Modeling of a permeate flux of cross-flow membrane filtration of colloidal suspensions: A wavelet network approach

Although traditional artificial neural networks have been an attractive topic in modeling membrane filtration, lower efficiency by trial-and-error constructing and random initializing methods often accompanies neural networks. To improve traditional neural networks, the present research used the wavelet network, a special feedforward neural network with a single hidden layer supported by the wavelet theory. Prediction performance and efficiency of the proposed network were examined with a published experimental dataset of cross-flow membrane filtration. The dataset was divided into two parts: 62 samples for training data and 329 samples for testing data. Various combinations of transmembrane pressure, filtration time, ionic strength and zeta potential were used as inputs of the wavelet network so as to predict the permeate flux. Through the orthogonal least square alogorithm, an initial network with 12 hidden neurons was obtained which offered a normalized square root of mean square of 0.103 for the training data. The initial network led to a wavelet network model after training procedures with fast convergence within 30 epochs. Futher the wavelet network model accurately depicted the positive effects of either transmembrane pressure or zeta potential on permeate flux. The wavelet network also offered accurate predictions for the testing data, 96.4 % of which deviated the measured data within the ± 10 % relative error range. Moreover, comparisons indicated the wavelet network model produced better predictability than the back-forward backpropagation neural network and the multiple regression models. Thus the wavelet network approach could be employed successfully in modeling dynamic permeate flux in cross-flow membrane filtration