Derivation of multi-dimensional ellipsoidal convex model for experimental data

This paper deals with determination of the best ellipsoidal model fitting the available limited experimental data. The problem is defined as that of finding the minimum volume ellipsoid containing all experimental data. A general transformation matrix for the rotation of N-dimensional coordinate system is first obtained by the Gramm-Schmidt orthogonalization procedure. The use of this matrix makes it possible to search in all possible directions to find an ellipsoid with a minimum volume. The general procedure is illustrated by examples in which the real data is utilized. An invariance property of the response with uncertain parameters of different physical nature is also discussed.