Mode Shape-Based Damage Localization in Steel Plates Using a Detection Index Based on 2D Wavelet Analysis

Document Type : Regular Paper

Authors

1 M.Sc. of Structural Engineering, Faculty of Civil Engineering, Semnan University, Semnan, Iran

2 Professor, Faculty of Civil Engineering, Semnan University, Semnan, Iran

3 Ph.D. of Structural Engineering, Faculty of Civil Engineering, Semnan University, Semnan, Iran

Abstract

Structures are subjected to a variety of environmental and loading conditions over time, and minor damage to structural elements may occur. By timely identifying damage and repairing damaged locations, it is possible to prevent the spread and development of damage to other elements and, as a result, the overall destruction of the structure. This article discusses the identification and determination of the location of damage in steel plates based on the use of the primary and secondary shapes of vibration modes and the analytical method of two-dimensional wavelet analysis. Modelling and frequency analysis of the plate were performed in ABAQUS software, and the primary and secondary mode shapes were extracted. To determine the location of the damage, a damage detection index (DDI) was proposed based on the angle between the primary and secondary mode shape vectors and the diagonal detail coefficients obtained from the wavelet analysis of the primary and secondary mode shapes. The results showed that by using this index, damage can be identified by identifying peaks resulting from irregularities and disturbances. Also, the DDI value of the damage was dependent on the severity of damage occurring in a damaged situation, and the height of the disorder peaks increased with increased damage only at that damage position.

