A functional global sensitivity measure and efficient reliability sensitivity analysis with respect to statistical parameters

Sensitivity analysis and reliability assessment are two important aspects of structural and system safety. Epistemic uncertainty with respect to probabilistic model of input parameters due to lack of knowledge is present in many scarce-data applications and complicates the characterization of uncertainty in model response. In this article, we present two importance measures to evaluate the impact of distribution parameters on the probability distribution function (PDF) of the output and the failure probability. The epistemic uncertainty associated with the distribution parameters is modeled as random variables. A modified extended polynomial chaos expansion (MEPCE) approach is introduced in which aleatory and epistemic random variables are modeled and propagated simultaneously while allowing the separate assessment for any single epistemic variable. A MEPCE-based kernel density estimation (KDE) construction provides a composite map from each epistemic variable to the response PDF. The functional global sensitivity index of the PDF with respect to the distribution parameters is thus derived, as a function of output, which is both more informative and more efficient than standard scalar sensitivity measures. Reliability sensitivity indices can be readily evaluated by integrating the global sensitivity index function over the failure zone. Three illustrative examples are used to demonstrate the proposed methodology.