Hybrid models are increasingly employed to simulate intricate physical processes by combining domain expertise embedded in physics-based models with process measurements-based data. The combination of domain knowledge and measurement data results in hybrid models that lead to high-accuracy decisions, extrapolation capabilities, and compliance with basic physical laws. Surrogate modeling, one aspect of hybrid modeling, involves a simplified model to capture the physics in a process, emphasizing an adaptable mathematical expression. This study applies hybrid modeling to address the intricate tool wear process in precision machining by developing a recursive model using symbolic regression.

In precision machining, predicting the tool health can improve productivity, job quality, and reduce machine downtime and energy consumption. While deep learning (DL) algorithms have garnered recent interest, they lack the physics understanding associated with machining processes. To address this limitation, we present a symbolic regression framework for tool wear diagnostics. The method explores analytical symbolic expressions using health indicators and cutting settings. Tool health indicators are computed from wavelet subspaces of vibration signals by applying a distance metric to the wavelet coefficients. These indicators are strongly correlated with tool wear measurements, making them suitable for tool wear diagnostics. We applied the developed framework to the IEEE PHM 2010 data, which comprises three sets of run-to-failure machining tests conducted with three tools. The framework predicted tool wear with an$R^{2}$of 0.947 and a mean absolute error (MAE) of 0.006 mm across test sets. The results demonstrate the effectiveness of the symbolic regression approach for tool wear diagnostics, showcasing the richness of information in the indicators and the quality of the developed model$\mathbf{for}$tool wear estimation.