Artificial neural network and differential evolution optimization of a circulated permeate gap membrane distillation unit

This study integrated an artificial neural network (ANN) model with a differential evolution (DE) optimization algorithm for cost optimization of a novel multi-stage permeate gap membrane distillation system with gap water circulation. A dataset with four inputs (feed temperature, feed flow rate, gap circulation rate, and coolant flow rate) and two outputs (flux and specific thermal energy consumption) was used to train the multi-layer perceptron-ANN. The ANN model was validated using the analysis of variance technique, and the resulting outputs were used to calculate water production costs. Differential evolution optimization model was employed to determine the lowest production cost. Results showed that the tan-sigmoid activation function outperformed the other tested activation functions with a mean average performance error of 1 %. The optimal number of neurons in the hidden layer was found to be 120, and the predicted output strongly agreed with the actual output with a regression coefficient greater than 99. The cost analysis for the waste-heat powered system revealed that under optimal conditions of feed temperature of 90 °C, number of stages of 12, and gap circulation rate per stage of 4.8 L/min, the cost of water production could be reduced to 1.8 US$/m³. Additionally, an optimum cost breakdown for the system was provided.