Smart Structures and Systems

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Mode shape expansion with consideration of analytical modelling errors and modal measurement uncertainty

  • Chen, Hua-Peng (School of Engineering, University of Greenwich) ;
  • Tee, Kong Fah (School of Engineering, University of Greenwich) ;
  • Ni, Yi-Qing (Department of Civil and Structural Engineering, The Hong Kong Polytechnic University)
  • Received : 2012.03.19
  • Accepted : 2012.06.27
  • Published : 2012.10.25
⟨ Previous Next ⟩

Abstract

Mode shape expansion is useful in structural dynamic studies such as vibration based structural health monitoring; however most existing expansion methods can not consider the modelling errors in the finite element model and the measurement uncertainty in the modal properties identified from vibration data. This paper presents a reliable approach for expanding mode shapes with consideration of both the errors in analytical model and noise in measured modal data. The proposed approach takes the perturbed force as an unknown vector that contains the discrepancies in structural parameters between the analytical model and tested structure. A regularisation algorithm based on the Tikhonov solution incorporating the L-curve criterion is adopted to reduce the influence of measurement uncertainties and to produce smooth and optimised expansion estimates in the least squares sense. The Canton Tower benchmark problem established by the Hong Kong Polytechnic University is then utilised to demonstrate the applicability of the proposed expansion approach to the actual structure. The results from the benchmark problem studies show that the proposed approach can provide reliable predictions of mode shape expansion using only limited information on the operational modal data identified from the recorded ambient vibration measurements.

Keywords

References

  1. Avitabile, P. (1999), "A review of modal model correlation techniques", Proceedings of the NAFEM World Congress 99, Rhode Island, USA.
  2. Chen, H.P. (2008), "Application of regularisation method to damage detection in plane frame structures from incomplete noisy modal data", Eng. Struct., 30(11), 3219-3227. https://doi.org/10.1016/j.engstruct.2008.04.038
  3. Chen, H.P. (2010), "Mode shape expansion using perturbed force approach", J. Sound Vib., 329(8), 1177-1190. https://doi.org/10.1016/j.jsv.2009.10.027
  4. Chen, H.P. and Bicanic, N. (2010), "Identification of structural damage in buildings using iterative procedure and regularisation method", Eng. Comput., 27(8), 930-950. https://doi.org/10.1108/02644401011082962
  5. Chen, W.H., Lu, Z.R., Lin, W., Chen, S.H., Ni, Y.Q., Xia, Y. and Liao, W.Y. (2011), "Theoretical and experimental modal analysis of the Guangzhou New TV Tower", Eng. Struct., 33(12), 3628-3646. https://doi.org/10.1016/j.engstruct.2011.07.028
  6. De Roeck, G. and Peeters, B. (2011), MACEC3.1 - Modal analysis on civil engineering constructions, Department of Civil Engineering, Catholic University of Leuven, Belgium.
  7. Guyan, R. (1965), "Reduction of stiffness and mass matrices", AIAA J., 3(2), 380-387. https://doi.org/10.2514/3.2874
  8. Hansen, P.C. and O'Leary, D.P. (1993), "The use of the L-curve in the regularisation of discrete ill-posed problems", SIAM J. Sci. Comput., 14(6), 1487-1503. https://doi.org/10.1137/0914086
  9. Hua, X.G., Ni, Y.Q. and Ko, J.M. (2009), "Adaptive regularization parameter optimization in output-errorbased finite element model updating", Mech. Syst. Signal Pr., 23(3), 563-579. https://doi.org/10.1016/j.ymssp.2008.05.002
  10. Kammer, D.C. (1987), "Test-analysis model development using an exact modal reduction", Int. J. Anal. Exper. Modal Anal., 2(4), 174-179.
  11. Kammer, D.C. (1991), "A hybrid approach to test-analysis-model development for large space structures", J. Vib. Acoust., 113(3), 325-332. https://doi.org/10.1115/1.2930188
  12. Kidder, R.L. (1973), "Reduction of structural frequency equations", AIAA J., 11(6), 892. https://doi.org/10.2514/3.6852
  13. Levine-West, M., Milman, M. and Kissil, A. (1996), "Mode shape expansion techniques for prediction: Experimental evaluation", AIAA J., 34(4), 821-829.
  14. Mottershead, J.E. and Friswell, M.I. (1993), "Model updating in structural dynamics: a survey", J. Sound Vib., 167(3), 347-375. https://doi.org/10.1006/jsvi.1993.1340
  15. Ni, Y.Q., Wong, K.Y. and Xia, Y. (2011), "Health checks through landmark bridges to sky-high structures", Adv. Struct. Eng., 14(1), 103-119. https://doi.org/10.1260/1369-4332.14.1.103
  16. Ni, Y.Q., Xia, Y., Liao, W.Y., and Ko, J.M. (2009), "Technology innovation in developing the structural health monitoring system for Guangzhou New TV Tower", Struct. Control Health Monit., 16(1), 73-98. https://doi.org/10.1002/stc.303
  17. Ni, Y.Q., Xia, Y., Lin, W., Chen, W.H., and Ko, J.M. (2012), "SHM benchmark for high-rise structures: a reduced-order finite element model and field measurement data", Smart Struct. Syst., in this issue.
  18. O'Callahan, J.C. (1989), "A procedure for an improved reduced system (IRS)", Proceedings of the 7th International Modal Analysis Conference, Las Vegas, Nevada, USA.
  19. O'Callahan, J.C., Avitabile, P. and Riemer, R. (1989), "System equivalent reduction expansion process", Proceedings of the 7th International Modal Analysis Conference, Las Vegas, Nevada, USA.
  20. Peeters, B. and De Roeck, G. (1999), "Reference-based stochastic subspace identification for output-only modal analysis", Mech. Syst.Signal Pr., 13(6), 855-878. https://doi.org/10.1006/mssp.1999.1249
  21. Tee, K.F., Koh, C.G. and Quek, S.T. (2009), "Numerical and experimental studies of a substructural identification strategy", Struct. Health Monit., 8(5), 397-410. https://doi.org/10.1177/1475921709102089
  22. Tikhonov, A.N. and Arsenin, V.Y. (1977), Solutions of ill-posed problems, Wiley, New York.

Cited by

  1. Active mass driver control system for suppressing wind-induced vibration of the Canton Tower vol.13, pp.2, 2014, https://doi.org/10.12989/sss.2014.13.2.281
  2. Operational modal analysis of Canton Tower by a fast frequency domain Bayesian method vol.17, pp.2, 2016, https://doi.org/10.12989/sss.2016.17.2.209
  3. Structural health monitoring of Shanghai Tower during different stages using a Bayesian approach vol.23, pp.11, 2016, https://doi.org/10.1002/stc.1840
  4. Efficiency of grey wolf optimization algorithm for damage detection of skeletal structures via expanded mode shapes vol.23, pp.13, 2012, https://doi.org/10.1177/1369433220921000
  5. Stiffness Modification-Based Bayesian Finite Element Model Updating to Solve Coupling Effect of Structural Parameters: Formulations vol.11, pp.22, 2012, https://doi.org/10.3390/app112210615