Uncertainty Analysis Applied to Least Squares Curve and Surface Fits.
Abstract
The application of uncertainty analysis to curve and surface fits obtained by the method of Least Squares is described. The primary obstacle to the routine implementation of the uncertainty analysis procedure: the derivation of the sensitivity derivatives, has been removed. Analytic expressions for the derivatives applicable to fits of arbitrary order have been derived, and a step-by-step procedure for their incorporation within a computer program provided. A review of the techniques for the construction of curve and surface fits of arbitrary order is included. The use of uncertainty analysis as an aid to the assessment of the suitability of a particular fit is demonstrated by the application of these procedures to a series of examples employing a generic data set typical of experimentally derived data. Some results include: quantification of the penalty for using a higher-order fit when it is not appropriate, and the fact that reduction of uncertainty in the data to be fitted is more effective at reducing the uncertainty in fit coefficients and fitted values than simply increasing the amount of data used to construct the fit. A computer program implementing these procedures is available from the authors.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1998
- Accession Number
- ADA360063
Entities
People
- David E. Hess
- William E. Smith
Organizations
- Naval Surface Warfare Center Carderock Division