Improving the robust design of piezoelectric energy harvesters by using polynomial chaos expansion and multiobjective optimization

Harvesting electrical energy from mechanical vibrations through piezoelectric-based resonant devices is a suitable form of generating alternative electrical sources for several applications, most dedicated to powering small electronic devices. This technique has attracted considerable attention over the past decades, mainly due to piezoelectric materials’ high electrical charge density. However, the amount of harvestable energy is usually small and sensitive to variabilities in design, manufacturing, operation, and environmental conditions. Hence, it is essential to account for predictable and potentially relevant uncertainties during the design of energy harvesting devices. This work presents strategies for the robust design of resonant piezoelectric energy harvesters, considering the presence of uncertainties in design, manufacturing, and mounting conditions, such as the bonding of the piezoelectric materials and the clamping of the resonant device. The work proposes and discusses strategies for finite element modeling, accounting for adhesive bonding of piezoelectric materials and imperfect clamping; harvestable power output mean value and dispersion estimation with Polynomial Chaos Expansion; and robust optimization using multiobjective optimization techniques. Relevant general conclusions concerning harvesting devices include but are not limited to, devices with shorter resonating beams and larger tip masses tend to present performances that are nominally better but also less robust. Additionally, reducing the effective electrical resistance may improve robustness without significantly losing the mean value performance. Also, through an assessment of the most relevant design variables and uncertain parameters, some aspects that should receive special attention when designing, manufacturing, and mounting these devices are discussed, such as the bonding of piezoelectric patches and the clamping of cantilever beams due to their essential effect on the robustness of the device. It is also shown that including well-selected design variables may mitigate the impact of uncertainties and, thus, improve the robustness of the device.