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A two-stage and two-step algorithm for the identification of structural damage and unknown excitations: numerical and experimental studies

  • Lei, Ying (School of Architecture and Civil Engineering, Xiamen University) ;
  • Chen, Feng (School of Architecture and Civil Engineering, Xiamen University) ;
  • Zhou, Huan (School of Architecture and Civil Engineering, Xiamen University)
  • Received : 2013.11.20
  • Accepted : 2014.04.05
  • Published : 2015.01.25

Abstract

Extended Kalman Filter (EKF) has been widely used for structural identification and damage detection. However, conventional EKF approaches require that external excitations are measured. Also, in the conventional EKF, unknown structural parameters are included as an augmented vector in forming the extended state vector. Hence the sizes of extended state vector and state equation are quite large, which suffers from not only large computational effort but also convergence problem for the identification of a large number of unknown parameters. Moreover, such approaches are not suitable for intelligent structural damage detection due to the limited computational power and storage capacities of smart sensors. In this paper, a two-stage and two-step algorithm is proposed for the identification of structural damage as well as unknown external excitations. In stage-one, structural state vector and unknown structural parameters are recursively estimated in a two-step Kalman estimator approach. Then, the unknown external excitations are estimated sequentially by least-squares estimation in stage-two. Therefore, the number of unknown variables to be estimated in each step is reduced and the identification of structural system and unknown excitation are conducted sequentially, which simplify the identification problem and reduces computational efforts significantly. Both numerical simulation examples and lab experimental tests are used to validate the proposed algorithm for the identification of structural damage as well as unknown excitations for structural health monitoring.

Acknowledgement

Supported by : National Natural Science Foundation of China (NSFC)

