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Determination of pressure balance distortion coefficient andzero-pressure effective area uncertainties

Published online by Cambridge University Press:  10 January 2012

V. Ramnath
V. Ramnath*
Affiliation:
Pressure & Vacuum Laboratory, National Metrology Institute of South Africa, Private Bag X34, Lynnwood Ridge, 0040 Pretoria, South Africa
*
⋆Correspondence: vramnath@nmisa.org
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Abstract

The behaviour of piston-cylinder operated pressure balances is characterized by thedistortion coefficient λ and zero-pressure effective areaA0 which model the variation of a pressure balance’s area interms of the applied pressure. This paper determines the uncertainties inλ and A0 when utilizing the method ofcross-floating with another pressure balance standard whose parameters and associateduncertainties are known. A limitation that is frequently encountered in many attempts ofthe uncertainty analysis for a pressure balance is that no readily accessible uncertaintyquantification framework for the distortion coefficient is present. As a result theuncertainty in a pressure balance’s area at elevated applied pressures is typicallyunderestimated in the absence of this uncertainty information. We firstly review theuncertainty formulation for a pressure balance generated pressure involving correlationeffects in terms of an implicit multivariate matrix equation approach and then utilizingthe resulting solution present the methodology to consistently perform the uncertaintyanalysis for λ and A0.

Keywords

Pressure balanceeffective areadistortion coefficientuncertainty analysisparameter estimation
Type
Research Article
Information
International Journal of Metrology and Quality Engineering , Volume 2 , Issue 2 , 2011 , pp. 101 - 119
Copyright
© EDP Sciences 2012

