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Mathematical Modelling and Data Analysis

Department 8.4

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Title: On challenges in the uncertainty evaluation for time-dependent measurements
Author(s): S. Eichstädt, V. Wilkens, A. Dienstfrey, P. Hale, B. Hughes and C. Jarvis
Journal: Metrologia
Year: 2016
Volume: 53
Issue: 4
DOI: 10.1088/0026-1394/53/4/S125
Keywords: dynamic measurement, dynamic uncertainty, deconvolution
Tags: 8.42, Dynamik
Abstract: The measurement of quantities with time-dependent values is a common task in many areas of metrology. Although well established techniques are available for the analysis of such measurements, serious scientific challenges remain to be solved to enable their routine use in metrology. In this paper we focus on the challenge of estimating a time-dependent measurand when the relationship between the value of the measurand and the indication is modeled by a convolution. Mathematically, deconvolution is an ill-posed inverse problem, requiring regularization to stabilize the inversion in the presence of noise. We present and discuss deconvolution in three practical applications: thrust-balance, ultra-fast sampling oscilloscopes and hydrophones. Each case study takes a different approach to modeling the convolution process and regularizing its inversion. Critically, all three examples lack the assignment of an uncertainty to the influence of the regularization on the estimation accuracy. This is a grand challenge for dynamic metrology, for which to date no generic solution exists. The case studies presented here cover a wide range of time scales and prior knowledge about the measurand, and they can thus serve as starting points for future developments in metrology. The aim of this work is to present the case studies and demonstrate the challenges they pose for metrology.

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