Multivariate Calibration Models Based on Functional Space and Partial Least Square for Batch Processes

Abstract

In this paper, the multivariate calibration model of complicated batch processes based on functional space analysis and PLS (partial least square), called FPLS, is explored. This method extends our previous research topic (Chen and Liu, 2001; Chen and Liu, 2000) which focuses on the FPCA (functional principal component analysis) model without considering the relationship between independent and dependent variables. In FPLS, the trajectories of tbe process measurements in the batch are mapped onto the new feature parameters in the functional space. Then PLS can be performed using the feature parameters and the product quality data. Modeling FPLS models in this way has the advantage over the FPCA model because FPLS concentrates more on the events that will cause the offset product quality or the abnormal behavior. Besides, FPLS, like FPCA, can be used to build the model with different duration data. The methodology is shown through two examples, the fluorescence data and an exothermic batch chemical reactor, to illustrate the general use of this proposed method. The two examples are performed on the fixed and the varying operating time, respectively.