Least squares approach to standard platinum resistance thermometer subrange inconsistency reduction with redundant gallium and indium fixed points

Žužek, Vincencij (author), Rusby, Richard (author), Pearce, Jonathan (author), Peruzzi, Andrea (author), Bojkovski, Jovan (author)

The International Temperature Scale of 1990 (ITS-90) defines several different and sometimes overlapping temperature subranges. Where overlap occurs, different definitions of the temperature t$_{90}$ exist that have equal status but produce different results. This discrepancy is called type 1 non-uniqueness or subrange inconsistency (SRI). In this paper, the SRI of the water-aluminum/water-zinc (SRI(Al:Zn)) and of the water-zinc/water-tin (SRI(Zn:Sn)) subranges of the ITS-90 were investigated for three cases. In the first case, the calculations followed the ITS-90 prescribed procedure. In the second case, the SPRT was calibrated at all fixed points of the subrange and its deviation function was then determined using the least squares method. In the third case, the least squares method was weighted by the uncertainties at each of the fixed points. One benefit of the least squares approach over exact interpolation is the reduction in uncertainty propagated from the fixed points. The calculations were applied to a large ensemble of 30 different SPRTs from the database of the Laboratory of Metrology and Quality at the University of Ljubljana, Slovenia. The sample consisted mainly of SPRTs manufactured by Fluke, Rosemount and AccuMac. The difference in the mean and standard deviation of SRI(Al:Zn) for the three cases was small, amounting to less than 0.06 mK. On the other hand, the mean of SRI(Zn:Sn) decreased from 0.73 mK to 0.01 mK and the standard deviation decreased from 1.25 mK to 0.43 mK when the weighted least squares approach was applied. Furthermore, the total propagated uncertainty from the fixed points decreased in particular temperature ranges with weighted least squares, especially from 50 °C to 300 °C (by about 50% compared to the ITS-90 case) and to a lesser extent from 400 °C to 600 °C (by about 10% compared to the ITS-90 case). The contribution of the difference in the uncertainty propagation between pairs of subranges to SRI was estimated to be at least 50% in all cases. According to the presented results, it can be advantageous to calibrate the SPRT at all available fixed points in the selected temperature subrange and then determine its deviation function using the weighted least squares method.

• Language: English
• Keywords: standard platinum resistance thermometer, SPRT, subrange inconsistency, SRI, non-uniqueness, International Temperature Scale of 1990, ITS-90, polynomial least squares, propagation of uncertainty, PoU
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FE - Faculty of Electrical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2023
• Number of pages: 7 str.
• Numbering: Vol. 220, art. 113400
• PID: 20.500.12556/RUL-153052
• UDC: 006.91
• ISSN on article: 0263-2241
• DOI: 10.1016/j.measurement.2023.113400
• COBISS.SI-ID: 167928067
• Publication date in RUL: 15.12.2023

Record is a part of a journal

• Title: Measurement : journal of the International Measurement Confederation
• Shortened title: Measurement
• Publisher: Elsevier, International Measurement Confederation
• ISSN: 0263-2241
• COBISS.SI-ID: 25917696

Licences

• License: CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Description: The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.

Secondary language

• Language: Slovenian
• Keywords: standardni platinasti uporovni termometer, neskladnost podobmočij, Mednarodna temperaturna lestvica iz leta 1990, metoda najmanjših kvadratov, končna negotovost