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.

翻译：维度分解广义多项式混沌展开（DD-GPCE）能够高效地对具有任意分布的高维随机输入的复杂工程系统进行前向不确定性量化（UQ）。然而，在DD-GPCE中构造与测度一致的正交多项式基需要输入分布的先验知识，而这在实际中往往难以获得。本文提出了一种数据驱动的DD-GPCE方法，消除了对此类先验知识的依赖，从而将其适用范围扩展至高维输入的UQ问题。输入分布通过平滑自助核密度估计（KDE）直接从样本数据中推断，而DD-GPCE框架则使KDE能够通过低维边缘估计来处理高维输入。随后，我们利用估计的输入分布，通过蒙特卡洛模拟进行白化变换，从而生成与测度一致的正交基函数。我们通过数学算例及一个涉及二十个随机输入的实际三维移动性设计的随机动力学分析，验证了所提方法的准确性。结果表明，与假设输入服从高斯分布的传统数据驱动方法相比，所提方法能够更精确地估计输出的均值与方差。