A Methodology for Imprecise Moment-Independent Global Sensitivity Analysis with Limited Data of Copula-Dependent Inputs: Application for Slopes

Abstract

Importance ranking of rock properties is important in allocating investigation resources, and then performing probabilistic analysis efficiently. Traditional global sensitivity analysis (GSA) can be employed to perform this ranking; however, it neglects (1) the epistemic uncertainties in the probability models and their parameters due to small sample sizes of inputs, and (2) the mutual dependence of inputs. This paper overcomes these limitations by introducing a stratified Bayesian multimodel inference (BMMI) coupled with moment independent GSA to estimate the imprecise sensitivity indexes (SIs) with complex copula-dependent inputs. The methodology initially identifies candidate marginal models and the uncertainties in their parameters by BMMI, which is employed to construct a model set comprising an ensemble of marginals estimated via the reweighting approach. Subsequently, this model set is used to quantify the uncertainties in the copula-based dependent structure using BMMI. The final step is to estimate the inaccurate SIs using the Monte Carlo–based moment independent GSA framework, which propagates an ensemble of joint densities to represent the overall uncertainty. The methodology is generalized in a way that it can be used for any number of complexly dependent inputs and eliminates the need to estimate conditional probability density functions (PDFs) and a precise copula otherwise required in mapping-based and traditional GSA. The methodology is demonstrated for two slopes, i.e., an infinite soil slope (two inputs) and a rock slope (four inputs). The methodology was accurate for both examples, and more informative than traditional GSA because it estimates the bounds of SIs reflecting the effect of epistemic uncertainties associated with dependent inputs with their point estimates from traditional GSA lying in their bounds.