Power expectation as a unified metric for the evaluation of vibration energy harvesters

Vibration energy harvesters (VEHs) allow the extraction of ambient mechanical energy. The proposed analysis focuses on bistable harvesters with Duffing nonlinearity. Bistable harvesters exhibit larger frequency bandwidth than linear monostable harvesters, but they exhibit complex behaviors (i.e., multiple periodic orbits and chaos), making their evaluation challenging. To assess the quality of a VEH, it is necessary to evaluate its energy performance generically. In this paper, we offer a new quantitative metric that can be used to evaluate bistable harvesters while taking into account the richness and diversity of their dynamics. This metric – called power expectation – is based on the average harvested power of each existing orbit weighted by its occurrence probability. The value of this power expectation depends on the harvester characteristics and potential orbit jump strategy implemented. Finally, we define a new figure of merit (FoM) based on the integral of the power expectation over all vibration frequencies. This FoM can be used for a generic evaluation of nonlinear vibration energy harvesters (NVEHs), by taking into account the various orbits and their respective probability of occurrence depending on the orbit jump strategy used. The proposed FoM also makes it possible to ensure a fair comparison with linear VEHs and quantitatively assess the effectiveness of orbit jump strategies for a given VEH.