This paper presents a method for performing Uncertainty Quantification in high-dimensional uncertain spaces by combining arbitrary polynomial chaos with a recently proposed scheme for sensitivity enhancement (1). Including available sensitivity information offers a way to mitigate the curse of dimensionality in Polynomial Chaos Expansions (PCEs). Coupling the sensitivity enhancement to arbitrary Polynomial Chaos allows the formulation to be extended to a wide range of stochastic processes, including multi-modal, fat-tailed, and truncated probability distributions. In so doing, this work addresses two of the barriers to widespread industrial application of PCEs. The method is demonstrated for a number of synthetic test cases, including an uncertainty analysis of a Finite Element structure, determined using Topology Optimisation, with 306 uncertain inputs. We demonstrate that by exploiting sensitivity information, PCEs can feasibly be applied to such problems and through the Sobol sensitivity indices, can allow a designer to easily visualise the spatial distribution of the contributions to uncertainty in the structure.

翻译：本文提出了一种通过将任意多项式混沌与近期提出的灵敏度增强方案相结合（1），在高维不确定空间中进行不确定性量化的方法。纳入可用的灵敏度信息为缓解多项式混沌展开（PCE）中的维数灾难提供了一条途径。将灵敏度增强与任意多项式混沌耦合，使得该公式能够扩展到广泛的随机过程，包括多模态、厚尾和截断概率分布。因此，本文解决了PCE在工业领域广泛应用的障碍之一。该方法在多个合成测试案例上进行了验证，包括对一个采用拓扑优化确定、具有306个不确定输入的有限元结构进行不确定性分析。我们证明，通过利用灵敏度信息，PCE可以实际应用于此类问题，并且通过Sobol灵敏度指数，设计人员能够轻松可视化结构中不确定性贡献的空间分布。