Design of vibratory energy harvesters under stochastic parametric uncertainty: a new optimization philosophy
Vibratory energy harvesters as potential replacements for conventional batteries are not as robust as batteries. Their performance can drastically deteriorate in the presence of uncertainty in their parameters. Parametric uncertainty is inevitable with any physical device mainly due to manufacturing tolerances, defects, and environmental effects such as temperature and humidity. Hence, uncertainty propagation analysis and optimization under uncertainty seem indispensable with any energy harvester design. Here we propose a new modeling philosophy for optimization under uncertainty; optimization for the worst case scenario (minimum power) rather than for the ensemble expectation of the power. The proposed optimization philosophy is practically very useful when there is a minimum requirement on the harvested power. We formulate the problems of uncertainty propagation and optimization under uncertainty in a generic and architecture independent fashion, and then apply them to a single degree of freedom linear piezoelectric energy harvester with uncertainty in its different parameters. The simulation results show that there is a significant improvement in the worst case power of the designed harvester compared to that of a naively optimized (deterministically optimized) harvester. For instance, for a 10% uncertainty in the natural frequency of the harvester (in terms of its standard deviation) this improvement is about 570%