Keywords

Main Subjects

References

[1]     Rytter A. Vibrational based inspection of civil engineering structures. Fract Dyn 1993. https://doi.org/10.1016/j.jsv.2016.06.047.
[2]     Farrar CR, Doebling SW, Nix DA. Vibration–based structural damage identification. Philos Trans R Soc London Ser A Math Phys Eng Sci 2001;359:131–49. https://doi.org/10.1098/rsta.2000.0717.
[3]     Montalvao D. A review of vibration-based structural health monitoring with special emphasis on composite materials. Shock Vib Dig 2006;38:295–324. https://doi.org/10.1177/0583102406065898.
[4]     Chatterjee A. Structural damage assessment in a cantilever beam with a breathing crack using higher order frequency response functions. J Sound Vib 2010;329:3325–34. https://doi.org/10.1016/j.jsv.2010.02.026.
[5]     Majumdar A, Maiti DK, Maity D. Damage assessment of truss structures from changes in natural frequencies using ant colony optimization. Appl Math Comput 2012;218:9759–72. https://doi.org/10.1016/j.amc.2012.03.031.
[6]     Bai RB, Ostachowicz W, Cao MS, Su Z. Crack detection in beams in noisy conditions using scale fractal dimension analysis of mode shapes. Smart Mater Struct 2014;23:065014. https://doi.org/10.1088/0964-1726/23/6/065014.
[7]     Yazdanpanah O, Seyedpoor SM, Bengar HA. A new damage detection indicator for beams based on mode shape data. Struct Eng Mech 2015;53:725–44. https://doi.org/10.12989/sem.2015.53.4.725.
[8]     Pandey AK, Biswas M, Samman MM. Damage detection from changes in curvature mode shapes. J Sound Vib 1991;145:321–32. https://doi.org/10.1016/0022-460X(91)90595-B.
[9]     Tomaszewska A. Influence of statistical errors on damage detection based on structural flexibility and mode shape curvature. Comput Struct 2010;88:154–64. https://doi.org/10.1016/j.compstruc.2009.08.017.
[10]   Cao M, Radzieński M, Xu W, Ostachowicz W. Identification of multiple damage in beams based on robust curvature mode shapes. Mech Syst Signal Process 2014;46:468–80. https://doi.org/10.1016/j.ymssp.2014.01.004.
[11]   Khanahmadi M, Garfamy HM, Gholhaki M, Rezaifar O, Pouraminian M. Curvature-based damage detection in a column under the effect of axial load. J Struct Steel 2022;16:65–75.
[12]   Khanahmadi M, Pouramonian M, Garfamy HM, Dezhkam B. Damage detection and identification in a column under the effect of axial load using modal properties and mode shape-based detection index. Sharif J Civ Eng 2023;38.2:53–62. https://doi.org/10.24200/j30.2022.60873.3129.
[13]   Daneshvar MH, Saffarian M, Jahangir H, Sarmadi H. Damage identification of structural systems by modal strain energy and an optimization-based iterative regularization method. Eng Comput 2023;39:2067–87. https://doi.org/10.1007/s00366-021-01567-5.
[14]   Hu M, He J, Zhou C, Shu Z, Yang W. Surface damage detection of steel plate with different depths based on Lamb wave. Measurement 2022;187:110364. https://doi.org/10.1016/j.measurement.2021.110364.
[15]   Liu X, Lieven NAJ, Escamilla-Ambrosio PJ. Frequency response function shape-based methods for structural damage localisation. Mech Syst Signal Process 2009;23:1243–59. https://doi.org/10.1016/j.ymssp.2008.10.002.
[16]   Bandara RP, Chan THT, Thambiratnam DP. Frequency response function based damage identification using principal component analysis and pattern recognition technique. Eng Struct 2014;66:116–28. https://doi.org/10.1016/j.engstruct.2014.01.044.
[17]   Bakhary N, Hao H, Deeks AJ. Substructuring technique for damage detection using statistical multi-stage artificial neural network. Adv Struct Eng 2010;13:619–39. https://doi.org/10.1260/1369-4332.13.4.619.
[18]   Shu J, Zhang Z, Gonzalez I, Karoumi R. The application of a damage detection method using Artificial Neural Network and train-induced vibrations on a simplified railway bridge model. Eng Struct 2013;52:408–21. https://doi.org/10.1016/j.engstruct.2013.02.031.
[19]   He R-S, Hwang S-F. Damage detection by a hybrid real-parameter genetic algorithm under the assistance of grey relation analysis. Eng Appl Artif Intell 2007;20:980–92. https://doi.org/10.1016/j.engappai.2006.11.020.
