Time–space locality preserving coordination for multimode process monitoring

• An original multimode process monitoring method-TSLPC is developed.
• A block-wise matrix with multimodality labels is defined to solve the multimodality issue.
• A novel distance which contains neighborhood information is proposed.
• Not only the nearest data based on the distance but also adjacent data based on the time are selected in TSLPC.

In this paper, an original algorithm called time–space locality preserving coordination (TSLPC) is put forward to monitor multimode processes. First, a block-wise matrix with multimodality labels is defined for dealing with the multimode problem. The information of internal representations and posterior probabilities is contained in the defined block-wise matrix. In order to make the posterior probabilities of data belonging to each mode more accurate, a novel distance applying the neighborhood information is developed. Next, considering the within-mode serial correlation, not only nearest data based on the distance but also adjacent data based on the time are selected as neighbors in the proposed TSLPC algorithm. Then, the low-dimensional global characterization of the defined block-wise matrix can be acquired by optimally preserving the neighborhood structure of the dataset. In addition, the proposed TSLPC algorithm establishes a global model for multimode processes on the basis of the defined block-wise matrix, which is different from traditional multimode process monitoring methods where multiple local models corresponding to multiple modes are constructed. Finally, the multimode continuous stirred tank reactor (CSTR) process and the multimode Tennessee Eastman (TE) process are studied to show the advantage of the proposed TSLPC method.