This file was created by the TYPO3 extension bib --- Timezone: CEST Creation date: 2024-04-24 Creation time: 05-01-03 --- Number of references 42 article EichstadtW2017 J. Acoust. Soc. Am. 2017 6 6 141 6 4155--4167 8.4,8.42,Unsicherheit,Dynamik 10.1121/1.4983827 SEichstädt VWilkens article KobuschE2017 Acta IMEKO 2017 4 1 6 1 3--12 Abstract: Investigations of the model-based dynamic calibration of a small strain gauge force transducer of high bandwidth revealed new challenges for parameter identification. This paper discusses a more generalized mechanical model of the calibration set-up employed taking account of the transducer’s connection to its mechanical environment at both ends. Based on new experimental sine and shock force data, the improved model is studied and its parameters are identified. It is shown that the proposed model is capable of linking the calibration results of both calibration methods to a much better degree. This paper is an extended version of the original contribution to the IMEKO 2015 conference in Prague, Czech Republic. dynamic modelling, parameter identification, sine force calibration, shock force calibration 8.4,8.42,Dynamik 10.21014/acta_imeko.v6i1.433 MKobusch SEichstädt article EichstadtESE2017 J. Sens. Sens. Syst. 2017 2 14 6 97-105 8.4,8.42,Unsicherheit,Dynamik 10.5194/jsss-6-97-2017 SEichstädt CElster I MSmith T JEsward article Eichstaedt2016d Measurement Science and Technology 2016 10 20 27 12 125009 The Kalman filter is an established tool for the analysis of dynamic systems with normally distributed noise, and it has been successfully applied in numerous areas. It provides sequentially calculated estimates of the system states along with a corresponding covariance matrix. For nonlinear systems, the extended Kalman filter is often used. This is derived from the Kalman filter by linearization around the current estimate. A key issue in metrology is the evaluation of the uncertainty associated with the Kalman filter state estimates. The “Guide to the Expression of Uncertainty in Measurement” (GUM) and its supplements serve as the de facto standard for uncertainty evaluation in metrology. We explore the relationship between the covariance matrix produced by the Kalman filter and a GUM-compliant uncertainty analysis. In addition, the results of a Bayesian analysis are considered. For the case of linear systems with known system matrices, we show that all three approaches are compatible. When the system matrices are not precisely known, however, or when the system is nonlinear, this equivalence breaks down and different results can then be reached. For precisely known nonlinear systems, though, the result of the extended Kalman filter still corresponds to the linearized uncertainty propagation of the GUM. The extended Kalman filter can suffer from linearization and convergence errors. These disadvantages can be avoided to some extent by applying Monte Carlo procedures, and we propose such a method which is GUM-compliant and can also be applied online during the estimation. We illustrate all procedures in terms of a two-dimensional dynamic system and compare the results with those obtained by particle filtering, which has been proposed for the approximate calculation of a Bayesian solution. Finally, we give some recommendations based on our findings. Kalman filter, uncertainty, dynamic measurement, state-space system, state estimation 8.4, 8.42, Dynamik 10.1088/0957-0233/27/12/125009 SEichstädt NMakarava CElster article DierlEFKEE2016 Journal of the Optical Society of America A 2016 6 23 33 7 1370--1376 dynamic measurement, dynamic uncertainty, deconvolution 8.42, Dynamik, Regression 10.1364/JOSAA.33.001370 MDierl TEckhard BFrei MKlammer SEichstädt CElster article Eichstaedt2016c Metrologia 2016 6 53 4 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. dynamic measurement, dynamic uncertainty, deconvolution 8.42, Dynamik 10.1088/0026-1394/53/4/S125 SEichstädt VWilkens ADienstfrey PHale BHughes CJarvis article e73c330da32016 Measurement Science and Technology 2016 3 22 27 5 055001 The Fourier transform and its counterpart for discrete time signals, the discrete Fourier transform (DFT), are common tools in measurement science and application. Although almost every scientific software package offers ready-to-use implementations of the DFT, the propagation of uncertainties in line with the guide to the expression of uncertainty in measurement (GUM) is typically neglected. This is of particular importance in dynamic metrology, when input estimation is carried out by deconvolution in the frequency domain. To this end, we present the new open-source software tool GUM2DFT , which utilizes closed formulas for