Deep Learning-Based Prediction of Machining Response Embedding Parameters

Cutting force signals reflect the underlying dynamics of machining systems and are intrinsically linked to tool–workpiece interactions. One fundamental characteristic of these dynamics is the embedding dimension, which serves as a proxy for the system's degrees of freedom and complexity. Accurate and automated prediction of this parameter can provide valuable insight into process stability, enable classification of machining regimes, and inform adaptive control strategies. In this study, the False Nearest Neighbours (FNN) algorithm was first employed to estimate the embedding dimension and corresponding time delay across different stages of the Cutter-Workpiece Engagement (CWE) cycle, which includes tool entry (Stage 1), full engagement (Stage 2), and tool exit (Stage 3). Distinct attractor geometries were observed in reconstructed state-space plots, reflecting stage-specific dynamical behaviour. To automate embedding dimension prediction, the deep learning technology was applied. Results show that the Stage 2 signals, corresponding to stable full engagement, yielded the most accurate predictions, with low variance between estimated and predicted embedding parameters. Stages 1 and 3 exhibited greater noise and waveform distortion, leading to slightly reduced performance, though prediction errors remained within ±1 dimension. Training performance was found to be stable across runs, with close alignment between final training and validation losses. These findings demonstrate the feasibility of combining FNN-based estimation with deep learning models to achieve robust, stage-aware embedding dimension prediction for intelligent machining process monitoring.