Published Jul 14, 2022



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Juan Daniel Molina, MSc https://orcid.org/0000-0001-8583-8889

Luis Fernando Giraldo-Jaramillo, MSc https://orcid.org/0000-0002-8539-6475

Edilson Delgado-Trejos, PhD https://orcid.org/0000-0002-4840-478X

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Abstract

Objective: To propose a methodological procedure that serves as a guide for applying techniques in the measurement uncertainty evaluation, such as GUM, MMC, and Bayes; in addition, to develop an application in a non-trivial case study. Materials and methods: In this paper, a set of steps are proposed that allow validating the measurement uncertainty evaluation from techniques such as GUM, MMC, and Bayes; these were applied as a strategy to evaluate the uncertainty of an indirect measurement process that sought to determine the level of a fluid by measuring the hydrostatic pressure generated by it at rest on the bottom of a container. The results obtained with each technique were compared. Results and discussion: the use of the GUM was found to be valid for the case under study, and the results obtained by applying the Bayesian approach and the MC technique provided highly useful complementary information, such as the Probability Density Function (PDF) of the measurand, which enables a better description of the phenomenon. Likewise, the posterior PDF obtained with Bayes allowed us to approximate closer values around the true values of the measurand, and the ranges of the possible values were broader than those offered by the MMC and the GUM. Conclusions: In the context of the case under study, the Bayesian approach presents more realistic results than GUM and MMC; in addition to the conceptual advantage presented by Bayes, the possibility of updating the results of the uncertainty evaluation in the presence of new evidence.

Keywords

Uncertainty estimation, GUM, Monte Carlo method, Bayesian inference, indirect measurement Evaluación de incertidumbre, GUM, Método de Monte Carlo, Inferencia Bayesiana, Medición indirecta

