Sensitivity and Uncertainty Analysis of Models and Data

Abstract

This chapter highlights the characteristic features of statistical and deterministic methods currently used for sensitivity and uncertainty analysis of measurements and computational models. The symbiotic linchpin between the objectives of uncertainty analysis and those of sensitivity analysis is provided by the “propagation of errors” equations, which combine parameter uncertainties with the sensitivities of responses (i.e., results of measurements and/or computations) to these parameters. It is noted that all statistical uncertainty and sensitivity analysis methods first commence with the “uncertainty analysis” stage, and only subsequently proceed to the “sensitivity analysis” stage. This procedural path is the reverse of the procedural (and conceptual) path underlying the deterministic methods of sensitivity and uncertainty analysis, where the sensitivities are determined prior to using them for uncertainty analysis. In particular, it is emphasized that the Adjoint Sensitivity Analysis Procedure (ASAP) is the most efficient method for computing exactly the local sensitivities for large-scale nonlinear problems comprising many parameters. This efficiency is underscored with illustrative examples. The computational resources required by the most popular statistical and deterministic methods are discussed comparatively. A brief discussion of unsolved fundamental problems, open for future research, concludes this chapter.