## 3 Predictor of the Harvestable Power from Vibrations (PHPV) Design
### Brief State of the Art on Linear Power Prediction
However, it requires many calculations, which can cause delays in decision-making. In addition, to store the data obtained during the previous time  
Figure 7: Fluctuations in the harvestable power at the different measuring points. (**a**) Harvestable powers on the Crusher Pinion and Crusher Gearbox (outlet). (**b**) Harvestable power on the Crusher Gearbox (Inlet), Internal Engine and Gearbox at the Output Side. (**c**) Harvestable power on the Gearbox Output SHaft, Radial Shaft 1 and Radial Shaft 2. (**d**) Harvestable powers on the Radial Shaft 3, Ventilation Side of the Engine and Engine Fan. slots, the processor calculates the power gap each time; this can induce delays (depending on the processor's speed). In [44], a new solar energy predictor designated by Solar Energy Predictor for Communicating Sensor (SEPCS) is proposed. The day is divided into 24 slots of time, and the power harvested during the time slot \(t\) is defined as:  
\[\hat{p}(t)=\sum_{i=1}^{N_{H}}\alpha_{i}\cdot p(t-i)+\sum_{j=1}^{N_{J}}\beta_{j} \cdot p(t-24j) \tag{6}\]  
where \(N_{H}\) is the number of hours in a day, \(p(t-i)\) is the harvested solar power in the earlier \(N_{H}\) period intervals, \(N_{J}\) is the number of days considered in the database, and \(p(t-24j)\) is the power harvested in the same time slot of the previous \(N_{J}\) days. \(\alpha_{i}\) and \(\beta_{j}\) are the weights of filters with values between 0 and 1. This method uses a more extensive database than the EWMA algorithm; however, it is appropriate for slowly varying processes because the duration of a time slot was fixed at 30 min. Recently, it has been proposed in [7] a Predictor of the Harvestable Energy from vibrations (PHEV). The method uses a more extensive database to reduce the RMSE from 28.63 to 19.52 mW when compared to the EWMA algorithm. The predicted power is expressed as follows:  
\[\hat{p}_{d}\ (t,d)=\sum_{i=1}^{N_{D}}\alpha_{i}\cdot p_{d-i}(t)+\sum_{j=1}^{T} \left[\sum_{i=1}^{N_{D}}\beta_{i,j}\cdot p_{d-i}(t+j)+\sum_{i=0}^{N_{D}}\gamma _{i,j}\cdot p_{d-i}(t-j)\right] \tag{7}\]  
where \(N_{D}\) represents the number of previous days, and \(T\) is the assumed periodicity observed in vibration signals due to repetitive tasks in the process. \(p_{d-i}(t)\) is the harvested power in the previous days at the same moment \(t\). \(p_{d-i}(t-j)\) and \(p_{d-i}(t+j)\) are, respectively, the powers harvested during previous days in earlier and successive periods. \(\alpha_{i}\), \(\beta_{i,j}\), and \(\gamma_{i,j}\) are weights of the filters. The database in this equation is huge, and this would require a lot of storage space. Taking multiple data into account when calculating power could also lead to a delay in decision-making. In addition, in this method, periodicity is considered in the vibration signals due to the habits of the process, which operates 24 h a day. However, it should be noted that this periodicity, assumed to be constant in the algorithm, could not remain so in an actual industrial application, because the wear of the equipment would influence the energy consumption profile of the engine, which would impact the characteristics of the acceleration signals [48]. These three observations taken together could then contribute to increasing the prediction errors. In [46], a prediction based on machine learning of piezoelectric energy harvesting from wake gallop was proposed; the method does not deal with a real case but analyzes the vibration response of piezoelectric energy recuperators to wake gallop in different configurations. Once again, the actual implementation would be complex, given the wear and tear of the equipment.