A new methodology for the prediction of optimal conditions for dyes' electrochemical removal; Application of copula function, machine learning, deep learning, and multi-objective optimization

In the present study, a new methodology has been introduced for predicting the simultaneous removal optimal conditions of Acid red 33 (AR33), Reactive orange 7 (RO7), Acid yellow 3 (AY3), and Malachite green (MG) dyes. Since industrial wastewater contains a variety of dyes, simultaneous prediction of their removal efficiency is a practical issue. The goal of this research was to address challenges associated with modeling this type of removal process. In the first part of this methodology, the c-vine copula function was used to generate synthetic data since the use of most modeling methods requires a large number of data, and studying different experimental conditions is time- and cost-consuming. Besides, Artificial neural network, Adaptive neuro-fuzzy inference system, Least-square support vector machine, and Long-short term memory algorithms were applied for modeling the dyes' removal efficiency using experimental and synthetic data. Utilizing synthetic data significantly improved the accuracy of modeling. For the purpose of finding the optimal amount of dyes' removal efficiency simultaneously, the removal efficiency of each dye is defined as an objective function. This leads to a problem requiring multi-objective optimization. Hence, the Multi-Objective Adaptive Guided Differential Evolution was employed for multi-objective optimization of dyes' removal efficiency. The optimization process was carried out based on the four objective functions including AR33, RO7, AY3, and MG dyes' removal efficiency. The results indicated a direct relationship between dyes' removal efficiency on the Pareto front as well as a highly oscillating and nonlinear relationship with decision variables (pH, NaCl concentration, current, and Time) under optimal conditions. Finally, the average results of Technique for Order of Preference by Similarity to Ideal Solution and VIekriterijumsko KOmpromisno Rangiranje were utilized to select the best optimal conditions from the Pareto front. With pH, NaCl, Time, and current inputs at 6.60, 0.67 (g/L), 96.93 (min), 0.01 (A) (optimal conditions), the best removal efficiencies of 98.88, 37.02, 91.19, and 98.33 (%) were obtained for AR33, RO7, AY3, and MG dyes, respectively. The introduced method demonstrated excellent promise for predicting optimal conditions for dyes' removal efficiency as well as for making wastewater treatment systems easier to design.