Abstract
Relationships characterizing measuring instruments are determined in a measuring experiment called calibration. The values of the parameters describing calibrated curves are measured with associated uncertainties. Identification of a given type of dependency is made based on the obtained values of the measured parameters. The most popular method of this identification is the least squares method, well implemented for polynomial relationships. In metrological practice, when identifying a non-linear calibrated relationship, it very often happens that increasing the polynomial degree within reasonable limits does not lead to a significant reduction of the approximation error. In that case, the primary dependence is transformed into a linear one by changing the variables. Then parameters of such a linearized relationship are determined by the least squares’ method. The article discusses the solution of estimating the uncertainty of parameters identified for the non-polynomial dependence, considering the instrumental uncertainties for the measured values.
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References
EA-4/02 M: Evaluation of the Uncertainty of Measurement in Calibration (2013)
Laaneots, R., Mathiesen, O.: An Introduction to Metrology, p. 271. TUT Press, Tallinn (2006)
Rabinovich, S.G.: Evaluating Measurement Accuracy: A Practical Approach, 3rd edn., p. 313. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-60125-0
COOMET R/GM/32:2017. Calibration of measuring instruments. Algorithms of processing measurement results and uncertainty evaluation
Vodyka, S., Zaharov, I.: Using PUMA for coefficients estimation of calibration dependences. In: Proceedings of XI International Ph. D. Workshop OWD 17–19 October 2009, Silesian TU, pp. 97–99 (2009)
Siraja, T.: Certification of algorithms for constructing calibration curves of measuring instruments. In: Advanced Mathematical and Computational Tools in Metrology and Testing X. Advanced in Mathematics for Applied Sciences, vol. 86, pp. 368–376. World Scientific Publications, London (2015). ISBN: 978-981-4678-61-2
Zakharrov, I., Neyezhmakov, P.: Peculiarity of measurement instruments verification by results of their calibration. In: Proceedings of 11th International Conference of Measurements, Smolenice, Slovakia, 29–31 May 2017, pp. 19–22 (2017). ISBN: 978-80-972629-0-7
Vitkovsky, V., Wimmer, G.: Inverse and direct prediction and its effect on measurement uncertainty in polynomial comparative calibration. In: Proceedings of 12th International Conference of Measurements, Smolenice, Slovakia, 27–29 May 2019, pp. 62–65 (2019). ISBN: 978-80-972629-2-1
Wimmer, G., Vitkovsky, V.: Two-dimensional linear comparative calibration and measurement uncertainty. In: Proceedings of 12th International Conference of Measurements, Smolenice, Slovakia, 27–29 May 2019, pp. 66–69 (2019). ISBN: 978-80-972629-2-1
Chunovkina, A., Stepanov, A.: Estimation of linear regression confidence bands in case of correlated noise. In: Proceedings of 12th International Conference of Measurements, Smolenice, Slovakia, 27–29 May 2019, pp. 58–61 (2019). ISBN: 978-80-972629-2-1
Vitkovsky, V., Wimmer, G.: Generalized polynomial comparative calibration: parameter estimation and application. In: Yurish, S.Y. (ed.) Advances in Measurements and Instrumentation: Reviews, chap. 1, vol. 1, pp. 15–52. IFSA International Frequency Sensor Association Publishing (2018). ISBN: 978-84-09-07321-4, e-ISBN: 978-84-09-07322-1
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Zakharov, I., Neyezhmakov, P., Semenikhin, V., Warsza, Z.L. (2022). Measurement Uncertainty Evaluation of Parameters Describing the Calibrated Curves. In: Szewczyk, R., Zieliński, C., Kaliczyńska, M. (eds) Automation 2022: New Solutions and Technologies for Automation, Robotics and Measurement Techniques. AUTOMATION 2022. Advances in Intelligent Systems and Computing, vol 1427. Springer, Cham. https://doi.org/10.1007/978-3-031-03502-9_38
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DOI: https://doi.org/10.1007/978-3-031-03502-9_38
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