33 Comparative Study on Modal Identification of a 10 Story RC Structure Using Free, Ambient and Forced Vibration Data 271 Table 33.1 Summary of free vibration measurements properties Damage state Number of recordings Signal duration range (s) Impulse direction Max. acceleration range in all 40 channels (mg) DS0 12 6–25 Y 1.5–15 DS1 12 8–14 Y 1.2–14.5 DS2 17 6–10 X 0.4–4.66 DS3 19 5–12 X 0.5–28 Table 33.2 Cases studied for NexT-ERA method Case # # of reference channels Location of reference channels Reference channel measurement direction(s) 1 4 10th floor: SW and NE corners XandY 2 2 10th floor: SW corner XandY 3 1 10th floor: SW corner X 4 1 10th floor: SW corner Y 5 1 5th floor: SW corner Y 6 1 1st floor: SW corner X 0 2 4 6 8 10 12 14 16 18 0 10 20 30 40 50 60 Identification order Mode 1 Mode 2 Mode 3 Mode 4 Maximum acceleration recorded among all channels (milli g) Fig. 33.6 Identification order dependency on maximum acceleration of the free vibration measurements in Y direction at DS0 are estimated, they are used to form a block Hankel matrix of (40 200) ((50 72) (# of reference channels)). Table 33.2 presents the cases considered in this study. For the forced vibration recordings the power spectral densities (PSD) of the acceleration measurements are estimated using the Welch method. The signals are averaged over Hamming windows of 8000 points and 50% window overlap. The PSDs are used to obtain the transfer functions. The acceleration measurements in X and Y directions at the SW corner of the 2nd floor are considered as the input excitation due to the proximity to the shaker. 33.4.1 Identification Orders and Stabilization Diagrams According to a previous study on system identification of the same structure [19], the first mode of the structure is identified at an order of 130 at DS0. Therefore, the system identification process for both ambient vibration and free vibration measurements is performed up to the order of 150. Figure 33.6 illustrates the identification order for the first four modes of the structure plotted against the maximum acceleration recorded among all of the 40 channels during the free vibration response at DS0 using the ERA method. Typically, identification orders as low as 10 are sufficient to identify the first two modes, and orders between 20 and 30 are sufficient for modes 3 and 4. It can be also observed in Fig. 33.6 that in the case of free vibrations no relation can be established between the identification order and the amplitude of the impulse excitations. The identification orders from the ambient vibration are compared to the average order needed in the analysis of the free vibration recordings at DS0 in Fig. 33.7. It can be observed that the identification orders are much higher using the ambient vibration data for modes 1–3 in all cases of reference channels considered for the first three modes, and in a few cases the modes are not identified at all. The difficulty in identifying the modes in lower system orders may be caused by processing of the signal used to convert the ambient vibration to free vibration as discussed in a previous section. This process is based on the assumption that the signal is broadband excitation which is not accurate. The unavoidable error in this simplifying
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