Multispace Total Projection to Latent Structures and its Application to Online Process Monitoring

In this paper, the use of multiple variable spaces is proposed for monitoring modern industrial processes where data for a large number of process variables may be collected from different sources to reveal different characteristics. The easiest method of modeling a process is to treat all variables in a single data space, but then the information inherent in different types of variables would be mixed together and there would be no local view of each variable space. An extended algorithm based on the concept of total projection to latent structures, which we call multispace T-PLS (MsT-PLS), is thus developed to treat variables in multiple data spaces. Multiple variable spaces that are separated from the measurement space are composed of different sets of process variables measured at the same time and responsible for the same response data. Using the proposed algorithm, the relationships among multiple variable spaces are studied under the supervision of quality characteristics. Thus, comprehensive information decomposition is obtained in each variable space, which can be separated into four systematic subspaces in response to the cross-space common and specific process variability and one final residual subspace. The theoretical support for MsT-PLS is analyzed in detail and its statistical characteristics are compared with those of single-space T-PLS (SsT-PLS) algorithm. A process monitoring strategy is developed based on the MsT-PLS subspace decomposition result and applied to the Tennessee Eastman process for illustration purposes.