Biosorption of copper(II) ions by flax meal: Empirical modeling and process optimization by response surface methodology (RSM) and artificial neural network (ANN) simulation

•Potential of waste flax meal for the removal of copper(II) ions was investigated.•The effect of the operating parameters was modeled by RSM and ANN methods.•Box–Behnken, central composite and full factorial designs were compared.•ANN simulation was more accurate than RSM in prediction of biosorption efficiency.•ANN topology was optimized by RSM based on BBD.

In the present study, application of waste flax meal was investigated for the removal of copper(II) ions from aqueous solution. The effect of operating parameters such as metal ions concentration (20–200 ppm), biosorbent dosage (1–10 g/L) and solution pH (2–5) was modeled by both response surface methodology (RSM) and artificial neural network (ANN). This study compares central composite design (CCD), Box–Behnken design (BBD) and full factorial design (FFD) utility for modeling and optimization by response surface methodology. The best statistical predictability and accuracy resulted from CCD (R2 = 0.997, MSE = 0.34). Maximum biosorption efficiency expressed as the sorption capacity, which was found to be 34.4 mg/g, at initial Cu2+ concentration of 200 ppm, biosorbent dosage of 1 g/L and initial solution pH of 5. The precision of the equation obtained by RSM was confirmed by the analysis of variance and calculation of correlation coefficient relating the predicted and the experimental values of biosorption efficiency. A feed-forward neural network with a topology optimized by response surface methodology was applied successfully for prediction of biosorption performance for the removal of Cu2+ ions by waste flax meal. The number of hidden neurons, the number of epochs, the adaptive value and the training goal were chosen for optimization. The multilayer perceptron with three neurons in one input layer, twenty two neurons in one hidden layer and one neuron in one output layer were required to build the model. The neural network turned out to be more accurate than RSM model in the prediction of Cu2+ biosorption by flax meal. The novelty of this paper is application of response surface methodology in order to optimize artificial neural network topology. The research on modeling biosorption by RSM and ANN has been highly developed and new waste material flax meal as potential biosorbent has been proposed.