DOI QR코드

DOI QR Code

A simple method to detect cracks in beam-like structures

  • Xiang, Jiawei (Department of Mechanical Science and Engineering, Nagoya University) ;
  • Matsumoto, Toshiro (Department of Mechanical Science and Engineering, Nagoya University) ;
  • Long, Jiangqi (College of Mechanical and Electrical Engineering, Wenzhou University) ;
  • Wang, Yanxue (School of Mechanical and Electrical Engineering, Guilin University of Electronic Technology) ;
  • Jiang, Zhansi (School of Mechanical and Electrical Engineering, Guilin University of Electronic Technology)
  • 투고 : 2011.12.15
  • 심사 : 2012.03.12
  • 발행 : 2012.04.25

초록

This study suggests a simple two-step method for structural vibration-based health monitoring for beam-like structures which only utilizes mode shape curvature and few natural frequencies of the structures in order to detect and localize cracks. The method is firstly based on the application of wavelet transform to detect crack locations from mode shape curvature. Then particle swarm optimization is applied to evaluate crack depth. As the Rayleigh quotient is introduced to estimate natural frequencies of cracked beams, the relationship of natural frequencies and crack depths can be easily obtained with only a simple formula. The method is demonstrated and validated numerically, using the numerical examples (cantilever beam and simply supported shaft) in the literature, and experimentally for a cantilever beam. Our results show that mode shape curvature and few estimated natural frequencies can be used to detect crack locations and depths precisely even under a certain level of noise. The method can be extended for health monitoring of other more complicated structures.

