Reduction and control of flux decline in cross-flow membrane processes modeled by artificial neural networks and hybrid systems Stefano Curcio*, Vincenza Calabro `, Gabriele Iorio Department of Engineering Modeling, University of Calabria, Rende, Italy email: stefano.curcio@unical.it, vincenza.calabro@unical.it, gabriele.iorio@unical.it Received 30 June 2007; revised accepted 7 October 2007 Abstract The aim of the present paper is the development of a hybrid system to model the behavior of membrane units operating in pulsating conditions. In two previous papers the authors already showed how efficiently advanced models based on artificial neural networks (ANN) could be used to predict the behavior of unsteady-state mem- brane processes. Nevertheless, a ‘‘pure’’ neural model does not make use of any equation that could help to deter- mine, on the basis of fundamental principles, the mutual relationships existing between the inputs and the outputs. A hybrid system represents an alternative method that may allow predicting the behavior of complex systems, in a more efficient way. Hybrid model predictions are given as a combination of both a theoretical and a neural net- work approach, together concurring to the obtainment of system responses. In this way, some well-assessed phe- nomena can be described by a fundamental theoretical approach; some others, being very difficult to interpret, can be analyzed by means of rather simple ‘‘cause-effect’’ models, based on ANN. Keywords: Ultrafiltration; Modeling; Transport phenomena; Hybrid models 1. Introduction In a previous work [1], the authors of the pre- sent paper developed an artificial neural network (ANN) model capable to analyze the behavior of membrane systems operating in pulsating con- ditions. The network was trained through a selected set of experimental data collected dur- ing the ultrafiltration of aqueous BSA solutions through PES membranes. All the experiments were performed in a lab-scale flat sheet mem- brane module equipped with a device that gener- ated periodic and repeated pulses of both the applied trans-membrane pressure (TMP) and the feed flow rate (Q). During each pulse, operating *Corresponding author. Presented at the International Membrane Science and Technology Conference, IMSTEC 07, 5–9 November 2007, Sydney, Australia 0011-9164/09/$– See front matter # 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.desal.0000.00.000 Desalination 236 (2009) 234–243