Data-Driven Machine Learning Intelligent Tools for Predicting Chromium Removal in an Adsorption System

Abstract

This study investigates chromium removal onto modified maghemite nanoparticles in batch experiments based on a central composite design. The effect of modified maghemite nanoparticles on the adsorptive removal of chromium was quantitatively elucidated by fitting the experimental data using artificial neural network (ANN) and adaptive neuro-fuzzy interference system (ANFIS) modeling approaches. The ANN and ANFIS models, relating the inputs, i.e., pH, adsorbent dose, and initial chromium concentration to the output, i.e., chromium removal efficiency (RE), were developed by comparing the predicted value with that of the experimental values. The RE of chromium ranged from 49.58% to 92.72% under the influence of varying pH (i.e., 2.6–9.4) and adsorbent dose, i.e., 0.8 g/L to 9.2 g/L. The developed ANN model fits the experimental data exceptionally well with correlation coefficients of 1.000 and 0.997 for training and testing, respectively. In addition, the Pearson’s Chi-square measure (χ²) of 0.0004 and 0.0673 for the ANN and ANFIS models, respectively, indicated the superiority of ANN over ANFIS. However, a small discrepancy in the predictability of the ANFIS model was observed owing to the fuzzy rule-based complexity and overtraining of data. Thus, the developed models can be used for the online prediction of RE onto synthesized maghemite nanoparticles with different sets of input parameters and it can also predict the operational errors in the system.

1. Introduction

A variety of industrial processes such as leather tanning, electroplating, pulp and paper, printing, and dyeing are known to release high concentration (i.e., >200 mg/L) of chromium (VI) into the water environment [1,2]. Chromium in such quantities is well beyond the recommended effluent concentration levels recommended by national and various international regulatory agencies [3,4]. Being classified as a group 1 carcinogen, the long term exposure to Cr (VI) can be a serious public health and environmental hazard [5,6]. The removal and control of chromium in all its forms (IV and VI) is, therefore, of utmost importance in the arena of wastewater treatment.

The removal technologies that are currently in use include adsorption, bioremediation, magnetic separation, the use of nanoparticles, adsorbing membranes, reverse osmosis, ion exchange, precipitation, and ozonation [7,8,9,10,11]. Although biological removal of chromium is considered to be a sustainable approach, adsorption remains the effective, low energy-intensive, cheaper incumbent for large-scale wastewater treatment [8,12]. Since the mechanism and efficacy of adsorption are well known, what remains is the selection of adsorbents and developing them for full-scale applications [13]. Modifications of adsorbents for improved physicochemical properties and increased chromium removal efficiencies (REs) are very important [14,15]. The use of modified maghemite nanoparticles was reported to remove about 95.8% of chromium at a pH of 2.6 and adsorbent dosage of 5 g/L, with an initial chromium concentration of 20 mg/L [12]. A mathematical modeling-based optimization technique may be able to locate the optimal conditions (e.g., dosage and pH) required for improved adsorption efficiency, without the need for comprehensive experimental exploration of the operating conditions.

Several mathematical modeling techniques have been used for optimizing the adsorption of chromium that include artificial neural networks (ANNs), adaptive neuro-fuzzy interface system (ANFIS), and polynomial regression models, such as the response surface methodology (RSM) [16]. These machine learning techniques find relations between nonlinear data and help in the prediction of future observations. The training scheme for each of these techniques is different and has its own advantages [17]. For instance, the adaptive nature of ANN allows it to be used in varieties of applications where nonlinear RSM may not be appropriate. ANN excludes the need to design the model, reducing the complexity and providing the optimum parameters to be used for a unit’s operation [18]. Solgi et al. [19] observed that ANN-support vector regression was on par with the SVR-genetic algorithm in prediction of chromium removal with activated carbon. The input parameters that are generally selected include initial pollutant concentration, adsorbent dosage, pH, and temperature. A chromium adsorption magnetic separation system was modeled using backpropagation with a regression coefficient of 99.9% [20]. In another study, ANN was successfully implemented to model chromium biosorption, with unmodeled variance of <5% [21]. Although ANN is widely implemented in real-life systems, long learning intervals, performance variations, difficulty in handling ambiguous data, or incorporating complete domain knowledge still remains a challenge [22].

