## 1 Introduction
### Related Work and Main Contribution
In addition, the proposed solutions only consider optimizing the capacity of a single WS located at a predetermined location in the network. This does not guarantee that all WSs in the network can be self-sufficient as the expected energy harvest rate depends on the location of the WS. Unlike these previous studies, this paper first proposed to design a _Predictor of the Harvestable Power from Vibrations (PHPV)_. Regarding power management solutions, although many solutions have been proposed in recent years for battery-powered WSs, the possibilities in terms of EH-WS are still limited. Most energy management techniques proposed in the literature only concern a single harvester node [24; 25]. The general method proposed uses ultra-low consumption components and the duty cycle strategy [26]. Since reducing the duty cycle is achieved by increasing the WS's sleep mode duration, most of the proposed solutions do not regard of the Quality of Service (QoS). For example, in [27], a WS equipped with a piezoelectric vibration harvesting system with a 0.33 pF supercapacitor could transmit data after 12 h.  
In [24], for example, a PID (Proportional Integral Derivative) controller for measuring the difference between the energy harvested and the energy stored in the WS battery is designed to adjust the WS specifications at each measurement cycle automatically. In [25], the duty cycle adaptation strategy was used to enslave the performance of the WS to the capacities of a piezoelectric beam fed by the vibration of 0.15 g at 40 Hz. The results obtained in this work show that the WS can transmit data every minute. A few solutions have nonetheless been proposed to efficiently manage energy in ambient energy-harvesting networks [28; 29; 30]. Most of these solutions are variants of the Low-Energy Adaptive Clustering Hierarchy (LEACH) protocol initially proposed in [31], intending to balance the energy expenditure of nodes powered by a battery. The initial version of the protocol suggests local data processing and a rotation of the cluster head (CH) at each measurement cycle. The cluster head's choice is based on each node's residual energy. Minimization of energy consumption is thus achieved by reducing the transmission range of each WS; this is achieved by local data processing. Since the work in [31], many variants of the LEACH protocol have been proposed, but always for battery-powered WSs. Some of the most important propositions are summarized in [32]. Only recently have some studies considered adapting the LEACH protocol to ambient energy-harvesting networks [28; 29; 30; 33]. In [28], a CH selection scheme is proposed, and compared to the original LEACH; three types of WS coexisted in each cluster. These were the CH, the WS members, and a scheduling WS whose function is to record the residual energy of each WS. The role of the WS scheduler is to designate the cluster head at the start of the measuring cycle. In [28], the energy harvest rate for the current cycle was not considered; this resulted in a decrease in the QoS of the network, by increasing the delay in data transmission. In [29], authors used the same scheme as that of [28] with only two types of nodes in the cluster (the CH and the WS members). Again, the predictor was not built into the design, and QoS was defined under the basis of the available energy. In addition, the analyzes in [29] were based on solar power. In [33], a new adaptive clustered protocol for ambient energy harvesting WS was proposed. First, a hierarchy was established based on the network's energy level of the different WSs. The active phases of each WS were adapted according to the availability or not of the ambient energy, as in the case of the duty cycle strategy [26]. The proposed method makes it possible to ensure the perpetual operation of the network under the base of the harvested energy.