the efficient propagation of uncertainties for the application of the DFT, inverse DFT and input estimation in the frequency domain. It handles different frequency domain representations, accounts for autocorrelation and takes advantage of the symmetry inherent in the DFT result for real-valued time domain signals. All tools are presented in terms of examples which form part of the software package. GUM2DFT will foster GUM-compliant evaluation of uncertainty in a DFT-based analysis and enable metrologists to include uncertainty evaluations in their routine work. dynamic measurements; deconvolution; discrete Fourier transform; uncertainty; 8.42, Dynamik 10.1088/0957-0233/27/5/055001 SEichstädt VWilkens article Eichstadt2016 tm - Technisches Messen 2016 1 6 83 2 66-70 Dynamische Messungen spielen eine zunehmend wichtigere Rolle in der metrologischen und industriellen Praxis. Zugleich stellt die Analyse dynamischer Messungen unter Berücksichtigung metrologischer Gesichtspunkte neue Herausforderungen an die mathematische und statistische Modellierung. Dieser Artikel stellt eine Reihe aktueller Modellierungskonzepte zu den einzelnen Aspekten der Messkette einer dynamischen Messungen vor. Es werden Vor- und Nachteile der Modellierungskonzepte diskutiert und Zielstellungen für zukünftige Forschungsarbeiten herausgestellt. 8.42, Dynamik http://www.degruyter.com/view/j/teme.2016.83.issue-2/teme-2015-0098/teme-2015-0098.xml?format=INT 0171-8096 10.1515/teme-2015-0098 SEichstädt CElster article Kobusch2015 ACTA IMEKO 2015 1 5 4 2 45-51 Within the scope of the joint research project EMRP IND09 “Traceable dynamic measurements of mechanical quantities”, numerous measurements were performed at PTB’s 20 kN primary shock force calibration device to investigate and validate the approach of a model-based dynamic calibration of force transducers by using shock excitations. The tests included several strain gauge force transducers of greatly differing structural design, size, weight and mechanical coupling. By looking at a few examples, some investigated physical models of the measurement set-up and a developed data analysis procedure for parameter identification based on measured shock data are presented and discussed. The models reproduce the dynamic response including the observed modal oscillations of various origins that limit the usable measurement bandwidth. Moreover, these modal oscillations may have an important role for the parameter identification process, which is further discussed. This paper is an extended version of the original contribution to the IMEKO 2014 conference in Cape Town, South Africa. Open Access model-based dynamic calibration, dynamic calibration, dynamic modelling,editor,force transducers, imeko 8.42, Dynamik fileadmin/internet/fachabteilungen/abteilung_8/8.4_mathematische_modellierung/Publikationen_8.4/ACTA_IMEKO_2014_Kobusch_et_al_preprint.pdf http://acta.imeko.org/index.php/acta-imeko/article/view/IMEKO-ACTA-04%20%282015%29-02-08/384 MKobusch SEichstädt LKlaus TBruns article Klaus2014a ACTA IMEKO 2015 1 4 3 1 1-6 For the dynamic calibration of torque transducers, a model of the unmounted transducer and an extended model of the mounted transducer including the measuring device have been developed. The dynamic behaviour of a torque transducer under test will be described by its model parameters. This paper presents the models comprising the known parameters of the measuring device andthe unknown parameters of the transducer and how the calibration measurements are going to be carried out. The principle for the identification of the transducer’s model parameters from measurement data is described using a least squares approach. The influence of a variation of the transducer’s parameters on the frequency response of the expanded model is analysed. Open Access mechanical model,model parameter identification 8.42, Dynamik http://acta.imeko.org/index.php/acta-imeko/article/view/IMEKO-ACTA-04%20%282015%29-02-07/385 LKlaus BArendacká MKobusch TBruns article Matthews2014e Metrologia 2014 51 3 326-338 dynamic measurement, pressure, parametric model 8.42, Dynamik, Regression fileadmin/internet/fachabteilungen/abteilung_8/8.4_mathematische_modellierung/Publikationen_8.4/Mathematical_Modelling_Dynamic_Pressure_preprint.pdf http://iopscience.iop.org/article/10.1088/0026-1394/51/3/326 IOP Publishing en doi:10.1088/0026-1394/51/3/326 0026-1394 10.1088/0026-1394/51/3/326 CMatthews FPennecchi SEichstädt AMalengo TEsward I MSmith CElster AKnott FArrhén ALakka article Eichstaedt2014 EPJ Web of Conferences 2014 77 3 One of the main challenges in the analysis of dynamic measurements is the estimation of the time-dependent value of the measurand and the