Evaluating the performance of extended and unscented Kalman filters in the reverse osmosis process

A Kalman filter (KF) algorithm is a recursive data processing algorithm typically recommended for estimating unmeasured state variables in chemical engineering processes. We studied the performance of a KF algorithm in a range of noise levels as well as indirectly observed data from the process model. For this study, two versions of the KF algorithm widely adopted for a nonlinear system, the extended Kalman filter and the unscented Kalman filter, were applied to 1-year time series data monitored during the operation of the Fujairah seawater reverse osmosis desalination plant. We found that variables indicating the state of fouling, membrane resistance, and solute permeability agreed well with those estimated by the two KF algorithms, specifically in terms of noise reduction and peak detection. When the two KF algorithms were exposed to various noise levels, they showed a corresponding increase in the error rates (for unmeasured state variables) according to the noise levels varying from 10% to 50%, regardless of the algorithms used. The two KF algorithms provided a good prediction performance only for the permeate flow rate rather than for the permeate concentration, out of the two types of measured data. However, the individual KF algorithms still showed different performances in computing estimated and predicted data in the reverse osmosis process. This result calls for further research on the determination of the best KF algorithms for either estimation or prediction of directly and indirectly measured state variables in various chemical processes.