Development of experimental design approach and ANN-based models for determination of Cr(VI) ions uptake rate from aqueous solution onto the solid biodiesel waste residue

•This paper investigates the Cr(VI) uptake rate on DPOC in batch and continues mode.•RSM and ANN models were used for removal of Cr(VI) ion in batch and continuous mode.•ANN had better prediction capability than RSM for Cr(VI) uptake rate on DPOC.•pH and temperature are significant factors for removal of Cr(VI) ions in batch mode.•Metal ions concentration and bed height are significant factors in continuous mode. In the present work, the evaluation capacities of two optimization methodologies such as RSM and ANN were employed and compared for predication of Cr(VI) uptake rate using defatted pongamia oil cake (DPOC) in both batch and column mode. The influence of operating parameters was investigated through a central composite design (CCD) of RSM using Design Expert 8.0.7.1 software. The same data was fed as input in ANN to obtain a trained the multilayer feed-forward networks back-propagation algorithm using MATLAB. The performance of the developed ANN models were compared with RSM mathematical models for Cr(VI) uptake rate in terms of the coefficient of determination (R2), root mean square error (RMSE) and absolute average deviation (AAD). The estimated values confirm that ANN predominates RSM representing the superiority of a trained ANN models over RSM models in order to capture the non-linear behavior of the given system.