Root sensitivity to parameter uncertainties: a statistical approach

Abstract

A statistical approach to calculating the sensitivity of characteristic roots to plant parameter uncertainties is presented. Means and variances of the eigenvalues are obtained in terms of the statistical moments of the system parameters, the sensitivity of an eigenvalue being defined by its relative standard deviation. The method allows for correlation among the system parameters and therefore among the elements of the plant matrix. The approach is a first-order random perturbation analysis that implicitly assumes gaussian random variables. The results derived by this statistical procedure are shown to be a generalization of the norm sensitivity results previously obtained in the literature by calculating the norm of the sensitivity matrix. Indeed, the two approaches are shown to be equivalent for uncorrelated and identically distributed plant matrix elements. The statistical measure of root sensitivity presented here is believed to be more representative than the usual norm sensitivity measure.