Sensitivity and Uncertainty Analyses

Abstract

The aim of sensitivity and uncertainty analysis methods is to determine the influence of changes in model input parameters on the output of mathematical models. Such methods can help to highlight key model inputs that drive uncer-tainties in model predictions. Here we describe a range of mathematical tools for sensitivity and uncertainty analysis which may assist in the evaluation of large kinetic mechanisms. Approaches based on local sensitivity, local uncertainty and global uncertainty analysis are covered, as well as examples of their application to a variety of chemical kinetic models. Local sensitivity analysis is a routinely used method for the investigation of models and the theory behind it is discussed. Uncertainty analysis reveals the uncertainty of the simulation results caused by the uncertainty of model input parameters. Such uncertainties can be estimated using local sensitivity coefficients, but global uncertainty methods based on sam-pling approaches usually provide more realistic results. Global sensitivity methods can then be applied which determine how each input parameter contributes to the overall output uncertainty based on measures such as output variance. Various global methods for sensitivity analysis are discussed here, including the Morris screening method, the calculation of sensitivity indices based on random sampling, the Fourier Amplitude Sensitivity Test (FAST) method and the different surface response methods. All of these methods can be applied generally to mathematical models, but we also include a discussion of topics specifically related to reaction kinetics such as uncertainties in rate coefficients and the characterisation of the uncertainty of Arrhenius parameters. 5.1 Introduction The term sensitivity analysis defines a collection of mathematical methods that can be used to explore the relationships between the values of the input parameters of a mathematical model and its solutions. Uncertainty analysis tells us how our lack of knowledge of model inputs propagates to the predictive uncertainty of key model outputs. This could include the equivalent of determining experimental error bars but for model outputs. The sources of such uncertainty can include lack of