References
[1] Joint Committee for Guides in Metrology, Evaluation of measurement data – guide to the expression of uncertainty in measurement, BIPM, 2008. [Online]. Available: https://www.bipm.org/documents/20126/2071204/JCGM_100_2008_E.pdf/cb0ef43f-baa5-11cf-3f85-4dcd86f77bd6
[2] T. Dietza, K. Klamrothb, K. Kraus, et al., “Introducing multiobjective complex systems,” European Journal of Operational Research, vol. 280, no. 2, pp. 581-596, 2020. https://doi.org/10.1016/j.ejor.2019.07.027
[3] C. Cai, J. Wang and Z. Li, “Assessment and modelling of uncertainty in precipitation forecasts from TIGGE using fuzzy probability and Bayesian theory,” Journal of Hydrology, vol. 577, 2019. https://doi.org/10.1016/j.jhydrol.2019.123995
[4] T. B. Schön, , A. Svensson, L. Murray and F. Lindsten, “Probabilistic learning of nonlinear dynamical systems using sequential Monte Carlo,” Mechanical Systems and Signal Processing, vol. 104, pp. 866-883, 2018. https://doi.org/10.48550/arXiv.1703.02419
[5] T. Hou, D. Nuyens, S. Roles and H. Janssen, “Quasi-Monte Carlo based uncertainty analysis: Sampling efficiency and error estimation in engineering applications,” Reliability Engineering and System Safety, vol. 191, 2019. https://doi.org/10.1016/j.ress.2019.106549
[6] Joint Committee for Guides in Metrology, JCGM 101:2008 – Evaluation of measurement data - Supplement 1 to the “Guide to the expression of uncertainty in measurement” – Propagation of distributions using a Monte Carlo method, BIPM, 2008.
[7] J. M. M. R. Roberto Arias R., “Determinación de la incertidumbre de medición del volumen de patrones volumétricos, determinado a partir del método de pesado de doble sustitución,” Santiago de Querétaro, 2002.
[8] M. A. Azpurua, C. Tremola and E. Paez, “Comparison of the gum and Monte Carlo methods for the uncertainty estimation in electromagnetic compatibility testing,” Progress In Electromagnetics Research B, vol. 34, pp. 125 - 144, 2011. https://doi.org/10.2528/PIERB11081804
[9] S. F. dos Santos and H. S. Brandi “Application of the GUM approach to estimate uncertainty in measurements of sustainability systems,” Clean. Techn. Environ. Policy, 2015. https://doi.org/10.1007/s10098-015-1029-3
[10] K. Weise and W. Woger, “A Bayesian theory of measurement uncertainty,” Meas. Sci. Technol, vol. 4, no. 1, 1992. https://doi.org/10.1088/0957-0233/4/1/001
[11] I. Lira, “The GUM revision: The Bayesian view toward the expression of measurement uncertainty,” European Journal of Physics, vol. 37, no. 2, p. 025803, 2016. [Online]. Available: https://iopscience.iop.org/article/10.1088/0143-0807/37/2/025803
[12] D. G. I Lira, “Bayesian assessment of uncertainty in metrology: a tutorial,” Metrologia, nº 47, pp. R1 - R14, 2010. [Online]. Available: https://iopscience.iop.org/article/10.1088/0026-1394/47/3/R01
[13] J.-H. Y. Heung-Fai Lam, “An innovative Bayesian system identification method using autoregressive model,” Mechanical Systems and Signal Processing, vol. 133, 2019. https://doi.org/10.1016/j.ymssp.2019.106289
[14] J. Berger, “The case for objective Bayesian analysis,” Bayesian Analysis, vol. 1, nº 3, pp. 385- 402, 2006. https://doi.org/10.1214/06-BA115
[15] L. S. Katafygiotis, “Sequential Bayesian estimation of state and input in dynamical systems using output-only measurements,” Mechanical Systems and Signal Processing, vol. 131, pp. 659-688, 2019. https://doi.org/10.1016/j.ymssp.2019.06.007
[16] I. Lira and W. Wöger “Bayesian evaluation of the standard uncertainty and coverage probability in a simple measurement model,” Measurement Science and Technology, vol. 12, no. 8, pp. 1172 –1179, 2001. [Online]. Available: https://iopscience.iop.org/article/10.1088/0957-0233/12/8/326/meta
[17] F. Attivissimo, N. Giaquinto and M. Savino, “A Bayesian paradox and its impact on the GUM approach to uncertainty,” Measurement, vol. 45, no. 9, pp. 2194-2202, 2012. https://doi.org/10.1016/j.measurement.2012.01.022
[18] C. Elster and Blaza Toman, “Bayesian uncertainty analysis under prior ignorance of the measurand versus analysis using the Supplement 1 to the Guide: a comparison,” Metrología, vol. 46, no. 3, pp. 261 – 266, 2009.
[19] M. Vilbaste, G. Slavin, O. Saks, V. Pihl and I. Leito, “Can coverage factor 2 be interpreted as an equivalent to 95% coverage level in uncertainty estimation? Two case studies,” Measurement, vol. 43, no. 3, pp. 392–399, 2010. https://doi.org/10.1016/j.measurement.2009.12.007
[20] A. Possolo, “Five examples of assessment and expression of measurement uncertainty,” Applied Stochastic Models Bussines and Industry, vol. 22, no. 1, pp. 1-18, 2012. https://doi.org/10.1002/asmb.1947
[21] A. Gelman, J. Carlin, H. Stern and D. Rubin, Bayesian data analysis, Boca Raton, FL, USA: Chapman & Hall/CRC, 2014.
[22] F. White, Fluid Mechanics, 6th Ed., McGraw-Hill, 2008.
[23] Centro Español de Metrología, Procedimiento ME - 017 para la calibración de transductores de presión con salida eléctrica, Madrid, España, 2003.
[24] Endress+Hauser. (2015). Technical Information Waterpilot FMX21. https://portal.endress.com/wa001/dla/5000557/8038/000/05/TI00431PEN_1413.pdf
[25] W. Hoeffding, “A non-parametric test of independence,” The annals of mathematical statistics, vol. 19, no. 4, pp. 546-557, 1948. https://doi.org/10.1214/aoms/1177730150
[26] R Core Team, “R: A language and environment for statistical computing,” R Foundation for Statistical Computing, Vienna, Austria, 2017.
[27] S. S. Shapiro and M. B. Wilk, “An analysis of variance test for normality (complete samples),” Biometrika, vol. 52, no. 3/4, pp. 591-611, 1965. https://doi.org/10.2307/2333709
[28] T. Pham-Gia, N. Turkkan and E. Marchand, “Density of the ratio of two normal random variables and applications,” Communications in Statistics-Theory and Methods, vol. 9, no. 35, pp. 1569-1591, 2006. https://doi.org/10.1080/03610920600683689
[29] J. A. Christen and F. Colin, “A general purpose sampling algorithm for continuous distributions (the t-walk),” Bayesian Analysis, vol. 2, no. 5, pp. 263-281, 2010. https://doi.org/10.1214/10-BA603
How to Cite
Molina-Muñoz, J. D., Giraldo-Jaramillo, L. F., & Delgado-Trejos, E. (2022). Bayesian Evaluation for Uncertainty of Indirect Measurements in Comparison with GUM and Monte Carlo. Ingenieria Y Universidad, 26. https://doi.org/10.11144/javeriana.iued26.beui
Section
Electrical and computer engineering