Batch process monitoring with tensor factorization

A batch process monitoring method using tensor factorization, tensor locality preserving projections (TLPP), is proposed. In many existing vector-based methods on batch process monitoring such as MPCA and MLPP, a batch data is represented as a vector in high-dimensional space. But vectorizing batch data will lead to information loss. Essentially, a batch data is presented as a second order tensor, or a matrix. In this case, tensor factorization may be used to deal with the two-way batch data matrix directly instead of performing vectorizing procedure. Furthermore, tensor representation has some advantages such as low memory and storage requirements and less estimated parameters for normal operating condition (NOC) model. On the other hand, different from principal component analysis (PCA) which aims at preserving the global Euclidean structure of the data, the TLPP aims to preserve the local neighborhood information and to detect the intrinsic manifold structure of the data. Consequently, TLPP may be used to find more meaningful intrinsic information hidden in the observations. The effectiveness and advantages of the TLPP monitoring approach are tested with the data from a benchmark fed-batch penicillin fermentation and two industrial fermentation processes, penicillin and cephalosporin, respectively.