Comparative development of single- and multi-output ANN surrogates for predicting natural frequencies from Chebyshev spectral simulation

This study presents a comparative development of single- and multi-output Artificial Neural Network (ANN) surrogate models for accurately predicting the first five natural frequencies of a rotating Timoshenko beam. Specifically, a comprehensive dataset consisting of 17,576 samples was generated using a high-fidelity Chebyshev spectral collocation method over a wide range of dimensionless design parameters. An initial correlation analysis has been conducted to effectively investigate the statistical relationships between the design parameters and the associated first five natural frequencies. Based on the initial screening, two ANN modeling strategies have been established: a unified multi-output ANN model capable of simultaneously predicting all five natural frequencies, and a set of five independent single-output ANN models, each optimized for a specific natural frequency. The models have been trained, validated, and evaluated using a 70–15–15 data split and compared against standard performance metrics from the literature, including the Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), and Coefficient of Determination (R2), along with the computational efficiency required for the model development. The results demonstrate that both ANN approaches significantly outperform a baseline linear regression model, confirming the strongly nonlinear nature of the problem under study. The single-output ANN models consistently achieved very high prediction accuracy across all modes, with R² values approaching unity and significantly lower RMSE and MAPE values compared to the multi-output model, particularly for higher vibration modes. Although the multi-output ANN provides a compact and unified modeling framework, it exhibited slightly reduced accuracy due to the need to generalize across multiple output natural frequencies. In terms of computational cost, the single-output models required less overall training time despite their higher predictive capability within the design parameter ranges investigated.