An enrichment scheme based upon the Neumann expansion method is proposed to augment the deterministic coefficient vectors associated with the polynomial chaos expansion method. The proposed approach relies upon a split of the random variables into two statistically independent sets. The principal variability of the system is captured by propagating a limited number of random variables through a low-ordered polynomial chaos expansion method. The remaining random variables are propagated by a Neumann expansion method. In turn, the random variables associated with the Neumann expansion method are utilised to enrich the polynomial chaos approach. The effect of this enrichment is explicitly captured in a new augmented definition of the coefficients of the polynomial chaos expansion. This approach allows one to consider a larger number of random variables within the scope of spectral stochastic finite element analysis in a computationally efficient manner. Closed-form expressions for the first two response moments are provided. The proposed enrichment method is used to analyse two numerical examples: the bending of a cantilever beam and the flow through porous media. Both systems contain distributed stochastic properties. The results are compared with those obtained using direct Monte Carlo simulations and using the classical polynomial chaos expansion approach.

提出了一种基于诺依曼展开方法的丰富方案，以增加与多项式混沌展开方法相关的确定性系数向量。所提出的方法依赖于将随机变量拆分为两个统计独立的集合。系统的主要可变性是通过低阶多项式混沌扩展方法传播有限数量的随机变量来捕获的。剩余的随机变量通过诺依曼展开方法传播。反过来，与诺依曼展开方法相关的随机变量被用来丰富多项式混沌方法。这种丰富的效果在多项式混沌展开系数的新增强定义中得到了明确的体现。这种方法允许人们以一种计算有效的方式在谱随机有限元分析的范围内考虑大量的随机变量。提供了前两个响应矩的闭式表达式。所提出的富集方法用于分析两个数值示例：悬臂梁的弯曲和通过多孔介质的流动。两个系统都包含分布式随机属性。将结果与使用直接蒙特卡罗模拟和使用经典多项式混沌扩展方法获得的结果进行比较。悬臂梁的弯曲和通过多孔介质的流动。两个系统都包含分布式随机属性。将结果与使用直接蒙特卡罗模拟和使用经典多项式混沌扩展方法获得的结果进行比较。悬臂梁的弯曲和通过多孔介质的流动。两个系统都包含分布式随机属性。将结果与使用直接蒙特卡罗模拟和使用经典多项式混沌扩展方法获得的结果进行比较。