Stochastic Model for a Piezoelectric Energy Harvester Driven by Broadband Vibrations

We present an experimental and numerical study of a piezoelectric energy harvester driven by broadband vibrations. This device can extract power from random fluctuations and can be described by a stochastic model, based on an underdamped Langevin equation with white noise, which mimics the dynamics of the piezoelectric material. A crucial point in the modelisation is represented by the appropriate description of the coupled load circuit that is necessary to harvest electrical energy. We consider a linear load (resistance) and a nonlinear load (diode bridge rectifier connected to the parallel of a capacitance and a load resistance), and focus on the characteristic curve of the extracted power as a function of the load resistance, in order to estimate the optimal values of the parameters that maximise the collected energy. In both cases, we find good agreement between the numerical simulations of the theoretical model and the results obtained in experiments. In particular, we observe a non-monotonic behaviour of the characteristic curve which signals the presence of an optimal value for the load resistance at which the extracted power is maximised. We also address a more theoretical issue, related to the inference of the non-equilibrium features of the system from data: we show that the analysis of high-order correlation functions of the relevant variables, when in the presence of nonlinearities, can represent a simple and effective tool to check the irreversible dynamics.