Abstract:Abstract: Based on the theories of Proper Orthogonal Decomposition(POD) and matrix analysis, the cross-correlation function matrix(CORM) of the mean values is introduced and decomposed, with which to demonstrate the influence mechanism of mean values on the application of POD for random fields with the whole signals or just the fluctuating signals(without the mean values included) concerned. With the section wind pressure fields of a cooling tower model and a box girder model, POD method is applied using the whole signals and just the fluttering signals. According to the POD results from two signals, the influence mechanism of mean values is illustrated, which is also a verification for the theoretical explanation obtaine. 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 signals are quite different because they are reflections of their original signals and shouldn’t be confused. If POD is applied on the cross-correlation function matrix of whole signals, POD results of all modes will be distorted by the mean values, especially the POD results of low order modes. As the mean values and fluctuating signals are always treaded separately, CORM should be formed by the fluctuating signals for POD application to reflect the characteristics genuinely and avoid the distortion of mean values.
张军锋 葛耀君 任鹏杰. 均值对随机场POD分解影响机理[J]. , 2012, 31(13): 46-52.
ZHANG Jun-feng;GE Yao-jun;REN Peng-jie. Influence mechanism of mean values on the application of POD for random fields. , 2012, 31(13): 46-52.