An extended polynomial chaos expansion for PDF characterization and variation with aleatory and epistemic uncertainties

This paper presents an extended polynomial chaos formalism for epistemic uncertainties and a new framework for evaluating sensitivities and variations of output probability density functions (PDF) to uncertainty in probabilistic models of input variables. An extended polynomial chaos expansion (PCE) approach is developed that accounts for both aleatory and epistemic uncertainties, modeled as random variables, thus allowing a unified treatment of both types of uncertainty. We explore in particular epistemic uncertainty associated with the choice of prior probabilistic models for input parameters. A PCE-based Kernel Density (KDE) construction provides a composite map from the PCE coefficients and germ to the PDF of quantities of interest (QoI). The sensitivities of these PDF with respect to the input parameters are then evaluated. Input parameters of the probabilistic models are considered. By sampling over the epistemic random variable, a family of PDFs is generated and the failure probability is itself estimated as a random variable with its own PCE. Integrating epistemic uncertainties within the PCE framework results in a computationally efficient paradigm for propagation and sensitivity evaluation. Two typical illustrative examples are used to demonstrate the proposed approach. (C) 2021 ElsevierB.V. All rights reserved.

Automated summary

This paper introduces an extended polynomial chaos formalism for addressing epistemic uncertainties and a new framework for evaluating sensitivities and variations of output probability density functions to uncertainty in probabilistic models of input variables. By combining aleatory and epistemic uncertainties in a unified treatment, a PCE-based approach is developed to evaluate sensitivities of outputs to input parameters efficiently. The integration of epistemic uncertainties within the PCE framework provides a computationally efficient paradigm for propagation and sensitivity evaluation.