Sensitivity Analysis of Dynamic Models to Uncertainties in Inputs Data With Time-Varying Variances

Abstract

This article deals with the differential computation of sensitivity functions and confidence intervals for model output, when model inputs are subject to systematic or stochastic uncertainties with time-varying variances. The nonlinear, time-varying systems dealt with correspond to the class of nonlinear systems with time-invariant dynamics and boundary conditions involving algebraic-only equations. It is shown that the first-order kernel of a Volterra series expansion of the time-invariant model, allied with a derivation of the algebraic equations, can be used to derive approached differential formulas. These are applied to the case study of a real-size building thermal dynamic model developed with the Clim2000 software; the results are compared with Monte Carlo sampling and show very good agreement.