114 K.A. Kvåle et al. 0 50 100 SWH [cm] 0.5 0.6 0.7 0.8 Natural frequency [rad/s] 0 50 100 SWH [cm] 0.6 0.8 1 1.2 0 50 100 SWH [cm] 0.6 0.8 1 1.2 0 50 100 SWH [cm] 0 5 10 15 Damping ratio [%] 0 50 100 SWH [cm] 0 5 10 15 0 50 100 SWH [cm] 0 5 10 15 (a) (b) Fig. 14.6 Effects on modal parameters from changing significant wave height. (a) Effect on natural frequency. (b) Effect on critical damping ratio 14.4.1 Automatic OMA and the Effect of Varying Environment By using the eigenvalue solution from the predictive numerical model as reference, the natural frequencies and critical damping ratios are automatically identified for various environmental conditions. The numerical prediction model is described in [7]. The MAC numbers between the predicted and measured mode shapes were required to have a value above 0:7, for storing as an identified mode. For the automatic OMA, the BR weighting is utilized due to higher robustness than the CVA weighting. The natural frequency and critical damping coefficients of mode 1, 2 and 3 are compared to the significant wave height (SWH) in Fig. 14.6. The SWH is defined as Hs D4 , where is the standard deviation of the wave elevation process. Large variability in the modal parameters, in particular the damping ratios, are observed. The plots indicate that the damping ratio is increasing for increased SWH. Increased SWH affects the three presented natural frequencies differently. Furthermore, the scatter of the natural frequencies are reduced for increasing SWH, i.e., increased excitation levels. This tendency is explained by the fact that a larger amount of the excitation is accounted for when the SWH is larger. 14.5 Concluding Remarks The Cov-SSI method is successfully applied with different weighting schemes on the Bergsøysund Bridge, an end-supported pontoon bridge in current operation, to identify the structure’s modal parameters. Damping ratios and MAC-values are poor for certain modes. The CVA weighting scheme improves the clarity of the stabilization plot to a great extent. When the CVA weighting is used in conjunction with a high stability level, the resulting stabilization plots become quite clear. On the other hand, the CVA weighting implementation used is observed as very sensitive to the input time series and parameters, and less robust than an unweighted analysis, i.e., BR weighting. The OMA procedure is made automatic by using the eigenvalue solution from a predictive numerical model as reference, which shows that the bridge’s natural frequencies’ variability is reduced when the excitation, represented by the SWH, is increased. Both mean value and variance of the damping ratios are in general increased as a consequence of increasing SWH. Acknowledgements The research was funded by the Norwegian Public Roads Administration. The authors gratefully acknowledge this support. References 1. Watanabe, E.: Floating bridges: past and present. Struct. Eng. Int. 13(2), 128–132 (2003) 2. Brownjohn, J.M.W., Magalhaes, F., Caetano, E., Cunha, A.: Ambient vibration re-testing and operational modal analysis of the Humber Bridge. Eng. Struct. 32, 2003–2018 (2010) 3. Magalhães, F., Cunha, Á., Caetano, E.: Dynamic monitoring of a long span arch bridge. Eng. Struct. 30, 3034–3044 (2008) 4. Farrar, C., James, G.: System identification from ambient vibration measurements on a bridge. J. Sound Vib. 205, 1–18 (1997)
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