
, J. R.
, 2003, “Using State Space Predictive Modeling with Chaotic Interrogation in Detecting Joint Preload Loss in a Frame Structure Experiment
,” Smart Mater. Struct.
0964-1726, 12
(4
), pp. 580
–601
.19.
Todd
, M. D.
, Erickson
, K.
, Chang
, L.
, Lee
, K.
, and Nichols
, J. M.
, 2004, “Using Chaotic Interrogation and Attractor Nonlinear Cross-Prediction Error to Detect Fastener Preload Loss in an Aluminum Frame
,” Chaos
1054-1500, 14
(2
), pp. 387
–399
.20.
Olson
, C. C.
, Overbey
, L. A.
, and Todd
, M. D.
, 2005, “A Comparison of State-Space Attractor Features in Structural Health Monitoring
,” Proceedings of the 23rd International Modal Analysis Conference (IMAC XXIII)
, Orlando, FL
, Jan. 31–Feb. 3.21.
Solbeck
, J. A.
, and Ray
, L. R.
, 2006, “Damage Identification Using Sensitivity-Enhancing Control and Identified Models
,” ASME J. Vibr. Acoust.
0739-3717, 128
(2
), pp. 210
–220
.22.
Ray
, L. R.
, and Marini
, S.
, 2000, “Optimization of Control Laws for Damage Detection in Smart Structures
,” Proceedings SPIE Smart Structures and Materials Conference
, March 6, Newport Beach, CA
, V. V.
Varadan
, ed., SPIE
, Bellingham, WA
, 3984
, pp. 395
–402
.23.
Mitchell
, M.
, 1996, An Introduction to Genetic Algorithms
, MIT Press
, Cambridge, MA
, Chap. 5.24.
Storn
, R.
, and Price
, R.
, 1997, “Differential Evolution—A Simple and Efficient Heuristic for Global Optimization Over Continuous Spaces
,” J. Global Optim.
0925-5001, 11
(4
), pp. 341
–359
.25.
Broomhead
, D. S.
, and King
, G. P.
, 1986, “Extracting Qualitative Dynamics from Experimental Data
,” Physica D
0167-2789, 20
, pp. 217
–236
.26.
Mees
, A. I.
, Rapp
, P. E.
, and Jennings
, L. S.
, 1987, “Singular Value Decomposition and Embedding Dimension
,” Phys. Rev. A
1050-2947, 36
(1
), pp. 340
–346
.27.
Fraser
, A. M.
, and Swinney
, H. L.
, 1986, “Independent Coordinates for Strange Attractors from Mutual Information
,” Phys. Rev. A
1050-2947, 33
(2
), pp. 1134
–1140
.28.
Kennel
, M. B.
, and Abarbanel
, H. D. I.
, 1992, “Determining Embedding Dimension for Phase-Space Reconstruction Using a Geometrical Construction
,” Phys. Rev. A
1050-2947, 45
(6
), pp. 3403
–3411
.29.
Schreiber
, T.
, 1997, “Detecting and Analyzing Nonstationarity in a Time Series Using Nonlinear Cross Predictions
,” Phys. Rev. Lett.
0031-9007, 78
(5
), pp. 843
–846
.30.
Theiler
, J.
, 1986, “Spurious Dimension from Correlation Algorithms Applied to Limited Time-Series Data
,” Phys. Rev. A
1050-2947, 34
(3
), pp. 2427
–2432
.31.
Pecora
, L. M.
, and Carroll
, T. L.
, 1996, “Discontinuous and Nondifferentiable Functions and Dimension Increase Reduced by Filtering Chaotic Data
,” Chaos
1054-1500, 6
, 432
–439
.32.
Sprott
, J. C.
, 1994, “Some Simple Chaotic Flows
,” Phys. Rev. E
1063-651X, 50
(2
), pp. R647
–R650
.33.
Rossler
, O. E.
, 1976, “An Equation for Continuous Chaos
,” Phys. Lett.
0375-9601 A, 57
(5
), pp. 397
–398
.34.
Lorenz
, E. N.
, 1963, “Deterministic Nonperiodic Flow
,” J. Atmos. Sci.
0022-4928, 20
, pp. 130
–141
.35.
Worden
, K.
, Manson
, G.
, Sohn
, H.
, and Farrar
, C. R.
, 2005, “Extreme Value Statistics from Differential Evolution for Damage Detection
,” Proceedings of the 23rd International Modal Analysis Conference (IMAC XXIII)
, Orlando, FL
, Jan. 31–Feb. 3.36.
Theiler
, J.
, Eubank
, S.
, Longtin
, A.
, Galdrikian
, B.
, and Farmer
, J. D.
, 1992, “Testing for Nonlinearity in Time Series: The Method of Surrogate Data
,” Physica D
0167-2789, 58
, pp. 77
–94
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