Application neural network approach for the estimation of heavy metal concentrations in the Inaouen watershed

This paper describes how the multilayer perceptron neural network (MLPNN) trained by the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-newton back-propagation approach was used to estimate heavy metal concentrations: Aluminum (Al), Lead (Pb), Copper (Cu), and Iron (Fe), in the province of Taza using sixteen physicochemical factors measured from 100 samples collected from surface water sources by our team, according to the protocol of the national water office (ONE). We chose a network with only one hidden layer to identify the network architecture to employ. The number of neurons in the hidden layer was varied, as were the types of transfer and activation functions, and the BFGS learning method was used. The following statistical metrics were used to evaluate the performance of the neural network’s stochastic models: Examining the adjustment graphs and residue, as well as the Error Sum of Squares (SSE); the mean bias error (MBE) and determination coefficient (R²). The results reveal that the predictive models created using the artificial neural network method (ANN) are quite efficient, thanks to the BFGS algorithm’s efficiency and speed of convergence. An architectural network [16-8-1] (16: number of variables in input layer, 8: number of hidden layer, 1: number of variables in output layer) produced the best results,{R²: Al(0.954), Pb(0.942), Cu(0.921), Fe(0.968)}, {SSE: Al(0.396), Pb(0.0059), Cu(0.252), Fe(4.29)} and {MBE: Al(–0.033), Pb(0.008), Cu(–0.004), Fe(0.091)}, which is developed so that each model is responsible for estimating the concentration of a single heavy metal. This result demonstrates that there is a non-linear relationship between the physical-chemical properties evaluated and the heavy metal content of surface water in the Taza province.