166 S. S. Christensen et al. (a) (b) Fig. 15.3 Frequency-damping ratio plot for the first mode using the modal parameters estimated from (a) PLSCF algorithm and (b) MITD algorithm. The black +(plus) denotes the lower half of the modal parameter estimates while the gray ×(cross) represents the upper half of the modal parameter estimates as seen in the stabilisation diagrams, Figs. 15.1 and 15.2 defined so that the correlation function value at the end of the measurement time was reduced to 0.01%. By increasing or decreasing this value by a multiple of 10, no noticeable differences were observed in the modal parameter estimates. Also for the MITD algorithm it was attempted to vary the number of time lag values used in the correlation function estimates from 70 to 130, which had minimal impact on the modal parameter estimates. The random error for the damping ratio estimates is not definitively lower whether the PLSCF or the MITD algorithm are used. For instance high standard deviations are attributed to the damping ratio estimates for the fourth, seventh and the ninth mode when using the MITD algorithm. The standard deviation associated with the damping ratio estimates, for the first mode, is high when using the PLSCF algorithm. By taking a closer look at the frequency-damping ratio plot for this mode, seen in Fig. 15.3, it is observed that the frequency and damping ratio estimates follow a trend. Upon further inspection it is seen that the pole estimates for the upper half (grey cross) of the stabilization diagram have lower standard deviation than those for the lower half (black plus). For the MITD algorithm the frequency and damping ratio estimates are neatly clustered, but it is also observed that the upper half of the estimates are clustered better than the lower half. Since the random error is dependent on the measurement duration, it was attempted to double the measurement time from 300 to 600 s, which would allow twice the number of averages. This barely had any impact on the standard deviations of modal parameter estimates output by either of the two algorithms. It was mentioned in Sect. 15.2 and in Sect. 15.4, that the PLSCF algorithm is sensitive to the number of references chosen. A study [28] using the MITD algorithm showed that the modal parameter estimates were almost unaffected whether all or only a few references were used when constructing the block Hankel matrix. This is expected since the MITD algorithm employs SVD, and thus removes redundant information, making the selection of poorly located references irrelevant as long as optimal reference locations are available. It was also reported in the study that by choosing fewer references a higher variance was obtained on the modal parameter estimates. Although the PLSCF algorithm uses fewer references than the MITD algorithm, the standard deviations of the modal parameters output were not much different. The frequency-damping ratio plot for the fourth mode is seen in Fig. 15.4. As for the first mode it is seen that the upper half of the modal parameter estimates have the lowest variation when using the PLSCF algorithm. For the MITD algorithm the complete opposite is seen, compared to the behaviour observed for the first mode, that the modal parameter estimates for the lower half of the stabilization diagram have the lowest variation. For both methods, still considering the fourth mode, it is seen that a number of potential outliers are present. The outliers seem to be more profound for the modal parameter estimates output by the MITD algorithm. Potential outliers were also present for the modal parameter estimates output for the seventh and the ninth mode when using the MITD algorithm. This naturally contributes to higher standard deviations, and may also affect the mean values. By omitting the four pole estimates furthest to the right in Fig. 15.4a and those seven pole estimates furthest to the left in Fig. 15.4b, the variation of pole estimates appear to be similar for the two methods. However, the PLSCF algorithm still underestimates the damping ratio more than the MITD algorithm does. Outlier detection is outside the scope of this paper, but it seems that when using a AMA algorithm, outlier detection should be employed. When an operator interprets a stabilisation diagram, that person may also assess whether one or more
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