[20]   Meruane V, Heylen W. Structural damage assessment with antiresonances versus mode shapes using parallel genetic algorithms. Struct Control Heal Monit 2011;18:825–39. https://doi.org/10.1002/stc.401.
[21]   Chandrashekhar M, Ganguli R. Damage assessment of structures with uncertainty by using mode-shape curvatures and fuzzy logic. J Sound Vib 2009;326:939–57. https://doi.org/10.1016/j.jsv.2009.05.030.
[22]   Nguyen SD, Ngo KN, Tran QT, Choi SB. A new method for beam-damage-diagnosis using adaptive fuzzy neural structure and wavelet analysis. Mech Syst Signal Process 2013;39:181–94. https://doi.org/10.1016/j.ymssp.2013.03.023.
[23]   Reda Taha MM, Noureldin A, Lucero JL, Baca TJ. Wavelet transform for structural health monitoring: A compendium of uses and features. Struct Heal Monit 2006;5:267–95. https://doi.org/10.1177/1475921706067741.
[24]   Andreaus U, Baragatti P, Casini P, Iacoviello D. Experimental damage evaluation of open and fatigue cracks of multi-cracked beams by using wavelet transform of static response via image analysis. Struct Control Heal Monit 2017;24. https://doi.org/10.1002/stc.1902.
[25]   Zhou S, Tang B, Chen R. Comparison between non-stationary signals fast Fourier transform and wavelet analysis. Int Asia Symp Intell Interact Affect Comput ASIA 2009 2009:128–9. https://doi.org/10.1109/ASIA.2009.31.
[26]   Newland DE. Wavelet Analysis of Vibration, Part 1: Theory; Part 2: Wavelet Maps. J Vib Acoust 1994;116:409–25.
[27]   Masuda, A., Nakaoka, A., Sone, A., and Yamamoto S. Health monitoring system of structures based on orthonormal wavelet transform. Seism Engrg 1995;312:161–7.
[28]   Wang Q, Deng X. Damage detection with spatial wavelets. Int J Solids Struct 1999;36:3443–68. https://doi.org/10.1016/S0020-7683(98)00152-8.
[29]   Hou Z, Hera A, Noori M. Wavelet-based techniques for structural health monitoring. Heal Assess Eng Struct Bridg Build Other Infrastructures 2013:179–202. https://doi.org/10.1142/9789814439022_0007.
[30]   Douka E, Loutridis S, Trochidis A. Crack identification in plates using wavelet analysis. J Sound Vib 2004;270:279–95. https://doi.org/10.1016/S0022-460X(03)00536-4.
[31]   Ovanesova A V., Suárez LE. Applications of wavelet transforms to damage detection in frame structures. Eng Struct 2004;26:39–49. https://doi.org/10.1016/j.engstruct.2003.08.009.
[32]   Loutridis S, Douka E, Trochidis A. Crack identification in double-cracked beams using wavelet analysis. J Sound Vib 2004;277:1025–39. https://doi.org/10.1016/j.jsv.2003.09.035.
[33]   Chang CC, Chen LW. Detection of the location and size of cracks in the multiple cracked beam by spatial wavelet based approach. Mech Syst Signal Process 2005;19:139–55. https://doi.org/10.1016/j.ymssp.2003.11.001.
[34]   Khatam H, Golafshani AA, Beheshti-Aval SB, Noori M. Harmonic class loading for damage identification in beams using wavelet analysis. Struct Heal Monit 2007;6:67–80. https://doi.org/10.1177/1475921707072064.
[35]   Fan W, Qiao P. A 2-D continuous wavelet transform of mode shape data for damage detection of plate structures. Int J Solids Struct 2009;46:4379–95. https://doi.org/10.1016/j.ijsolstr.2009.08.022.
[36]   Gökdaǧ H, Kopmaz O. A new damage detection approach for beam-type structures based on the combination of continuous and discrete wavelet transforms. J Sound Vib 2009;324:1158–80. https://doi.org/10.1016/j.jsv.2009.02.030.
[37]   Katunin A. Identification of multiple cracks in composite beams using 2010:41–52.
[38]   Zhong S, Oyadiji SO. Crack detection in simply supported beams using stationary wavelet transform of modal data. Struct Control Heal Monit 2011;18:169–90. https://doi.org/10.1002/stc.366.
[39]   Bagheri A, Kourehli S. Damage detection of structures under earthquake excitation using discrete wavelet analysis. Asian J Civ Eng 2013;14:289–304.
[40]   Xu W, Radzieński M, Ostachowicz W, Cao M. Damage detection in plates using two-dimensional directional Gaussian wavelets and laser scanned operating deflection shapes. Struct Heal Monit 2013;12:457–68. https://doi.org/10.1177/1475921713492365.