corresponding propagation of uncertainties. In this paper we outline the design of appropriate digital compensation filters as a means of estimating the quantity of interest. For the propagation of uncertainty in the application of such digital filters we present online formulae for finite impulse response and infinite impulse response filters. We also demonstrate a recently developed efficient Monte Carlo method for uncertainty propagation in dynamic measurements which allows calculating point-wise coverage intervals in real-time. 8.42, Dynamik fileadmin/internet/fachabteilungen/abteilung_8/8.4_mathematische_modellierung/Publikationen_8.4/epjconf_icm2014_00003.pdf EPJ Web of Conferences 10.1051/epjconf/20147700003 SEichstädt BArendacká ALink CElster article Eichstadt2014a Journal of Physics: Conference Series 2014 490 1 012230 Regression, ODE, parameter identification, dynamic calibration, modelling 8.42,Dynamik, Regression http://iopscience.iop.org/article/10.1088/1742-6596/490/1/012230 IOP Publishing en 1742-6596 10.1088/1742-6596/490/1/012230 SEichstädt CElster article Arendacka2014a Measurement Science Review 2014 14 2 52-61 In Annex H.5, the Guide to the Evaluation of Uncertainty in Measurement (GUM) [1] recognizes the necessity to analyze certain types of experiments by applying random effects ANOVA models. These belong to the more general family of linear mixed models that we focus on in the current paper. Extending the short introduction provided by the GUM, our aim is to show that the more general, linear mixed models cover a wider range of situations occurring in practice and can be beneficial when employed in data analysis of long-term repeated experiments. Namely, we point out their potential as an aid in establishing an uncertainty budget and as means for gaining more insight into the measurement process. We also comment on computational issues and to make the explanations less abstract, we illustrate all the concepts with the help of a measurement campaign conducted in order to challenge the uncertainty budget in calibration of accelerometers. dynamic measurement, acceleration, dynamic calibration, mixed model, design of experiment 8.42, Dynamik, Unsicherheit fileadmin/internet/fachabteilungen/abteilung_8/8.4_mathematische_modellierung/Publikationen_8.4/epjconf_icm2014_00003.pdf http://www.degruyter.com/view/j/msr.2014.14.issue-2/msr-2014-0009/msr-2014-0009.xml 1335-8871 10.2478/msr-2014-0009 BArendacká ATäubner SEichstädt TBruns CElster article Eichstadt2013a Metrologia 2013 50 2 107-118 Bandpass correction in spectrometer measurements using monochromators is often necessaryin order to obtain accurate measurement results. The classical approach of spectrometer bandpass correction is based on local polynomial approximations and the use of finite differences. Here we compare this approach with an extension of the Richardson–Lucy method, which is well known in image processing, but has not been applied to spectrum bandpass correction yet. Using an extensive simulation study and a practical example, we demonstrate the potential of the Richardson–Lucy method. In contrast to the classical approach, it is robust w.r.t. wavelength step size and measurement noise. In almost all cases the Richardson–Lucy method turns out to be superior to the classical approach both in terms of spectrum estimate and its associated uncertainties. dynamic measurement, bandwidth correction, spectral estimation, deconvolution 8.42, Dynamik fileadmin/internet/fachabteilungen/abteilung_8/8.4_mathematische_modellierung/Publikationen_8.4/Eichstaedt_bandwidth_correction.pdf http://iopscience.iop.org/article/10.1088/0026-1394/50/2/107 IOP Publishing en 10.1088/0026-1394/50/2/107 SEichstädt FSchmähling GWübbeler KAnhalt LBünger UKrüger CElster article Eichstaedt2012a Metrologia 2012 49 3 401 Measurement of quantities having time-dependent values such as force, acceleration or pressure is a topic of growing importance in metrology. The application of the Guide to the Expression of Uncertainty in Measurement (GUM) and its Supplements to the evaluation of uncertainty for such quantities is challenging. We address the efficient implementation of the Monte Carlo method described in GUM Supplements 1 and 2 for this task. The starting point is a time-domain observation equation. The steps of deriving a corresponding measurement model, the assignment of probability distributions to the input quantities in the model, and the propagation of the distributions through the model are all considered. A direct implementation of a Monte Carlo method can be intractable on many computers since the storage requirement of the method can be large compared with the available computer memory. Two memory-efficient alternatives to the direct implementation are proposed. One approach is based on applying updating formulae for calculating means, variances and point-wise histograms. The second approach is based on evaluating the measurement model sequentially in time. A simulated example is used to compare the performance of the direct and alternative procedures. 