Abstract
This article describes the measurement uncertainty evaluation of the dew-point temperature when using a two-pressure humidity generator as a reference standard. The estimation of the dew-point temperature involves the solution of a non-linear equation for which iterative solution techniques, such as the Newton–Raphson method, are required. Previous studies have already been carried out using the GUM method and the Monte Carlo method but have not discussed the impact of the approximate numerical method used to provide the temperature estimation. One of the aims of this article is to take this approximation into account. Following the guidelines presented in the GUM Supplement 1, two alternative approaches can be developed: the forward measurement uncertainty propagation by the Monte Carlo method when using the Newton–Raphson numerical procedure; and the inverse measurement uncertainty propagation by Bayesian inference, based on prior available information regarding the usual dispersion of values obtained by the calibration process. The measurement uncertainties obtained using these two methods can be compared with previous results. Other relevant issues concerning this research are the broad application to measurements that require hygrometric conditions obtained from two-pressure humidity generators and, also, the ability to provide a solution that can be applied to similar iterative models. The research also studied the factors influencing both the use of the Monte Carlo method (such as the seed value and the convergence parameter) and the inverse uncertainty propagation using Bayesian inference (such as the pre-assigned tolerance, prior estimate, and standard deviation) in terms of their accuracy and adequacy.
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References
Guide to the Expression of Uncertainty in Measurement (GUM), 1st edn. (International Organization for Standardization, Genève, Switzerland, 1995)
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 (JCGM), 2008)
P. Huang, Determining uncertainties of relative humidity, dew/frost-point temperature and mixing ratio in a humidity standard generator, in Proceedings of the 3rd Symposium on Humidity & Moisture, Teddington, London, UK, 1998
Carpentier V., Megharfi M., Quint J., Priel M., Desenfant M., Morice R.: Metrologia 41, 432 (2004)
D. Soontag, The history of formulations and measurements of saturation water vapor, in Proceedings of the 3rd Symposium on Humidity & Moisture, Teddington, London, UK, 1998
Wexler A.: J. Res. Natl. Bur. Stand. (U.S.) 80, 775 (1976)
Greenspan L.: J. Res. Natl. Bur. Stand. (U.S.) 80, 41 (1976)
Press W., Flannery B., Teukolsky T., Vetterling W.: Numerical Recipes—The Art of Scientific Computing. Cambridge University Press, New York (1986)
J.A. Sousa, A.S. Ribeiro, The choice of method to the evaluation of measurement uncertainty in metrology, in Proceedings of the IMEKO XIX World Congress—Fundamental and Applied Metrology, Lisbon, Portugal, 2009
Matsumoto M., Nishimura T.: ACM T. Model. Comput. Simul. 8, 3 (1998)
Box G., Muller M.: Ann. Math. Stat. 29, 610 (1958)
Cox M., Dainton M., Harris P.: Software Specifications for Uncertainty Calculation and Associated Statistical Analysis, NPL Report CMSC 10/01. National Physical Laboratory, Teddington (2001)
A.B. Forbes, J.A. Sousa, The GUM, Bayesian inference and forward and inverse uncertainty evaluation, in Proceedings of the 2nd National Conference—Metrology and Inovation—of the Portuguese Metrology Society, Funchal, Madeira, Portugal, 2007
Boudjemaa R., Cox M.G., Forbes A.B., Harris P.M.: Automatic differentiation and its applications to metrology. In: Ciarlini, P., Cox, M.G., Pavese, F., Rossi, G.B. (eds) Advanced Mathematical and Computational Tools in Metrology VI, pp. 170–179. World Scientific, Singapore (2004)
Squire W., Trapp G.: SIAM Rev. 40, 110 (1998)
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Martins, L.L., Ribeiro, A.S., Alves e Sousa, J. et al. Measurement Uncertainty of Dew-Point Temperature in a Two-Pressure Humidity Generator. Int J Thermophys 33, 1568–1582 (2012). https://doi.org/10.1007/s10765-011-1005-z
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DOI: https://doi.org/10.1007/s10765-011-1005-z