#
Modeling and Optimizing of NH_{4}^{+} Removal from Stormwater by Coal-Based Granular Activated Carbon Using RSM and ANN Coupled with GA

^{*}

## Abstract

**:**

_{4}

^{+}removal from stormwater by coal-based granular activated carbon (CB-GAC), a novel approach, the response surface methodology (RSM), back-propagation artificial neural network (BP-ANN) coupled with genetic algorithm (GA), has been applied in this research. The sorption process was modeled based on Box-Behnben design (BBD) RSM method for independent variables: Contact time, initial concentration, temperature, and pH; suggesting a quadratic polynomial model with p-value < 0.001, R

^{2}= 0.9762. The BP-ANN with a structure of 4-8-1 gave the best performance. Compared with the BBD-RSM model, the BP-ANN model indicated better prediction of the response with R

^{2}= 0.9959. The weights derived from BP-ANN was further analyzed by Garson equation, and the results showed that the order of the variables’ effectiveness is as follow: Contact time (31.23%) > pH (24.68%) > temperature (22.93%) > initial concentration (21.16%). The process parameters were optimized via RSM optimization tools and GA. The results of validation experiments showed that the optimization results of GA-ANN are more accurate than BBD-RSM, with contact time = 899.41 min, initial concentration = 17.35 mg/L, temperature = 15 °C, pH = 6.98, NH

_{4}

^{+}removal rate = 63.74%, and relative error = 0.87%. Furthermore, the CB-GAC has been characterized by Scanning electron microscopy (SEM), X-ray diffraction (XRD) and Brunauer-Emmett-Teller (BET). The isotherm and kinetic studies of the adsorption process illustrated that adsorption of NH

_{4}

^{+}onto CB-GAC corresponded Langmuir isotherm and pseudo-second-order kinetic models. The calculated maximum adsorption capacity was 0.2821 mg/g.

## 1. Introduction

_{3}

^{-}), nitrite (NO

_{2}

^{-}), ammonia and ammonium (NH

_{3}and NH

_{4}

^{+}), and organic N. The distribution between NH

_{3}versus NH

_{4}

^{+}is pH dependent (pK

_{a}= 9.25), but NH

_{4}

^{+}dominates in stormwater (typical pH values are 6–8) [7]. The high level of ammonia in water imparts taste and odor problems, can cause symptoms in aquatic organisms such as hypoxia, coma, and decreased immunity, resulting in slow growth and even a large numbers of deaths [8,9].

_{4}

^{+}removal process from stormwater by coal-based granular activated carbon (CB-GAC). RSM experimental design was selected to establish the regression model. The model involved four parameters (i.e., contact time, initial concentration, temperature, and pH) as independent variables and NH

_{4}

^{+}removal rate as dependent variable. The interaction effect of the independent variables with the response using the response surface plots was illustrated. Meanwhile, the back-propagation artificial neural network BP-ANN model was also developed and the optimal number of hidden neurons was determined by trial and error method. Coupled with GA, the ANN-GA model was used for optimization of the operating conditions to determine the maximum NH

_{4}

^{+}removal rate. The predictive capabilities and modelling efficiencies of the two models are compared and verified. Furthermore, the CB-GAC has been characterized by scanning electron microscopy (SEM), X-ray diffraction (XRD), and Brunauer-Emmett-Teller (BET). Finally, adsorption isotherm model (Langmuir, Freundlich, and Temkin) and adsorption kinetics model (pseudo-first-order, pseudo-second-order) had been investigated to explore the mechanisms of the NH

_{4}

^{+}removal process.

## 2. Materials and Methods

#### 2.1. Materials and Characterization

_{4}Cl, NaOH, HCl) used were analytical grade and were purchased from Beijing Yili Fine Chemicals Co., Ltd. (Beijing, China). The coal based granular activated carbon (CB-GAC) is columnar and has a diameter of 2–3 mm, washed three times with deionized water, then drying at 105 °C for 24 h before use. All the solutions were prepared by the deionized water.

_{2}at 77 K in a Surface Area and Pore Size Analyzer (Micromeritics Instruments, ASAP 2460, Norcross, GA, USA).

