A Comparative Review of Sensitivity and Uncertainty Analysis of Large-Scale Systems—II: Statistical Methods

Abstract

Part II of this review paper highlights the salient features of the most popular statistical methods currently used for local and global sensitivity and uncertainty analysis of both large-scale computational models and indirect experimental measurements. These statistical procedures represent sampling-based methods (random sampling, stratified importance sampling, and Latin Hypercube sampling), first- and second-order reliability algorithms (FORM and SORM, respectively), variance-based methods (correlation ratio-based methods, the Fourier Amplitude Sensitivity Test, and the Sobol Method), and screening design methods (classical one-at-a-time experiments, global one-at-a-time design methods, systematic fractional replicate designs, and sequential bifurcation designs). It is emphasized that all statistical uncertainty and sensitivity analysis procedures first commence with the “uncertainty analysis” stage and only subsequently proceed to the “sensitivity analysis” stage; this path is the exact reverse of the conceptual path underlying the methods of deterministic sensitivity and uncertainty analysis where the sensitivities are determined prior to using them for uncertainty analysis.By comparison to deterministic methods, statistical methods for uncertainty and sensitivity analysis are relatively easier to develop and use but cannot yield exact values of the local sensitivities. Furthermore, current statistical methods have two major inherent drawbacks as follows:1. Since many thousands of simulations are needed to obtain reliable results, statistical methods are at best expensive (for small systems) or, at worst, impracticable (e.g., for large time-dependent systems).2. Since the response sensitivities and parameter uncertainties are inherently and inseparably amalgamated in the results produced by these methods, improvements in parameter uncertainties cannot be directly propagated to improve response uncertainties; rather, the entire set of simulations and statistical postprocessing must be repeated anew. In particular, a “fool-proof” statistical method for correctly analyzing models involving highly correlated parameters does not seem to exist currently, so that particular care must be used when interpreting regression results for such models.By addressing computational issues and particularly challenging open problems and knowledge gaps, this review paper aims at providing a comprehensive basis for further advancements and innovations in the field of sensitivity and uncertainty analysis.