Batch process monitoring based on functional data analysis and support vector data description

Since the batch dataset is often organized as a special three-way array, i.e. (batches × variables × time), the research of data-based batch process monitoring has attracted much attention. This paper introduces a novel batch process monitoring framework based on functional data description (FDD), which treats each variable's trajectory varying with time in a batch process as a typical functional datum. Thus, the original batch process data can be transformed into a two-way manner (batches × functions of the variable trajectories) by describing each variable trajectory as a function. The FDD-based batch process monitoring method not only is effective to distinguish the subtle differences in the shape of variables' trajectories between normal batches and faulty batches, but also can easily handle some off-line data preprocessing steps, such as recovery of the missing data and trajectory alignment. Based on FDD, this paper extends a one-class classification method called support vector data description (SVDD) to its functional counterpart, which is called functional SVDD (FSVDD), and further proposes the algorithm of FSVDD-based batch process monitoring. Finally, two case studies, including a simulation example and an industrial semiconductor etch process, are used to illustrate the validity of the proposed FSVDD-based batch process monitoring method.