# Piezoelectric Energy Harvesting Prediction and Efficient Management for Industrial Wireless Sensor
## 1 Introduction
### Literature Overview and Main Problematic  
Three transduction mechanisms, namely electrostatic, electromagnetic, and piezoelectric, are considered to convert vibrations into electrical energy. Piezoelectric transducers (PTs) are the most considered because of their strong electromechanical coupling and the ease of integrating them into the desired applications [11]. As most vibration applications in industrial processes are low frequency, PT architecture is of the cantilever type [12]. The main problem linked to cantilever PTs' design is their narrow bandwidth, resulting in low conversion efficiency when the main vibration frequency fluctuates. The main techniques for increasing the PT's efficiency include non-linearity and de circuit management [13]. The research carried out in non-linear modules offers solutions to amplify the voltage and the maximum energy transferred to the load. The most used non-linear techniques are the Synchronized Switch Harvesting on Inductor (SSHI) [14], the Synchronized Switch Harvesting on Capacitor (SSHC) [15], and the Synchronous Electric Charge Extraction (SECE) [16]. These techniques are derived from the Synchronized Switch Damping on Inductor (SSDI) proposed in [17] to cushion vibrations in mechanical systems. In the SSDI technique, by connecting to the piezoelectric material, a passive electrical load, it can transfer some of the mechanical energy in an electrical form, leading to mechanical damping [18]; therefore, maximizing the recovered electrical power. Practically, a switch is used to insert into the PT's circuit as it passes through its maximum voltage, an impedance that is dual to the PT's internal impedance; this has caused an increase in the current through the dual impedance. This current decreases by recharging the PT's impedance to a voltage reverse to its initial voltage, giving rise to a voltage greater than the PT's maximum initial voltage [19]. For example, using the SSHI technique was possible in [20] to harvest 200% more power than with a standard PT at a frequency of 30 Hz. In [15], using the SSHC technique, it was possible to amplify the harvested power six times compared to the standard PT this at an excitation frequency of 22 Hz. As can be seen, although these solutions help to amplify the level of harvestable power, they are still offered for a fixed excitation of the PT. Unfortunately, in actual use, the vibrations' fundamental frequency changes according to the engine's operating speed, which generates the waves. In most industrial processes, the motor at a given moment may find itself at full load or overload and even sometimes at no charge. These different operating regimes will cause a fluctuation in the harvestable energy. The vibrations' primary frequency changes give rise to the PTs' low efficiencies in real situations. Other design methods aim to tune the transducer's resonant frequency to the main frequency of the vibrations to overcome this limitation. For this, some research suggests broadband or multiband transducers [21; 22]. However, designing such kinds of PT is accompanied by an increase in the size of the circuits, which can prove to be cumbersome for miniature components such as IWS. Another method to make an IWS operational under the harvested energy, without resorting to bulky circuits consists of storing energy until it is enough to allow the node to transmit data. This research field concerns the management of harvestable energy, and this energy harvesting technique is known in the literature as Harvest-Store-Use (HSU) [23]. Very often, the method allows the node to operate perpetually, but this is to the detriment of the Quality of Service (QoS) since it is difficult to predict the frequency of data transmission and the amount of data that the IWS can transmit at a given time. For example, in [19], the vibration data from a mining locomotive are used to design a piezoelectric micro-generator, which incorporates most of the optimizations proposed in the literature, in particular, the non-linear SSHI technique.