Abstract
The continuous wavelet transform (CWT) is one of the crucial damage identification tools in the vibration-based damage assessment. Because of the vanishing moment property, the CWT method is capable of featuring damage singularity in the higher scales, and separating the global trends and noise progressively. In the classical investigations about this issue, the localization property of the CWT is usually deemed as the most critical point. The abundant information provided by the scale-domain information and the corresponding effectiveness are, however, neglected to some extent. Ultimately, this neglect restricts the sufficient application of the CWT method in damage localization, especially in noisy conditions. In order to address this problem, the wavelet correlation operator is introduced into the CWT damage detection method as a post-processing. By means of the correlations among different scales, the proposed operator suppresses noise, cancels global trends, and intensifies the damage features for various mode shapes. The proposed method is demonstrated numerically with emphasis on characterizing damage in noisy environments, where the wavelet scale Teager-Kaiser energy operator is taken as the benchmark method for comparison. Experimental validations are conducted based on the benchmark data from composite beam specimens measured by a scanning laser vibrometer. Numerical and experimental validations/comparisons present that the introduction of wavelet correlation operator is effective for damage localization in noisy conditions.
Similar content being viewed by others
References
Liu Z, He Z, Guo W, et al. A hybrid fault diagnosis method based on second generation wavelet de-noising and local mean decomposition for rotating machinery. ISA Trans, 2016, 61: 211–220
Jiang H K, He Z J, Duan C D, et al. Gearbox fault diagnosis using adaptive redundant Lifting Scheme. Mech Syst Signal Process, 2006, 20: 1992–2006
Jiang H, He Z, Duan C, et al. Gearbox fault diagnosis using adaptive redundant second generation wavelet. Key Eng Mater, 2005, 293-294: 95–102
Zhang X, Gao R X, Yan R, et al. Multivariable wavelet finite elementbased vibration model for quantitative crack identification by using particle swarm optimization. J Sound Vibr, 2016, 375: 200–216
Zhang X, Zuo H, Liu J, et al. Analysis of shallow hyperbolic shell by different kinds of wavelet elements based on B-spline wavelet on the interval. Appl Math Model, 2016, 40: 1914–1928
Yang Z B, Chen X F, Yu J, et al. A damage identification approach for plate structures based on frequency measurements. Nondestruct Test Eval, 2013, 28: 321–341
Yan R, Gao R X. Harmonic wavelet-based data filtering for enhanced machine defect identification. J Sound Vibr, 2010, 329: 3203–3217
Yan R, Gao R X, Chen X. Wavelets for fault diagnosis of rotary machines: A review with applications. Signal Process, 2014, 96: 1–15
Gao R X, Yan R. Wavelets: Theory and Applications for Manufacturing. Berlin Springer Science & Business Media, 2010
Wang Q, Deng X M. Damage detection with spatial wavelets. Int J Solids Struct, 1999, 36: 3443–3468
Cai G, Chen X, He Z. Sparsity-enabled signal decomposition using tunable Q-factor wavelet transform for fault feature extraction of gearbox. Mech Syst Signal Process, 2013, 41: 34–53
Rucka M, Wilde K. Crack identification using wavelets on experimental static deflection profiles. Eng Struct, 2006, 28: 279–288
Rucka M, Wilde K. Application of continuous wavelet transform in vibration based damage detection method for beams and plates. J Sound Vibr, 2006, 297: 536–550
Katunin A, Dragan K, Dziendzikowski M. Damage identification in aircraft composite structures: A case study using various non-destructive testing techniques. Compos Struct, 2015, 127: 1–9
Katunin A. Diagnostics of composite structures using wavelets. The Publishing House of the Institute for Sustainable Technologies-National Research Institute. Place Radom, 2015, 128
Cao M, Ye L, Zhou L, et al. Sensitivity of fundamental mode shape and static deflection for damage identification in cantilever beams. Mech Syst Signal Process, 2011, 25: 630–643
Xu W, Radzienski M, Ostachowicz W, et al. Damage detection in plates using two-dimensional directional Gaussian wavelets and laser scanned operating deflection shapes. Struct Health Monit, 2013, 12: 457–468
Yang Z, Chen X, Jiang Y, et al. Generalised local entropy analysis for crack detection in beam-like structures. Nondestruct Test Eval, 2014, 29: 133–153
Zhang C L, Li B, Yang Z B, et al. Crack location identification of rotating rotor systems using operating deflection shape data. Sci China Tech Sci, 2013, 56: 1723–1732
Yang Z B, Chen X F, Xie Y, et al. The hybrid multivariate analysis method for damage detection. Struct Control Health Monit, 2016, 23: 123–143
Katunin A. Damage identification in composite plates using two-dimensional B-spline wavelets. Mech Syst Signal Process, 2011, 25: 3153–3167
Katunin A, Przystalka P. Damage assessment in composite plates using fractional wavelet transform of modal shapes with optimized selection of spatial wavelets. Eng Appl Artif Intel, 2014, 30: 73–85
Xiang J W, Liang M. Wavelet-based detection of beam cracks using modal shape and frequency measurements. Comput-Aided Civ Inf, 2012, 27: 439–454
