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8 December 2025

Multi-Task Deep Learning for Surface Metrology

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1
Division of Metrology and Measurement Systems, Institute of Mechanical Technology, Faculty of Mechanical Engineering, Poznan University of Technology, 60-965 Poznan, Poland
2
Laboratory of Coordinate Metrology, Faculty of Mechanical Engineering, Cracow University of Technology, 31-864 Cracow, Poland
3
Institute of Metrology and Biomedical Engineering, Faculty of Mechatronics, Warsaw University of Technology, 02-525 Warsaw, Poland
4
Department of Metrology and Modern Manufacturing, Faculty of Mechatronics and Mechanical Engineering, Kielce University of Technology, 25-314 Kielce, Poland
This article belongs to the Special Issue Measurement Sensors and Machine Learning Applications in Modern Manufacturing

Abstract

A reproducible deep learning framework is presented for surface metrology to predict surface texture parameters together with their reported standard uncertainties. Using a multi-instrument dataset spanning tactile and optical systems, we jointly address measurement system type classification and regression of key surface parameters—arithmetic mean roughness (Ra), mean peak-to-valley roughness (Rz), and total roundness deviation (RONt)—alongside their reported standard uncertainties. Uncertainty is modelled via quantile and heteroscedastic regression heads, with post hoc conformal calibration used to obtain calibrated prediction intervals. On a held-out test set, high fidelity was achieved by single-target regressors (coefficients of determination: Ra 0.9824, Rz 0.9847, RONt 0.9918), with two uncertainty targets also well modelled (standard uncertainty of Ra 0.9899, standard uncertainty of Rz 0.9955); the standard uncertainty of RONt remained more difficult to learn (0.4934). The classifier reached 92.85% accuracy, and probability calibration was essentially unchanged after temperature scaling (expected calibration error 0.00504 → 0.00503 on the test split). Negative transfer was observed for naive multi-output trunks, with single-target models performing better. These results provide calibrated predictions suitable for informing instrument selection and acceptance decisions in metrological workflows.

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