Research On Relative PCA Theory With Its Application

Principal component analysis (PCA) is one of the most important methods for statistical control of multivariate process, which has been widely used at present in such fields as fault diagnosis, data compression, signal processing, pattern recognizing and so on. However, in traditional PCA, because of the neglect for influence of dimensions on system, the selected principal components (PCs) often fail to have representative. Moreover, according to the obtained approximately equal eigenvalues after dimensionless standardization, it is more difficulty to select PCs effectively. These questions all will impact the application of PCA algorithms in the practical systems. Based on the previous works, an improved algorithm called as relative principal component analysis (RPCA) is proposed with its application inito process monitoring. Achievements obtained are as follows:1. Discuss the influence of dimensionless standardization on system structure in detail, based on which an new algorithm called as RPCA is proposed by introducing"rotundity"scatter, relative transform(RT), relative principal components (RPCs) and so on. Firstly, standardize the system for dimensionless. Secondly, according to priori information, analyze and determine the different important levels of different variables. And then allocate weights for each variable under the criterion of conservation of system energy. Finally, utilize the relative-principal-component model established in this paper to analyze system. Both theoretic analysis and simulation have shown that RPCs selected by our method are more representative and their significance of geometry is more notable.2. Study on RPCA with its application on process monitoring and data compress, aiming at the problems happened in practical application. For example, data compression may be insufficiency, monitoring results are not exactly because of the unproperly PC selection, and outlier problems exist. Firstly, a mahalanobis distance (MD) method is proposed to reduce false alarms from outliers and data missing; and then a data compression ability performance index is built to verify validity of RPCA on process monitoring and data compression. By comparing with traditional PCA method, the new one can better utilize prior system information, make the PCs selection easier and thereby greatly improve the representing ability of RPCs.3. Analyze the change of T 2statistics mean in PCs subspace as while as statistics mean in residual subspace, on the basis of which, a method to determine proportional factor is given. SPE...