Selection Of The Number Of Principal Component Based On The Explanation Of Variability

Principal component analysis (PCA) finds wide application in chemical monitoring and fault isolation as a data-driven modeling method. Current studies show that PCA combined with data filters can effectively enhance the detectability for incipient faults. Research shows that the number of principal component, as the most important parameters in the process monitoring model, directly determines the detection performance of the process monitoring. In the process of modeling, selecting the correct number of data can effectively extract the main information from the data, eliminate the interference of the noise, and improve the effect of condition monitoring and the accuracy of fault diagnosis. There are several methods about the number selection of the principal component, such as, cumulative percent variance, average eigenvalue, cross-validation, variance of the reconstruction error, fault signal-to-noise ratio and so on.A novel method for selecting the number of PCs is proposed in this paper, which called variability explained by principal component. By calculating the variability of each variable that can be explained by every PC, we can obtain the correct number of PC by choosing the suitable PCs and calculating its collection. In this paper, we firstly discuss the definition and calculation method of VEPC and proposed two kind of rule used in the VEPC which called cumulative contribution rate rule and average contribution rate rule. After that, we carry out a detailed analysis of two kinds of rule and get the conclusion that the average contribution rate rule has a stronger adaptability. Furthermore, a Monte Carlo simulation model and a quadruple-tank process model are used to verify the feasibility of VEPC, and the VEPC is compared with several other conventional methods to illustrate its advantages.