#### 2.2. Batch Adsorption Experiments

_{4}

^{+}. The initial pH was adjusted to the desired value by using 0.1 mol/L HCl or 0.1 mol/L NaOH. After reaching the designed time, an aliquot of the sample was withdrawn and filtered through 0.45 μm poly tetra fluoroethylene (PTFE) filter (Anpel Co. Ltd., Shanghai, China) to remove suspended solids. The concentration of NH

_{4}

^{+}were measured by UV-visible Multi-parameter Analyzer (Lianhua Tech Co. Ltd., LH-3BA, Beijing, China). The removal rate and adsorption amount of NH

_{4}

^{+}were calculated using the following equations.

_{4}

^{+}, respectively. ${\mathrm{C}}_{0}$ (mg/L) and ${\mathrm{C}}_{\mathrm{t}}$ (mg/L) are the concentrations at time 0 and t, respectively. V (L) is the volume of the solution, and m (g) is the mass of adsorbent.

#### 2.3. Isotherm and Kinetics Study

_{4}

^{+}onto the CB-GAC. All of this part of the experiments were performed under the following conditions: 10 g of CB-GAC was mixed with 100 mL of ammonium chloride solution (5–30 mg/L), at pH 7.0 and room temperature (25 ± 1 °C).

#### 2.4. Experimental Design and Mathematical Models

#### 2.4.1. Response Surface Methodology

_{4}

^{+}removal rate and obtain an accurate model to predict the removal rate. The Box-Behnken design involves 4 variables and 3 levels. There were 29 runs, including 5 zeros, which usually represented repeated experiments, and were used to estimate experimental errors. Specifically, contact time, initial concentration, temperature, and pH were selected as independent variables, their levels were coded as: −1, 0, +1, and the NH

_{4}

^{+}removal rate as the dependent variable. The relationship between the dependent and the independent variables can be represented by the Equation (3). The variables and the levels for BBD-RSM used in this study are shown in Table 2.

_{4}

^{+}; ${\alpha}_{0}$ is a constant offset term; ${\alpha}_{1}$,${\alpha}_{2}$,${\alpha}_{3}$,${\alpha}_{4}$,${\alpha}_{12}$,${\alpha}_{13}$,${\alpha}_{14}$,${\alpha}_{23}$,${\alpha}_{24}$,${\alpha}_{34}$,${\alpha}_{11}$,${\alpha}_{22}$,${\alpha}_{33}$,${\alpha}_{44}$ are the estimated coefficients, respectively; $A$, $B$, $C$, $D$ are contact time, initial concentration, temperature, and pH, respectively.

#### 2.4.2. BP-ANN Modeling and Optimization

_{4}

^{+}removal rate).

#### 2.4.3. Genetic Algorithms

## 3. Results and Discussion

#### 3.1. Characterization of the CB-GAC

#### 3.2. Isotherm and Kinetics Studies

#### 3.2.1. Adsorption Isotherm

^{2}value of Langmuir isotherm model (0.9951) was higher than that of the Freundlich (0.9843) and Temkin models (0.9925), indicating that the adsorption behavior of CB-GAC for NH

_{4}

^{+}was more consistent with the Langmuir model. The Langmuir isotherm model assumes the number of active sites distributed homogeneously on the surface of the adsorbent followed by monolayer adsorption (physical adsorption) having high adsorptive power [37]. This suggested that the adsorption of NH

_{4}

^{+}takes place on the surface of the CB-GAC until a monolayer coverage was formed, after which the driving force of the sorption process decreases drastically [38]. The ${\mathrm{Q}}_{\mathrm{max}}$ calculated from the Langmuir model was 0.2821 mg/g.

#### 3.2.2. Adsorption Kinetics

_{4}

^{+}removal rate with time were illustrated in Figure 5. At the started phase, the adsorption efficiency was very high, and the amount of adsorbed ammonia nitrogen increased rapidly. After the started phase, the adsorption efficiency gradually slowed down and reached equilibrium at around 16 h. The fitting parameter values and errors of the adsorption kinetic models were shown in Table 6. It can be seen from the R

^{2}value that, compared with the pseudo-first-order kinetic model (0.9535), the adsorption kinetics behavior of NH

_{4}

^{+}-CB-GAC is more consistent with the pseudo-second-order kinetic model (0.9868), which suggested that the adsorption might depend on the availability of the adsorption sites. This is similar to the kinetic adsorption characteristics of many carbon materials [21,39,40,41]. The calculated value ${\mathrm{Q}}_{\mathrm{e}}$ from pseudo-second-order kinetic was 0.0956 mg/g, which is close to the experimental value of 0.0927 mg/g.

