A coherence-driven method for instability frequency identification and uncertainty evaluation in friction stir welding

Friction Stir Welding (FSW) exhibits non-stationary vibrations that challenge conventional vibration-based monitoring, where stability indicators are often extracted from single-sensor spectra without formal uncertainty assessment. This study proposes a coherence-filtered spectral framework for the quantitative evaluation of dynamic stability in FSW. Magnitude-squared coherence between translational acceleration and rotational velocity is used as a filtering criterion to restrict feature extraction to dynamically correlated frequency bands. Within these bands, Spectral Flatness (SF), Spectral Bandwidth (BW), and Spectral Centroid (FC) are employed as stability-related descriptors. Experiments conducted on aluminum alloy lap joints at 1400, 1800, and 3200 rpm show that stable regimes are associated with low SF (<0.1), narrow BW (<20 Hz), and relative uncertainties below 10%, whereas unstable conditions exhibit broadband spectra, loss of feature separability, and uncertainty levels up to 30%. Measurement uncertainty is evaluated through Monte Carlo propagation of inertial sensor noise and bias effects following GUM principles. The proposed methodology provides an uncertainty-qualified and measurement-oriented framework for discriminating stable and unstable FSW operating regimes.