References

  1. Azam, S.E. and Mariani S. (2007), "Unscented Kalman filtering for nonlinear structural dynamics", Nonlinear Dynam., 49(1-2), 131-150; https://doi.org/10.1007/s11071-006-9118-9
  2. Bernal, D. and Beck, J. (2004), "Special section: phase I of the IASC-ASCE structural health monitoring benchmark", J. Eng. Mech. - ASCE, 130(1), 1-127. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:1(1)
  3. Chen, H.P. (2008), "Application of regularization methods to damage detection in large scale plane frame structures using incomplete noisy modal data", Eng. Struct., 30(1), 3219-3227. https://doi.org/10.1016/j.engstruct.2008.04.038
  4. 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
  5. Feng, M.Q. (2009), "Application of structural health monitoring in civil infrastructure", Smart Struct. Syst., 5(4), 469-482. https://doi.org/10.12989/sss.2009.5.4.469
  6. Hoshiya, M. and Sutoh, A. (1993), "Kalman filter-finite element system method in identification", J. Eng. Mech. - ASCE, 119(2), 197-210. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:2(197)
  7. Hsu, T.Y., Huang, S.K., Lu, K.C. Loh, C.H., Wang, Y. and Lynch, J.P. (2011), "On-line structural damage localization and quantification using wireless sensors", Smart Mater. Struct., 20(10), 105025. https://doi.org/10.1088/0964-1726/20/10/105025
  8. Huang, H.W., Yang, J.N. and Zhou L. (2010), "Adaptive quadratic sum-squares error with unknown inputs for damage identification of structures", Struct. Control Health Monit., 17(4), 404-426. https://doi.org/10.1002/stc.318
  9. Johnson, E.A., Lam, H.F., Katafygiotis, L.S. and Beck, J.L. (2004), "The phase I IASC-ASCE structural health monitoring benchmark problem using simulated data", J. Eng. Mech. - ASCE, 130(1), 3-15. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:1(3)
  10. Julier, S., Uhlmann, J. and Durrant-Whyte, H.F. (2010), "A new method for the nonlinear transformation of means and covariances in filters and estimators", IEEE T. Automat. Contr., 45(3), 477-482;
  11. Karayannis, C.G., Favvata, M.J. and Kakaletsis, D.J. (2011), "Seismic behaviour of infilled and pilotis RC frame structures with beam-column joint degradation effect", Eng. Struct., 10, 821-2831.
  12. Katkhudat, H.N., Dwairi, H.M. and Shatarat, N. (2010), "System identification of steel framed structures with semi-rigid connections", Struct. Eng. Mech., 34(3), 351-366. https://doi.org/10.12989/sem.2010.34.3.351
  13. Kim, J.H., Kim, K.Y. and Sohn, H. (2013), "Data-driven physical parameter estimation for lumped mass structures from a single point actuation test", J. Sound Vib., 332(18), 4390-4402 https://doi.org/10.1016/j.jsv.2013.03.006
  14. Kim, J.H. and Lynch, J.P. (2012), "Subspace system identification of support-excited structures-part I: theory and black-box system identification", Earthq. Eng. Struct. D., 41(15), 2235-2251. https://doi.org/10.1002/eqe.2184
  15. Koh, C.G., See, L.M. and Balendra, T. (1991), "Estimation of structural parameters in time domain: a substructure approach", Earthq. Eng. Struct. D., 20(8), 787-801. https://doi.org/10.1002/eqe.4290200806
  16. Lee, K.J. and Yun, C.B. (2008), Parameter identification for nonlinear behavior of RC bridge piers using sequential modified extended Kalman filter. Smart Structures and Systems, 4(3), 319-342. https://doi.org/10.12989/sss.2008.4.3.319
  17. 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
  18. Lei, Y., Lai, Z.L., Liu, L.J., Tan, Y.L. and Wang X. J. (2011), "A new type wireless sensor network for distributed structural damage detection", Proceedings of the 1st Middle East Conference on Smart Monitoring, Assessment and Rehabilitation of Civil Structures, Feb. 8-10, Dubai UAE.
  19. Lei, Y., Liu, C., Jiang. Y.Q. and Mao, Y.K. (2013), "Substructure based structural damage detection with limited input and output measurements", Smart Struct. Syst., 12(6), 619-640. https://doi.org/10.12989/sss.2013.12.6.619
  20. Li, G.Q., Shi, W.L. and Xiao Y. (2007), "State of the art of research on semi-rigid composite beam-to-column joints", Progress Steel Build. Struct., 9(4), 11-22.
  21. Li, J.C., Dackermann, U., Xu, Y.L. (2011), "Damage identification in civil engineering structures utilizing PCA-compressed residual frequency response functions and neural network ensembles", Struct. Control Health Monit., 18(2), 207-226. https://doi.org/10.1002/stc.369
  22. Liu, X., Escamilla-Ambrosio, P.J. and Lieven, N.A. (2009), "Extended Kalman filtering for the detection of damage in linear mechanical structures", J. Sound Vib., 325, 1023-1046. https://doi.org/10.1016/j.jsv.2009.04.005
  23. Lu Z.R. and Law, S.S. (2007), "Identification of system parameters and input force from output only", Mech. Syst. Signal Pr., 21(5), 2099-2111. https://doi.org/10.1016/j.ymssp.2006.11.004
  24. Lynch, J.P. (2007), "An overview of wireless structural health monitoring for civil structures", Philos. T. R. Soc. A, 365, 345-372. https://doi.org/10.1098/rsta.2006.1932
  25. Mariani, S. and Ghisi, A. (2007), "Unscented Kalman filtering for nonlinear structural dynamics", Nonlinear Dynam., 49(1-2), 131-150; https://doi.org/10.1007/s11071-006-9118-9
  26. Ou, J.P. and Li, H. (2010), "Structural health monitoring in mainland China: Review and future trends", Struct. Health Monit., 9(3), 219-231. https://doi.org/10.1177/1475921710365269
