EMUE-D4-3-QuantifyUncertaintiesInCalibration

Calibration of a sonic nozzle as an example for quantifying all uncertainties involved in straight-line regression

When calibrating a sonic nozzle, it is recommended to estimate the straight-line relationship between the discharge coefficient of the nozzle and the square root of the inverse Reynolds number for a gas. The slope and intercept of this relation characterize the nozzle, and reliable estimates and uncertainties for this multivariate measurand are mandatory for its use as transfer or working standard.

This example emphasizes the importance of accounting for correlation for a reliable uncertainty evaluation. The use of common reference standards and instruments causes correlation among and between the discharge coefficient and the Reynolds number, and impacts significantly on the uncertainty of the characteristic parameters of the nozzle. To show this, a measurement model based on the weighted total least-squares (WTLS) method is applied and its input quantities are fully characterized. In particular, we demonstrate in detail how to jointly evaluate the correlation, uncertainties and estimates for the input quantities of least-squares methods applying the Monte Carlo method. As a result, sonic nozzles can be characterized in line with the Guide to the expression of uncertainty in measurement (GUM).

Files contained in the dataset are:

Example_A223.pdf: Report “Calibration of a sonic nozzle as an example for quantifying all uncertainties involved in straight-line regression”;

Example_A223.tex: LaTeX file to be compiled in order to produce Example_A223.pdf;

Compendium_A223.bib: bibliography file;

Fig1.pdf: PDF file needed to compile Example_A223.tex;

Fig2.pdf: PDF file needed to compile Example_A223.tex;

Fig2.png: PNG file needed to compile Example_A223.Rmd;

Fig3a.pdf: PDF file needed to compile Example_A233.tex;

Fig3b.pdf: PDF file needed to compile Example_A233.tex;

Fig4.pdf: PDF file needed to compile Example_A223.tex;

Fig5a.pdf: PDF file needed to compile Example_A223.tex;

Fig5b.pdf: PDF file needed to compile Example_A223.tex;

Fig6a.pdf: PDF file needed to compile Example_A223.tex;

Fig6a.png: PNG file needed to compile Example_A223.Rmd;

Fig6b.pdf: PDF file needed to compile Example_A223.tex;

Fig6b.png: PNG file needed to compile Example_A223.Rmd;

data_A223.csv: data file containing the estimates and associated standard uncertainties for the measurements;

MC_data_A223.xslx: excel file containing the estimates and associated covariance matrix for the intermediate measurands;

Example_A223.Rmd: R Markdown file for quantifying all uncertainties involved in straight-line regression. As output an HTML file similar to Example_A223.pdf is created with results dynamically produced by underlying R code;

ieee.csl: CSL file needed to cite the reference in example_A223.Rmd according to the Institute of Electrical and Electronics Engineers style.