## 1 Introduction
### Related Work and Main Contribution  
To answer the issue of the randomness of the harvestable power, two lines of research must be combined. This includes research in optimizing the performance of the harvesting circuits [8] and the efficient managing of the available energy [9]. Very little research, however, integrates these two aspects into their designs. There are four main mechanisms for converting vibration into electrical energy in harvesting circuits. These mechanisms are electrostatic, electromagnetic, piezoelectric, and triboelectric. A comparison of these different transduction mechanisms has been proposed in [10; 11; 12; 13]. It emerges from a synthesis of these previous works that piezoelectric materials are the most used due to their high output voltage and the facility of shaping the harvested energy. It should be noted that the transducer's performance is also determined by its geometry. To harvest the maximum power, the transducer's resonant frequency must match the surrounding vibrations' main frequency [14]. There are three main types: cantilever, circular, and cymbal-type transducers [15]. Given the low frequencies in most applications, cantilever beams are the most considered structures because they make it possible to reach low resonance frequencies while maintaining acceptable dimensions [15; 16]. The major disadvantage of piezoelectric cantilever-type beams is their narrow bandwidth; however, most vibration spectra are wideband [16]. The optimizations are then mechanical in nature, using multi-beam harvesters to increase the transducer's bandwidth [17]. For example, in [18], five piezoelectric beams connected in series are used to harvest 66.75 uW for an acceleration of 5 m/s\({}^{2}\) at 234.5 Hz of frequency. Reconfigurable transducers are also being considered to overcome the fluctuation observed in most vibration spectra. The general principle of the technique is based on adjusting the proof mass of the cantilever beam. In [19], a stepper motor performed the proof mass adjustment. Although the results yielded a 60.56% bandwidth improvement with a conversion efficiency of 84.8%, the engine used to adapt the system consumed some of the harvested energy. In [20], the power harvested on the different axes was analyzed beforehand. The harvesting system's location was defined according to the level of harvestable energy. Although effective, these solutions were suitable for applications where the amounts of vibrations are important, since the adjustment systems consume a part of the harvested energy. Moreover, improvements on the mechanical level are achieved at the expense of the congestion generated by the circuits' size. Electrical solutions are also proposed to amplify the power at the output of the piezoelectric transducer. For example, non-linear processing techniques to amplify the amount of power harvested have been proposed. Non-linear techniques consist of intermittently switching the piezoelectric transducer on a resonant electrical network for a short time [21]. The main method is the synchronized switch harvesting on the inductor [7]. Thanks to this technique, it is possible to amplify the transducer's output power and output voltage, but this is generally for a fixed excitation frequency [17], which is difficult to maintain in real applications. It has also been shown experimentally in [22] that these optimization techniques are only gainful when the transducer's open-circuit voltage is greater than 5.84 V; this is at a frequency of 30 Hz. It has nevertheless recently been proposed in [23] a reconfigurable nonlinear method, efficient for open-circuit voltage levels of the transducer between 0.03 V and 4.39 V. Although the simulated results of the proposed circuit demonstrated the efficiency of 66%, it remained that this performance was achieved by using several (up to 8 eight piezoelectric transducers, which once again contributed to increasing the size of the circuits.