To overcome the drawbacks of ANN, ANFIS has started to replace it for modeling complex industrial systems, including wastewater treatment plants [23,24]. In addition to solving the issues with ANN, ANFIS offers a simple architecture, ease of implementation, and good reasoning capability [22,25]. Very few studies have adopted ANFIS modeling in adsorptive chromium removal. Chromium adsorption from leather industry wastewater using clay-based adsorbent was modeled with ANFIS to predict the removal efficiency, where the error between the observed and experimental values was nominal [26]. In another study, ANFIS coupled with a particle swarm optimization algorithm was developed to model chromium adsorption on nickel oxide nanoparticles. This developed model was highly effective as deviations were <0.1% with a correlation of >99% [27]. Various studies further indicate the superiority of ANN over ANFIS for wastewater systems, as ANFIS tends to oversimplify the data (

Table 1. Summary of investigations on ANN modeling for different adsorption systems.

Pollutant (s)	Adsorbent	Batch/Continuous	Type of Algorithm	Input Parameters	Output Parameters	Data Points Used	Network Architecture	References
Arsenic	Iron/olivine composite	Batch	Levenberg-Marquardt (LM) BP algorithm	Cad, Ci, time, qag, and pH	REAs	38	5:12:1 (As (III)T) 5:14:1 (As (V)T)	[28]
Ethanol mediated-Arsenic (III)	Zn-loaded pinecone (PC) biochar	Batch	BP algorithm and genetic algorithm	CAs, CEtOH, and pH	ACAs	17	3:4:1	[29]
Fluoride	Protonated clinoptilolite	Batch	Hybrid feedforward algorithm	pH, Ci, and temperature	ACF	99	3:3:1	[30]
Methylene blue (MB)	Biowaste AC 1	Batch	BP algorithm	Ci, Cad, pH, temperature, and time	ACdye	88	5:10:1	[31]
Zinc (II)	Palm kernel shell AC 1	Batch	PSO and LM-BP algorithm	Ci, pH, time, Cad, and temperature	REZn	270	5:7:1	[32]
Methyl orange dye	Polyaniline nano-adsorbent	Batch	LM-BP algorithm	pH, Ci, Cad, temperature, and time	REdye	322	5:12:1	[33]
Phenol	Scoria stone	Batch	CS-NN 3	Cad, Ci, and time	REPh	100	3:10:1	[34]
Arsenic	Opuntia ficus indica biomass	Batch	Hybrid model	Ci, temperature, pH, and time	ACAs	81	4:3:1	[21]
AB and AR 4	Chitosan hydrogels	Batch	LM-BP algorithm	Ci-AB, Ci-AR, time, ϕ, and w/w%	ACAB-AC	315	5:10:10:10:1	[35]
Copper and Manganese	GN-SDS 2	Continuous	Quick prop algorithm	Ci, Cad, pH, and temperature	RECu,Mg	40	4:10:1	[36]
Cadmium, nickel, zinc, and copper	Bone Biochar	Continuous	LM-BP algorithm	Ci and time	Ct/C0	1420	2:6:1	[37]
Coal-based pollutant	AC 1	Continuous	LM–BP algorithm	β, ReL, t/tmax, and Ck/C0	qt/qmax	208	4:9:1	[38]
Triclosan and ibuprofen	AC	Continuous	Gradient descent algorithm	Ci and q	C-t	10	2:4:1	[39]

Note: Neural network terminologies: BP—back propagation algorithm, PSO—particle swarm optimization. Input parameters: C_ad = adsorbent dosage, C_i = Inlet concentration, q_ag = agitation rate, C_As = Arsenic concentration, C_EtOH = ethanol concentration, β = average high gravity factor, Re_L = Liquid Reynolds number, t/t_max = adsorption time to the maximum adsorption time, C_k/C₀ = packing density to liquid concentration, _q = flow rate, ϕ = porosity and w/w% = mass percentage of carbonaceous material. Output parameters: RE_As = Arsenic removal efficiency, C_t = concentration at time t, C₀ = initial concentration, AC_As = Arsenic Adsorption capacity, RE_Cu,Mg—Manganese and copper removal efficiency, AC_F = Fluoride adsorption capacity, AC_dye = Dye adsorption capacity, RE_Zn = Zinc removal efficiency, q_t/q_max = adsorption amount to the maximum adsorption amount, C-t = concentration time pairs, RE_dye = Dye removal efficiency, RE_Ph = Phenol removal efficiency and AC_AB-AC = adsorption capacity of Acid Blue 9 and Allura Red AC. Superscripts: 1—Activated carbon; 2—Sodium dodecyl sulphate modified graphene; 3—Clonal selection algorithm; 4—Acid Blue 9 and Allura Red activated carbon.

