Convergence Behaviour of Numerical Measurement Uncertainty Evaluation using a Virtual Metrological Computed Tomography System

Abstract

Digital twins of measurement devices offer fascinating applications, e.g. systematic error correction [12] or numerical uncertainty evaluation according to GUM Supplement 1 [5]. The latter is state of the art for tactile coordinate measurements [3]. For Computed Tomography (CT), this is currently not the case [18]. Prior work at the Institute of Manufacturing Metrology showed the potential to numerically evaluate task-specific measurement uncertainties in good agreement with values determined experimentally in accordance with the VDI/VDE standard 2630 Part 2.1 [18] for an unproblematic measurement task (see [8]). Details on the digital twin and the Monte Carlo method used can be found in [19]. In this prior work, the number of simulations for the Monte Carlo trials was chosen based on computational feasibility and expert knowledge. A systematic study of the convergence behaviour is the object of this contribution. Other contributions towards the numerical evaluation of task-specific measurement uncertainties can be found in [9, 15].

Charting the course towards dimensional measurement traceability by x-ray computed tomography

“…Using a modified version [60] of the aRTist simulation software [61] developed by the Bundesanstalt für Materialforschung und -prüfung (BAM), Helmecke et al [62] and Wohlgemuth et al [63] perform 50 simulations, each comprising 800-projection acquisitions, to determine the uncertainty in the measurement of four cylindrical hole diameters and six hole-to-hole center distances on an aluminum rotor head, and the uncertainty in measuring 12 bi-directional lengths on a polycarbonate LEGO connector. An initial set of 21 geometrical parameters (table 3) are randomly sampled from uniform distributions for each Monte Carlo trial.…”

“…Helmecke et al [62] and Wohlgemuth et al [63] assume a normal distribution in the outputs and therefore use the standard deviation as the estimate of uncertainty for a 68.27% confidence interval. Uncertainties estimated for similar features, e.g.…”

“…diameters and hole-to-hole distances, in Table 3. Varied parameters and corresponding distributions in [62] and [63], as described in [60], where the distribution parameters are not provided. the rotor head were averaged and compared to equivalent uncertainties determined by the substitution method [15].…”

“…[65][66][67][68]]. An additional validation can be performed by comparing reconstructed datasets [62,63]. The simulation model is then adapted to reduce any discrepancies between the two datasets.…”

“…Segmenting artifact-laden data will result in the generation of false surfaces and thus presents a fundamental dilemma to the question of traceability. In fact, incomplete modelling and characterization of artifact-inducing physical phenomena in the simulations is believed to be the reason for discrepancies between numerically and experimentally determined uncertainties [62,63]. Currently, numerical uncertainty determination only holds for simple measurement tasks, i.e.…”