Active learning assisted strategy of constructing hybrid models in repetitive operations of membrane filtration processes: Using case of mixture of bentonite clay and sodium alginate

•A hybrid active learning TMP model is developed.•Novel probabilistic modeling is used to approximate nonlinear fouling mechanism.•The hybrid TMP model can be updated efficiently without unnecessary data samples.•Accurate hybrid TMP models for both filtration and backwashing phases are built.•Superiority of active learning TMP models is shown via simulation and experiments.

Reliable prediction of the transmembrane pressure (TMP) in membrane filtration systems often encounters different challenges in practice, including process nonlinearity, cycle-to-cycle change, and multiple operating conditions. In this work, an active learning TMP model with the hybrid structure is developed to predict the short-term fouling formation. The advantages of the physical and empirical models are integrated into this hybrid model. For construction of the empirical model, the Gaussian process regression model (GPRM) is adopted to approximate the complex fouling mechanism with fouling propensity in the short-term period. It can be a useful complement to the physical model with inaccuracy. Moreover, GPRM can simultaneously provide the prediction variance. Using this appealing property, the hybrid TMP model can be updated in an active and efficient manner without introducing additional unnecessary data samples. Consequently, accurate hybrid TMP models for the repetitive operations of membrane filtration processes are established. The superiority of the proposed hybrid TMP models is demonstrated through simulation and short-term experiments. The experimental results show the hybrid TMP models have better prediction performance (with R2 values larger than 0.9) than the physical model (with R2 about 0.5).