Artificial Neural Network Modelling of Multi-system Dynamic Adsorption of Organic Pollutants on Activated Carbon

The aim of this work was to model multi-system dynamic adsorption using an artificial intelligence technique. A set of data points, collected from scientific papers containing the dynamic adsorption kinetics on activated carbon, was used to build the artificial neural network (ANN). The studied parameters were molar mass, initial concentration, flow rate, bed height, particle diameter, BET surface area, average pore diameter, time, and concentration of dimensionless effluents. Results showed that the optimized ANN was obtained with a high correlation coefficient, R = 0.997, a root mean square error of RMSE = 0.029, and a mean absolute deviation of AAD (%) = 1.810 during the generalisation phase. Furthermore, a sensitivity analysis was also conducted using the inverse artificial neural network method to study the effect of all the inputs on the dynamic adsorption. Also in this work, the traceability of the estimated results was conducted by developing a graphical user interface.


Introduction
Industrialization is vital to sustainable development, and water resource management is essential in protecting the environment. However, the increase in world population leads to industrial growth and low quality wastewater containing pollutants harmful to human health and the environment. 1 The wastewater generated in industrial processes requires the use of pre-treatment methods and processes to reduce and/or eliminate all types of pollutants before discharge of the effluent into nature 2 . Wastewaters travel through the treatment plants to remove pollutants from them. Most of the wastewaters contain many substances that could be categorised into organic and inorganic pollutants. 3 Most of the organic pollutants in industrial effluents are difficult to analyse and cannot be treated using conventional methods. 4,5 This is due to the unlimited flow rates and excessively high concentrations, and their presence could cause significant environmental damage and health risks. Several studies and research have been conducted on the removal of these environmental organic pollutants using various physical and chemical methods. These methods include chemical precipitation, oxidation, ion exchange, coagulation/flocculation, solvent extraction, membrane separation, and adsorption. 6,7 Dynamic and/ or fixed bed adsorption is one of the most widely used processes in the environmental applications of chemical industries, especially for the separation and purification of effluents, due to its high efficiency, low cost, and easy operation. 8,9 The dynamic conduct of a fixed-bed column is described according to the breakthrough curve resulting from the adsorbent-adsorbate system analysis. 8,10 Artificial neural networks (ANNs) have also proven to be a suitable modelling tool to deal with complicated problems, especially when physical phenomena are present within the system. 11,12 (ANN) models can also be used as an alternative prediction method in analysis and engineering. They work like "black box" models, and require no detailed information about the system. 13 In many applications, ANNs have proven to be a valuable tool for creating databased empirical models. The great number of scientific papers that are being published recently, containing experimental data about the adsorption process, reflects the importance of this phenomenon; therefore, it is of the highest interest to exploit these results available in the literature. They can be used for development, monitoring, and design of the separation process with the help of informatics tools, where the spearhead of any innovative technique is modelling, optimisation, and simulation. Among these applications found in the literature, ANNs have been applied to describe the dynamic, p-nitrophenol, 14 the complex system, 15 and multi-component system of heavy metals, 16,17 with the adsorption process.
The aim of this research was to develop a multi-layer ANN to predict the dynamic adsorption of the adsorbent-adsorbate system consisting of 15 components as organic pollutants in the presence of multi-characteristic activated carbon under different operating conditions using the largest and most representative database in comparison with other studies. The performance of the ANN model was evaluated using classical analysis methods; the correlation coefficient (R), statistical root mean square error (RMSE), and average absolute deviation (AAD).

Artificial neural networks (ANNs)
ANNs are defined by a set of algorithms graphically derived from the performance of biological neurons, and have many uses for process modelling and analysis, as well as for predicting a particular system. 18 They are characterised by simple processing units known as nodes that perform certain mathematical functions. They are also known for their similarity to the structure of the human brain, having the potential to learn (store experimental knowledge) and automatically extract rules from complicated data. 19,20 The architecture of ANN consists of one or more hidden input layer(s), and an output layer. Each layer of the network consists of neurons, which are inter-connected processing elements. Each neuron is connected to all the neurons in the next layer. The output of the neural network is given by the output layer for the given input data. 21,22 The hidden layers enable these networks to compute complicated relations between inputs and outputs. The architecture of the ANN model is shown in Fig. 1. The mathematical expression between the input vector X i and output vector Z j of this element ( Fig. 1) can be defined as follows: 23,24 where f(x) is the linear or nonlinear transfer function, Z j is the output from the hidden layers, and are weighted outputs from the preceding layer as its input result. It propagates the resulting value to output Y: Combining Eqs. 1 and 2, the relation between the output Y and the inputs X i of the ANN is obtained: Shown below are three transfer functions that are the most commonly used for back-propagation (BP). 23 The logarithmic sigmoid transfer function (logsig): The hyperbolic tangent sigmoid transfer function (tansig): The pure linear transfer function (purelin): The procedure for updating the synaptic weights is called back-propagation (BP). BP refers to the way error computed at the output side is propagated backward from the output to the hidden layer(s), and finally to the input layer. 23
The used database for the ANN model is shown in Table 2.
Linear scaling in the range of [−1, +1] was used in the present study by calculating the minimum and maximum of each variable vector and scaling the data with respect to these limits. Normalisation function used in this work is given by Eq. 7, and it was programmed in MATLAB as (mapminmax, [−1, +1]): 42-44 where X i is the input or output variable X, and X min and X max are the minimum and maximum values of variable X.

