A Bayesian multi-model inference methodology for imprecise moment-independent global sensitivity analysis of rock structures

Abstract

Traditional global sensitivity analysis (GSA) neglects the epistemic uncertainties associated with the probabilistic characteristics (i.e. type of distribution type and its parameters) of input rock properties emanating due to the small size of datasets while mapping the relative importance of properties to the model response. This paper proposes an augmented Bayesian multi-model inference (BMMI) coupled with GSA methodology (BMMI-GSA) to address this issue by estimating the imprecision in the moment-independent sensitivity indices of rock structures arising from the small size of input data. The methodology employs BMMI to quantify the epistemic uncertainties associated with model type and parameters of input properties. The estimated uncertainties are propagated in estimating imprecision in moment-independent Borgonovo's indices by employing a reweighting approach on candidate probabilistic models. The proposed methodology is showcased for a rock slope prone to stress-controlled failure in the Himalayan region of India. The proposed methodology was superior to the conventional GSA (neglects all epistemic uncertainties) and Bayesian coupled GSA (B-GSA) (neglects model uncertainty) due to its capability to incorporate the uncertainties in both model type and parameters of properties. Imprecise Borgonovo's indices estimated via proposed methodology provide the confidence intervals of the sensitivity indices instead of their fixed-point estimates, which makes the user more informed in the data collection efforts. Analyses performed with the varying sample sizes suggested that the uncertainties in sensitivity indices reduce significantly with the increasing sample sizes. The accurate importance ranking of properties was only possible via samples of large sizes. Further, the impact of the prior knowledge in terms of prior ranges and distributions was significant; hence, any related assumption should be made carefully.