A new statistical moment-based structural damage detection method

  • Zhang, J. (Department of Civil and Structural Engineering, The Hong Kong Polytechnic University) ;
  • Xu, Y.L. (Department of Civil and Structural Engineering, The Hong Kong Polytechnic University) ;
  • Xia, Y. (Department of Civil and Structural Engineering, The Hong Kong Polytechnic University) ;
  • Li, J. (Department of Building Engineering, Tongji University)
  • Received : 2007.09.27
  • Accepted : 2008.08.01
  • Published : 2008.11.10


This paper presents a novel structural damage detection method with a new damage index based on the statistical moments of dynamic responses of a structure under a random excitation. After a brief introduction to statistical moment theory, the principle of the new method is put forward in terms of a single-degree-of-freedom (SDOF) system. The sensitivity of statistical moment to structural damage is discussed for various types of structural responses and different orders of statistical moment. The formulae for statistical moment-based damage detection are derived. The effect of measurement noise on damage detection is ascertained. The new damage index and the proposed statistical moment-based damage detection method are then extended to multi-degree-of-freedom (MDOF) systems with resort to the leastsquares method. As numerical studies, the proposed method is applied to both single and multi-story shear buildings. Numerical results show that the fourth-order statistical moment of story drifts is a more sensitive indicator to structural stiffness reduction than the natural frequencies, the second order moment of story drift, and the fourth-order moments of velocity and acceleration responses of the shear building. The fourth-order statistical moment of story drifts can be used to accurately identify both location and severity of structural stiffness reduction of the shear building. Furthermore, a significant advantage of the proposed damage detection method lies in that it is insensitive to measurement noise.


  1. Alvandi, A. and Cremona, C. (2006), "Assessment of vibration-based damage identification techniques", J. Sound Vib., 292, 179-202
  2. Chen, B. and Xu, Y.L. (2007), "A new damage index for detecting sudden change of structural stiffness", Struct. Eng. Mech., 26(30), 315-341
  3. Cho, H.N., Cho, Y.M., Lee, S.C. and Hur, C.K. (2004), "Damage assessment of cable stayed bridge using probabilistic neural network", Struct. Eng. Mech., 17(3-4), 483-492
  4. Doebling, S.W., Farrar, C.R. and Prime, M.B. (1998), "A summary review of vibration-based damage identification methods", Shock Vib. Dig., 30, 91-105
  5. Farrar, C.R. and Jauregui, D.A. (1998), "Comparative study of damage identification algorithms applied to a bridge: I. experiment", Smart Mater. Struct., 7, 704-719
  6. DAMAS 97, Dulieu-Smith, J.M., Staszewski, W.J. and Worden, K. (editors), Sheffield Academic Press, Sheffield, 351-362
  7. Kim, B.H., Joo, H.J. and Park, T. (2006), "Nondestructive damage evaluation of a curved thin beam", Struct. Eng. Mech., 24(6), 665-682
  8. Link, M. (2001), "Updating of analytical models - review of numerical procedures and application aspects", Structural Dynamics @2000: Current Status and Future Directions, Ewins, D.J., Inman, D.J. (editors), Research Studies Press, Philadelphia,193-223
  9. Martin, H.R. (1989), "Statistical moment analysis as a means of surface damage detection", Proceedings of the 7th International Modal Analysis Conference, Las Vegas, Nevada, 1016-1021
  10. Meirovitch, L. (1975), Elements of Vibration Analysis, McGraw-Hill, New York
  11. Pandey, A.K., Biswas, M. and Samman, M.M. (1991), "Damage detection from changes in curvature mode shapes", J. Sound Vib., 145, 321-332
  12. Salawu, O.S. (1997), "Detection of structural damage through changes in frequency: A review", Eng. Struct., 19, 718-723
  13. Shinozuka, M. and Jan, C.M. (1972), "Digital simulation of random processes and its applications", J. Sound Vib., 25(1), 111-128
  14. Xu, Y.L., Zhu, H.P. and Chen, J. (2004), "Damage detection of mono-coupled multistory buildings: Numerical and experimental investigations", Struct. Eng. Mech., 18(6), 709-729
  15. Zhao, J. and DeWolf, J.T. (2007), "Modeling and damage detection for cracked I-shaped steel beams", Struct. Eng. Mech., 25(2), 131-146
  16. Zhao, X., Xu, Y.L., Chen, J. and Li, J. (2005), "Hybrid identification method for multi-story building with unknown ground motion: Experimental investigation", Eng. Struct., 27, 1234-1247

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