Single- and multi-output data-driven surrogate modelling for design optimization of multi-DOF piezoelectric energy harvesters

This study proposes single- and multi-output machine learning surrogate modeling for response prediction and design optimization of multimodal piezoelectric energy harvesters. The framework is demonstrated on a Quad-Finger harvester with closely spaced resonance frequencies to evaluate its capability in a high-dimensional design setting. Datasets are generated from an experimentally validated finite element (FE) model and used to train three ensemble regression algorithms: Random Forest Regression (RFR), Gradient Boosting Regression Tree (GBRT), and eXtreme Gradient Boosting Regression (XGBR). Two modeling strategies are examined. In Case Study I, a single-output model predicts the peak power at the first vibration mode. In Case Study II, a multi-output model simultaneously predicts the peak powers of the first four vibration modes, enabling direct representation of the coupled response. Model performance is evaluated using reliability metrics (R2, MAE, and MSE), residual analysis, and comparison with FE-computed results. GBRT demonstrates the highest predictive accuracy and is therefore integrated with genetic algorithm (GA) for optimization. The GA evaluates the objective function using the trained surrogate model instead of repeated FE simulations. The optimized configurations are validated through separate FE simulations, showing close agreement. Significant improvements in peak and total harvested power are achieved compared to the initial configuration.