Pseudo-cubic thin-plate-type spline method for analysing experimental data

Abstract

A mathematical tool, using pseudo-cubic thin-plate-type splines, has been developed for analysis of experimental datum points. The main purpose is to obtain, without any a priori given model, a mathematical predictor with related uncertainties, usable at any point in the multidimensional parameter space. The smoothing parameter is determined by a generalized cross-validation method implemented using Monte Carlo techniques. The residual standard deviation obtained is significantly smaller than that of a least-squares regression. An example of use is given with critical heat flux data, showing a significant decrease in the conception criterion.