Particle Swarm Optimization for broadband energy harvesting of ambient mechanical vibrations

We consider the model of a networked energy harvester for ambient dispersed vibrations, based on coupled mechanical resonators and a piezoelectric transduction mechanism. The networked harvester is equivalent to a mechanical filter that can be optimized for broadband energy harvesting. Using mechanical-to-electrical analogies, we derive an equivalent circuit model for the energy harvester, and we calculate the transfer function, output voltage, average harvested power and power efficiency in the frequency domain. We discuss the problem of the energy harvester optimization. Because analytical formulas for the objective function and its derivatives are not available, we apply a gradient-free method, based on Particle Swarm Optimization, to find the network parameters that maximize the scavenged energy. We demonstrate that, after proper optimization, the networked energy harvester scavenges more than 100% additional power compared to a simple, single mechanical degree-of-freedom energy harvester. We show that increasing the number of mass-spring pairs beyond three offers negligible returns in terms of increased scavenged power. Additionally, we reveal that the networked harvester functions as a broadband mechanical filter, with a decrease in the power scavenged at the resonance frequency in exchange for a wider bandwidth, thus collecting more energy by exploiting a broader frequency range. Furthermore, we demonstrate that broadband optimization using Particle Swarm Optimization achieves superior performance compared to analytical methods based on broadband impedance matching designed at the resonance frequencies.