1. A method for analyzing high cycle fatigue (HCF) in a design of a gas turbine engine, comprising: identifying a component of the gas turbine engine for high cycle fatigue analysis; inputting parametric data of the component over a predetermined parameter space into at least one computer processor; using the at least one computer processor to build a plurality of flexible models of the component based on the parametric data of the component over the predetermined parameter space; using the at least one computer processor to build a plurality of emulators of the component based on the plurality of flexible models; and using the at least one computer processor to predict a probability of HCF based at least in part on the parametric data of the component over the predetermined parameter space and the plurality of emulators.