1 Automated Operational Modal Analysis on a Full-Scale Wind Turbine Tower 5 Fig . 1. 4 Histogram of the frequencies inside the area of interest. Time series start point is 40 hours into the data and the time series length is 30 minute s Fig . 1. 5 Model order of each extracted natural frequency of the two closely spaced modes. Here, the time instance of 40 hours into the signal is still used is larger than 50 in the case of this algorithm, the current time series is skipped as two modes cannot be discerned inside the frequency resolution. If two suspected physical modes can be discerned, the two bins of natural frequencies are isolated. Optimally, there will now be two bins from the histogram, each with 100 natural frequencies of similar values because of the maximum chosen model order of 100, but in practice because of noise and frequency resolution there will be fewer poles left. The optimal two poles and two modal vectors have to be chosen, a set from the bin with the lowest frequency and a set from the bin with the highest frequency. Each model order corresponding to a pole is plotted against the natural frequency to visualize the two closely spaced modes in frequency. This is shown in Fig. 1.5. To find the optimal pole and modal vector, an AMAC calculation is performed. In Fig. 1.5, each model order indicates a different pole and modal vector, and ideally all the blue points are the same mode shape and all the orange points are the same mode shape. Figure 1.6a shows each modal vector of the blue points in Fig. 1.5 compared to each other in the AMAC. This results in a contour plot where the color bar indicates the MAC value of each modal vector compared with the other modal vectors. The diagonal is unity since this is when a modal vector is compared to itself. To find the optimal modal vector—which determines the choice of the set of extracted poles and modal vectors—an acceptance threshold for the MAC value must be set where the number of model order’s corresponding modal vectors in Fig. 1.6a that fulfill the threshold is summed for each model order. The acceptance threshold is set at .MACthreshold ≥0.9. (1.3 ) The model order with the most modal vectors that comply with the acceptance threshold is the most consistent model order and determines the set which is picked by the algorithm. The consistency plot of the model orders in Fig. 1.6a is shown in Fig. 1.6b. For this particular example, the most consistent model order is found to be 26, which is consistent with 24 other modes at the threshold set in Eq. (1.3).
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