This paper presents a statistical measure for the identification of the presence, the location, and the calibration of the strength of singularity in a signal or in any of its derivatives in the presence of measurement noise without the requirement of a baseline using a wavelet based detection technique. For this proposed wavelet based detection of singularities present in a signal, the problem of false alarm and its significant reduction by use of multiple measurements is presented. The importance of the proposed measure on baseline and nonbaseline damage calibration has been discussed from the aspect of structural health monitoring. The findings in this paper can also be used for cross-checking of background noise level in an observed signal. The detection of the existence, location, and extent of an open crack from the first fundamental modeshape of a simply supported beam is presented as an example problem.
Issue Section:
Research Papers
1.
Robertson
, A. N.
, Farrar
, C. R.
, and Sohn
, H.
, 2003, “Singularity Detection for Structural Health Monitoring Using Holder Exponents
,” Mech. Syst. Signal Process.
0888-3270, 17
(6
), pp. 1163
–1184
.2.
Zimmermann
, C. G.
, 2006, “The Impact of Mechanical Defects on the Reliability of Solar Cells in Aerospace Applications
,” IEEE Trans. Device Mater. Reliab.
1530-4388, 6
(3
), pp. 486
–494
.3.
Zhang
, H. Q.
, and Yan
, Y.
, 2001, “Wavelet-Based Approach to Abrupt Fault Detection and Diagnosis of Sensors
,” IEEE Trans. Instrum. Meas.
0018-9456, 50
(5
), pp. 1389
–1396
.4.
Addison
, P. S.
, 2005, “Wavelet Transforms and the ECG: A Review
,” Clin. Phys. Physiol. Meas.
0143-0815, 26
, pp. R155
–R199
.5.
Ide
, K.
, and Sornette
, D.
, 2002, “Oscillatory Finite-Time Singularities in Finance, Population and Rupture
,” Physica A
0378-4371, 307
, pp. 63
–106
.6.
Mallat
, S.
, 2001, A Wavelet Tour on Signal Processing
, Academic
, New York
.7.
Chiementin
, X.
, Bolaers
, F.
, and Dron
, J. P.
, 2007, “Early Detection of Fatigue Damage on Rolling Element Bearings Using Adapted Wavelet
,” ASME J. Vibr. Acoust.
0739-3717, 129
(4
), pp. 495
–506
.8.
Zhong
, S.
, and Oyadiji
, S. O.
, 2008, “Identification of Cracks in Beams With Auxiliary Mass Spatial Probing by Stationary Wavelet Transform
,” ASME J. Vibr. Acoust.
0739-3717, 130
(4
), p. 041001
.9.
Al-Raheem
, K. F.
, Roy
, A.
, Ramachandran
, K. P.
, Harrison
, D. K.
, and Grainger
, S.
, 2008, “Application of the Laplace-Wavelet Combined With ANN for Rolling Bearing Fault Diagnosis
,” ASME J. Vibr. Acoust.
0739-3717, 130
(5
), p. 051007
.10.
Lam
, H. F.
, Lee
, Y. Y.
, Sun
, H. Y.
, Cheng
, G. F.
, and Guo
, X.
, 2005, “Application of the Spatial Wavelet Transform and Bayesian Approach to the Crack Detection of a Partially Obstructed Beam
,” Thin-Walled Struct.
0263-8231, 43
(1
), pp. 1
–21
.11.
Gentile
, A.
, and Messina
, A.
, 2003, “On the Continuous Wavelet Transforms Applied to Discrete Vibrational Data for Detecting Open Cracks in Damaged Beams
,” Int. J. Solids Struct.
0020-7683, 40
(2
), pp. 295
–315
.12.
Dado
, M. H.
, 1997, “A Comprehensive Crack Identification Algorithm for Beams Under Different End Conditions
,” Appl. Acoust.
0003-682X, 51
(4
), pp. 381
–398
.13.
Loutridis
, S.
, Douka
, E.
, and Trochidis
, A.
, 2004, “Crack Identification in Double Cracked Beams Using Wavelet Analysis
,” J. Sound Vib.
0022-460X, 277
(4–5
), pp. 1025
–1039
.14.
Pakrashi
, V.
, Basu
, B.
, and O’ Connor
, A.
, 2007, “Structural Damage Detection and Calibration Using a Wavelet-Kurtosis Technique
,” Eng. Struct.
0141-0296, 29
(9
), pp. 2097
–2108
.15.
Chang
, C. C.
, and Chen
, L. W.
, 2003, “Vibration Damage Detection of a Timoshenko Beam by Spatial Wavelet Based Approach
,” Appl. Acoust.
0003-682X, 64
(12
), pp. 1217
–1240
.16.
Okafor
, A. C.
, and Dutta
, A.
