Comparison of GUM and Monte Carlo Methods in Air Flow Measurement System Uncertainty

Abstract

Measurement uncertainty and measurement error are the most important parameters for reliable measurement results. Measurement uncertainty becomes important, especially for comparing new measurement systems with nonlinear characteristics with traditional systems. In this study, the measurement uncertainty of a new air speed and flow measurement system with non-linear characteristics was calculated using both Guide to the Expression of the Uncertainty in Measurement (GUM) and Monte Carlo simulation. GUM results were compared with Monte Carlo simulation results. The standard uncertainty is calculated for six speed levels from approximately 1 m/s to 20 m/s. Comparison of measurement uncertainty values ​​showed that the uncertainty values ​​obtained from the Monte Carlo simulation were higher than those from the GUM method. The results showed that it is impossible to validate GUM methods for two significant digits according to GUM. The study also showed that in such measurement systems with nonlinear properties, Monte Carlo simulation should be considered to validate the GUM method for more reliable and consistent results.

Keywords

• Flow
• GUM
• Monte Carlo
• Uncertainty
• Measurement

Hava Akış Ölçüm Sistemi Belirsizliğinde GUM ve Monte Carlo Yöntemlerinin Karşılaştırılması

Öz

Ölçüm belirsizliği ve ölçüm hatası, güvenilir ölçüm sonuçları için en önemli parametrelerdir. Özellikle doğrusal olmayan karakteristiklere sahip yeni ölçüm sistemlerinin geleneksel sistemlerle karşılaştırılması için ölçüm belirsizliği önemli hale gelmektedir. Bu çalışmada, doğrusal olmayan karakteristiklere sahip yeni bir hava hızı ve akış ölçüm sisteminin ölçüm belirsizliği hem Guide to the Expression of the Uncertainty in Measurement (GUM) hem de Monte Carlo simülasyonu ile hesaplanmıştır. GUM sonuçları Monte Carlo simülasyon sonuçları ile karşılaştırılmıştır. Standart belirsizlik yaklaşık 1 m/s hız seviyesi ile 20 m/s hız seviyesi arasındaki altı hız seviyesi için hesaplanmıştır. Ölçüm belirsizliği değerlerinin karşılaştırılması, Monte Carlo simülasyonundan elde edilen belirsizlik değerlerinin GUM yönteminden daha yüksek olduğunu göstermiştir. Sonuçlar, GUM'a göre iki anlamlı basamak için GUM yöntemlerini doğrulamanın imkânsız olduğunu göstermiştir. Çalışma ayrıca, doğrusal olmayan özelliklere sahip bu tür ölçüm sistemlerinde, daha güvenilir ve tutarlı sonuçlar için GUM yöntemini geçerli kılmak amacıyla Monte Carlo simülasyonunun göz önünde bulundurulması gerektiğini göstermiştir.

Anahtar Kelimeler

• Akış
• Monte Carlo
• GUM
• Belirsizlik
• Ölçüm

Kaynakça

1. [1] Joint Committe for Guides in Metrology, (2008), JCGM 100:2008 Guide to the Expression of the Uncertainty in Measurement, Joint Committe for Guides in Metrology, Sevres: 3,6,10,19
2. [2] International Standards Organization/ International Electrotechnic Committe, (2008), Uncertainty of measurement -- Part 3: Guide to the expression of uncertainty in measurement (GUM:1995), ISO/IEC, Geneva
3. [3] P.R.G. Couto, J.C. Damasceno, S.P. de Oliveira, (2013), Chapter 2: Monte Carlo simulations applied to uncertainty in measurement, Theory and Applications of Monte Carlo Simulations, InTech Publisher, 2013, Rijeka: 27-52
4. [4] Joint Committe for Guides in Metrology, (2008), Evaluation of measurement data — Supplement 1 to the “Guide to the expression of uncertainty in measurement, Joint Committe for Guides in Metrology, Sevres:5,7,28,30,31,34
5. [5] M.A. Herrador, A.G. González, Evaluation of measurement uncertainty in analytical assays by means of Monte-Carlo simulation, Talanta 64 (2004) 415–422.
6. [6] S.P. Oliveira, A.C. Rocha, J.T. Filho, P.R.G. Couto, Uncertainty of measurement by Monte-Carlo simulation and metrological reliability in the evaluation of electric variables of PEMFC and SOFC fuel cells, Measurement 42 (2009) 1497–1501.
7. [7] K. Shahanaghi, P. Nakhjiri, A new optimized uncertainty evaluation applied to the Monte-Carlo simulation in platinum resistance thermometer calibration, Measurement 43 (2010) 901–911.
8. [8] J. Sładek, A. Gaska, Evaluation of coordinate measurement uncertainty with use of virtual machine model based on Monte Carlo method, Measurement 45 (2012) 1564–1575.

9. [9] D. Theodorou, L. Meligotsidou, Sotirios Karavoltsos, A. Burnetas, M. Dassenakis, M. Scoullos, Comparison of ISO–GUM and Monte Carlo methods for the evaluation of measurement uncertainty: application to direct cadmium measurement in water by GFAAS, Talanta 83 (2011) 1568–1574.
10. [10] M. Azpurua, C. Tremola, E. Paez, Comparison of the GUM and MONTE CARLO methods for the uncertainty estimation in electromagnetic compatibility testing, Prog. Electrom. Res. B 34 (2011) 125–144.
11. [11] Chen A., Chen C., Comparison of GUM and Monte Carlo methods for evaluating measurement uncertainty of perspiration measurement systems, Measurement 87 (2016) 27-37
12. [12] González, C.; Vilaplana, J.M.; Parra-Rojas, F.C.; Serrano, A. Validation of the GUM uncertainty framework and the Unscented transformation for Brewer UV irradiance measurements using the Monte Carlo method. Measurement 2025, 239, 115466.
13. [13] Castro, H.F.F., Mathematical modeling applied to the uncertainty analysis of a tank prover calibration: Understanding the influence of calibration conditions on the GUM validation using the Monte Carlo method, Flow Measurement and Instrumentation, Volume 96, 2024,102547.
14. [14] Wei M. Chong W., Cao J., Zhou T., Zheng D., Uncertainty evaluation for wind speed measurement part (1): “GUM method and Monte Carlo method”, Flow Measurement and Instrumentation, Volume 97,2024,102607.
15. [15] Castro H.F.F., Validation of the GUM using the Monte Carlo method when applied in the calculation of the measurement uncertainty of a compact prover calibration, Flow Measurement and Instrumentation, Volume 77, 2021, 101877
16. [16] Hoerner. S. F., (1958) Fluid Dynamic Drag.", ABD: Author, 3-14,3-15
17. [17] Davis, R.S., “Equation for the determination of the density of moist air” (1981/91), Metrologia 29, 67 (1992)
18. [18] Giacomo, P., “Equation for the determination of the density of moist air” (1981), Metrologia 18, 33 (1982)
19. [19] International Organizatıon Of Legal Metrology, (2004), OIML R111-1 Weights of classes E1, E2, F1, F2, M1, M1–2, M2, M2–3 and M3 Part 1: Metrological and technical requirements, International Organizatıon Of Legal Metrology, Paris:76.