Different numerical estimators for main effect global sensitivity indices

Abstract

The variance-based method of global sensitivity indices based on Sobol' sensitivity indices became very popular among practitioners due to its easiness of interpretation. For complex practical problems computation of Sobol' indices generally requires a large number of function evaluations to achieve reasonable convergence. Four different direct formulas for computing Sobol’ main effect sensitivity indices are compared on a set of test models for which there are analytical results. Considered test functions represent various types of models that are found in practice. Formulas are based on high-dimensional integrals which are evaluated using Monte Carlo (MC) and Quasi Monte Carlo (QMC) techniques. Direct formulas are also compared with a different approach based on the so-called “double loop reordering” formula. It is found that the “double loop reordering” (DLR) approach shows a superior performance among all methods both for models with independent and dependent variables

Uncertainty and Sensitivity Analyses for Evaluating the Building Element‘s Replacement in Building LCA

“…The variance-based global sensitivity analysis was chosen, which decomposes the variance of the model (LCA) into fractions, that can be attributed to the inputs, here the building elements (Saltelli, 2004). This method is used in order to rank variables, fix unessential variables and decrease problem dimensionality (Kucherenko and Song, 2017), (Sobol′, 2001). Hence, the first and the total Sobol' Indices (main and total effect, respectively) were calculated, which represent the unique contribution of the parameters or the joint one with other parameters, respectively.…”

Key Characteristics identification by global sensitivity analysis

“…Among these sensitivity analysis methods, the variance-based method is considered in this article since the concern is to have the sensitivities by considering the variation on the whole domain and not only for a representative point (local sensitivities) and since the variance is considered as a good proxy of the uncertainty. Among the variance-based approaches, Sobol' approach is adopted in this study because of its efficient implementations that are well documented [25,26] and because of the possibility to perform the sensitivity analysis with moderate numerical efforts.…”

Sensitivity analysis in general metric spaces

“…As mentioned in the Introduction, many classical methods of estimation are available. Among them, one can cite estimation procedure based on polynomial chaos expansion [35], quasi Monte-Carlo scheme [18,25], the classical Pick-Freeze method [11,15], and more recently a method based on nested Monte-Carlo [13]. This last method seems to be numerically ecient.…”

“…Many dierent estimation procedures of the Sobol indices have been proposed and studied in the literature. Some are based on Monte-Carlo or quasi Monte-Carlo design of experiments (see [18,25] and references therein for more details). More recently a method based on nested Monte-Carlo [13] has been developed.…”