[41]   Lee SG, Yun GJ, Shang S. Reference-free damage detection for truss bridge structures by continuous relative wavelet entropy method. Struct Heal Monit 2014;13:307–20. https://doi.org/10.1177/1475921714522845.
[42]   Li J, Hao H. Substructure damage identification based on wavelet-domain response reconstruction. Struct Heal Monit 2014;13:389–405. https://doi.org/10.1177/1475921714532991.
[43]   Katunin A. Stone impact damage identification in composite plates using modal data and quincunx wavelet analysis. Arch Civ Mech Eng 2015;15:251–61. https://doi.org/10.1016/j.acme.2014.01.010.
[44]   Patel SS, Chourasia AP, Panigrahi SK, Parashar J, Parvez N, Kumar M. Damage Identification of RC Structures Using Wavelet Transformation. Procedia Eng 2016;144:336–42. https://doi.org/10.1016/j.proeng.2016.05.141.
[45]   Asgarian B, Aghaeidoost V, Shokrgozar HR. Damage detection of jacket type offshore platforms using rate of signal energy using wavelet packet transform. Mar Struct 2016;45:1–21. https://doi.org/10.1016/j.marstruc.2015.10.003.
[46]   Ashory MR, Ghasemi-Ghalebahman A, Kokabi MJ. Damage identification in composite laminates using a hybrid method with wavelet transform and finite element model updating. Proc Inst Mech Eng Part C J Mech Eng Sci 2018;232:815–27. https://doi.org/10.1177/0954406217692844.
[47]   Yang C, Oyadiji SO. Delamination detection in composite laminate plates using 2D wavelet analysis of modal frequency surface. Comput Struct 2017;179:109–26. https://doi.org/10.1016/j.compstruc.2016.10.019.
[48]   Zhao Y, Noori M, Altabey WA, Beheshti-Aval SB. Mode shape-based damage identification for a reinforced concrete beam using wavelet coefficient differences and multiresolution analysis. Struct Control Heal Monit 2018;25. https://doi.org/10.1002/stc.2041.
[49]   Younesi A, Rezaifar O, Gholhaki M, Esfandiari A. Structural health monitoring of a concrete-filled tube column. Mag Civ Eng 2019;85:136–45. https://doi.org/10.18720/MCE.85.11.
[50]   Younesi A, Rezaifar O, Gholhaki M, Esfandiari A. Damage detection in concrete filled tube columns based on experimental modal data and wavelet technique. Mech Adv Compos Struct 2020;7:245–54. https://doi.org/10.22075/macs.2020.17087.1195.
[51]   Younesi A, Rezaifar O, Gholhaki M, Esfandiari A. Active interface debonding detection of a concrete filled tube (CFT) column by modal parameters and continuous wavelet transform (CWT) technique. Struct Monit Maint 2021;8:69–90. https://doi.org/10.12989/smm.2021.8.1.069.
[52]   Wang S, Li J, Luo H, Zhu H. Damage identification in underground tunnel structures with wavelet based residual force vector. Eng Struct 2019;178:506–20. https://doi.org/10.1016/j.engstruct.2018.10.021.
[53]   Khanahmadi M, Rezaifar O, Gholhaki M. Damage detection in steel plates based on comparing analytical results of the discrete 2-D wavelet transform of primary and secondary modes shape. J Struct Constr Eng 2021;8:198–214. https://doi.org/10.22065/jsce.2019.174347.1799.
[54]   Khanahmadi M, Rezaifar O, Gholhaki M. Damage detection of prefabricated walls (panel 3D plates) based on wavelet transform detection algorithm. J Struct Constr Eng 2021;8:289–309. https://doi.org/10.22065/jsce.2019.197470.1923.
[55]   Khanahmadi M, Gholhaki M, Ghasemi-Ghalebahman A, Khademi-Kouhi M. Damage detection in laminated composite plates using wavelet analysis analytical method. J Vib Sound 2022;10:144–56.
[56]   Khanahmadi M, Gholhaki M, Rezaifar O. Damage identification of a column under the axial load based on wavelet transform and modal data. J Model Eng 2021;18:51–64. https://doi.org/10.22075/JME.2020.20940.1931.
[57]   Khanahmadi M, Garfamy HM, Gholhaki M, Dezhkam B, Miri ME. Wavelet-based damage detection of steel beam-structures. J Struct Steel 2021;15:15–27.
