A Methodology for Computing the Uncertainty of Curve Fitting Parameters Interpolating Experimental Data

Abstract

Abstract A general procedure to determine the experimental uncertainty of parameters obtained directly from equations curve fitting experimental data is presented. The procedure, valid for any curve fitting equation, is used for estimating the uncertainties of permeability and inertia coefficient characterizing the hydraulic behavior of mechanically compressed aluminum porous matrices. These parameters, to be obtained experimentally since predictive models do not exist, are frequently determined by extrapolation of the experimental pressure drop versus fluid speed data to asymptotic regimes. In this case the results are rigorously valid only at the asymptotes and their uncertainties are independent of the curve fitting uncertainty. We propose here a new methodology for determining the permeability and inertia coefficient of porous media based on the curve fitting of the experimental results without using extrapolation. This methodology is found to yield more consistent and accurate results than existing methods because the parameters are valid now throughout the entire experimental range. The corresponding uncertainties, calculated following a prescribed scheme, are no longer local but global because they are affected by the uncertainties of each and every experimental data point via the curve fitting equation.