| Popis: |
We pursue a multi-faceted exploration of the Challenge problem aimed at examining the suitability of a probabilistic characterization of the epistemic uncertainties included with the problem statement. In the process, we treat subproblems A through D and delineate the opportunities and challenges associated with a probabilistic description as it pertains to each of uncertainty characterization, uncertainty propagation, and uncertainty management, as well as to sensitivity analysis and to design. We replace all epistemic variables with random variables whose initial (prior) distribution is uniform and we rely chiefly on two mathematical constructs to pursue our analysis. According to the first construction, we pursue a Bayesian approach for parameter inference and update that is applied directly on the probability densities of the various uncertainty variables, and use sampling techniques for uncertainty propagation. The second construction is based on an adapted polynomial chaos expansions (PCE), that reflects acquired knowledge about the input-output map. Throughout the work, issues of efficiency are tackled with a combination of sparse quadrature methods and MCMC while proximity between probability densities is gaged using the Kullback-Leibler distance and new measures that are adapted to the structure and requirements of the Challenge problem. |
