A Method for Uncertainty Quantification in Virtual Metrology Models: Acoustic-emission-based Quality Prediction in Micro Crown Gear Manufacturing

This paper proposes a method to quantify the uncertainty of machine learning prediction-based measurement chains building on a feasibility investigation of AE-based virtual metrology for micro crown gear manufacturing. Providing reliable uncertainty statements is essential if regression models are to support conformity decisions or partially replace physical measurements.

The established metrological framework of the Guide to the Expression of Uncertainty in Measurement (GUM) and GUM Supplement 1 provides a basis for uncertainty propagation. However, it treats a learned model typically as deterministic and epistemic uncertainty is not represented. This limitation of application to data-driven models is discussed.

Building up on this discussion, we formulate an uncertainty model for virtual metrology that explicitly incorporates epistemic model uncertainty alongside stochastic input and label uncertainties, considering current state-of-the-art approaches. These contributions are combined within a Monte Carlo–based propagation framework.

The resulting methodology yields predictive distributions and coverage intervals for VM outputs, enabling traceable and decision-relevant uncertainty reporting for AE-based quality prediction in micro-machining.