Evaluation of the air density uncertainty: the effect of the correlation of input quantities and higher order terms in the Taylor series expansion

Abstract

Air density uncertainty is usually evaluated as if its input quantities were uncorrelated and as if the mathematical model was linear. The present work takes the CIPM 81/91 formula as a starting point and proposes arguments in favour or against in order to take into account the correlation components and the higher order terms of the Taylor series expansion in the analysis of air density uncertainty.

A compact tensor algebra expression of the law of propagation of uncertainty

“…In practice, some of the generated terms are usually zero; however, a substantial number of them can remain. Another example is the case of the model for the determination of the density of wet air [4], with four random variables: the temperature, the pressure, the relative humidity and the model fitting error, where the propagation formula involves 34 derivatives in total which combine into 22 different terms to sum to obtain the combined variance.…”

Milling optimisation of removal rate and accuracy with uncertainty: Part 2: parameter variation

“…Rooney and Biegler (2001) showed the importance of including parameter correlation in design problems by using elliptical joint confidence regions to describe the correlation among the uncertain model parameters. In a recent paper, Becerra and Hernandez (2006) deemed parameter correlation imperative to the proper evaluation of air density uncertainty. In our study, the variation and correlation in the model parameters are measured and propagated through the model using sampling methods.…”

Parametric uncertainty quantification in coalescene flutter

“…The results of this method show good agreement when compared with the MCS technique, but only for low uncertainty in the input. The perturbation method proves to be much more efficient than the MCS for low levels of uncertainty [54,53,55]. Oh and Librescu [56] present a method based on the Perturbation technique in order to obtain a measure of randomness within the modal parameters based on uncertainty contained within the structural properties of a composite cantilever wing.…”