).

This study aims to develop efficient models to determine the optimum conditions for chromium removal from synthetic wastewater onto modified maghemite nanoparticles. The main objectives of this study include (1) developing ANN and ANFIS models using different learning algorithms, using pH and adsorbent dose as the input and chromium RE as the output parameter, (2) testing the individual models with an external validation laboratory dataset, and (3) conducting a comparative analysis between the developed models.

2. Materials and Methods

2.1. Sample Preparation

Analytical grade K₂Cr₂O₇ (Nice Chemicals, Chennai, India) was dissolved in double distilled water to prepare a stock solution of chromium (250 mg/L), likely to be used within a month of preparation [40]. For batch experiments, the chromium solution was produced from the stock by diluting it with distilled water and adjusting the pH with 0.1 N HCl or NaOH as needed.

2.2. Adsorbent Preparation and Characterization

Maghemite nanoparticles (NPs) purchased from Sigma Aldrich, Bengaluru (India) were treated with Sodium dodecyl sulfate (SDS) to the improve surface characteristics of NPs, as described elsewhere [41]. Briefly, different volumes (1, 2, 3, and 4 mL) of SDS solution (5% w/v) were added to 0.1 g of NPs and stirred for 90 s. Following magnetic decantation, the modified NPs (MNPs) were repeatedly washed and dried overnight at 60 °C in a hot air oven. The dried particles were crushed with a marble mortar and pestle.

Optimal SDS concentration in MNPs preparation for chromium removal was established through an independent study where 0.1 g MNPs was incubated with 10 mL chromium solution (2000 mg/L, pH 5.0) in a 250 mL flask at ~37 °C for 30 min in an orbital shaker at 200 rpm [42]. Following magnetic decantation, the residual concentration of chromium was measured using atomic absorption spectroscopy. It was observed that the addition of 2 mL of SDS in MNPs preparation was most effective, and the same was maintained in further studies.

2.3. Batch Experiment and Chromium Analysis

Batch adsorption studies were conducted in 250 mL conical flasks containing 20 mL of chromium solution at the desired concentration. The pH of the solution was measured using a digital pH meter (Orion 3-star, Thermo Electron Corporation, Beverly, MA, USA). The required amount of adsorbents was added to these flasks, placed in an orbital shaker (200 rpm), and maintained at ~35 °C for 80 min, an equilibrium time based on preliminary kinetic studies. Following removal of the adsorbent, the supernatant was filtered through 2.5 µm filter paper (Whatman 42). The chromium concentration in the filtrate was measured with an AAS (Varian SPECTRA A240, Santa Clara, CA, USA). The current, detection wavelength, and slit bandwidth were set at 7.0 mA, 357.9 nm, and 0.2 nm, respectively, as recommended by the manufacturer. The percentage of chromium removal was calculated using Equation (1):

$$RE(\%)=\frac{C_0-C_e}{C_0}\times 100$$

(1)

where RE is the chromium RE (%), and C₀ and C_e are the initial and final concentrations in the solution (mg/L), respectively. The adsorption equilibrium time (i.e., 80 min) was established through preliminary experiments with 10 mL of chromium solution (20 mg/L) at pH 6.0 and 0.05 g of MNPs incubated at room temperature for 120 min.

The pH, adsorbent dosage, and initial chromium concentration were chosen as independent factors in this study because they are all likely to have an effect on the RE, the dependent variable. The pH and adsorbent dosage ranges were chosen based on earlier studies [40,43], while the initial concentration was selected based on the level of chromium contamination in groundwater in the surrounding areas [44]. In this work, we used a full-factorial central composite design (CCD) consisting of a complete 2k—factorial design, n₀—center point (n₀ > 1) and two axial points on the axis of each design variable at a distance of α = 1.682 from the design center [42]. For ‘k’ number of factors, a total of N = 2^k + 2k + n₀ design points were indicated, where n₀ was the number of center point replicates used to estimate design error. In this study for k = 3, and n₀ = 6, 20 experimental runs were projected. However, two experimental runs having high residuals were marked as outliers and excluded from testing in ANN and ANFIS modeling.

Table 2. Experimental design matrix and the response.

