Evaluation of measurement uncertainty is considered when the value of the measurand depends on the continuous variable time. A concept of dynamic measurement uncertainty is introduced by generalizing the GUM approach. The concept is applied to linear and time-invariant systems which are often appropriate to model dynamic measurements. Digital filtering is proposed for estimating the time-dependent value of the measurand and the design of an appropriate FIR filter is described. Dynamic uncertainty evaluation is then carried out for this analysis and conditions are specified for its proper use. The approach is illustrated for the particular example of a second-order model. It is shown in terms of simulations that the proposed analysis yields significantly improved results when compared with the sometimes applied quasi-static treatment.

https://iopscience.iop.org/article/10.1088/0026-1394/45/4/013/pdf

Uncertainty evaluation for dynamic measurements modelled by a linear time-invariant system

This paper reviews and analyzes studies concerning measurement uncertainty, examining 114 papers published between 2004 and 2010 in the following international journals: IEEE Transactions on Instrumentation and Measurement, Measurement, Flow Measurement and Instrumentation, and Precision Engineering. The papers were classified according to six different approaches identified during the research and six different methods of calculating uncertainty used by the authors of the researched articles. This paper provides a short summary of the state of the art of measurement uncertainty, analyzes the research scenario on the theme, and, finally, brings suggestions on future work based on the analysis.

Measurement Uncertainty: Literature Review and Research Trends

This paper focuses on the mathematical modelling required to support the development of new primary standard systems for traceable calibration of dynamic pressure sensors. We address two fundamentally different approaches to realizing primary standards, specifically the shock tube method and the drop-weight method. Focusing on the shock tube method, the paper presents first results of system identification and discusses future experimental work that is required to improve the mathematical and statistical models. We use simulations to identify differences between the shock tube and drop-weight methods, to investigate sources of uncertainty in the system identification process and to assist experimentalists in designing the required measuring systems. We demonstrate the identification method on experimental results and draw conclusions.

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Mathematical modelling to support traceable dynamic calibration of pressure sensors

Nine european national metrology institutes (NMIs) are collaborating in a new project funded by the european metrology research programme (EMRP) to establish traceable dynamic measurement of the mechanical quantities force, pressure, and torque. The aim of this joint research project (JRP) is to develop appropriate calibration methods, mathematical models, and uncertainty evaluation. The duration of the project is 3 years for a global amount of €3.6 million. It began in September 2011.

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Traceable dynamic measurement of mechanical quantities: objectives and first results of this european project

The task of analysing dynamic measurements is considered for the case that the input–output behaviour of the employed sensor can be described in terms of a second-order dynamic model. It is assumed that estimates of the parameters of this model are available which have been determined by the analysis of previous dynamic calibration measurements. The goal is to estimate the unknown input of the sensor given its discrete-time output signal. It is proposed to apply an FIR filter which is constructed according to the underlying dynamic model. The uncertainties associated with the obtained estimates of the time-dependent measurand are then determined by taking into account the uncertainty associated with the estimates of the parameters of the dynamic model, the uncertainty of the sensor's output signal and the applied signal processing steps. The proposed procedure allows real-time calculations including the real-time calculation of uncertainties, and it could therefore be directly integrated into the measurement chain. Utilizing dynamic calibration measurements of accelerometers, the proposed analysis is demonstrated by its application to acceleration measurements upon shock excitations.

https://iopscience.iop.org/article/10.1088/0957-0233/18/12/002/pdf

Analysis of dynamic measurements and determination of time-dependent measurement uncertainty using a second-order model

Modelling accelerometers for transient signals using calibration measurements upon sinusoidal excitation

A novel approach is proposed for the analysis of shock calibration measurements of accelerometers. The input/output behaviour of an accelerometer is represented by a physical model in terms of a second-order differential equation. The unknown model parameters, i.e. the coefficients of the differential equation, are estimated by a frequency domain least-squares approach. The derived model is then used to determine the frequency response of the accelerometer. The method was applied to calibration measurements upon shock excitations of two back-to-back accelerometers (ENDEVCO type 2270 and Bruel & Kjaer type 8305). The determined frequency response was then compared to additional calibration measurements upon sinusoidal excitation. The sinusoidal excitation measurements were analysed by means of the established sine approximation method. Consistent results were obtained by the two methods which confirm the validity of the proposed modelling approach.

https://iopscience.iop.org/article/10.1088/0957-0233/17/7/030/pdf

Calibration of accelerometers: determination of amplitude and phase response upon shock excitation

From oscillation to impact: the design of a new force calibration device at PTB

The primary calibration of pressure transducers is at present realized by static methods. This paper describes a new route to gaining traceability for dynamic calibration using the acousto-optic effect. The pressure range under consideration is up to 100 MPa. We set out a description of the general principle employed to gain traceability, the experimental set-ups that are used for the realization and the thermophysical background of the measurements, and some numerical estimates on the expected results for two different pressure-transmitting media are shown.

http://iopscience.iop.org/article/10.1088/0026-1394/50/6/580/pdf

Th Bruns

Papers

Analysis of dynamic measurements and determination of time-dependent measurement uncertainty using a second-order model

Modelling accelerometers for transient signals using calibration measurements upon sinusoidal excitation

Calibration of accelerometers: determination of amplitude and phase response upon shock excitation

From oscillation to impact: the design of a new force calibration device at PTB

Linking dynamic to static pressure by laser interferometry