Abstract. For probabilistic monitoring of multimode processes, this paper introduced a monitoring scheme that integrates joint probability density and weighted probabilistic principal component analysis based on coefficient of variation (CV-WPPCA). A joint probability based on 2 statistic was constructed for mode identification. After it concentrated maximum fault-relevant information into dominant subspace by identifying and extracting important noise factors from the residual subspace, the new approach utilized a weighting strategy based on coefficient of variation method to highlight the useful information in the reconstructed dominant subspace. A case study on the Tennessee Eastman process was applied to demonstrate the efficiency of the proposed method.

Probabilistic principal component analysis (PPCA) is widely used in process monitoring and has achieved effective fault detection and online fault identification. However, the relationship between fault information and certain probabilistic principal components has not been explicitly mapped. Therefore, fault information might be scattered across 2 different subspaces when probabilistic principal components are selected subjectively based on variance. Moreover, although the maximum useful information is collected into a new subspace by the selected elements, a large amount of useless information might cover up the fault-relevant information. Considering these shortcomings, weighted PPCA based on entropy method and moving window (EMW-PPCA) is applied in this study to improve the monitoring performance of traditional PPCA. After building a traditional PPCA model through normal observations, EMW-PPCA proposes a novel strategy to identify and extract as much fault-relevant information as possible from the residual subspace and then integrates the selected fault-relevant noise factors into the dominant subspace to create a new specific subspace for process monitoring. The entropy method is applied to this new subspace to define the importance degree of each direction and evaluate the weighting values objectively. Then, the weighting values are assigned to each of the corresponding elements to highlight the fault-relevant information for online monitoring within a moving window. Case studies on a simple numerical example are conducted, and the Tennessee Eastman process is applied to validate the effectiveness of the EMW-PPCA scheme.