Run	Actual Level of Factors			Chromium RE (%)
	X1	X2 (g/L)	X3 (mg/L)	Experimental	Predicted
1	4	2.5	10	80.54	84.38
2	8	2.5	10	69.79	69.87
3	4	7.5	10	92.72	94.54
4	8	7.5	10	90.36	89.56
5	8	2.5	30	52.35	49.72
6	8	7.5	30	82.20	77.54
7	2.64	5	20	95.48	93.94
8	9.36	5	20	73.95	74.85
9	6	0.795	20	49.58	49.69
10	6	9.204	20	88.34	87.69
11	6	5	3.182	92.81	91.28
12	6	5	36.82	72.15	72.98
13	6	5	20	80.85	80.99
14	6	5	20	80.89	80.99
15	6	5	20	80.84	80.99
16	6	5	20	80.87	80.99
17	6	5	20	83.49	80.99
18	6	5	20	81.02	80.99

provides the independent variables, experimental range, and the levels for chromium removal achieved.

3. Network Development

3.1. ANN Model

A multi-layered perceptron (MLP) using the backpropagation (BP) algorithm is the most widely used neural network (NN) for forecasting/predicting purposes [45]. The architecture of MLP NN consists of basic processing units (neurons which are interconnected to each other through different weights and bias values in a network form and transmit the signals between them during processing). This process mimics the human brain processing that accepts different inputs and produces the desired output. The MLP NN generally consists of three layers: an input layer, a hidden layer, and an output layer [45]. A suitable example of the architecture of an ANN is shown in Figure 1. The neurons of the input layers are interconnected to the neurons of the hidden layer using different connection weights (W_ij). The number of neurons in the hidden layer is optimized and selected based on their prediction ability with minimum statistical error. The bias term (b) is considered as an additional threshold in the activation of neuron and processing. The experimental variables with equal weightage (through suitable scaling) can be used as the input in NN architecture and, thus, equal to the number of input layer nodes/neurons. In this study, the input data (pH, adsorbent dose, and initial chromium concentration) were presented to the network through the input layer, which were then passed to the hidden layer along with the weights. Similarly, the number of nodes in the output layer was equal to the number of output parameters of the datasets, i.e., chromium RE (%) in this study [45].

Figure 1 shows the architecture of the constructed NN model with four neurons in the hidden layer. The ANN architecture with appropriate training (backpropagation) algorithm can be used to solve the problem by a trial-and-error methodology. It is noteworthy that the backpropagation algorithm, e.g., the Levenberg-Marquardt (LM) algorithm is the most robust learning algorithm whose performance is based on gradient descent with minimization of error at each iteration [46].

3.2. ANFIS Model

The Adaptive Neuro-Fuzzy Inference System (ANFIS) technique is a combined form of two machine learning approaches, namely fuzzy logic and neural network, wherein, fuzzy logic transforms a given input into the desired output through simultaneously interconnected neural network processing elements [47]. The general architecture of the ANFIS model is made up of six different layers including an input layer, (e.g., pH, adsorbent dose, and initial chromium concentration), a fuzzy operator (e.g., gaussmf) layer, a product/normalized layer (application method, e.g., HYBRID), an output aggregation layer, a defuzzification layer, and an output layer (e.g., chromium RE, %) as shown in Figure 2. The detailed parameters of nodes are given in

Table 3. The features of ANN and ANFIS structure used in modeling.

Characteristics	Features/Value
ANN model
Network type	Feed-forward backpropagation
Training function	Trainlm (Levenberg Marquardt)
Number of hidden layers	1
Number of data used for network training	14
Number of data used for testing	4
Transfer function in hidden layer	tansig (Sigmoid)
Optimum no. of neurons in hidden layer	3
Epoch number	164
ANFIS Model
Number of nodes	58
Number of linear parameters	72
Number of nonlinear parameters	24
Total number of parameters	96
Number of training data pairs	14
Number of validation data pairs	04
Number of fuzzy rules	18

. The nodes in fuzzy and defuzzy layers are adaptive, i.e., parameters in these nodes are determined through training; however, the nodes in a product, normalized, and the output layer are fixed [46].

3.3. Data Processing in ANN and ANFIS

In order to develop suitable ANN and ANFIS models in this study, the experimental datasets (18 experiments) were divided into training (about 75%) and testing/validation performance sets (about 25%). The data in the training and validation sets were selected randomly from the original dataset [12]. Before the start of ANN and ANFIS modeling, the experimental data were scaled in the suitable range of 0 to 1 in order to have equal weightage of each variable during processing and accuracy of the output [48].