, 2000, “Structural Damage Detection in Beams by Wavelet Transforms
,” Smart Mater. Struct.
0964-1726, 9
(6
), pp. 906
–917
.17.
Taha
, M. M. R.
, Noureldin
, A.
, Lucero
, J. L.
, and Baca
, T. J.
, 2006, “Wavelet Transform for Structural Health Monitoring: A Compendium of Uses and Features
,” Struct. Health Monit.
1475-9217, 5
(3
), pp. 267
–295
.18.
Hadjileontiadis
, L. J.
, Douka
, E.
, and Trochidis
, A.
, 2005, “Crack Detection in Beams Using Kurtosis
,” Comput. Struct.
0045-7949, 83
, pp. 909
–919
.19.
Hadjileontiadis
, L. J.
, Douka
, E.
, and Trochidis
, A.
, 2005, “Fractal Dimension Analysis for Crack Detection in Beam Structures
,” Mech. Syst. Signal Process.
0888-3270, 19
(3
), pp. 659
–674
.20.
Hadjileontiadis
, L. J.
, Leontios
, J.
, and Douka
, E.
, 2007, “Kurtosis Analysis for Crack Detection in Thin Isotropic Rectangular Plates
,” Eng. Struct.
0141-0296, 29
(9
), pp. 2353
–2364
.21.
Hadjileontiadis
, L. J.
, and Douka
, E.
, 2007, “Crack Detection in Plates Using Fractal Dimension
,” Eng. Struct.
0141-0296, 29
(7
), pp. 1612
–1625
.22.
Loutridis
, S.
, Douka
, E.
, Hadjileontiadis
, L. J.
, and Trochidis
, A.
, 2005, “A Two-Dimensional Wavelet Transform for Detection of Cracks in Plates
,” Eng. Struct.
0141-0296, 27
(9
), pp. 1327
–1338
.23.
Rucka
, M.
, and Wilde
, K.
, 2006, “Crack Identification Using Wavelets on Experimental Static Deflection Profiles
,” Eng. Struct.
0141-0296, 28
(2
), pp. 279
–288
.24.
Poudel
, U. P.
, Fu
, G.
, and Ye
, J.
, 2005, “Structural Damage Detection Using Digital Video Imaging Technique and Wavelet Transformation
,” J. Sound Vib.
0022-460X, 286
(4–5
), pp. 869
–895
.25.
Vanlanduit
, S.
, Guillaume
, P.
, Schoukens
, J.
, and Parloo
, E.
, 2000, “Linear and Nonlinear Damage Detection Using a Scanning Laser Vibrometer
,” Proc. SPIE
0277-786X, 4072
, pp. 453
–466
.26.
Khan
, A. Z.
, Stanbridge
, A. B.
, and Ewins
, D. J.
, 2000, “Detecting Damage in Vibrating Structures With a Scanning LDV
,” Opt. Lasers Eng.
0143-8166, 32
(6
), pp. 583
–592
.27.
Carneiro
, S. H. S.
, and Inman
, D. J.
, 2002, “Continuous Model for the Transverse Vibration of Cracked Timoshenko Beams
,” ASME J. Vibr. Acoust.
0739-3717, 124
(2
), pp. 310
–320
.28.
Narkis
, Y.
, 1994, “Identification of Crack Location in Vibrating Simply Supported Beams
,” J. Sound Vib.
0022-460X, 172
(4
), pp. 549
–558
.29.
Bovsunovsky
, A. P.
, and Matveev
, V. V.
, 2000, “Analytical Approach to the Determination of Dynamic Characteristics of a Beam With a Closing Crack
,” J. Sound Vib.
0022-460X, 235
(3
), pp. 415
–434
.30.
Misiti
, M.
, Misiti
, Y.
, Oppenheim
, G.
, and Poggi
, J. M.
, 2006, Wavelet Toolbox for Use With MATLAB
, The Mathworks Inc.
, Natick, MA
.31.
De Vries
, D. K.
, and Chandon
, Y.
, 2007, “On the False-Positive Rate of Statistical Equipment Comparisons Based on the Kruskal-Wallis H Statistic
,” IEEE Trans. Semicond. Manuf.
0894-6507, 20
(3
), pp. 286
–292
.32.
Bukkapatnam
, S. T. S.
, Nichols
, J. M.
, Seaver
, M.
, Trickey
, S. T.
, and Hunter
, M.
, 2005, “A Wavelet Based Distortion Energy Approach to Structural Health Monitoring
,” Struct. Health Monit.
1475-9217, 4
(3
), pp. 247
–258
.33.
Rouhan
, A.
, and Schoefs
, F.
, 2003, “Probabilistic Modelling of Inspection Results for Offshore Structures
,” Struct. Safety
0167-4730, 25
, pp. 379
–399
.Copyright © 2009
by American Society of Mechanical Engineers
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