Zhang X, Liu J, Chen X, et al. Multivariable wavelet finite element for plane truss analysis. CMES-Comp Model Eng, 2015, 109: 405–425
Zhang X W, Chen X F, Yang Z B, et al. Multivariable wavelet finite element for flexible skew thin plate analysis. Sci China Tech Sci, 2014, 57: 1532–1540
Yang Z, Chen X, He Y, et al. The analysis of curved beam using b-spline wavelet on interval finite element method. Shock Vib, 2014, 1–9
Zuo H, Yang Z B, Chen X F, et al. Static, free vibration and buckling analysis of functionally graded beam via b-spline wavelet on the interval and Timoshenko beam theory. CMES-Comp Model Eng, 2014, 100: 477–506
Zuo H, Yang Z, Chen X, et al. Bending, free vibration and buckling analysis of functionally graded plates via wavelet finite element method. CMC: Comput Mater Con, 2014, 44: 167–204
Yang Z B, Chen X F, Li B, et al. Vibration analysis of curved shell using b-spline wavelet on the interval (bswi) finite elements method and general shell theory. CMES-Comp Model Eng, 2012, 85: 129–155
Yang Z, Chen X, Tian S, et al. Multiple damages detection in beam based approximate waveform capacity dimension. Struct Eng Mech, 2012, 41: 663–673
Geng J, Zhang X W, Chen X F, et al. High-frequency vibration analysis of thin plate based on wavelet-based FEM using B-spline wavelet on interval. Sci China Tech Sci, 2017, 60: 792–806
Solís M, Algaba M, Galvín P. Continuous wavelet analysis of mode shapes differences for damage detection. Mech Syst Signal Process, 2013, 40: 645–666
Montanari L, Spagnoli A, Basu B, et al. On the effect of spatial sampling in damage detection of cracked beams by continuous wavelet transform. J Sound Vibr, 2015, 345: 233–249
Zhong S C, Oyadiji S O. Detection of cracks in simply-supported beams by continuous wavelet transform of reconstructed modal data. Composite Struct, 2011, 89: 127–148
Cao M, Radzienski M, Xu W, et al. Identification of multiple damage in beams based on robust curvature mode shapes. Mech Syst Signal Process, 2014, 46: 468–480
Cao M S, Xu W, Ren W X, et al. A concept of complex-wavelet modal curvature for detecting multiple cracks in beams under noisy conditions. Mech Syst Signal Process, 2016, 76-77: 555–575
Cao M, Xu W, Ostachowicz W, et al. Damage identification for beams in noisy conditions based on Teager energy operator-wavelet transform modal curvature. J Sound Vibr, 2014, 333: 1543–1553
Xu W, Cao M, Radzienski M, et al. Detecting multiple small-sized damage in beam-type structures by Teager energy of modal curvature shape. J Vibroeng, 2015, 17: 275–286
Yang Z B, Radzienski M, Kudela P, et al. Scale-wavenumber domain filtering method for curvature modal damage detection. Composite Struct, 2016, 154: 396–409
Yang Z B, Chen X F, Radzienski M, et al. A Fourier spectrum-based strain energy damage detection method for beam-like structures in noisy conditions. Sci China Tech Sci, 2017, 28
Yang Z B, Radzienski M, Kudela P, et al. Fourier spectral-based modal curvature analysis and its application to damage detection in beams. Mech Syst Signal Process, 2017, 84: 763–781
Yang Z B, Radzienski M, Kudela P, et al. Damage detection in beamlike composite structures via Chebyshev pseudo spectral modal curvature. Composite Struct, 2017, 168: 1–12
Yang Z, Chen X, Li X, et al. Wave motion analysis in arch structures via wavelet finite element method. J Sound Vibr, 2014, 333: 446–469
Chen X F, Yang Z B, Zhang X W, et al. Modeling of wave propagation in one-dimension structures using B-spline wavelet on interval finite element. Finite Elem Anal Des, 2012, 51: 1–9
Zuo H, Yang Z, Chen X, et al. Analysis of laminated composite plates using wavelet finite element method and higher-order plate theory. Composite Struct, 2015, 131: 248–258
Yang Z B, Chen X F, Xie Y, et al. Wave motion analysis and modeling of membrane structures using the wavelet finite element method. Appl Math Model, 2016, 40: 2407–2420
Yang Z, Chen X, Zhang X, et al. Free vibration and buckling analysis of plates using B-spline wavelet on the interval Mindlin element. Appl Math Model, 2013, 37: 3449–3466
Yang Z B, Radzienski M, Kudela P, et al. Two-dimensional Chebyshev pseudo spectral modal curvature and its application in damage detection for composite plates. Composite Struct, 2017, 168: 372–383
Rucka M. Damage detection in beams using wavelet transform on higher vibration modes. J Theor App Mech-Pol, 2011, 49: 399–417
Yang Z B, Radzienski M, Kudela P, et al. Two-dimensional modal curvature estimation via Fourier spectral method for damage detection. Composite Struct, 2016, 148: 155–167
Yang Z B, Chen X F, Xie Y, et al. Hybrid two-step method of damage detection for plate-like structures. Struct Control Health Monit, 2016, 23: 267–285
Katunin A. Nondestructive damage assessment of composite structures based on wavelet analysis of modal curvatures: State-of-the-art review and description of wavelet-based damage assessment benchmark. Shock and Vib, 2015, 501: 735219
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yang, Z., Chen, X., Radzienski, M. et al. Damage localization for beams based on the wavelet correlation operator. Sci. China Technol. Sci. 60, 1505–1517 (2017). https://doi.org/10.1007/s11431-016-9036-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11431-016-9036-7