Model performance evaluation
The performance of the ANN model was evaluated using the following statistical parameters, [45][46][47] as expressed below for the correlation coefficient (R): In this study, the database was randomly divided into three groups: training, test, and validation set, composed of 80 %, 10 %, and 10 %, respectively. Since there was no rule to determine the number of neurons in the hidden layers, a test and trial method was adopted in this work by repeating each architecture twenty times to avoid overfitting problem.
The optimised ANN architecture consisted of {8-45-1}, which means eight inputs forty-five neurons in the hidden layer and one output, as is shown in Fig. 2. The best ANN was found with the logarithmic sigmoid (logsig) given in Eqs. (4), and tangent hyperbolic (tansig) given in Eqs. (5) transfer functions for the hidden and the output layers, re- while the output of the network is given by: In Eqs. (11) and (12): w i,j is the weight of the connections between the input and the hidden neurons, x i are the input variables (relevant descriptors), b j is the bias on the hidden neuron similarly, w 1,j represents the weight of the connections between the hidden and output neuron, and b 1 is the bias on the output neuron.
The results showed that the ANN with one hidden layer was the best. Tests conducted for more than one of the hidden layers and different parameters showed no significant improvement. Table 3 shows the structure of the improved ANN model to obtain the highest correlation coefficient closer to 1, with the minimum RMSE error closer to 0. The linear regression parameters were obtained directly using the postreg MATLAB R2018a function.
The performance of the optimised network was evaluated for each epoch in the training through mean square error (MSE). Evolution of the mean square error for the training, validation, and testing stage vs. the number of epochs is shown in Fig. 3. The best ANN was found with a very acceptable validation performance at 4892 epochs, indicating an accurate mapping of the experimental data.  Table  3 suggest high performance of the optimised ANN with a correlation coefficient of R = 0.997, root mean square error of RMSE = 0.029, and the absolute deviation of AAD (%) = 1.810. It can be observed that ANN was able to capture the adsorption dynamics very well.
Detailed comparison between the calculated and the experimental values of each system in terms of correlation coefficient (R), root mean square error (RMSE), and average absolute deviation (AAD) is presented in Table 4.
Figs. 5 to 9 show comparison curves between experimental and ANN-predicted values illustrated in empty and full geometric shapes, respectively, of dynamic adsorption of     The last comparison, plotted in Fig. 9, of Norfloxacin, Ciprofloxacin, and Levofloxacin systems was conducted with the same three initial concentration values. Results show the ability of the ANN to model dimensionless effluent concentration of different dynamic adsorption systems at various operating conditions with high performance.

Sensitivity analysis
Sensitivity analysis is a critical tool for the determination of the relative importance of each input on the output variable. A sensitivity study was conducted by programming the Garson equation 48 in MATLAB software, and using the best model architecture {8, 45, 1} and parameters {weight matrix and vectors biases}.
where I j is the relative importance of the j input variable on the output variable; N i and N h are the number of input and hidden neurons, respectively; w are the connection weights; the superscripts i, h, and o refer to input, hidden, and output layers, respectively; and subscripts k, m, and n refer to input, hidden, and output neurons, respectively. 48,49 The contribution of the input variables obtained by the 'weight' method for the neural network is shown in Fig. 10.

Program for calculating the effluent concentration
In order to provide easy computing of effluent concentration, a computer program was designed based on the best ANN architecture {weights and biases}. All inputs were normalised and de-normalised via this interface to calculate the dimensionless effluent concentration (Fig. 11).

Conclusions
In this work, a methodology was proposed to predict the multi-system dynamic adsorption of organic pollutants on activated carbon. Conclusions are summarised as follows: • Before using ANN, the database used was collected from experimental data recently published in scientific articles, which include a relevant input matrix of [5951,8], as follows: molar mass, initial concentration, flow rate, bed height, particle diameter, BET surface area, average pore diameter, and dimensionless effluent concentration as an output. • Good agreement was shown between the experimental data and the data calculated by the ANN model, the correlation coefficients of the dataset (training, validation, and testing) were greater than 0.99, plus better robustness (R = 0.997, RMSE = 0.029, and AAD = 1.810 %) for the training group were obtained. • For determination of the importance of each input variable, a sensitivity analysis was conducted. The results showed that all input parameters had a significant relative importance on the output and could not be neglected. • Finally, a user-friendly graphical interface was designed based on the optimised ANN parameters.