Rigorous uncertainty quantification with correlated random variables from multiple sources

A method of quantification of margins and uncertainties (QMU) is developed for structures with correlated random variables originated from multiple sources. The QMU analysis aims to certify the concerned structure with a prescribed confidence factor (CF), and further determine an adequate design margin. After partitioning correlated random variables into different groups based on their uncertain sources, the multidimensional parallelepiped model is established to describe the uncertainty domain of these correlated random variables. Based on the grouped independent random vectors, McDiarmid's inequality is applied to realize rigorous uncertainty quantification of the structural performance. The computation of structural uncertainty is formulated as an optimization problem of variables within the multidimensional parallelepiped uncertainty domain. The QMU framework is then established and applied to low cycle fatigue life assessment of aero-engine turbine disc made of GH720Li superalloy. Stochastic parameters involving loads, geometries, and material properties, are chosen as input random variables. It is demonstrated that the turbine disc can be rigorously certified under the given design specification. By contrast, it will provide a wrong certification decision when the correlation of variables is not considered. The assessment provides an effective basis for the design with enough confidence in engineering applications from the perspective of QMU analysis.