Using neural networks coupled with particle swarm optimization technique for mathematical modeling of air gap membrane distillation (AGMD) systems for desalination process

Nowadays, membrane distillation (MD) systems have found considerable attention in separation processes, especially for desalination applications. Among different MD systems, air gap membrane distillation (AGMD) system is of the most appropriate choices for water desalination. In this system, the stagnant air gap between the membrane and condensation surface causes an increase in the thermal energy efficiency of the process. To understand the relationships between input and outputs parameters and variables, a mathematical technique was developed using Volterra functional series theory. The cold feed inlet temperature (T ₁), hot feed inlet temperature (T ₃), and feed-in flow rate (F) were considered as the input variables of the AGMD system, and distillate flux (J), cold feed outlet temperature (T ₂), and gained output ratio (GOR) were set as the output variables. The relationships between these variables were examined, and their effect on the performance of the AGMD system was evaluated in terms of GOR and J by using the presented mathematical techniques of multivariable function approximation. A particle swarm optimization-based controlled neural network was also performed to explore the effect of input operational parameters on GOR, J, and T2 in each model to determine the existence domain of model coefficients. The experimental data have been collected from the literature and analyzed to check the consistency and accuracy of proposed model. It was found that the presented models can reproduce the available experimental data with desirable accuracy.