This study addresses the critical need for sustainable energy by optimizing diaphragm-type piezoelectric elements for efficient waste vibration energy harvesting. Traditional experimental optimization of complex, non-linear design parameters including applied load, tapper diameter, and support structures is often resource-intensive and time-consuming. To overcome these limitations, we developed a novel hybrid machine learning framework that seamlessly integrates an Artificial Neural Network (ANN) with a Modified Grey Wolf Optimization (mGWO) algorithm. The ANN was rigorously trained on experimental data using Bayesian Regularization, establishing itself as a robust and high-fidelity surrogate model capable of accurately predicting voltage output based on diverse input parameters, evidenced by an R-value close to 1. This predictive model subsequently served as the fitness function for the mGWO algorithm, which incorporated a non-linear control parameter to efficiently explore the multi-dimensional design space and effectively balance exploration with exploitation. The framework successfully identified the optimal configuration for maximizing voltage output, predicting a theoretical maximum of approximately 70.67 V. This optimal setup notably involved a high applied load of 100 N, the 6CA multi-pointed tapper configuration, and the three-support boundary condition, which is consistent with the experimentally validated results. The computational findings demonstrated excellent agreement with empirical results while providing significantly higher resolution for design insights. This validated, predictive tool offers a substantial advancement for the future scaling and design optimization of piezoelectric energy harvesters, minimizing the need for extensive physical prototyping and ensuring efficient stress transfer without mechanical failure.
Yadav et al. (2026) studied this question.