3.4. Statistical Evaluation

The performance of the network developed under the ANN and ANFIS expert system was evaluated based on the following statistical parameters (Equations (2)–(11)).

• Correlation coefficient (R)

  $$R=\sqrt{1-\frac{{\displaystyle \sum _{i=1}^N{{(\stackrel{⌢}{\mathrm{y}}}_{{}_{\mathrm{i}}}-{\mathrm{y}}_{{}_{\mathrm{i}}})}^2}}{{\displaystyle \sum _{i=1}^N{{(\stackrel{⌢}{\mathrm{y}}}_{{}_{\mathrm{i}}}-{\overline{\mathrm{y}}}_{{}_{\mathrm{i}}})}^2}}}$$

  (2)
• Sum of squares error (SSE)

  $$SSE={\displaystyle \sum _{i=1}^N{{(\stackrel{⌢}{\mathrm{y}}}_{\mathrm{i}}-{\mathrm{y}}_{\mathrm{i}})}^2}$$

  (3)
• Sum of the absolute error (SAE)

  $$SAE={\displaystyle \sum _{i=1}^N\left|{\stackrel{⌢}{\mathrm{y}}}_{\mathrm{i}}-{\mathrm{y}}_{\mathrm{i}}\right|}$$

  (4)
• Average relative error (ARE)

  $$ARE=\frac{100}{N}{\displaystyle \sum _{i=1}^N\frac{\left|{\stackrel{⌢}{\mathrm{y}}}_{\mathrm{i}}-{\mathrm{y}}_{\mathrm{i}}\right|}{y_i}}$$

  (5)
• Absolute average deviation (AAD)

  $$AAD=100|\frac{1}{N}{\displaystyle \sum _{i=1}^N\frac{{(\stackrel{⌢}{\mathrm{y}}}_{\mathrm{i}}-{\mathrm{y}}_{\mathrm{i}})}{y_i}|}$$

  (6)
• Mean squared error (MSE)

  $$MSE=\frac{1}{N}{\displaystyle \sum _{i=1}^N{{(\stackrel{⌢}{\mathrm{y}}}_{\mathrm{i}}-{\mathrm{y}}_{\mathrm{i}})}^2}$$

  (7)
• Root mean square error (RMSE)

  $$RMSE=\sqrt{\frac{{\displaystyle \sum _{i=1}^N{{(\stackrel{⌢}{\mathrm{y}}}_{\mathrm{i}}-{\mathrm{y}}_{\mathrm{i}})}^2}}{\mathrm{N}}}$$

  (8)
• Hybrid fractional error function (HYBRID)

  $$HYBRID=\frac{100}{N-P}{\displaystyle \sum _{i=1}^N\frac{{{(\stackrel{⌢}{\mathrm{y}}}_{\mathrm{i}}-{\mathrm{y}}_{\mathrm{i}})}^2}{{\mathrm{y}}_{\mathrm{i}}}}$$

  (9)
• Marquart’s percentage standard deviation (MPSD)

  $$MPSD=100\sqrt{\frac{1}{N-P}{\displaystyle \sum _{i=1}^N\frac{{{(\stackrel{⌢}{\mathrm{y}}}_{\mathrm{i}}-{\mathrm{y}}_{\mathrm{i}})}^2}{{\mathrm{y}}_{\mathrm{i}}}}}$$

  (10)
• Chi-square $\left({\chi }^2\right)$

  $${\chi }^2={\displaystyle \sum _{i=1}^N\frac{{{(\stackrel{⌢}{\mathrm{y}}}_{\mathrm{i}}-{\mathrm{y}}_{\mathrm{i}})}^2}{{\mathrm{y}}_{\mathrm{i}}}}$$

  (11)

where $y_i$ is the experimentally measured value of the Cr⁺⁶ remaining in concentration, ${\widehat{y}}_i$ is the predicted value by ANN and ANFIS models, ${\overline{y}}_i$ is the mean value of $y_i$, N is the number of experiment points, and p is the number of parameters.