키워드

참고문헌

  1. Adams, R.D., Cawley, P., Pye, C.J. and Stone, B.J. (1978), "A vibration technique for non-destructively assessing the integrity of structures", J. Mech. Eng. Sci., 20(2), 93-100. https://doi.org/10.1243/JMES_JOUR_1978_020_016_02
  2. Amiri, G.G., Razzaghi, S.A.S. and Bagheri, A. (2011), "Damage detection in plates based on pattern search and Genetic algorithms", Smart Struct. Syst., 7(2), 117-132. https://doi.org/10.12989/sss.2011.7.2.117
  3. Begambre, O. and Laier, J.E. (2009), "A hybrid particle swarm optimization-simplex algorithm (PSOS) for structural crack identification", Adv. Eng. Softw., 40(9), 883-891. https://doi.org/10.1016/j.advengsoft.2009.01.004
  4. Birge, B. (2003), "PSOt-a particle swarm optimization toolbox for use with Matlab", In: Proceedings of the IEEE Swarm Intelligence Symposium (SIS03).
  5. Chaudhari, T.D. and Maiti, S.K. (2000), "A study of vibration of geometrically segmented beams with and without crack", Int. J. Solids. Struct., 37(5), 761-779. https://doi.org/10.1016/S0020-7683(99)00054-2
  6. Chen, X.F., He, Z.J. and Xiang, J.W. (2005), "Experiments on crack identification in cantilever beams", Exp. Mech., 45(3), 295-300. https://doi.org/10.1007/BF02427954
  7. Chen, X.F., Zi, Y.Y., Li, B. and He, Z.J. (2006), "Identification of multiple cracks using a dynamic meshrefinement method", J. Strain Anal. Eng., 41(1), 31-39. https://doi.org/10.1243/030932405X30911
  8. Higham, D.J. and Higham, N.J. (2005), MATLAB Guide, 2nd Ed., New York, Society for Industrial and Applied Mathematics.
  9. Dong, H.B., Chen, X.F., Li, B., He, Z.J. (2009), "Rotor crack detection based on highprecision modal parameter identification method and wavelet finite element model", Mech. Syst. Signal. Pr., 23, 69-883.
  10. Fan, W. and Qiao, P.Z. (2011), "Vibration-based damage identification methods: a review and comparative study", Struct. Health Monit., 10(1), 83-111. https://doi.org/10.1177/1475921710365419
  11. Fourie, P.C. and Groenwold, A.A. (2002), "The particle swarm optimization algorithm in size and shape optimization", Struct. Multidiscip. O., 23(4), 259-267. https://doi.org/10.1007/s00158-002-0188-0
  12. Gokdag, H. (2010), "A new structural damage detection index based on analyzing vibration modes by the wavelet transform", Struct. Eng. Mech., 35(2), 257-260. https://doi.org/10.12989/sem.2010.35.2.257
  13. Gokdag, H. (2011), "Wavelet-based damage detection method for a beam-type structure carrying moving mass", Struct. Eng. Mech., 38(1), 81-97. https://doi.org/10.12989/sem.2011.38.1.081
  14. Harris, C.M. and Piersol, A.G. (2002), Harris' Shock and Vibration Handbook, 5th Ed., New York, McGraw- Hill.
  15. Kennedy, J. and Eberhart, R. (1995), "Particle swarm optimization", Proceedings of IEEE International Conference on Neural Networks, Perth, Australia.
  16. Kim, J.T., Park, J.H., Yoon, H.S. and Yi, J.H. (2007), "Vibration-based damage detection in beams using genetic algorithm", Smart Struct. Syst., 3(3), 263-280. https://doi.org/10.12989/sss.2007.3.3.263
  17. Kim, J.T., Park, J.H., Koo, K.Y. and Lee, J.J. (2008), "Acceleration-based neural networks algorithm for damage detection in structures", Smart Struct. Syst., 4(5), 583-603. https://doi.org/10.12989/sss.2008.4.5.583
  18. Koo, K.Y., Lee, J.J., Yun, C.B. and Kim, J.T. (2008), "Damage detection in beam-like structures using deflections obtained by modal flexibility matrices", Smart Struct. Syst., 4(5), 605-628. https://doi.org/10.12989/sss.2008.4.5.605
  19. Lakshmanan, N., Raghuprasad, B.K., Muthurnani, K., Gopalakrishnan, N. and Basu, D. (2008), "Identification of reinforced concrete beam-like structures subjected to distributed damage from experimental static measurements", Comput. Concrete, 5(1), 37-60. https://doi.org/10.12989/cac.2008.5.1.037
  20. Lee, J.H. (2009), "Identification of multiple cracks in a beam using natural frequencies", J. Sound. Vib., 320(3), 482-490. https://doi.org/10.1016/j.jsv.2008.10.033
  21. Lele, S.P. and Maiti, S.K. (2002), "Modeling of transverse vibration of short beams for crack detection and measurement of crack extension", J. Sound. Vib., 257(3), 559-583. https://doi.org/10.1006/jsvi.2002.5059
  22. Li, B. Chen, X.F. and He, Z.J. (2005), "Detection of crack location and size in structures using wavelet finite element methods", J. Sound. Vib., 285(4-5), 767-782. https://doi.org/10.1016/j.jsv.2004.08.040
  23. Li, B. and He, Z.J. (2011), "Frequency-based crack identification for static beam with rectangular cross-section", J. Vibroeng., 13(3), 477-486.
  24. Liang, R.Y., Choy, F.K. and Hu, J. (1991), "Frequency-based crack identification for static beam with rectangular cross-section", J. Franklin I., 328(4), 505-518. https://doi.org/10.1016/0016-0032(91)90023-V
  25. Liang, R.Y., Hu, J. and Choy, F.K. (1992a), "Theoretical study of crack-induced eigenfrequency changes on beam structures", J. Eng. Mech.- ASCE, 118(2), 384-396. https://doi.org/10.1061/(ASCE)0733-9399(1992)118:2(384)
  26. Liang, R.Y., Hu, J. and Choy, F.K. (1992b), "A quantitative NDE technique for assessing damage in beam structures", J. Eng. Mech.- ASCE, 118(7), 1468-1487. https://doi.org/10.1061/(ASCE)0733-9399(1992)118:7(1468)
