This work develops a novel basis-adaptive method for constructing anisotropic polynomial chaos expansions of multidimensional (vector-valued, multi-output) model responses. The adaptive basis selection is based on multivariate sensitivity analysis metrics that can be estimated by post-processing the polynomial chaos expansion and results in a common anisotropic polynomial basis for the vector-valued response. This allows the application of the method to problems with up to moderately high-dimensional model inputs (in the order of tens) and up to very high-dimensional model responses (in the order of thousands). The method is applied to different engineering test cases for surrogate modeling and uncertainty quantification, including use cases related to electric machine and power grid modeling and simulation, and is found to produce highly accurate results with comparatively low data and computational demand.

翻译：本研究提出了一种新颖的基自适应方法，用于构建多维（向量值、多输出）模型响应的各向异性多项式混沌展开。自适应基选择基于多元敏感性分析指标，这些指标可通过后处理多项式混沌展开进行估计，并为向量值响应生成一个通用的各向异性多项式基。这使得该方法能够适用于模型输入维度中等偏高（数十维）且模型响应维度极高（数千维）的问题。该方法被应用于不同工程测试案例的代理建模与不确定性量化，包括与电机和电网建模仿真相关的应用场景，结果表明其能以相对较低的数据需求和计算成本获得高精度的结果。