Design optimization under uncertainty and speed variability for a piezoelectric energy harvester powering a tire pressure monitoring sensor

Energy harvesting (EH) technologies to power small sized electronic devices are attracting great attention. Wasted energy in a vehicle's rotating tire has a great potential to enable self-powered tire pressure monitoring sensors (TPMS). Piezoelectric type energy harvesters can be used to collect vibrational energy and power such systems. Due to the presence of harsh acceleration in a rotating tire, a design tradeoff needs to be studied to prolong the harvester's fatigue life as well as to ensure sufficient power generation. However, the design by traditional deterministic design optimization (DDO) does not show reliable performance due to the lack of consideration of various uncertainty factors (e.g., manufacturing tolerances, material properties, and loading conditions). In this study, we address a new EH design formulation that considers the uncertainty in car speed, dimensional tolerances and material properties, and solve this design problem using reliability-based design optimization (RBDO). The RBDO problem is formulated to maximize compactness and minimize weight of a TPMS harvester while satisfying power and durability requirements. A transient analysis has been done to measure the time varying response of EH such as power generation, dynamic strain, and stress. A conservative design formulation is proposed to consider the expected power from varied speed and stress at higher speed. When compared to the DDO, the RBDO results show that the reliability of EH is increased significantly by scarifying the objective function. Finally, experimental test has been conducted to demonstrate the merits of RBDO design over DDO.