A common strategy to handle simulation-based uncertainty quantification problems is adopting a metamodel to replace time-demanding calculations such as computational fluid dynamics simulation or finite element analysis within Monte Carlo simulation process. However, most of the so far metamodel-assisted uncertainty quantification methods suffer from the ‘curse of dimensionality.’ The required number of evaluations, which determines the computational cost, increases exponentially as the dimensionality of the input uncertainty increases, resulting in unaffordable computational cost for high-dimensional problems. Another challenge emerges when the output uncertainties are a spatially varying field accommodating a huge number of spatial nodes. To solve these issues, here we propose a dimension-reduction metamodeling approach, in which active subspace method is utilized to reduce the input dimensionality and proper orthogonal decomposition method is utilized to reduce the output dimensionality of the spatially varying field. The relationship between the two methods is established by using the support vector regression model. Through uncertainty quantification of seven stochastic analytical functions and one stochastic convection-diffusion equation, the proposed approach was verified to be fairly accurate in propagating high-dimensional input uncertainties to either a scalar value or a spatially varying output. The accuracy and efficiency of the proposed approach in dealing with even more practical simulation-based problems were then validated by uncertainty quantification of a compressor cascade with stochastic protrusions/dents distributed on the blade surface. This work provides an effective and versatile approach for simulation-based high-dimensional uncertainty quantification problems.

处理基于仿真的不确定性量化问题的常见策略是采用元模型来代替诸如蒙特卡洛仿真过程中的计算流体动力学仿真或有限元分析等时间要求较高的计算。但是，到目前为止，大多数由元模型辅助的不确定性量化方法都遭受“维数诅咒”的困扰。随着输入不确定性的维数增加，确定计算成本的所需评估数量呈指数增长，从而导致高维问题的计算成本无法承受。当输出不确定性是容纳大量空间节点的空间变化场时，就会出现另一个挑战。为了解决这些问题，我们在这里提出一种降维元建模方法，其中采用主动子空间方法降低输入维数，采用适当的正交分解方法降低空间变化场的输出维数。两种方法之间的关系是通过使用支持向量回归模型建立的。通过对七个随机分析函数和一个随机对流扩散方程的不确定性量化，该方法在将高维输入不确定性传播到标量值或空间变化的输出中时，被证明是相当准确的。然后，通过对在叶片表面分布有随机凸起/凹痕的压缩机叶栅进行不确定性量化，验证了所提出方法在处理更为实际的基于仿真的问题上的准确性和效率。