Quantification of margins and uncertainties using an active subspace method for approximating bounds

In many engineering application, bounds on the model output are sought to characterize safe operating conditions of a system. When a complex model contains many inputs, determining such bounds may be intractable. However, if one can determine that the model output varies with gross, global monotonic trends along a low-dimensional active subspace of the high-dimensional input space, then this information can be exploited to find corners of the input space that likely correspond to bounds on the output. We present a method for determining the active subspace, and we use it to determine the safe operating conditions of a hypersonic scramjet vehicle with 19 independent input parameters.