Quantifying Random Variable Dependence Structure Through Copulas Theory for Probabilistic Assessment

摘要

This paper is an initial contribution to the aerospace audience intended to disseminate copulas theory and showcase its capabilities. The applications demonstrate how the quantification of uncertainty in design can be improved using copulas to correlate variables that are traditionally and arbitrarily treated as independent or deterministic. Our canonical problem and subsequent applications only address a few technology impact factors applied to the aircraft wing tracked through a single aircraft level response metric, yet we have shown that inclusion of copulas theory has substantial impact on our results. There are many other engineering problems with a large variety of technologies and impacts on the entire aircraft that must be investigated and correlated as appropriate between themselves, across technologies, and with design variables to fully understand the implications of using copulas theory in the design of aircraft.