Data-driven topology optimization design of phononic crystals for vibration control

Phononic crystals, as artificial composite materials, exhibit bandgap characteristics that strongly depend on the geometry of the unit cell. This study proposes an innovative machine learning-driven framework for the inverse design of phononic crystals (PnCs). First, we developed a new hybrid framework that integrates variational autoencoders (VAE) with Light Gradient Boosting Machine (LightGBM), establishing a groundbreaking paradigm for bandgap prediction. Secondly, a genetic algorithm (GA) enhanced optimization strategy is proposed, combining machine learning (ML) prediction with multi-objective evolutionary search, enabling simultaneous optimization of filling rate minimization and precise low-frequency bandgap targets (50-70 Hz). Finally, the vibration isolation capability of the designed phononic crystal is verified by frequency domain analysis and time history analysis. In addition, the feasibility and reliability of the data-driven topology optimization design method are fully demonstrated. The results show that the LightGBM achieves fast and accurate bandgap boundary prediction with MSE as low as 0.015 after 100 iterations on the validation set and R2 as high as 0.999 on the test set. Four groups of low filling rate (39.1 %) metamaterials are designed to mitigate the subway vibration through the proposed machine learning-driven framework. It is also indicated that the optimized metamaterial barriers significantly attenuated the vibration wave by 90 %. The proposed framework can provide a new possibility for the design of multi-resonator and multi-function PnCs.