[58]   Khanahmadi M, Rezaifar O, Gholhaki M. Comparative study on steel beams damage detection based on continuous and discrete wavelet transforms of static and dynamic responses. J Struct Constr Eng 2021;8:166–83. https://doi.org/10.22065/JSCE.2020.216647.2058.
[59]   Khanahmadi M, Rezaifar O, Gholhaki M, Dezhkam B, Younesi A. Health monitoring and damage assessment of a column under the effect of axial load using modal dynamic data and wavelet analytical method. Modares Civ Eng J 2023;23:7–25. https://doi.org/10.22034/23.3.7.
[60]   Rezaifar O, Gholhaki M, Khanahmadi M, Amiri Y. A review of structural health monitoring and damage detection using wavelet transform: the case study of damage detection in cantilever beams. J Vib Sound 2022;11:157–71.
[61]   Jahangir H, Khatibinia M, Mokhtari Masi M. Damage detection in prestressed concrete slabs using wavelet analysis of vibration responses in the time domain. J Rehabil Civ Eng 2022;10:37–63. https://doi.org/10.22075/jrce.2021.23385.1510.
[62]   Jahangir H, Hasani H, Esfahani MR. Damage localization of RC beams via wavelet analysis of noise contaminated modal curvatures. J Soft Comput Civ Eng 2021;5:101–33. https://doi.org/10.22115/SCCE.2021.292279.1340.
[63]   Mamazizi A, Khanahmadi M, Nobakht Vakili K. Debonding damage detection and assessment in a CFST composite column using modal dynamic data. Sharif J Civ Eng 2022;38.2:53–63. https://doi.org/10.24200/j30.2022.59903.3075.
[64]   Khanahmadi M, Rezaifar O, Gholhaki M, Younesi A. Detection of debonding damage location of the concrete core from the steel tube of concrete-filled steel tube (CFST) columns using wavelet analysis analytical method. Modares Civ Eng J 2023;22:129–42.
[65]   Khanahmadi M, Gholhaki M, Rezaifar O, Dezhkam B. Damage identification in steel beam structures based on the comparison of analytical results of wavelet analysis. Civ Infrastruct Res 2023;8:173–83. https://doi.org/10.22091/cer.2022.8340.1407.
[66]   Benedetto JJ, Walnut DF. Gabor frames for L2 and related spaces. Wavelets 2021:97–162. https://doi.org/10.1201/9781003210450-4.
[67]   Rao KR, Kim DN, Hwang J-J. Fast Fourier Transform - Algorithms and Applications 2010:340.
[68]   Douka E, Loutridis S, Trochidis A. Crack identification in beams using wavelet analysis. Int J Solids Struct 2003;40:3557–69. https://doi.org/10.1016/S0020-7683(03)00147-1.
[69]   Zhong S, Oyadiji SO. Detection of cracks in simply-supported beams by continuous wavelet transform of reconstructed modal data. Comput Struct 2011;89:127–48. https://doi.org/10.1016/j.compstruc.2010.08.008.
[70]   Kim H, Melhem H. Damage detection of structures by wavelet analysis. Eng Struct 2004;26:347–62. https://doi.org/10.1016/j.engstruct.2003.10.008.
[71]   Abdulkareem M, Bakhary N, Vafaei M, Noor NM, Padil KH. Non-probabilistic wavelet method to consider uncertainties in structural damage detection. J Sound Vib 2018;433:77–98. https://doi.org/10.1016/j.jsv.2018.07.011.
[72]   Hoseini Vaez SR, Dehghani E, Babaei V. Damage Detection in Post-tensioned Slab Using 2D Wavelet Transforms. J Rehabil Civ Eng 2017;5:25–38. https://doi.org/10.22075/JRCE.2017.11561.1191.
[73]   Rezaifar O, Kabir MZ, Taribakhsh M, Tehranian A. Dynamic behaviour of 3D-panel single-storey system using shaking table testing. Eng Struct 2008;30:318–37. https://doi.org/10.1016/j.engstruct.2007.03.019.
[74]   Kabir MZ, Rezaifar O. Shaking table examination on dynamic characteristics of a scaled down 4-story building constructed with 3D-panel system. Structures 2019;20:411–24. https://doi.org/10.1016/j.istruc.2019.05.006.
[75]   Naderpour H, Fakharian P. A synthesis of peak picking method and wavelet packet transform for structural modal identification. KSCE J Civ Eng 2016;20:2859–67. https://doi.org/10.1007/s12205-016-0523-4.
[76]   Fakharian P, Naderpour H. Damage Severity Quantification Using Wavelet Packet Transform and Peak Picking Method. Pract Period Struct Des Constr 2022;27:1–11. https://doi.org/10.1061/(asce)sc.1943-5576.0000639.

Files

Cited by

History

  • Receive Date: 27 May 2022
  • Revise Date: 20 November 2022
  • Accept Date: 06 December 2022

Share

How to cite

Statistics