8.42, Dynamik, Unsicherheit 10.1088/0026-1394/49/3/401 SEichstädt ALink P MHarris CElster article Bruns2012 Metrologia 2012 49 1 27--31 dynamic calibration, accelerometer, dynamic measurement 8.42, Dynamik http://iopscience.iop.org/article/10.1088/0026-1394/49/1/005 IOP Publishing en 0026-1394 10.1088/0026-1394/49/1/005 TBruns ALink ATäubner article Fuser2012 Measurement Science and Technology 2012 23 2 025201 We have performed an optoelectronic measurement of the impulse response of an ultrafast sampling oscilloscope with a nominal bandwidth of 100 GHz within a time window of approximately 100 ps. Our experimental technique also considers frequency components above the cut-off frequency of higher-order modes of the 1.0 mm coaxial line, which is shown to be important for the specification of the impulse response of ultrafast sampling oscilloscopes. Additionally, we have measured the reflection coefficient of the sampling head induced by the mismatch of the sampling circuit and the coaxial connector which is larger than 0.5 for certain frequencies. The uncertainty analysis has been done using the Monte Carlo method of Supplement 1 to the ‘Guide to the Expression of Uncertainty in Measurement’ and correlations in the estimated impulse response have been determined. Our measurements extend previous work which deals with the characterization of 70 GHz oscilloscopes and the measurement of 100 GHz oscilloscopes up to the cut-off frequency of higher-order modes. dynamic measurement, oscilloscope, dynamic calibration, impulse response 8.42,Dynamik fileadmin/internet/fachabteilungen/abteilung_8/8.4_mathematische_modellierung/Publikationen_8.4/Fueser_Osci_preprint.pdf http://iopscience.iop.org/article/10.1088/0957-0233/23/2/025201 IOP Publishing en 0957-0233 10.1088/0957-0233/23/2/025201 HFüser SEichstädt KBaaske CElster KKuhlmann RJudaschke KPierz MBieler inbook Eichstaedt2012e 2012 Advanced Mathematical & Computational Tools in Metrology and Testing IX  126-135 dynamic measurement, continuous function, stochastic process, uncertainty 8.42, Dynamik, Unsicherheit F. Pavese, M. Bär, J.-R. Filtz, A. B. Forbes, L. Pendrill, K. Shirono World Scientific New Jersey Series on Advances in Mathematics for Applied Sciences 84 16 SEichstädt CElster inbook Esward2012 2012 Advanced Mathematical & Computational Tools in Metrology and Testing IX   143-151 dynamic pressure, calibration, dynamic measurement 8.42, Dynamik, Unsicherheit F. Pavese, M. Bär, J.-R. Filtz, A. B. Forbes, L. Pendrill, K. Shirono World Scientific New Jersey Series on Advances in Mathematics for Applied Sciences 84 19 T JEsward CMatthews SDownes AKnott SEichstädt CElster phdthesis Eichstaedt_Thesis 2012 Metrology is concerned with the establishment of measurement units and the transfer of measurement standards to industry. International comparability of measurement results requires internationally agreed guidelines for specific measurement tasks and a standardised treatment of measurement uncertain- ties. To this end, the Guide to the Expression of Uncertainty in Measurement (GUM) provides the framework for the evaluation and interpretation of mea- surement uncertainty in metrology. However, it does not address dynamic measurements, which are of growing importance for industry and metrology. Typical examples of dynamic measurements are in-cylinder measurements in the automotive industry (pressure), crash tests (e.g., acceleration and force) or assembly line measurements (e.g., torque and force). A reliable calibra- tion of the measurement systems employed, which can be related to national standards, requires a consistent evaluation of measurement uncertainty for dynamic measurements.The goal of this thesis is to develop a framework for the evaluation of uncer- tainty in dynamic measurements in metrology that are closely related to the treatment of static measurements. The measurement systems considered are those that can be modelled by a linear and time-invariant (LTI) system since such models cover a wide range of metrological applications. The measured values are the values of the system output signal, whereas the values of the quantity of interest serve as the system input signal. Estimation of the in- put signal is considered to be carried out by means of digital filtering in the discrete time domain from which