# Accuracy Characterization of a MEMS Accelerometer for Vibration Monitoring in a Rotating Framework
## 2 Materials and Methods
### Measurement Test Protocol  
In order to test the most structurally severe operating conditions, the measurements were performed simultaneously with both the acceleration systems, while exciting the first four eigenfrequencies of the blade and selecting different rotor angular speeds. The four natural frequencies correspond to 80 Hz, 302 Hz, 818 Hz and 1220 Hz, and they were used to generate the corresponding harmonic voltage \(V_{PZT}(t)\), as reported in Section 2.1. Experimental trials were carried out for the following conditions: 0 rpm (static), 120 rpm, 180 rpm, 240 rpm, and 300 rpm. Before carrying out the acceleration measurements by inducing the resonance of the blade via PZT actuators, noise baseline measurements (with de-activated PZT actuators) were carried out for every considered condition. In this way, the sensor's noise, due to any electromagnetic interferences and vibrations caused by the rotating framework imbalances, was recorded. The measurement range of \(\pm\)98.1 m/s\({}^{2}\) was chosen for the MEMS accelerometer in order to exploit the sensor's highest sensitivity (Table 2). The overall measurement campaign consists of 20 test conditions, and each one was repeated a minimum of six times. The trials were randomized in order to make the experimental and control groups probabilistically equal with respect to all potential confounding variables, and thus minimizing the bias due to the initial differences between the treatment conditions. The data acquisitions were performed simultaneously for both the measurement systems. A sampling rate of 16 k sample/s was set for both the DAQs and each trial was acquired for 4 s. The data were subsequently processed with an _in-house_ routine developed in the _MATLAB_ environment. In particular, a fast Fourier's transform (FFT) of all the signals was performed to analyze the accelerations in the frequency domain. The spectral components of the baseline noise detected by the two accelerometers in each test condition were filtered. Thereby, the acceleration amplitudes of both the accelerometers were evaluated, and the MAPE was calculated between the reference accelerometer (considered as the actual value) and the MEMS accelerometer in order to estimate the proposed wireless vibration monitoring system accuracy. The MAPE was evaluated as follows:  
\[MAPE=\frac{100\%}{n}\sum_{i=1}^{n}\left|\frac{x_{R,i}-x_{M,i}}{x_{R,i}}\right| \tag{2}\]  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Specification** & **Reference System** & **Wireless System** \\ \hline \multicolumn{3}{c}{**Accelerometer**} \\ \hline Model & PCB 352A56 & ADXL 356C \\ \hline Measurement range & \(\pm\)490 m/s\({}^{2}\) & \(\pm\)98.1 or \(\pm\)392.3 m/s\({}^{2}\) \\ \hline Sensitivity & 10.2 \(\pm\) 5\% mV/m/s\({}^{2}\) & 8 \(\pm\) 8\% or 2 \(\pm\) 8\% mV/m/s\({}^{2}\) \\ \hline Bandwidth & 0.5–10,000 Hz (\(\pm\)5\%) & 0–2400 Hz \\ \hline Resonant frequency & \(\geq\)45 kHz (\(\pm\)5\%) & 5.5 kHz \\ \hline Transverse sensitivity & \(\leq\)5\% (\(\pm\)5\%) & 1\% \\ \hline Mass & 1.8 g & 1.6 g \\ \hline \multicolumn{3}{c}{**DAQ**} \\ \hline Model & NI USB 6341 & MCC 118 \\ \hline \multirow{2}{*}{Channels} & 16 single ended or & \multirow{2}{*}{8 single ended} \\  & 8 differential & \\ \hline ADC resolution & 16 bit & 12 bit \\ \hline Sample rate & up to 500 kSample/s & up to 100 kSample/s \\ \hline Input voltage range & \(\pm\)10 V & \(\pm\)10 V \\ \hline Selectable input voltage range & yes & no \\ \hline \hline \end{tabular}
\end{table}
Table 2: Main specifications of both the acceleration measurement systems.  
with \(n\), \(x_{R}\) and \(x_{M}\) being, respectively, the number of trials and the acceleration measurement obtained, respectively, with the reference and MEMS-based system.