Data-driven dimensionally decomposed generalized polynomial chaos expansion for forward uncertainty quantification

TL;DR

This paper presents a data-driven approach for high-dimensional uncertainty quantification that infers input distributions from data and constructs orthonormal polynomial bases without prior distribution knowledge, improving accuracy.

Contribution

It introduces a novel data-driven DD-GPCE method that infers input distributions from samples and constructs measure-consistent bases, extending UQ applicability to high-dimensional, unknown-input scenarios.

Findings

More accurate estimates of output mean and variance.

Effective handling of high-dimensional inputs via marginal KDE.

Validated on mathematical and practical engineering examples.

Abstract

Dimensionally decomposed generalized polynomial chaos expansion (DD-GPCE) efficiently performs forward uncertainty quantification (UQ) in complex engineering systems with high-dimensional random inputs of arbitrary distributions. However, constructing the measure-consistent orthonormal polynomial bases in DD-GPCE requires prior knowledge of input distributions, which is often unavailable in practice. This work introduces a data-driven DD-GPCE method that eliminates the need for such prior knowledge, extending its applicability to UQ with high-dimensional inputs. Input distributions are inferred directly from sample data using smoothed-bootstrap kernel density estimation (KDE), while the DD-GPCE framework enables KDE to handle high-dimensional inputs through low-dimensional marginal estimation. We then use the estimated input distributions to perform a whitening transformation via Monte Carlo Simulation, which enables generation of measure-consistent orthonormal basis functions. We demonstrate the accuracy of the proposed method in both mathematical examples and stochastic dynamic analysis for a practical three-dimensional mobility design involving twenty random inputs. The results indicate that the proposed method produces more accurate estimates of the output mean and variance compared to the conventional data-driven approach that assumes Gaussian input distributions.