A review of global sensitivity analysis for uncertainty structure

Abstract

This paper mainly reviews some widely used global sensitivity analysis methods for uncertainty structure, in which the uncertainty is described by probability theory. Global sensitivity analysis can be divided into single output global sensitivity analysis and multivariate global sensitivity analysis based on the number of output response of the structure. The single output global sensitivity analysis has been studied by many researchers and obtains widely development. Due to the different ways of representing uncertainty in probability theory (variance, probability density function, cumulative distribution function, etc.), different global sensitivity analysis methods (variance based method, moment-independent method, etc.) have been proposed. For example, the variance based global sensitivity analysis method can reflect the structure of the model itself and has been widely studied and applied in engineering; while the moment independent global sensitivity analysis method has a more comprehensive description of the uncertainty and reflects more uncertainty information. The multivariate output global sensitivity analysis is developed based on the single output global sensitivity analysis and it mainly focuses on the effects of input variables on the uncertainty of the whole multivariate output. For the models with multivariate outputs, the correlation between different outputs exists and it should be considered when performing the global sensitivity analysis. Comparing to the single output global sensitivity analysis, the multivariate output global sensitivity analysis is much more complicated and computational demanding since there are more uncertainty information for the multivariate outputs. The basic theories of different global sensitivity analysis methods are described in detail in order to have better understanding of these methods. Numerical examples are also used to compare these different methods. Through the comparison, the advantages and shortage of different global sensitivity analysis methods are obtained.