Structural Monitoring and Maintenance

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Detection of structural damage via free vibration responses by extended Kalman filter with Tikhonov regularization scheme

  • Zhang, Chun (Department of Civil Engineering and Architecture School, Nanchang University) ;
  • Huang, Jie-Zhong (Department of Civil Engineering and Architecture School, Nanchang University) ;
  • Song, Gu-Quan (Department of Civil Engineering and Architecture School, Nanchang University) ;
  • Dai, Lin (Department of Civil Engineering and Architecture School, Nanchang University) ;
  • Li, Huo-Kun (Department of Civil Engineering and Architecture School, Nanchang University)
  • Received : 2014.10.24
  • Accepted : 2015.11.30
  • Published : 2016.06.25
⟨ Previous Next ⟩

Abstract

It is a challenging problem of assessing the location and extent of structural damages with vibration measurements. In this paper, an improved Extended Kalman filter (EKF) with Tikhonov regularization is proposed to identify structural damages. The state vector of EKF consists of the initial values of modal coordinates and damage parameters of structural elements, therefore the recursive formulas of EKF are simplified and modal truncation technique can be used to reduce the dimension of the state vector. Then Tikhonov regularization is introduced into EKF to restrain the effect of the measurement noise for improving the solution of ill-posed inverse problems. Numerical simulations of a seven-story shear-beam structure and a simply-supported beam show that the proposed method has good robustness and can identify the single or multiple damages accurately with the unknown initial structural state.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China

References

  1. Corigliano, A. and Mariani, S. (2004), "Parameter identification in explicit structural dynamics: performance of the extended Kalman filter", Comput. Method. Appl M., 193(36-38), 3807-3835. https://doi.org/10.1016/j.cma.2004.02.003
  2. ELSheikh, A.H., Pain, C.C., Fang, F., Gomes, J.M.A. and Navon, I.M. (2013), "Parameter estimation of subsurface flow models using iterative regularized ensemble Kalman filter", Stoch Environ. Res Risk Assess., 27(4), 877-897. https://doi.org/10.1007/s00477-012-0613-x
  3. Friswell, M. and Mottershead, J.E. (1995), Finite Element Model Updating in Structural Dynamics, Kluwer Academic Publishers. The Netherlands.
  4. Gao, F. and Lu, Y. (2006), "A Kalman-filter based time-domain analysis for structural damage diagnosis with noisy signals", J. Sound. Vib., 297(3-5), 916-930. https://doi.org/10.1016/j.jsv.2006.05.007
  5. Hansen, P.C. and O'Leary, D.P. (1993), "The use of the L-curve in the regularization of discrete ill-posed problems", SIAM J. Sci Comput., 14(6), 1487-1503. https://doi.org/10.1137/0914086
  6. Hoshiya, M. and Saito, E. (1984), "Structural identification by extended Kalman filter", J. Eng. Mech. - ASCE., 110(12), 1757-1770. https://doi.org/10.1061/(ASCE)0733-9399(1984)110:12(1757)
  7. Jazwinski, A.H. (1970), Stochastic Process and Filtering Theory, Academic Press, New York.
  8. Lei, Y., Jiang, Y.Q. and Xu, Z.Q. (2012), "Structural damage detection with limited input and output measurement signals", Mech. Syst. Signal Pr., 28, 229-243. https://doi.org/10.1016/j.ymssp.2011.07.026
  9. Liu, X., Escamilla-Ambrosio, P. and Lieven, N. (2009), "Extended Kalman filtering for the detection of damage in linear mechanical structures", J. Sound. Vib., 325(4-5), 1023-1046. https://doi.org/10.1016/j.jsv.2009.04.005
  10. Loh, C.H., Lin, C.Y. and Huang, C.C. (2000), "Time domain identification of frames under earthquake loadings", J. Eng. Mech. - ASCE, 126(7), 693-703. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:7(693)
  11. Masri, S.F. and Caughey, T.K. (1979), "A nonparametric identification technique or nonlinear dynamic problems", Int. J. Appl. Mech., 46(2), 433-447. https://doi.org/10.1115/1.3424568
  12. Straser, E.G. and Kiremidjian, A.S. (1996), "Monitoring and evaluating of civil structures using measured vibration", Proceedings of the SPIE's Conference on Smart Structures and Smart Materials, 2719, 112-121, San Diego, CA, USA.
  13. Weber, B., Paultre, P. and Proulx, J. (2009), "Consistent regularization of nonlinear model updating for damage identification", Mech. Syst. Signal Pr., 23(6), 1965-1985. https://doi.org/10.1016/j.ymssp.2008.04.011
  14. Xing, S.T., Halling, M.W. and Pan, S.W. (2014), "Application of substructural damage identification using adaptive Kalman filter", J. Civil Struct. Health Monit., 4(1), 27-42. https://doi.org/10.1007/s13349-013-0054-3
  15. Yang, J.N., Pan, S. and Huang, H. (2007), "An adaptive extended Kalman filter for structural damage identification II: unknown inputs", Struct Control. Health, 14(3), 497-521. https://doi.org/10.1002/stc.171
  16. Yang, J.N., Lin, S., Huang, H. and Li, Z. (2006), "An adaptive extended Kalman filter for structural damage identification", Struct Control. Health., 13(4), 849-867. https://doi.org/10.1002/stc.84
  17. Zheng, Y., Wang, M., He, L. and Zhou, X. (2004), "Time-domain identification of dynamic properties of layered soil by using extended Kalman filter and recorded seismic data", Earthq. Eng. Eng. Vib., 3(2), 237-247. https://doi.org/10.1007/BF02858238
  18. Zhou, L., Wu, S. and Yang, J.N. (2008), "Experimental Study of an Adaptive Extended Kalman Filter for Structural Damage Identification", J. Infrastruct. Syst., 14, 42-51. https://doi.org/10.1061/(ASCE)1076-0342(2008)14:1(42)

Cited by

  1. Condition assessment of bridge pier using constrained minimum variance unbiased estimator vol.7, pp.4, 2016, https://doi.org/10.12989/smm.2020.7.4.319