# Piezoelectric Energy Harvesting Prediction and Efficient Management for Industrial Wireless Sensor
## 1 Introduction
### The Method, Assumptions, and Paper Organization  
In this work, it is proposed to analyze the vibrations at the location of the IWS before conception. The analysis of fluctuations over a very long-time interval will make it possible to design a predictor of the harvestable energy subsequently. The specifications of the IWS will be defined beforehand based on the estimated energy harvesting rate. To define the maximum data size, an IWS's consumption model based on IoT protocols is established. Then the PMM is programmed so that the IWS sends its maximum amount of data to the base station at the end of each measurement cycle. The protocol implemented in the PMM will be called the Maximizing Data Size Protocol (MDSP). It will make it possible to maximize the size of the data transmitted to the base station by harnessing harvestable energy during the measurement cycle. The design steps to develop the new design method proposed here are shown on the functional diagram in Figure 2.  
Overall, in Figure 2, the first step will be to analyze vibration signals at the IWS location. An electromechanical conversion model of the MATLAB/SIMULINK software will be used to observe fluctuations in harvestable power at the sensor location. An Exponentially Weighted Moving-Average (EWMA) filter will then be used to predict harvestable power levels in each measurement cycle. The predictor's performance will then be analyzed through the maximum absolute error and the  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**PT** & **Frequency Range (Hz)** & **Power** & **Size (cm\({}^{3}\))** \\ \hline \hline Mode volume [37; 39] & 50–200 & 9 mW @ 1 g & 3 \\ Piezo System [40] & 52 & 7.1 mW @ 2.6 mm (deflexion) & 3.3 \\ MicroGen System [41] & 100, 120 and 600 & 0.85 mW @ 600 Hz; 0.5 g & 0.7 \\ PMG Perpetuum [42] & 50 and 60 Hz & 25.5 mW & — \\ \hline \hline \end{tabular}
\end{table}
Table 2: Some marketed piezoelectric transducer.  
Figure 2: Functional diagram of the workflow of the design method.  
Root Mean Square Error (RMSE). Subsequently, based on the temporal analysis of power, the PHEV predictor will be set up to minimize prediction errors. The harvestable power will be combined with a long-range consumption model of the IWS to implement the MDSP in the PMM to maximize the data transmitted to the base station. Finally, an evaluation of the design method's performance will be provided as well as a comparison in terms of throughput with related work.  
The following assumptions will be made throughout this work:  
* The memory for storing data in the IWS is assumed to be unlimited.
* The conditioning of the energy coming from the PT is not treated since, in most designs, Maximum Power Point Tracking (MPPT) is used to keep track of the maximum efficiency operating condition [43]. This issue is not discussed here as MPPT is now a classical function. The maximum power transfer is studied here by varying the resistive load of the PT.  
According to the functional diagram of Figure 2, in Section 2, the vibration measurements on the industrial process to be automated will be reported as well as the mechanical-electric conversion model. Section 3 is devoted to the design of the PHEV. In Section 4, a consumption model of the IWS based on the IoT requirements is proposed to precisely quantify the transferable data size during each measurement cycle. The MDSP will then be set up to transmit the maximum amount of data to the base station. Section 5 provides a comparison of the results obtained with some related work. Finally, the paper is concluded in Section 6.