3.5. Software Used

The predictive modeling work using ANN was carried out using the shareware version of the neural network and the multivariable statistical modeling software, MATLAB^®, Neural Network and ANFIS Toolboxes (MathWorks Inc., Natick, MA, USA, R2016a). For ANN modeling, the trainlm function related to backpropagation LM algorithm, the tansig function with backpropagation algorithm in the hidden layer, and purelin, i.e., linear transfer function at the output layer, were used. In ANFIS modeling, the genfis1 function using Gaussian (gaussmf) as the membership function and a combination of least squares and a backpropagation algorithm (HYBRID method) was used.

4. Results and Discussion

4.1. ANN Performance

The dataset viz. pH, adsorbent dose, and initial concentration used for the ANN modeling of chromium RE is given in Table 2. The dataset was divided into training (75%) and testing (25%) of the network. A maximum of 164 epochs was observed to achieve the required gradient tolerance, i.e., 2.98 × 10⁻⁵ during the training process. During the training process, a sigmoidal function was used as the activation function for each neuron. The input and output data were normalized within the range of 0.1 and 0.9 using Equation (12) to reduce the saturation problem in the sigmoidal function and also to reduce the influence of the higher magnitude of factors on the architecture [49]. After training, the optimized value of the variable (X) was rescaled using Equation (13).

$$X^{\ast }=0.8\frac{X-X_{\min }}{X_{\max }-X_{\min }}+0.1$$

(12)

$$X=\frac{(X_{\max }-X_{\min })(X^{\ast }-0.1)}{0.8}+X_{\min }$$

(13)

where X* is the normalized value of the input/output variables X, and X_max and X_min are their maximum and minimum values, respectively.

Figure 3 shows the experimental data with the predicted values of the actual adsorption capacity of chromium for the training and testing datasets using the ANN model. The results indicated a similar trend between the training and testing dataset, which shows the predictive ability of the trained network.

4.2. ANFIS Performance

The same data given in Table 2 were used for the ANFIS modeling, and the entire data were randomly divided into training (75%) and testing (25%) sets. One hundred epochs were used to train the network. The best testing performance of the model occurred in epoch 23, which presented the lowest MSE error value of 0.60334. Figure 4 illustrates the ANFIS model’s predictive capability during both the training and testing phases, as well as the experimental and model-predicted values of chromium RE on modified maghemite nanoparticles. There was agreement between the predicted and experimental values. However, the ANFIS model was capable of predicting the chromium RE with less precision than that of the ANN model.

4.3. Comparison of ANN and ANFIS Models

The efficiency of the ANN and ANFIS models and their performances were evaluated by several statistical indices and are shown in

Table 4. Statistical analysis of the ANN and ANFIS models.

Parameters	ANN Model		ANFIS Model
	Training	Testing	Training	Testing
R	1.00	0.97	0.99	0.82
R2	1.00	0.98	0.99	0.94
SSE	0.03	60.58	5.57	233.15
SAE	0.51	10.89	4.60	19.12
ARE	0.05	2.88	0.40	5.51
AAD	0.23	1009.72	39.75	3885.83
MSE	<0.01	10.10	0.40	38.85
RMSE	0.05	3.18	0.63	6.23
HYBRID	<0.01	33.66	0.61	144.72
MPSD	6.03	580.16	78.24	1203.03
Chi-Square	<0.01	1.01	0.07	4.34

. In the case of the ANN model, the low values of the conventional error functions such as SSE (0.0320), MSE (0.0023), and RMSE (0.0478) are within the acceptable range [46,50]. In addition, the correlation coefficient (R) of 0.999 indicates a satisfactory agreement between the experimental data and predicted values by the ANN model.

For the ANFIS model, a comparatively high value of SSE (5.565), MSE (0.397), RMSE (0.630), and correlation coefficient (R) of 0.993 were observed. This indicates better predictability of the ANN model than the ANFIS model toward the experimental data. To evaluate the training of each approach, the statistical matrices were conducted; ARE for the ANN and ANFIS models was 0.0458 and 0.4004, while the AAD was 0.2287 and 39.7537, respectively. The sum of the absolute error (SAE) was found to be 0.5086 and 4.5955 for the ANN and ANFIS models, respectively. The other matrices such as HYBRID and MPSD were found to be higher for the ANFIS model (0.6121 and 78.2399, respectively) compared to these matrices for the ANN model (0.0036 and 6.0346, respectively). The Pearson’s Chi-square measure (χ²) was found to be 0.0004 and 0.0673 for the ANN and ANFIS models, respectively. On the basis of these matrices, it can be stated that the ANN model suited the experimental data well, with a high degree of accuracy and a suitable measuring scale for determining the goodness of fit. Thus, the ANFIS model has no benefit over the ANN model in terms of predicting the chromium RE on modified maghemite nanoparticles.

