Principal Component Analysis on multi-rate sampling system

Till now, principal component analysis (PCA) has not concerned about groups of variables from different sampling rates yet, because the data on one rate are not correlated with the data on another one directly in multi-sampling system. Firstly, the mathematical characteristics of PCA comprised with data on different sampling rate are introduced now. Moreover, several helpful data interpolation approaches for a common sampling rate are proposed to make all groups of data on various sampling rate uniformly for building PCA model. The simulation from Tennessee Eastman process discusses PCA in different ways of sampling rate transformation, and proves that several PCA algorithms concerned about above transformations have similar process monitoring results despite of different ways of data process.