Browse > Article
http://dx.doi.org/10.12989/smm.2016.3.2.115

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)
Publication Information
Structural Monitoring and Maintenance / v.3, no.2, 2016 , pp. 115-127 More about this Journal
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
extended Kalman filter; structural damage identification; Tikhonov regularization; ill-posed inverse problem;
Citations & Related Records
연도 인용수 순위
  • Reference
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.   DOI
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.   DOI
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.   DOI
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.   DOI
6 Hoshiya, M. and Saito, E. (1984), "Structural identification by extended Kalman filter", J. Eng. Mech. - ASCE., 110(12), 1757-1770.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI