均值对奇异特征值分解算法的影响机制

Influence Mechanism of the Mean Values on POD Method

该文研究了均值在奇异特征分解算法(POD)中的影响机制.首先,给出了POD方法中时间系数的相关基本性质.其次,基于矩阵分析理论,引入全信号及去除均值部分信号的相关矩阵,且从理论上推导了均值对POD方法的影响机制,这在以往研究中较少见到.最后,通过数值算例对均值场在POD过程中的影响机理进行验证.

The proper orthogonal decomposition(POD) has been known as an efficient reduction technique in simulating physical process which governed by partial differential equations.In this paper,the basic properties of time coefficients in POD method are studied.Based on the theories and matrix analysis,by introducing the cross-correlation matrix(CROM) of the whole signals and the covariance matrix of the fluctuating parts of signals(in which the mean values have been cancelled,COVM),we derive the influence mechanism of mean values on the POD method in theory.There are fewer relevant studies in previous works.Finally,numerical examples are provided for verification and demonstration the influence mechanism in POD process.