272 S. Yousefianmoghadam et al. 0 20 40 60 80 100 120 140 Mode 1 Mode 2 Mode 3 Mode 4 Identification order Demolition Average Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Not identified Not identified Fig. 33.7 Comparison of identification orders between the studied cases assumption along with the computational error added to the system identification because of the conversion process can increase the identification order and required computational resources. Figure 33.7 also demonstrates the importance of the number and location of the reference channels in the modal identification of ambient vibration recordings using NExT-ERA method. When four, two, or one reference channels at the 10th floor are considered in cases 1, 2, and 4, respectively, the identification order slightly increases as the number of reference channels decreases. However, the computational time needed to run the identification algorithm increases significantly by increasing the number of reference channels as the Henkel matrix size is proportional to the number of channels. Case 5 which considers one reference channel at the fifth floor requires a higher identification order than case 4 which includes one reference channel in the 10th floor. This can be attributed to the fact that the higher floors experience more motion which increases the signal-to-noise ratio. In case 3, which considers one reference channel at the 10th floor measuring the acceleration in a direction perpendicular to the that of case 4 (X-direction), only mode 2 can be identified at DS0. This can also be observed in Table 33.3 which summarizes the identification order of the considered cases at all damage states. In all damage states, case 3 identifies modes in higher orders than those of case 4. As shown in Fig. 33.8, which illustrates the mode shapes of the structure, the reference channel selected for case 3 (X-direction in the South-West corner at the 10th floor) has a relatively small modal component in all modes except for mode 2. Therefore, if this channel is used as a reference, the relatively low signal-to-noise ratio in the free vibrations is produced from the NExT process. Case 6 which uses reference signal obtained from an accelerometer in the first floor at the direction with small modal components, combines the drawbacks of cases 3 and 5. This results in the highest identification orders among all the considered cases. 33.4.2 Modal Frequencies and Mode Shapes Table 33.3 also presents the identified natural frequencies of the building for all considered cases. The values match well between cases 1, 2, and 4 with maximum difference within 1%. In cases 3, 5, and 6 the results are more scattered; however, the difference is not considerable. One can note that the natural frequencies identified from the free vibration measurements are lower than those obtained from the recordings of ambient and forced vibrations. This difference can be attributed to the level of motion of the structure as reflected in the acceleration amplitude. As shown in Fig. 33.4, the acceleration of the structure after the jack hammer impulses has a higher amplitude than those resulted from forced and ambient vibrations. The higher amplitude causes opening of minor cracks which reduce the overall stiffness of the structure and therefore the identified natural frequencies. This can be also seen in Fig. 33.9 which presents the identified natural frequency at different damage states for the first two modes of the structure using the different data sets. In all cases, the identified frequencies indicate the same frequency change between the damage states. Figure 33.8 presents the mode shapes obtained from the average of the free vibration, ambient vibration in cases 1, 2, and 4, and the forced vibration measurements. The modal assurance criterion (MAC) [22] values are also calculated using
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