Dynamic learning on the manifold with constrained time information and its application for dynamic process monitoring

- A novel process monitoring method called time information constrained embedding is proposed.
- The time window with a certain length is adopted to restrict the scope of the neighbors' selection.
- A new expression of time weight based on the distance in the time scale is given to quantify the importance of the sequential neighbors.
- To reveal the distance in the time scale, an enhanced object function is constructed to calculate the projection.

Complex industrial processes exhibit dynamic behavior. Typically, samples are correlate in time. Therefore monitoring methods based on a single process may not perform well under such conditions. In this paper, a novel algorithm named time information constrained embedding (TICE) is proposed to improve the monitoring performance for the dynamic process. In this study, the neighbors are selected to reconstruct the current data point. With the consideration of the serial correlation, the time window with a certain length is adopted to restrict the scope of the neighbors' selection. To reveal the distance in the time scale as well as to preserve the neighborhood structure, a new expression of time weight is given to quantify the importance of sequential neighbors. Furthermore, an enhanced objective function is constructed to calculate the transformation matrix. Finally, the superiority of the proposed method is illustrated by an application example (TecQuipment CE117 process trainer) and the Tennessee Eastman (TE) process.