# Accuracy Characterization of a MEMS Accelerometer for Vibration Monitoring in a Rotating Framework
## 3 Results and Discussion  
In this section, the results obtained with both the vibration monitoring systems are presented with the corresponding uncertainties expressed as standard deviations. Figure 3 illustrates the raw data of two signals acquired with the reference and MEMS accelerometers in two different test configurations. It can be seen that the data acquisitions were simultaneously performed. In particular, the first 10 oscillation periods are plotted for both cases: Figure 3a,b show, respectively, the acceleration measured in the case of the first resonant mode at a rotor angular speed of 180 rpm and the acceleration obtained by exciting the blade at the second eigenmode for a rotor speed of 300 rpm. It can be seen that the signal acquired by the wireless system appears much smoother than the reference one. This is mainly due to the slip ring used to bring back the reference accelerometer signal that might introduce noise, and the 2.4 kHz bandwidth of the MEMS accelerometer. Figures 4 and 5 show the spectra calculated from the reference and MEMS accelerometers at two rotor angular speeds, namely 180 and 300 rpm, and by exciting the first four blade-bending eigenmodes via PZT actuators. The spectral components of the baseline noise were assessed in tests performed with de-activated PZT actuators at each considered rotor speed and removed from the depicted spectra. The FFTs were plotted within a 0-1500 Hz frequency range in order to appreciate the components of all the four resonant modes with the same frequency scale. From a closer inspection of the Figures 4 and 5, it can be seen that the frequency component corresponding to the highest acceleration amplitude always corresponds to the excited eigenmode, considering a standard uncertainty of \(\pm\)0.14 Hz due to the frequency resolution given by the time window for acquisition (4 s). The peak values, expressed in m/s\({}^{2}\), were then compared to evaluate the accuracy of the wireless vibration monitoring system. Table 3 summarizes the results obtained for all the considered rotor angular velocities and resonant modes. The proposed wireless system always showed an overall maximum error less than 5%, while the maximum difference between the average acceleration values measured by means of both systems was 0.39 m/s\({}^{2}\) in the case of the third resonant mode at an angular speed of 240 rpm. Figure 6 reports the results expressed in terms of mean and standard deviation, obtained by comparing the FFT peaks derived from each accelerometer and evaluating the MAPE. It appears that the MAPE grows with the rotor angular speed; this behaviour could be due to the increasing centrifugal acceleration, which affects the MEMS accelerometer accuracy. Figure 3: Plots of accelerations measured over time in the case of: (**a**) the first resonant mode at a rotor speed of 180 rpm and (**b**) the second resonant mode at 300 rpm. Figure 6 also shows the results obtained by comparing the peaks of the spectra which have been used for the evaluation of the MAPE (Equation (2)). It is worth noting that, for all the test configurations, both the acceleration amplitude and the corresponding frequency evaluated through the MEMS-based wireless system are compatible with the ones assessed with the reference monitoring system. According to the presented outcomes, the proposed inexpensive vibration monitoring system may be deployed both in wind turbine and turbomachinery fan blades by positioning the accelerometer at a proper distance from the rotation axis. The power consumption of both the reference and MEMS-based wireless systems is another critical feature that should be compared. In fact, while the reference system includes benchtop instruments that require hundreds of watts, without considering the reference and MEMS-based wireless systems, the reference and MEMS-based wireless systems are compatible with the ones assessed with the reference monitoring system.