  27. Hu, J. and Liang, R.Y. (1993), "An integrated approach to detection of cracks using vibration characteristics", J. Franklin I., 330(5), 841-853. https://doi.org/10.1016/0016-0032(93)90080-E
  28. Maiti S.K. and Patil, D.P. (2004), "A method of analysis for detection of multiple cracks in beams based on vibration", Adv. Vib. Eng., 3(4), 348-369.
  29. Mallat, S.G. (1999). A Wavelet Tour of Signal Processing, NewYork: Academic Press.
  30. Mendrok, K. and Uhl, T. (2010), "The application of modal filters for damage detection", Smart Struct. Syst., 6(2), 115-133. https://doi.org/10.12989/sss.2010.6.2.115
  31. Montejo, L.A. (2011), "Signal processing based damage detection in structures subjected to random excitations", Struct. Eng. Mech., 40(6).
  32. Nandwana, B.P. and Maiti, S.K. (1997), "Detection of the location and size of a crack in stepped cantilever beams based on measurements of natural frequencies", J. Sound. Vib., 203(3), 435-446. https://doi.org/10.1006/jsvi.1996.0856
  33. Ostachowicz, W.M. and Krawczuk (1991), "Analysis of the effect of cracks on the natural frequencies of a cantilever beam", J. Sound Vib., 150(2), 191-201. https://doi.org/10.1016/0022-460X(91)90615-Q
  34. Pandey, A.K., Biswas, M. and Samman, M.M. (1991), "Damage detection from changes in curvature mode shapes", J. Sound Vib., 145(2), 321-332. https://doi.org/10.1016/0022-460X(91)90595-B
  35. Papadopoulos, C.A. and Dimarogonas, A.D. (1987), "Coupled longitudinal and bending vibrations of a rotating shaft with an open crack", J. Sound. Vib., 117(1), 81-93. https://doi.org/10.1016/0022-460X(87)90437-8
  36. Patil, D.P. and Maiti, S.K. (2003), "Detection of multiple cracks using frequency measurements", Eng. Fract. Mech., 70(12), 1553-1572. https://doi.org/10.1016/S0013-7944(02)00121-2
  37. Patil, D.P. and Maiti, S.K. (2005), "Experimental verification of a method of detection of multiple cracks in beams based on frequency measurements", J. Sound Vib., 281(1-2), 439-451. https://doi.org/10.1016/j.jsv.2004.03.035
  38. Rajasekaran, S. and Varghese, S.P. (2005), "Damage detection in beams and plates using wavelet transforms", Comput. Concrete, 2(6), 481-498. https://doi.org/10.12989/cac.2005.2.6.481
  39. Shi, Y.H. and Eberhart, R. (1998), "A modified particle swarm optimizer", Proceedings of the IEEE International Conference on Evolutionary Computation, Anchorage, USA.
  40. Shih, H.W., Thambiratnam, D.P. and Chan, T.H.T. (2009) "Vibration based structural damage detection in flexural members using multi-criteria approach", J. Sound Vib., 323(3-5), 645-661. https://doi.org/10.1016/j.jsv.2009.01.019
  41. Shih, H.W., Thambiratnam, D.P. and Chan, T.H.T. (2011), "Damage detection in truss bridges using vibration based multi-criteria approach", Struct. Eng. Mech., 39(2), 187-206. https://doi.org/10.12989/sem.2011.39.2.187
  42. Sinou, J.J. (2007), "A robust identification of single crack location and size only based on pulsations of the cracked system", Struct. Eng. Mech., 25(6), 691-716. https://doi.org/10.12989/sem.2007.25.6.691
  43. Suk, M. and Gillis, E.D. (2005), "Effect of mechanical design of the suspension on dynamic loading process", Microsyst. Techol., 11(8-10), 846-850. https://doi.org/10.1007/s00542-005-0545-1
  44. Tada, H., Paris, P.C. and Irwin, G.R. (2000), The Stress Analysis of Cracks Handbook, 3rd Ed., New York, The American Society of Mechanical Engineers.
  45. Timoshenko, S., Young, D.H. and Weaver, W. (1974), Vibration Problems in Engineering, 4th Ed., London, John Wiley and Sons.
  46. Xiang, J.W., Chen, X.F., Mo, Q.Y. and He, Z.J. (2007a), "Identification of crack in a rotor system based on wavelet finite element method", Finite. Elem. Anal. Des., 43(14), 1068-1081. https://doi.org/10.1016/j.finel.2007.07.001
  47. Xiang, J.W., Chen, X.F., He, Z.J. and Zhang, Y.H. (2007b), "The construction of 1D wavelet finite elements for structural analysis", Comput. Mech., 40(2), 325-339. https://doi.org/10.1007/s00466-006-0102-5
  48. Xiang, J.W., Zhong, Y.T., Chen, X.F. and He, Z.J. (2008), "Crack detection in a shaft by combination of waveletbased elements and genetic algorithm", Int. J. Solids. Struct., 45(17), 4782-4795. https://doi.org/10.1016/j.ijsolstr.2008.04.014
  49. Xiang, J.W., Chen, X.F. and Yang, L.F. (2009), "Crack identification in short shafts using wavelet-based element and neural network", Struct. Eng. Mech., 33(5), 571-589.
  50. Xiang, J.W., Wang, Y.X., Jiang, Z.S. and Chen, X.F. (2011a), "Study on damage detection software of beam-like structures", Struct. Eng. Mech., 39(1), 77-91. https://doi.org/10.12989/sem.2011.39.1.077
  51. Xiang, J.W. and Liang, M. (2011), "Multiple damage detection method for beams based on multi-scale elements using Hermite cubic spline wavelet", CMES-Comput. Model. Eng. Sci., 73(3), 267-298.
  52. Yun, G.J., Ogorzalek, K.A., Dyke, S.J. and Song, W. (2009), "A two-stage damage detection approach based on subset selection and genetic algorithms", Smart Struct. Syst., 5(1), 1-21. https://doi.org/10.12989/sss.2009.5.1.001
  53. Zhong, Y. and Ye, Z.F. (2009), "Particle swarm optimisation algorithm for crack shape reconstruction in magnetic flux leakage nondestructive testing", Nondestruct. Test. Eva., 24(1-2), 243-250. https://doi.org/10.1080/10589750802375962

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