Microscale piezoelectric energy harvesters (PEHs) are promising devices for converting ambient thermal and vibrational energy into usable electrical power. However, their performance is strongly influenced by geometric, material, and thermal parameters, leading to nonlinear behavior that complicates accurate prediction. This study investigates a three-layer clamped bimorph beam consisting of PZT-5H piezoelectric outer layers and an aluminum core, modeled using Euler–Bernoulli beam theory under base excitation and thermal gradients. To overcome the high computational cost of solving the governing equations, a surrogate model based on Gaussian Process Regression (GPR) is developed. The training dataset is generated using Latin Hypercube Sampling, enabling efficient exploration of the design space. The surrogate model accurately predicts both output power and natural frequency across diverse design configurations. Validation against numerical simulations demonstrates excellent agreement, with coefficient of determination ( R 2 ) values exceeding 0.99. The proposed framework significantly reduces computational effort while maintaining high predictive accuracy. It provides a reliable tool for design optimization of thermal–vibrational energy harvesting systems, enhancing their efficiency and robustness.
Shirbani et al. (Wed,) studied this question.