inference of the continuous-time signal is sought.This requires the design of digital filters, an uncertainty evaluation for regu- larised deconvolution and a framework for the definition and propagation of the uncertainty of a continuous function. The design of digital filters for de- convolution is well-established in the signal processing literature. The same holds true for the propagation of variances through LTI systems. However, propagation of variances through uncertain LTI systems for evaluation of uncertainty in the sense of GUM has only recently been considered. The methods developed so far focus on the evaluation of uncertainties and do not address regularisation errors. Moreover, the relation of the discrete-time es- timate to the actual continuous-time measurand has not yet been addressed.We extend the available results for the evaluation of uncertainties to the propagation of associated probability density functions and propose efficient calculation schemes. Moreover, the ill-posed deconvolution problem requires regularisation. We develop a reliable quantitative evaluation of the uncer- tainty contribution due to regularisation assuming a particular type of prior knowledge. We present a framework for the evaluation of uncertainty for con- tinuous measurements, which addresses the definition, assignment and prop- agation of uncertainty. Finally, we develop a technique for the calculation of uncertainty associated with a continuous-time estimate of the measurand from a discrete-time estimate.The proposed techniques provide a complete framework for the consistent and reliable evaluation of uncertainty in the analysis of a dynamic measurement. dynamic measurement, dynamic uncertainty, digital filter, deconvolution 8.42, Dynamik fileadmin/internet/fachabteilungen/abteilung_8/8.4_mathematische_modellierung/Publikationen_8.4/842_Dynamik_Diss_Eichstaedt.pdf

Berlin

TU Berlin PhD Thesis SEichstädt article Eichstadt2010i Sensors 2010 10 8 7621-31 The compensation of LTI systems and the evaluation of the according uncertainty is of growing interest in metrology. Uncertainty evaluation in metrology ought to follow specific guidelines, and recently two corresponding uncertainty evaluation schemes have been proposed for FIR and IIR filtering. We employ these schemes to compare an FIR and an IIR approach for compensating a second-order LTI system which has relevance in metrology. Our results suggest that the FIR approach is superior in the sense that it yields significantly smaller uncertainties when real-time evaluation of uncertainties is desired. dynamic model, digital filter, deconvolution, dynamic measurement 8.42, Dynamik http://www.mdpi.com/1424-8220/10/8/7621/htm Molecular Diversity Preservation International en 10.3390/s100807621 SEichstädt ALink CElster article Eichstadt2010k Measurement 2010 43 5 708-713 The output signal of an accelerometer typically contains dynamic errors when a broadband acceleration is applied. In order to determine the applied acceleration, post-processing of the accelerometer’s output signal is required. To this end, we propose the application of a digital FIR filter. We evaluate the uncertainty associated with the filtered output signal and give explicit formulae which allow for on-line calculation. In this way, estimation of the applied acceleration and the calculation of associated uncertainties may be carried out during the measurement. The resulting uncertainties can strongly depend on the design of the applied filter and we describe a simple method to construct an uncertainty-optimal filter. The benefit of the proposed procedures is illustrated by means of simulated measurements. Accelerometer,Digital filter,Dynamic measurements,Dynamik,Uncertainty 8.42, Dynamik, Unsicherheit http://www.sciencedirect.com/science/article/pii/S0263224110000023 10.1016/j.measurement.2009.12.028 SEichstädt ALink TBruns CElster article Eichstadt2010j Metrologia 2010 47 5 522-533 deconvolution, digital filter, dynamic measurement 8.42, Dynamik IOP Publishing en 10.1088/0026-1394/47/5/003 SEichstädt CElster T JEsward J PHessling article Link2009b Measurement Science and Technology 2009 20 5 055104 dynamic measurement, digital filter, deconvolution, dynamic uncertainty 8.42,Dynamik, Unsicherheit IOP Publishing 10.1088/0957-0233/20/5/055104 ALink CElster inbook Wuebbeler2009 2009 Advanced Mathematical & Computational Tools in Metrology VIII 369-374 dynamic measurement, frequency response, dynamic calibration 8.42, Dynamik, Unsicherheit F. Pavese, M. Bär, J.M. Limares, C. Perruchet, N.F. Zhang World Scientific New Jersey Series on Advances in Mathematics for Applied Sciences 78 52 GWübbeler ALink TBruns CElster inbook Elster2009m 