  27. Park, J.W., Sim, S.H. and Jung, H.J. (2013), "Wireless sensor network for decentralized damage detection of building structures", Smart Struct. Syst., 12(3-4), 399-414. https://doi.org/10.12989/sss.2013.12.3_4.399
  28. Ren, W.X., Lin, Y.Q. and Fang, S.E. (2011), "Structural damage detection based on stochastic subspace identification and statistical pattern recognition: I. Theory", Smart Mater. Struct., 20(11),115009. https://doi.org/10.1088/0964-1726/20/11/115009
  29. Sim, S.H., Spencer, B.F., Jr. and Zhang, M. (2010), "Automated decentralized modal analysis using smart sensors", Struct. Control Health Monit., 17(8), 872-894. https://doi.org/10.1002/stc.348
  30. Sirca, Jr. G.F. and Adeli, H. (2012), "System identification in structural engineering", Scientia Iranica A., 19 (6), 1355-1364 https://doi.org/10.1016/j.scient.2012.09.002
  31. Sohn, H., Farrar, C.R., Hemez, F.M., Shunk, D.D., Stinemates, D.W. and Nadler, B.R. (2003), A review of structural health monitoring literature: 1996-2001, Los Alamos National Laboratory Report LA-13976-MS.
  32. Spencer, Jr. B.F., Ruiz-Sandova, M.E. and Kurata, N. (2004), "Smart sensing technology: opportunities and challenges", Struct. Control Health Monit., 11(4), 349-368. https://doi.org/10.1002/stc.48
  33. Wan E.A. and Van der Merwe, R. (2001), The unscented Kalman filter, Kalman Filtering and Neural Networks, (Ed. Haykin, S.), Wiley.
  34. Weng, J.H., Loh, C.H. and Yang, J.N. (2009), "Experimental study of damage detection by data-driven subspace identification and finite-element model updating", J. Struct. Eng. - ASCE, 135(12), 1533-1544. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000079
  35. Wu, Z.S., Xu, B. and Yokoyama, K. (2002), "Decentralized parametric damage detection based on neural network", Comput. -Aided Civil Infrastruct. Eng., 17(3), 175-184. https://doi.org/10.1111/1467-8667.00265
  36. Wu, Z.S., Xu, B. and Harada, T. (2003), "Review on structural health monitoring for infrastructures", J. Appl. Mech. - JSCE , 6, 1043-1054. https://doi.org/10.2208/journalam.6.1043
  37. Xia, Y. (2011), System Identification and Damage Detection of Nonlinear Structures, PhD Dissertation, Department of Civil and Environmental Engineering, University of California, Irvine, CA.
  38. Xu, B., He, J., Rovekamp, R. and Dyke, S.J. (2012), "Structural parameters and dynamic loading identification form incomplete measurements: approach and validation", Mech. Syst. Signal Pr., 28, 244-257. https://doi.org/10.1016/j.ymssp.2011.07.008
  39. Xu, B., Song, G.B. and Masri, S.F. (2012), "Damage detection for a frame structure model using vibration displacement measurement", Struct. Health Monit., 11(3), 281-292. https://doi.org/10.1177/1475921711430437
  40. Yang, J.N., Huang, H.W. and LIN S.L. (2006), "Sequential non-linear least-square estimation for damage identification of structures", Int. J. Nonlinear Mech., 41, 124-140. https://doi.org/10.1016/j.ijnonlinmec.2005.06.006
  41. Yang, J.N. and Huang, H.W. (2009), "Adaptive quadratic sum-squares error for structural damage identification", J. Eng. Mech. - ASCE, 135(2), 67-77. https://doi.org/10.1061/(ASCE)0733-9399(2009)135:2(67)
  42. Yang, J.N., Pan, S.W. and Huang, H.W. (2007), "An adaptive extended Kalman filter for structural damage identification II: unknown inputs", Struct. Control Health Monit., 14(3), 497-521. https://doi.org/10.1002/stc.171
  43. Yi, T.H., Li, H.N. and Gu M. (2011), "Optimal sensor placement for structural health monitoring based on multiple optimization strategies", Struct. Des. Tall Spec., 20(7), 881-900. https://doi.org/10.1002/tal.712
  44. Yi, T.H., Li, H.N. and Sun, H.M. (2013), "Multi-stage structural damage diagnosis method based on "energy-damage" theory", Smart Struct. Syst., 12(3-4), 345-361. https://doi.org/10.12989/sss.2013.12.3_4.345
  45. Yuen, K.V., Liang, P.F. and Kuok, S.C. (2013), "Online estimation of noise parameters for Kalman filter", Struct. Eng. Mech., 47(3), 361-381. https://doi.org/10.12989/sem.2013.47.3.361
  46. Yun, C.B. and Min, J.Y. (2011), "Smart sensing, monitoring, and damage detection for civil infrastructures", J. Civil Eng. - KSCE, 15(1), 1-14.
  47. Yun, C.B., Lee, J.J. and Koo, K.Y. (2011), "Smart structure technologies for civil infrastructures in Korea: recent research and applications", Struct. Infrastruct. E., 7(9), 673-688. https://doi.org/10.1080/15732470902720109
  48. Yun, G.J., Lee, S.G., Carletta, J. and Nagayama, T. (2011), "Decentralized damage identification using wavelet signal analysis embedded on wireless smart sensors", Eng. Struct., 33(7), 2162-2172. https://doi.org/10.1016/j.engstruct.2011.03.007
  49. Zhang, H.D. and Han, Q.H. (2013), "Numerical investigation of seismic performance of large span single-layer latticed domes with semi-rigid joints", Struct. Eng. Mech., 48(1), 57-75. https://doi.org/10.12989/sem.2013.48.1.057
  50. Zhang, Q., Jankowski, L. and Duan Z. (2012), "Simultaneous identification of excitation time histories and parameterized structural damages", Mech. Syst. Signal Pr., 33,56-68. https://doi.org/10.1016/j.ymssp.2012.06.018

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