## 4 Conclusions  
In this paper, the current method to detect erosive cavitation in hydraulic turbines by analyzing high-frequency vibrations has been revised by studying its main existing uncertainties. This method is based on measuring high-frequency vibrations provoked by the collapse of cloud cavitation bubbles near the runner in different parts of the machine. It compares RMS values and amplitude demodulation of different high-frequency bands and different sensors. However, the transmission path from the runner to the measuring points is not known when the machine is under operating conditions, as there is no visual correlation of cavitation and the measured signals, and it is still not clear which high-frequency bands have to be used for every sensor located in every position of the machine.  
To optimize this current method, a simplified test rig based on a rotating disk submerged in water has been used. The disk has been excited with a PZT reproducing the excitation patterns caused by erosive cavitation, hence, the phenomenon of cavitation is not present in the test rig. Several sensors, including accelerometers, AE sensors, and a microphone, have been installed in the rotating and stationary parts of this test rig. This way, the excitation is completely known and, therefore, the transmission path between the excitation and the measuring point is obtained for every sensor. Different high-frequency bands have also been tested to study which are the best to detect the excitation for the different sensors. Thus, the best sensor and position to measure the given excitation is obtained.  
The results obtained show that the sensors installed in the rotating frame are the best to detect the excitation at high-frequency given to the disk. Especially, the AE sensor installed in the shaft was the best sensor to detect the excitation, since it is able to eliminate the structural response of the shaft and only obtain the information of the excitation, for all kinds of frequency bands tested. Accelerometers located in the shaft and in the disk detect both excitation and structural response, which can be  
Figure 12: Amplitude demodulation for the sensors on the stationary frame and the excitation with two modulating frequencies. Rotating case (\(f_{\mathrm{f}}\) = 4.1 Hz).  
distinguished using the amplitude demodulation analysis. For these sensors, the excitation is better transmitted at high frequency (10 to 11 kHz or 20 to 21 kHz).  
For the sensors installed in the stationary part, it has been demonstrated that the transmission of the disk vibration was better when the disk was submerged in water than in the case of the disk in air. This means that the disk vibration is mainly transmitted through the water. The accelerometer in the bearing presents similar results than the one located in the shaft, and the accelerometer in the upper cover shows relevant information also obtained by the accelerometer in the disk. The microphone and AE sensor located in the stationary frame are contaminated by the vibration of the motor and, in this case, they are not very useful to obtain the excitation in the disk.  
The comparison made in the present study permits improving the current method to detect cavitation in hydraulic turbines. In this case, the best position and sensor have been selected as an AE sensor in the shaft, which works properly in both low- and high-frequency bands.  
The authors would like to acknowledge the HYPERBOLE research project, granted by the European Commission (ERC/FP7-ENERGY-2013-1-Grant 608532) for the economic support received. We would also like to thank Voith Hydro(r) for helping to design, economically and technically, the test rig.  
[PERSON], [PERSON], [PERSON], and [PERSON] conceived and designed the experiments; [PERSON] performed the experiments; [PERSON], [PERSON], and [PERSON] analyzed the data; and [PERSON] wrote the paper.  
The authors declare no conflict of interest.