均值对随机场POD分解影响机理

基于POD方法的理论基础与数学矩阵分析,通过引入随机场均值的相关矩阵及对均值相关矩阵的POD分解,阐述均值对随机场完整信号和脉动信号POD分解的影响机理。以双曲冷却塔模型和闭口箱梁模型的断面风压场POD分解实例,分析风压均值的影响,并验证上述理论解释的合理性。尽管随机场均值并不影响POD方法对随机场的分解和重建过程,但两种信号分解得到的各阶参数如本征值、本征模态及主坐标都只是所采用信号特性的反映而不能相互混淆。以完整信号分解得到的各阶参数都将受到随机场均值的影响,尤其是低阶参数。由于实际使用中对随机场的信号均值和脉动信号多分别对待,因此在POD分解中应使用脉动信号构建相关矩阵以完全反映脉动信号的特性,从而避免信号均值的影响。

Influence mechanism of mean values on POD of signals in random fields

Based on the theories of proper orthogonal decomposition(POD) and matrix analysis,the cross-correlation function matrix(CORM) of the mean values was introduced and decomposed to demonstrate the influence mechanism of mean values on the POD of the whole signals or of the fluctuating parts of signals(with the mean values cancelled).The sectional wind pressure fields of a cooling tower model and a box girder model were taken as examples to expound the influence of mean values on the POD method.According to the POD results of the two kinds of signals,the influence mechanism of mean values was discussed,which is also a verification of the theoretical explanation obtained.The mean values have no effects on the decomposition or reconstruction of random fields,but the POD results such as spatial modes,eigenvalues and principle coordinates got form the two kinds of signals are quite different because they are reflections of their original signals and shouldn’t be confused.In the case of CORM from whole signals,POD results of all modes will be distorted by mean values,especially the POD results of low order modes.As the mean values and fluctuating parts of signals are always processed separately,CORM should be formed from the fluctuating parts of signals to reflect the characteristics genuinely and avoid the distortion by mean values.