Figure 5 and Figure 6 suggest a good agreement between the experimental and modeled chromium adsorption onto modified maghemite nanoparticles, using “in sample” and external validation datasets, respectively. The highest prediction discrepancies of the ANFIS model can be demonstrated for experimental run 2 in the testing data. It is noteworthy that the ANN model is simple in structure and training in comparison to the ANFIS model. However, the complexity of the ANFIS model lies in the dependence of this model on a fuzzy rule and overtrained the network when it implied FIS and employed a hybrid learning rule during training. Thus, these distinctions were attributed to an ANN’s relatively basic structure and the learning process of input, output, and hidden layers in a feedback mode [48].

4.4. Practical Implications of the Work and Future Research Perspectives

Despite the large number of studies in the literature on the adsorption of various pollutants using adsorbents with ANN (Table 1), the use of machine learning in the actual world has received relatively little attention. From the table, it is possible to examine the differences in input and output parameters that were employed, with almost all of the outcomes being satisfactory and the accuracy being comparable. Slowly these techniques are being recognized and implemented at the large scale [51]. Table 1 also shows the comparisons made between the two modeling techniques (ANN and ANFIS) and portrays that most systems display an affinity towards, ANN which was also the case for the current study. As discussed earlier, ANN seems to be a better option with a lower SSE, MSE, and RMSE than that of ANFIS. The developed model for chromium adsorption by modified maghemite shows a correlation coefficient (R) closer to one and is also proposed as a relatively simple model suited for real-world applications. This model has the additional advantage of having an input parameter that is directly measurable, namely the adsorbent dosage, which can be measured at the beginning and altered as needed. Behera et al. [12] have implicated further research in the area of maghemite recovery following chromium adsorption. One can develop predictive models for maghemite recovery with ANN or ANFIS. For practical application, an ANN model with simple network must be integrated into an online user interface that enables one to estimate the RE and predict future errors in a systematic manner. ANN models may be trained online or offline depending on the situation, and this flexibility allows them to be used in processes, i.e., with good process control systems and online measurement devices, that can be tested and trained regularly to achieve greater performance in real-world situations. New raw data can be provided with data filtering that can incorporate any limitations which may arise due to data discrepancy (e.g., data collected during a shorter interval of time and/or with a transition period between different loads). As mentioned previously, the model can yield much better results when the online/offline control system can be integrated with application-specific programs such as pH control and initial concentration control systems to monitor the removal efficiencies. Both ANN and ANFIS should be combined with a priori process-structure knowledge, quantitative structure-activity relationship (QSAR) models, and the internet of things (IoT) in the future to anticipate the hydrodynamics of wastewater treatment facilities and the physical, chemical and biological properties of treated water.

5. Conclusions

This study focused on the application of two intelligent modeling approaches, viz. ANN and ANFIS for modeling chromium RE (%) adsorbed onto modified MNPs. The prediction ability of ANN and ANFIS was compared with experimental chromium RE (%) in terms of R, ARE, AAD, MSE, RMSE, HYBRID, MPSD, correlation coefficient (R²), and Pearson’s Chi-square measure (χ²). The efficiency of the ANN and ANFIS models and their performances were evaluated by several statistical indices, which indicated a satisfactory agreement between the experimental data and predicted values with the low values of SSE (0.0320), MSE (0.0023), and RMSE (0.0478). However, a comparatively high value of SSE (5.565), MSE (0.397), and RMSE (0.630) were observed in case of ANFIS modeling. This indicates a better predictability of ANN over the ANFIS model toward the experimental data. Furthermore, the statistical matrices such as ARE for the ANN and ANFIS models were estimated to be 0.0458 and 0.4004; while the AAD was 0.2287 and 39.7537, respectively. Other statistical matrices, viz. HYBRID and MPSD were found to be higher for the ANFIS model (0.6121 and 78.2399, respectively) compared to these matrices for the ANN model (0.0036 and 6.0346, respectively). The Pearson’s Chi-square measure (χ²) was found to be 0.0004 and 0.0673 for the ANN and ANFIS models, respectively. In summary, the ANN model fitted well the experimental data with high accuracy as compared to the ANFIS model for predicting the adsorptive removal of chromium onto modified MNPs.