45 Modal Identification and Damage Detection of Railway Bridges Using. . . 409 0 1 2 3 4 5 6 7 6 8 10 12 Time (sec) Freq. (Hz) Identified FE 1 2 3 4 5 6 7 8 -1 0 1 Sensor Mode shape Identified FE Fig. 45.4 Identified time-varying first modal frequency and mode shapes of train-bridge system for healthy bridge, compared with first modal frequency and mode shape of FE model of healthy bridge 0 1 2 3 4 5 6 7 10 15 Time (sec) Freq. (Hz) Identified FE 1 2 3 4 5 6 7 8 -1 0 1 Sensor Mode shape Identified FE Fig. 45.5 Identified time-varying second modal frequency and mode shapes of train-bridge system for healthy bridge, compared with second modal frequency and mode shape of FE model of healthy bridge introduced in the left support conditions, and hence in the first element. Additionally, the absence of rotational measurements may also contribute to discrepancies in the damage detection results. 45.5 Conclusion In this paper, an approach is presented to obtain the time-varying modes of a train-bridge system when a heavy train passes over the bridge. The gradual variation of the system modes is utilized to identify the modal parameters within small overlapping time windows sweeping across the entire time duration of the measured response. In each time window, an auto-regressive model of the system is first identified, followed by the modes obtained using the Eigensystem Realization Algorithm. The modes identified in the different time windows collectively represent the time-varying modes of the trainbridge system as the train passes over the bridge. A damage index, based on the damage locating vectors obtained using such
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