Abstract
Generalized Polynomial Chaos Expansion (gPCE) is widely used in uncertainty quantification and sensitivity analysis for applications in the aerospace industry. gPCE uses the spectrum projection to fit a polynomial model, the gPCE model, to a sparse grid Design of Experiments (DOEs). The gPCE model can be used to make predictions, analytically determine uncertainties, and calculate sensitivity indices. However, the model’s accuracy is very dependent on having complete DOEs. When a sampling point is missing from the sparse grid DOE, this severely impacts the accuracy of the gPCE analysis and often necessitates running a new DOE. Missing data points are a common occurrence in engineering testing and simulation. This problem complicates the use of the gPCE analysis.
In this paper, we present a statistical imputation method for addressing this missing data problem. This methodology allows gPCE modeling to handle missing values in the sparse grid DOE. Using a series of numerical results, the study demonstrates the convergence characteristics of the methodology with respect to reaching steady state values for the missing points. The article concludes with a discussion of the convergence rate, advantages, and feasibility of using the proposed methodology.
2pCA5 - Uncertainty quantification in acoustics through generalized polynomial chaos expansions
