## 4 Results of the Acoustic method for Mistuning Identification
### Measurement Results  
For the individual blades, the FFT analyses of the measured responses from laser vibrometer and microphone were obtained. When measuring without additional weights on the other blades, the response also includes slightly different frequencies of the other mistuned blades, and it is practically impossible to evaluate the eigenfrequencies of the measured blade, see Figure 10.  
Figure 8: Some computed blade dominated mode shapes of the turbine impeller. Figure 9: Examples of computed mode shapes and corresponding distribution of the strain energy. The results of calculated FFT analysis of measured response signals of the first blade are shown in Figures 11 and 12. In this blade vibration measurement, weights were placed on other blade tips. When using a laser vibrometer, the frequencies of such detuned blades are significantly suppressed in the measured blade response. Similarly, by measuring with a microphone, repeated experiments have shown that with a suitable location of the microphone and due to its directional characteristic, the effect of detuned blades in the response of the measured blade is also negligible. The additional weights with optimal size are very effective in suppressing the influence of the slightly different eigenfrequencies of the unmeasured blades. They make it possible to obtain the eigenfrequencies of individual blades of a real impeller and to create a mistuned 3D model for further detailed computational analysis. In Figures 11 and 12, red lines are drawn to indicate the eigenfrequencies of the one impeller segment from the FE simulation. A comparison of the measurement results of the methods using a laser vibrometer and a measuring microphone shows a good agreement of the results. Figure 11: FFT analysis of measured response signal using the laser vibrometer and eigenfrequencies from the FE model—measured with additional weights. Figure 10: Fast Fourier transform (FFT) analysis of measured response signal using the laser vibrometer and eigenfrequencies from the FE model—measured without additional weights. It is undoubtedly that the method using the FE model to assign the respective mode shapes to the individual peaks of the FFT analysis is suitable for further use with much simpler instruments than the use of an expensive single-beam laser or even a 3D scanning laser. Using this method, the user can only concentrate on the blade-dominated eigenfrequencies and does not have to pay attention to other FFT peaks that belong entirely or primarily to the turbine disk or shaft. The size of the FFT spectral components in the measured response depends, when measured with a laser vibrometer or a microphone, among other things at the location of the force pulse on the blade. The location of the force pulse should not be close to the nodal lines of the blade mode shapes, but their position varies for each mode. Based on the results of the modal analysis of the blade, the location for the force pulse was chosen as a certain compromise. When it comes to choosing a measuring point for a laser vibrometer, the blade tip is a suitable place for all mode shapes. The F3 peak (Figure 11) can be highlighted and its presence confirmed by a more suitable location of the force pulse when measured by laser. The measuring microphone captures this F3 peak quite significantly already in the basic set-up of the experiment (Figure 12). However, the size of the individual detected frequency components in the measured response is not significant for the application of this method, whether it is measured by a laser vibrometer or a microphone. Since the measured response was recorded in a time window of 0.2 s, the frequency resolution of the FFT is 5 Hz, and thus the uncertainty of the position of each spectral component on the frequency axis is 2.5 Hz, which is quite satisfactory for determining of the impeller mistuning. From the performed measurements, similar diagrams as in Figures 11 and 12 were evaluated for all 13 blades of the turbine impeller.