2009 Advanced Mathematical & Computational Tools in Metrology VIII 80-89 8.42, Dynamik, Unsicherheit F. Pavese, M. Bär, J.M. Limares, C. Perruchet, N.F. Zhang World Scientific New Jersey Series on Advances in Mathematics for Applied Sciences 78 13 CElster ALink article Elster2008c Metrologia 2008 45 4 464-473 dynamic measurement, digital filter, deconvolution, dynamic uncertainty 8.42,Dynamik, Unsicherheit IOP Publishing 10.1088/0026-1394/45/4/013 CElster ALink article Link2007b Measurement 2007 40 9-10 928-935 A recently proposed accelerometer model is applied for determining the accelerometer's output to transient accelerations. The model consists of a linear, second-order differential equation with unknown coefficients. It is proposed to estimate these model parameters from sinusoidal calibration measurements, and an estimation procedure based on linear least-squares is presented. In addition, the uncertainties associated with the estimated parameters are determined utilizing a Monte Carlo simulation technique. The performance of the proposed modelling approach was tested by its application to calibration measurements of two back-to-back accelerometers (ENDEVCO type 2270 and Br<prt>ü</prt>el <prt>&amp;</prt> Kjær type 8305). For each of the two accelerometers, the model was first estimated from sinusoidal calibration measurements and then used to predict the accelerometer's behaviour for two shock calibration measurements. Measured and predicted shock sensitivities were found consistent with differences below 1<prt>%</prt> in most cases which confirms the benefit of the proposed modelling approach. IIR filter,Modelling,Shock excitation,Sinusoidal excitation,Uncertainty, dynamic measurement 8.42,Dynamik 10.1016/j.measurement.2006.10.011 ALink ATäubner WWabinski TBruns CElster article Elster2007b Measurement Science and Technology 2007 18 12 3682-3687 dynamic measurement 8.42,Dynamik, Unsicherheit IOP Publishing en 10.1088/0957-0233/18/12/002 CElster ALink TBruns article Martens2006 Metrologia 2006 43 1A 09002-09002 8.42,Dynamik,KC IOP Publishing 10.1088/0026-1394/43/1A/09002 H-Jvon Martens CElster ALink ATäubner TBruns article Link2006a Measurement Science and Technology 2006 17 7 1888-1894 8.42,Dynamik IOP Publishing en 10.1088/0957-0233/17/7/030 ALink ATäubner WWabinski TBruns CElster article Link2006 tm - Technisches Messen 2006 73 12 675-683 8.42,Dynamik 10.1524/teme.2006.73.12.675 ALink MKobusch TBruns CElster article VonMartens2005 Technisches Messen 2005 72 141-152 8.42,Dynamik 10.1524/teme.72.3.141.60281 H-Jvon Martens WWabinski ALink H-JSchlaak ATäubner UGöbel article Link2005 tm - Technisches Messen 2005 72 3-2005 153-160 8.42,Dynamik 10.1524/teme.72.3.153.60277 ALink WWabinski H-Jvon Martens article Link2004b Measurement 2004 35 1 191-199 8.42, Dynamik 10.1016/j.measurement.2003.08.007 ALink H-JMartens incollection Link2004a 2004 5503 580-587 8.42, Dynamik Proceedings of SPIE SPIE ALink WWabinski H-JMartens article Elster2000b Measurement Science and Technology 2000 11 9 1359 The evaluation of the uncertainty in measurement in the presence of combined random errors and errors due to the analogue-to-digital conversion of measuring signals is studied. The following situation is investigated. Analogue measuring signals of a measurand under study are obtained. The signals are assumed to contain random errors with a Gaussian distribution and they are converted into the digital form. Only the resulting digital signals are to be available. The Bayesian theory of measurement uncertainty is applied to the analysis. An estimator is assigned to the measurand and the distribution of this estimator is determined. This distribution can then be used to numerically calculate a best estimate of the measurand and its associated uncertainty. The application of this approach to some examples is presented and compared with results obtained by treating random and analogue-to-digital conversion errors additively and independently, which is frequently done. In some cases, remarkable differences are found which can justify the increased time and effort involved in the approach proposed. 8.42, Dynamik http://stacks.iop.org/0957-0233/11/i=9/a=315 10.1088/0957-0233/11/9/315 CElster article Martens2000 Measurement 2000 28 1 3-20 8.42, Dynamik 10.1016/S0263-2241(00)00003-8 H-Jvon Martens ATäubner WWabinski ALink H-JSchlaak article Gerhardt2000 tm - Technisches Messen 2000 6 1 274-282 8.42, Dynamik 10.1524/teme.2000.67.6.274 JGerhardt H-JSchlaak article Link2000a Shock. Vib. 2000 7 1 101-112 8.42, Dynamik 10.1155/2000/531718 ALink H-JMartens incollection Link2000b 2000 126-136 8.42, Dynamik Proceedings of SPIE SPIE 4072 ALink WWabinski APohl H-Jvon Martens