Removal efficiency optimization of Pb2+ in a nanofiltration process by MLP-ANN and RSM


Using computational intelligence for prediction, modeling, and optimization of chemical process behavior could save costs and time. This study’s main goal was to predict and optimize removal efficiency and permeate flux behavior of Pb2+ aqueous solution in a nanofiltration process through using response surface methodology (RSM) and multilayer perceptron (MLP) neural network. A regression coefficient R2=0.99 was obtained for both removal efficiency and permeate flux in the RSM model. Also, the F-value for the removal efficiency and permeate flux was 394.79 and 1888.85, respectively. Different MLP structures for predicting removal efficiency and permeate flux behavior of lead ion in aqueous solutions were investigated. The best structure was obtained for two hidden layers with nine (tansig transfer function) and three (logsig transfer function) neurons. The values of R=0.9993, R2=0.9986, MSE=0.402 and MAE=0.409 for the best structure were obtained. Finally, the the removal efficiency was optimized through RSM based on the experimental data. It was concluded that optimum mode selected for membrane composition of PSF=10.04%, NMP=88.98%, and PAN-CMC-41=0.98% (wt%) 53.17 ppm as lead ion concentration in solution and 30.31 min for filtration time achieved the maximum value of removal efficiency equal to 90.68%.

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artificial neural network


analysis of variance


degrees of freedom


design of experiments


log sigmoid transfer function


mean absolute error


multilayer perceptron


margin of deviation


mean square error


hyperbolic tangent sigmoid transfer function

R2 :

regression coefficient


response surface methodology


root mean square error




temperature [°C]



Pb2+ :

lead ion


ultra filtration


nano filtration


reverse osmosis


removal efficiency


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Correspondence to Mohammad Reza Sarmasti Emami.

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Emami, M.R.S., Amiri, M.K. & Zaferani, S.P.G. Removal efficiency optimization of Pb2+ in a nanofiltration process by MLP-ANN and RSM. Korean J. Chem. Eng. 38, 316–325 (2021).

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  • Membrane
  • Modeling
  • Prediction
  • RSM
  • MLP
  • Lead Ion
  • Filtration