D3-2.1 - Representing Measurement Uncertainty by Gaussian Mixtures

Event

23. ITG/GMA-Fachtagung Sensoren und Messsysteme 2026
2026-06-09 - 2026-06-10
Nürnberg

Band

Vorträge

Chapter

Messunsicherheit und Selbstvalidierung

Author(s)

L. Hoffmann, M. Y. Alayoubi, M. Heizmann - Karlsruhe Institute of Technology, Karlsruhe, A. Darijani, J. Beyerer - Fraunhofer IOSB, Karlsruhe

Pages

258 - 263

DOI

10.5162/sensoren2026/D3-2.1

ISBN

978-3-910600-11-9

Price

free

Abstract

This paper presents a probabilistic framework for uncertainty quantification in nonlinear measurement systems Instead of relying on local linearization as often used according to the based on Gaussian mixture models. Guide to the Expression of Uncertainty in Measurement (GUM), the proposed approach represents the measurement model as a joint probability density function of input and output quantities. This joint distribution is approximated using a Gaussian mixture, the parameters of which are estimated from data via the Expectation–Maximization (EM) algorithm. Posterior distributions of the measurand are obtained by conditioning the Gaussian mixture on observed input values, enabling the characterization of non-Gaussian, asymmetric, and multimodal uncertainty structures. This formulation allows for a flexible and computationally efficient alternative to classical uncertainty propagation methods, particularly in the presence of nonlinear relationships. The approach is demonstrated using fatigue strength estimation of materials, where uncertainties in hardness, residual stress, and surface roughness are propagated through a nonlinear model. Monte Carlo simulation is used as a reference, and the resulting distributions are approximated by Gaussian mixtures. The results show that the proposed method provides a consistent and compact representation of uncertainty while preserving relevant distributional features.