Abstract
Linear uncertainty analysis based on a first order Taylor series expansion, described in ASME PTC (Performance Test Code) 19.1 “Test Uncertainty” and the ISO Guide for the “Expression of Uncertainty in Measurement,” has been the most widely technique used both in industry and academia. A common approach in linear uncertainty analysis is to use local derivative information as a measure of the sensitivity needed to calculate the uncertainty percentage contribution (UPC) and uncertainty magnification factors (UMF) due to each independent variable in the measurement/process being examined. The derivative information is typically obtained by either taking the symbolic partial derivative of an analytical expression or the numerical derivative based on central difference techniques. This paper demonstrates that linear multivariable regression is better suited to obtain sensitivity coefficients that are representative of the behavior of the data reduction equations over the region of interest. A main advantage of the proposed approach is the possibility of extending the range, within a fixed tolerance level, for which the linear approximation technique is valid. Three practical examples are presented in this paper to demonstrate the effectiveness of the proposed least-squares method.
Highlights
The topic of estimation of experimental uncertainty is covered in a wide variety of forums
There are more sophisticated uncertainty quantification methods, including Monte Carlo [13], Bayesian [14], Latin square sampling techniques [15, 16], by far ASME PTC 19.1-1998 “Test Uncertainty” standard [1] is the most widely adopted in the current industrial applications
Most approaches [Coleman and Steele [7], Abernethy et al [17], International Organization for Standardization (ISO) Guide [2], etc. to engineering uncertainty propagation are based on the assumption of linear behavior for small perturbations in the measured variables
Summary
The topic of estimation of experimental uncertainty is covered in a wide variety of forums. The International Organization for Standardization (ISO) publishes a guide on uncertainty calculation and terminology entitled “Guide to the Expression of Uncertainty in Measurement” [2] These two approaches are compared by Steele et al [3]. To engineering uncertainty propagation are based on the assumption of linear behavior for small perturbations in the measured variables These approaches rely on a first order Taylor series approximation at a nominal location obtained from the mean of the measured variables. While the Taylor series approximation is usually quite good over regions of high probability, it can give a very poor estimate of the 95 % confidence interval for highly non-linear functions. The authors describe a least-squares approach to obtain better sensitivity coefficients that result in better predictions for the 95 % confidence interval
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