Predicting Optimized Dissolution of Selected African Copperbelt Copper-cobalt-bearing Ores by Means of Neural Network Prediction and Response Surface Methodology Modeling

Abstract

AbstractWhile the uncertainty brought about by a varying feed mineralogy was taken into consideration, the paper investigated the modeling and prediction of the leaching behavior of complex copper-cobalt bearing ores, using an artificial neural network (ANN) with a backforward algorithm. The process optimization is further conducted using the response surface methodology (RSM) employing the Box-Behnken design (BBD). Seven (7) parameters were considered in a multiple linear regression according to the L12screening plan (27) of Plackett–Burman. From the seven parameters, four including solid percentage (15, 27.5, 40%), time (45, 90, 135 min), particle size passing (53, 75, 105 µm), and Fe2+ion concentration (2, 4, 6 g/L) are modeled with L27(34) BBD. With a composite desirability of 0.94, leaching yields of 93.46% Cu and 89.43% Co were obtained. The neural network algorithm used is the BFGS (Broyden, Fletcher, Goldfarb and Shanno) algorithm multilayer perceptron with the hyperbolic tangent activation function for the hidden layer and a linear activation function for the neural output. The Multilayer perceptron {4–7-1} structure was chosen as a suitable arrangement for Cu leaching. Comparing the predicted values and those obtained experimentally resulted with a correlation coefficient of 0.9552 for the data trained in the artificial neural network and 0.8742 for the data obtained with the response surface methodology. The synergy of these 2 techniques shows that the prediction can be achieved by means of the ANN giving the values of the root mean square errors (RMSE) of 0.0115, 0.00624, 0.0229, respectively, for the training, testing and validation sets for copper recovery while the correlational study between variables could be done through the RSM. The above includes only the 95% confidence interval while the remaining 5% would be uncertain. The above results and conclusion are accompanied by the relative uncertainty as the ore mineralogy varies. The combination of the synergistic use of ANN and RSM with the sensitivity analysis has approached the process to the physics of the Multi-criteria decision-making.Graphical Abstract