Enhancing dynamic soft sensors based on DPLS: A temporal smoothness regularization approach. (April 2015) - Shang, Chao; Huang, Xiaolin; Suykens, Johan A.K.; Huang, Dexian
Abstract : Highlights: Temporal smoothness regularizations are applied to dynamic soft sensor modeling. Unlikely abrupt changes in model dynamics are penalized. The over-fitting problem is alleviated compared to traditional methods. The model has smoothed dynamic parameters and clearer interpretations. Abstract: Without an inclusion of process dynamics, traditional data-driven soft sensors are termed as static because only single snapshots of process samples are used. It leads to a series of limitations, such as sensitivity to temporal noises and inaccurate description in process dynamics. To this end, static models have been extended to dynamic versions thereof like dynamic partial least squares (DPLS) with lagged inputs for the sake of process dynamics. The dimension of soft sensor models' inputs, however, could be considerably larger than static ones, which leads to the over-fitting problem. In this paper, we introduce the concept of temporal smoothness as a novel approach to DPLS-based dynamic soft sensor modeling. The starting point is to not only include historical process data but also impose smoothness regularization on proximal dynamic parameters. The smoothness regularization assumes that historical inputs have smoothly varying impacts on the latent variables as a valid prior knowledge, which is in consensus with the physical truth of industrial processes. Therefore abrupt changes in model dynamics are desirably penalized and the DPLS-based soft sensors enjoy better generalizations and interpretations. A numerical example is given to demonstrate the advantages of temporal smoothness. A simulated Tennessee Eastman process study and a real quality prediction task in a crude distillation unit process are provided to show the feasibility as well as effectiveness of our method.