Wavelet-based multi-branch deep learning for tool wear monitoring with physics-informed label construction

The production of mechanical parts predominantly relies on material removal processes, where cutting tools play a critical role in ensuring dimensional accuracy and surface quality. However, cutting tools are subjected to severe operating conditions, including high mechanical loads, elevated temperatures, and friction, which lead to progressive tool wear. This wear is a major source of dimensional errors, scrap, and unplanned downtime, highlighting the need for reliable real-time monitoring and remaining useful life (RUL) prediction. However, accurate tool wear prediction and RUL estimation remain challenging due to noisy supervision, cross-tool variability, and the lack of physically consistent learning in existing approaches. To address these challenges, this paper proposes a physics-informed, modality-aware hybrid framework for tool wear prediction and RUL estimation. Force and vibration signals are first denoised using wavelet packet decomposition (WPD). To reduce label noise and enforce physical plausibility, a health indicator (HI) is constructed and aligned with a generic wear model, with its weights optimized via a genetic algorithm for cross-tool consistency. Wear prediction is performed by a dual-branch CNN-Transformer that processes force and vibration through separate CNN encoders, followed by attention-based fusion and Transformer-based temporal modeling, with an additional monotonic regularization loss to encourage physically consistent degradation trends. Experiments on the PHM-2010 dataset show that the proposed CNN-Transformer achieves lower error than CNN and CNN-LSTM baselines (RMSE down to 0.00847 in normalized scale) and strong cross-tool generalization (mean RMSE of 0.0194 and coefficient of determination (\(\varvec{R}^{\varvec{2}}\)) up to 0.99). When direct wear labels are unavailable, HI-based supervision remains effective (RMSE of 0.0264 and \(\varvec{R}^{\varvec{2}}\) up to 0.98). The method also generalizes to the HMoTP dataset (mean RMSE of 0.0380 and mean \(\varvec{R}^{\varvec{2}}\) of 0.98). Runtime benchmarking indicates an end-to-end latency of 133 ms per cut. These results demonstrate the applicability of the proposed framework for real-time tool condition monitoring, predictive maintenance, and production planning in industrial machining environments.