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Analysis of dynamic measurements

Working Group 8.42


Dynamic measurements can be found in many areas of metrology and industry such as, for instance, in the measurement of time-dependent forces or accelerations. Methods from signal processing are often applied in the analysis of dynamic measurements. In many applications linear time-invariant systems are appropriate to model dynamic measurements, where the output signal is obtained as a convolution of the input signal and the measurement system’s impulse response. Input and output signal are not proportional to each other, and estimation of the system’s input signal from its output signal constitutes one important task in the analysis of dynamic measurements. Often digital filters are employed for this purpose. The evaluation of the uncertainty associated with the estimated input signal is particularly important from a metrological perspective.

Typical dynamic measurement with time-dependent errors in the output signal caused by the dynamic behavior of the measurement system.

Typical examples are measurements of mechanical quantities as, for example, force, torque and pressure. Further examples are oscilloscope measurements for the characterization of high speed electronics, hydrophone measurements for the characterization of medical ultrasound devices, the spectral characterization of radiation sources, spectral color measurements and camera-aided temperature measurements.



One focus of PTB‘s Working Group 8.42 is the development of methods for the estimation of the input signal from the output signal when the dynamic behavior of the measurement system has been characterized. This includes the development of procedures for the evaluation of the uncertainty associated with the estimated input signal. Another focus is the development of methods for the analysis of dynamic calibration measurements aimed at determining the dynamic behavior of a measurement system.



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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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