(605c) Two-Stage Subspace Identification for High Performance Softsensor Design

Product quality is not always measured on-line and its estimates are useful for realizing feedback control; thus softsensors play an important role in achieving better industrial productivity. To build softsensors, statistical methods have been widely used. When many process variables are used as input variables of a statistical model, the highly correlated nature of process data must be taken into account. In distillation processes, for example, tray temperatures close to each other change in nearly the same way. Applying a statistical modeling method to such highly correlated data causes a collinearity problem. To solve this problem, composition estimators using partial least squares (PLS) have been widely used. Kano et al. (J. Proc. Cont., 2000) investigated PLS-based inferential models, which can estimate product compositions of a multicomponent distillation column from on-line measured process variables. They compared steady-state, static, and dynamic inferential models and found that the estimation accuracy could be greatly improved by using dynamic models.

In recent years, much research on subspace identification (SSID) has been conducted, and several applications of SSID to softsensor design have been reported (for example, Amirthalingam and Lee, J. Proc. Cont., 1999). However, the performance of the conventional methods based on the Kalman filtering technique is limited due to the assumption that innovations are Gaussian white noises and the properties of disturbances stay constant with time. In other words, the conventional methods do not use measured variables effectively, while measured variables contain valuable information on a process including unmeasured disturbances that have serious influence on key variables.

In the present work, two-stage SSID is proposed to develop highly accurate softsensors that can take into account the influence of unmeasured disturbances on key variables explicitly. The procedure of two-stage SSID is as follows: 1) identify a state space model by using measured input and output variables, 2) estimate unmeasured disturbance variables from residual variables, and 3) identify a state space model to estimate key variables from the estimated disturbance variables and the other measured input variables. The proposed method can estimate unmeasured disturbances without assumptions that the conventional Kalman filtering technique must make. The usefulness of the proposed method is demonstrated through its applications to illustrative numerical examples and an industrial ethylene fractionator. To develop accurate softsensors, it is very effective to use measured input variables including manipulated variables and disturbances and also estimated unmeasured disturbance variables. The proposed two-stage SSID can cope with these three types of inputs systematically; thus it can realize highly accurate softsensors and outperform the conventional methods.