Simplified robust and multiobjective optimization of piezoelectric energy harvesters with uncertain parameters

Harvesting energy from mechanical vibrations using piezoelectric materials presents itself as an interesting alternative energy source, particularly for embedded and integrated designs considering the high electric charge density that can be stored in these materials. To amplify the amount of energy available at narrow predefined frequency ranges, resonant cantilever devices are usually considered. Nevertheless, energy output is still small and highly sensitive to device parameters, mounting and operating conditions. Thus, these devices must be designed using optimization techniques, to ensure maximum extraction of energy available, and accounting for uncertainties in parameters, mounting and operating conditions. This work presents two methodologies to design cantilever piezoelectric energy harvesters using deterministic and robust optimization and accounting for the presence of uncertain parameters. The proposed methodology employs an electromechanical coupled finite element model to estimate mean and variance of harvestable power for given base excitation and parametric uncertainties. The electromechanical model is then used in two design methodologies, a robust design based on Taguchi’s method and a multiobjective deterministic Compromise Programming method. Both methods are shown to be capable of providing design solutions that allow maximization of nominal or mean harvesting performance and minimization of variability (increased robustness). As general design guidelines, it is shown that devices with larger mass lead to better mean performance but also to higher variability, thus a compromise solution is advisable. Also, a reduction of the effective harvesting circuit resistance, from nominally optimal value, may improve robustness without substantial decrease in mean performance.