A re-sampling statistics based imprecise moment independent global sensitivity analysis methodology with limited data of uncorrelated and correlated geotechnical properties

Abstract

Traditional Global Sensitivity Analysis (GSA) is often performed using variance-based Sobol’s GSA, considering statistics of inputs estimated from limited data to be precise. This can lead to inaccuracies in the importance ranking of inputs due to negligence of – i) epistemic uncertainties in their statistics, and ii) role of other moments of outputs in Sensitivity Indices (SIs). This study overcomes these limitations by proposing an imprecise moment independent GSA methodology. The methodology couples re-sampling statistical techniques, i.e., Jackknifing and Bootstrapping with Monte-Carlo Simulations based Borgonovo’s moment independent GSA to estimate distributions of SIs. The re-sampling techniques estimate epistemic uncertainties in the statistics of inputs by generating re-constituted samples. These epistemic uncertainties are then propagated via Borgonovo’s GSA to estimate their imprecise moment independent SIs. The methodology is further coupled with Nataf’s transformation and Moving Least Square-Response Surface Methods to deal with problems of correlated inputs and lack of explicit input-output relationships. The generalized nature of methodology is demonstrated for three real case studies (one tunnel and two slopes), with different correlation structures between inputs, input-outputs relationships (explicit/implicit), and failure mechanisms. The methodology estimated the distributions of SIs of inputs instead of their point estimates, indicating the propagation of epistemic uncertainties truthfully. The Jackknife-GSA was significantly efficient (∼99 %) with negligible differences in statistics of SIs as compared to Bootstrap-GSA. The correlation between inputs significantly affects the statistics of SIs. Further, a reduction in the imprecision of SIs of inputs with their increasing sample sizes was observed, which is consistent with the general understanding.