## 3 Predictor of the Harvestable Power from Vibrations (PHPV) Design
### Proposed Predictor
This discrepancy can be explained by the fact that the periodicity in the signals is shifted because of wear in the equipment. For all the measurement points, we first observed that the power predicted with the PHPV (blue curve) is more in phase with the real power. In addition, it is noted that considering the power difference during the time slots makes it possible to reduce the absolute error. To conclude this part, Table 2 summarizes the performance of the three predictors. In Table 2, the RMSE is minimal with the PHPV when compared to the values reached with the EWMA and PHEV algorithms. Improvements range from 37.2% for vibrations taken at the inlet of the crusher gearbox to 78.32% for vibration signals measured from radial shaft 2. With this ability to calculate the quantity of harvestable power at each controlled location with the slightest error, a protocol is proposed in the following section to optimize the performance of the wireless sensor network. \begin{table}
\begin{tabular}{c c c c c c|c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Measuring** \\ **Points** \\ \end{tabular} } & \multicolumn{3}{c}{**Absolute Error**} & \multicolumn{3}{c}{**RMSE**} \\ \cline{2-9}  & **EWMA** & **PHEV** & **PHPV** & **EWMA** & **PHEV** & **PHPV** & **Improvement** \\ \hline \(V_{EPB}\) & 9.7 \(\mu\)W & 5.1 \(\mu\)W & 1.42 \(\mu\)W & 0.6 \(\mu\)W & 0.29 \(\mu\)W & 0.08 \(\mu\)W & 72.41\% \\ \(V_{IPB}\) & 34.4 \(\mu\)W & 18.92 \(\mu\)W & 5.34 \(\mu\)W & 7.4 \(\mu\)W & 2.9 \(\mu\)W & 0.84 \(\mu\)W & 71\% \\ \(V_{OCG}\) & 9.8 \(\mu\)W & 2.6 \(\mu\)W & 0.8 \(\mu\)W & 1.7 \(\mu\)W & 0.71 \(\mu\)W & 0.22 \(\mu\)W & 69\% \\ \(V_{ICG}\) & 440 \(\mu\)W & 162.97 \(\mu\)W & 116.8 \(\mu\)W & 7.8 \(\mu\)W & 9.4 \(\mu\)W & 5.9 \(\mu\)W & 37.2\% \\ \(VI_{IE}\) & 6.7 mW & 9.3 mW & 2 mW & 1.3 mW & 3.27 mW & 0.73 mW & 77.6\% \\ \(V_{GOS}\) & 26.7 mW & 24 mW & 5.22 mW & 3 mW & 6.7 mW & 1.5 mW & 77.6\% \\ \(V_{OSH}\) & 7.9 \(\mu\)W & 4.92 \(\mu\)W & 1 \(\mu\)W & 2.4 \(\mu\)W & 1.7 \(\mu\)W & 0.37 \(\mu\)W & 78.24\% \\ \(V_{RS1}\) & 55 \(\mu\)W & 10.41 \(\mu\)W & 6.77 \(\mu\)W & 1.54 \(\mu\)W & 1.77 \(\mu\)W & 0.4 \(\mu\)W & 77.4\% \\ \(V_{SR2}\) & 81.3 \(\mu\)W & 49.09 \(\mu\)W & 9.46 \(\mu\)W & 26.5 \(\mu\)W & 18.45 \(\mu\)W & 4 \(\mu\)W & 78.32\% \\ \(V_{SR3}\) & 6.8 \(\mu\)W & 4.55 \(\mu\)W & 1.42 \(\mu\)W & 1.54 \(\mu\)W & 1.53 \(\mu\)W & 0.5 \(\mu\)W & 67.3\% \\ \(V_{VSE}\) & 2.3 mW & 1.94 mW & 0.55 mW & 0.3 mW & 0.62 mW & 0.17 mW & 72.58\% \\ \(V_{EF}\) & 4.9 \(\mu\)W & 2.2 \(\mu\)W & 0.6 \(\mu\)W & 1.7 \(\mu\)W & 0.71 \(\mu\)W & 0.18 \(\mu\)W & 74.65\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of EWMA and PVHE performance. Figure 10: PHPV performance compared to EWMA and PHEV. (**a**) Power on External and Inside Crusher Pinion. (**b**) Power at the Outlet and Inlet of the Crusher Gearbox. (**c**) Power at Internal Engine and Gearbox at the Output Side. (**d**) Power on the Gearbox at the gearbox output Shaft and on the on the Radial Shaft 1. (**e**) Power on the Radial Shaft 2 and 3. (**f**) Power at the Ventilation Side of the Engine and Engine fan.