Data-driven sparse regression for a complex zigzag structure: Frequency response in low-frequency vibrations

Abstract

In this study, we develop a sparse regression framework to predict the frequency response of a complex zigzag structure using frequency domain data from experimental setups. Such structures are widely used in MEMS (Micro-Electro-Mechanical Systems) and vibration energy harvesters where small structures with low-natural frequencies are desired. Our approach employs sparsity-promoting techniques, including LASSO (Least Absolute Shrinkage and Selection Operator) regression, to selectively identify the most relevant nonlinear terms based on the LASSO regression technique, thereby avoiding exhaustive searches across all potential models. The machine learning framework proposed in this research consists of standard scaling for data normalization, trigonometric and polynomial feature transformations, and regularization through LASSO regression, followed by optimization using a genetic algorithm to fine-tune LASSO parameters like regularization strength, maximum iterations, and tolerance. This method ensures a generalized and interpretable model capable of addressing the complexities of dynamic systems with external excitations. The present model achieves an R² score of 0.9998, a root mean squared error (RMSE) of 0.021947, and a mean absolute error (MAE) of 0.002580, demonstrating exceptional predictive accuracy. The accuracy and robustness of our model are verified by comparing its predictions with those of the finite element simulations using COMSOL (Computational Software for Multiphysics Simulation). The integration of machine learning with symbolic regression in this framework allows for precise characterizations of system performance and provides a methodological bridge between data-driven models and conventional physics-based analyses. This research demonstrates significant potential for advancing dynamic system modeling and analysis in complex structures, where governing equations are unknown or difficult to determine.