Assessment of machine learning methods predicting the axial vibration frequencies of microbars

Microbars are one of the important components of microelectromechanical systems. With the recent increase in their applications, the importance of understanding their mechanical response has become an important topic. In this study, for the first time, the mechanical behavior of microbars based on the strain gradient theory is investigated using a machine learning (ML) approach. Four distinct ML models, namely artificial neural network (ANN), support vector regression (SVR), decision tree regression (DTR), and random forest regression (RFR), are developed for microbars with clamped boundary conditions. The performance of these models is individually assessed using five different metrics: coefficient of determination (R2), Mean Absolute Error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE) and Nash-Sutcliffe efficiency coefficient (NSE). The best-performing model is selected based on these comparisons. Additionally, a semi-analytical approach is employed to determine the natural frequencies of microbars under general elastic boundary conditions using the Fourier sine series and Stokes' transform. While the R2 value for all four models indicated a good fit of 0.999, the percentage difference in MAE and RMSE values between the training and testing data for DTR and RFR models was relatively higher as compared to ANN and SVR. The results showed that ANN and SVR models exhibit the best performance in predicting the natural frequencies on both training and testing data across all three metrics. Finally, a study on the free axial vibration frequencies of microbar under various effects was conducted.