(669e) Selection of Similarity Measure for Locally Weighted Partial Least Squares Regression
AIChE Annual Meeting
Thursday, October 20, 2011 - 9:55am to 10:15am
Soft-sensors are widely used in various industrial processes to realize high product quality and productivity. However, their estimation accuracy deteriorates due to changes in processes characteristics and operating condition. In fact, the recent questionnaire survey confirms that model maintenance is the most important issue concerning soft-sensors (Kano and Ogawa, 2010). Since model maintenance or reconstruction is demanding for operators and engineers, practical, adaptive modeling techniques that can maintain high estimation accuracy need to be developed.
Locally weighted partial least squares (LW-PLS) is an adaptive modeling technique that builds a local linear regression model based on the similarity between a query and sample data stored in the database when output estimation is required. LW-PLS combines the capabilities of locally weighted regression and PLS; thus it can cope with the nonlinearity, the time-varying nature, and the colinearity. In the recent years, LW-PLS has been applied to various industrial processes including chemicals, semiconductor, and pharmaceuticals.
The estimation accuracy of LW-PLS depends on the definition of similarity between a query and samples. Thus, the present research focuses on the selection of similarity measure. The similarity is generally defined on the basis of the distance such as Euclidean distance and Mahalanobis distance; it is determined by using exponential function of the distance in conventional methods. In this work, new weighted distances are investigated; each input variable is weighted by its corresponding regression coefficient derived by LW-PLS or conventional PLS. In addition, various functions such as Sigmoid function are investigated to improve the prediction performance.
Various LW-PLS methods were applied to actual operation data of the ethylene fractionator at Showa Denko K.K. in Japan. As a result, the best estimation accuracy was achieved by the LW-PLS model based on the new similarity determined by Sigmoid function of the weighted distance in which each input variable is weighted by its corresponding regression coefficient derived by conventional PLS; the estimation accuracy was improved by 20 % in Root Mean Square Error of Prediction (RMSEP) and by 6.9 % in multiple correlation coefficient compared with the LW-PLS model based on the conventional similarity determined by exponential function of Euclidean distance. The results clearly show the proposed method is superior to the conventional method.
M. Kano and M. Ogawa: The State of the Art in Chemical Process Control in Japan: Good Practice and Questionnaire Survey. J. Proc. Cont., 20, 969-982 (2010)