Dynamic hypersphere based support vector data description for batch process monitoring

Support Vector Data Description (SVDD) is an efficient monitoring method that captures the spherically shaped boundary around the normal batch data and sets the control limit related to support vectors (SVs) for online monitoring. Using nonlinear transformation functions, SVDD constructs an irregular hypersphere in high dimensional space. When the batch process is complicated, the accuracy of monitoring will decrease with traditional control limit of SVDD. In this paper, dynamic hypersphere based support vector data description (DH-SVDD) is proposed for batch process monitoring. In training process, static hypersphere is built by the important SVs of training dataset. In testing process, dynamic hypersphere is built by the important SVs of combined dataset with current test sample and training dataset. If there is a significant change between these two hyperspheres, it means that the current test sample is an outlier. Thus, DH-SVDD has a relatively high monitoring accuracy because it fully considers relationship between the current test sample and the historical training dataset in high dimensional space. Comparison is conducted between the proposed DH-SVDD and traditional methods such as K-chart-SVDD, max limit SVDD and validation limit SVDD. The effectiveness of the DH-SVDD is also verified by a semiconductor etch process and a fed-batch penicillin fermentation process.