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References

Sutton, C.M., Fitzgerald, M.P., Giardini, W., A Method of analysis for cross-floats between pressure balances, Metrologia 42, S212–S215 (2005) CrossRefGoogle Scholar
B. Blagojevic, I. Bajsic, Determination of the Effective Area of a Gas-Pressure Balance for Low Pressures, in XVII IMEKO World Congress, edited by K. Havrilla (2003)
R.S. Dadson, S.L. Lewis, G.N. Peggs, The Pressure Balance: Theory and Practice (HMSO, London, 1982)
Forbes, A.B., Harris, P.M., Estimation algorithms in the calculation of effective area of pressure balances, Metrologia 36, 689–692 (1999) CrossRefGoogle Scholar
J.W. Wilkinson, Exact Expressions for the Covariances Between Products of Randoms Variables, Technical report ORNL-TM-1977, Oak Ridge National Laboratory, Atomic Energy Commission, USA, 1967
BIPM, IEC, IFCC, ISO, IUPAC, OIML, Guide to the Expression of Uncertainty in Measurement, 2nd edn., BIPM (1995), ISBN 92-67-10188-9
Efron, B., Gong, G., A Leisurely look at the bootstrap, the Jackknife, and cross-validation, Am. Stat. 37, 36–48 (1983) Google Scholar
W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd edn. (Cambridge University Press, 2007)
Cox, M.G., Siebert, B.R.L., The use of a Monte Carlo method for evaluating uncertainty and expanded uncertainty, Metrologia 43, S178–S188 (2006) CrossRefGoogle Scholar
Ramnath, V., Comparison of the GUM and Monte Carlo measurement uncertainty techniques with application to effective area determination in pressure standards, Int. J. Metrol. Qual. Eng. 1, 51–57 (2010) CrossRefGoogle Scholar
D. Zvizdic, L.G. Bermanec, G. Bonnier, E. Renaot, Uncertainty Budget of Pressure Balance Effective Area Determined by Comparison Method, in XVII IMEKO World Congress (2003)
Picard, A., Davis, R.S., Glaser, M., Fujii, K., Revised formula for the density of moist air (CIPM-2007), Metrologia 45, 149–155 (2007) CrossRefGoogle Scholar
E.C. Morris, K.M.K. Fen, The Calibration of Weights and Balances, Monograph 4: NML Technology Transfer Series, 3rd edn. (CSIRO National Measurement Laboratory, 2003)
D. Tabor, Gases, Liquids and Solids, 2nd edn. (Cambridge University Press, 1985)
P.J. Mohr, B.N. Taylor, D.B. Newell, CODATA recommended values of the fundamental physical constants: 2006, Rev. Mod. Phys. 80 (2008)
I. Kocas, Technical Protocol of EURAMET.M.P-K13 (500 MPa), Technical report, TUBITAK UME, 2009
M.G. Cox, P.M. Harris, Software Support for Metrology Best Practice Guide No. 6 – Uncertainty Evaluation, Technical report, NPL, UK, 2004
B.R.L. Siebert, P. Ciarlini, D. Sibold, Monte Carlo Study on Logical and Statistical Correlation, in VII IMEKO World Congress, edited by P. Ciarlini, E. Filipe, A.B. Forbes, F. Pavese, C. Perruchet, B.R.L. Siebert (2005)
Krystek, M., Anton, M., A least-squares algorithm for fitting data points with mutually correlated coordinates to a straight line, Meas. Sci. Technol. 22, 1–9 (2011) CrossRefGoogle Scholar
P. Penfield, Principle of Maximum Entropy, in Information, Entropy and Computation (2010), www.mit.edu, http://www.mtl.mit.edu/Courses/6.050/2010/notes/chapter9.pdf
S. Lewis, G. Peggs, The Pressure Balance: A Practical Guide to its Use, 2nd edn. (HMSO, London, 1992), ISBN 0114800618
W. Schelter, Maxima – A Computer Algebra System (Version 5.23.2) (Free Software Foundation, 2011), http://maxima.sourceforge.net/
J.W. Eaton, GNU Octave Manual, Network Theory Limited (2002), ISBN 0-9541617-2-6, www.gnu.org/software/octave
J.E. Shigley, C.R. Mischke, Mechanical Engineering Design, 6th edn. (Metric Edition, McGraw-Hill, 2003)
Dogra, S., Yadav, S., Bandyopadhyay, A.K., Computer simulation of a 1.0 GPa piston-cylinder assembly using finite element analysis (FEA), Measurement 43, 1345–1354 (2010) CrossRefGoogle Scholar
Bandyopadhyay, A.K., Olson, D.A., Characterization of a compact 200 MPa controlled clearance piston gauge as a primary pressure standard using the heydemann and welch method, Metrologia 43, 573–582 (2006) CrossRefGoogle Scholar
P.L.M. Heydemann, B.E. Welch, Piston Gauges, in Experimental Thermodynamics, Experimental Thermodynamics of Non-Reacting Fluids, edited by B. Le Neindre, B. Vodar (Butterworth and Co., 1975), Chap. 4, pp. 147–202
F.M. White, Viscous Fluid Flow, 2nd edn. (McGraw-Hill, 1991)
JCGM/WG1, Evaluation of Measurement Data – Supplement 1 to the Guide to the Expression of Uncertainty in Measurement – Propagation of Distributions using a Monte Carlo Method, 1st edn., Joint Committee for Guides in Metrology (2007)
Elster, C., Toman, B., Bayesian uncertainty analysis for a regression model versus application of GUM supplement 1 to the least-squares estimate, Metrologia 48, 233–240 (2011) CrossRefGoogle Scholar
A.B. Forbes, Nonlinear Least Squares and Baysesian Inference, in Advanced Mathematical and Computational Tools in Metrology and Testing, edited by F. Pavese, M. Bar, A.B. Forbes, J.M. Linares, C. Perruchet, N.F. Zhang (World Scientific Publishing Company, 2009), pp. 104–112
M.G. Cox, P.M. Harris, Software Specifications for Uncertainty Evaluation, Technical report, NPL, UK, 2006
W. Bich, Uncertainty Evaluation by Means of a Monte Carlo Approach, in BIPM Workshop 2 on CCRI (II) Activity Uncertainties and Comparisons (2008), www.bipm.org, http://www.bipm.org/wg/CCRI–%"28II–%"29/WORKSHOP–%"28II–%"29/Allowed/2/Bich.pdf
R.L. Burden, J.D. Faires, Numerical Analysis (Brooks/Cole, 2001), ISBN 0-534-38216-9
Krystek, M., Anton, M., A weighted total least-squares algorithm for fitting a straight line, Meas. Sci. Technol. 18, 3438–3442 (2007) CrossRefGoogle Scholar
M. Krystek, M. Anton, Weighted total least squares for mutually correlated coordinates (2011), www.mathworks.com