#### 3.3. Modeling and Optimization by BBD-RSM

#### 3.3.1. Modeling

_{4}

^{+}removal rate Y as response value.

_{4}

^{+}removal rate for its highest positive coefficient value, which is consistent with the conclusion of kinetic model that the NH

_{4}

^{+}removal rate increases with time. The second important variable is temperature with negative sign. This suggested that the adsorption capacity of the adsorbent decreased with the increase of temperature. Similar results were obtained by Ren et al. in the experiment of the adsorption of ammonia nitrogen by iron-loaded activated carbon [42].

#### 3.3.2. Analyzing

^{2}> 0.95, R

_{pred}

^{2}> 0.7, R

_{adj}

^{2}-R

_{pred}

^{2}< 0.2, C.V. < 10%, Adeq Precision > 4 [20]. F-value and p-value was used to determine the statistical significance of the model. It can be seen that the F value of this model is 40.94 > 0.1, p < 0.0001, showing that the model is reliable and fits well in the whole regression area. R

_{adj}

^{2}− R

_{pred}

^{2}= 0.0785 < 0.2, C.V. = 1.54% < 10%, indicating high reliability and accuracy of the experiment. Adeq Precision is the ratio of effective signal to noise. The experimental model Adeq Precision = 22.8713 > 4, indicating that the model is reliable and has enough signals to respond to the design. As shown in Figure 6, the high determination coefficient (R

^{2}= 0.9762) indicated a strong correlation between the predicted and actual values. Hence, the obtained model provided a good estimation of the predicted response within the studied range. The parameters were considered significant if p-value (Prob > F) is lower than 0.05. From the ANOVA (Table 8), the coded parameters A, C, D, A

^{2}, C

^{2}, D

^{2}are significant parameters, i.e., (p > F) < 0.05.

_{4}

^{+}removal rate was displayed in Figure 7. The results showed that with the increase of pH, the removal of NH

_{4}

^{+}increased first and then decreased, reaching the maximum value around 7.2. For the contact time, as the contact time increases, the NH

_{4}

^{+}removal rate also increased, and the trend slowed down after reaching a certain value, indicating that the contribution of the contact time to the NH

_{4}

^{+}removal rate gradually tends to be saturated. This is consistent with the kinetic results. The research showed that in response surface analysis, if the contour shape is elliptic, it means that the interaction between factors is significant, while the circle means that the interaction between factors is not significant [43]. As can be seen intuitively from the contour plot, the interaction between contact time and pH is relatively significant. When pH is close to the optimal value, the removal rate of NH

_{4}

^{+}gradually reaches the limit value with the increase of contact time, and the value is closer to the optimal removal rate. This can be explained by the morphology transform of NH

_{4}

^{+}: in the acidic environment, high amount of H

^{+}caused a strong competition with NH

_{4}

^{+}, while in the alkaline environment, NH

_{4}

^{+}was converted into the NH

_{3}·H

_{2}O molecular form [42]. Both the conditions can result in a reduction in NH

_{4}

^{+}removal rate. The interaction between contact time and pH indicated that there is an optimal NH

_{4}

^{+}removal area, that is, the area with a contact time of 700~900 min and pH of 7.2, with NH

_{4}

^{+}removal rate of over 62%.

_{4}

^{+}removal rate was displayed in Figure 8. The results showed that with the increase of contact time and decrease of temperature, NH

_{4}

^{+}removal rate increased, then the trend was gradually slowed. In the contour plot, the contour was thinning, which suggested that contact time and temperature on the contribution of NH

_{4}

^{+}removal rate were both gradually tending to saturation. It can be intuitively seen from the contour plot that the interaction between contact time and temperature is relatively significant, which is reflected in that when the temperature approaches the optimal value, with the increase of contact time, the removal rate of NH

_{4}

^{+}gradually reaches the limit value, and the value is closer to the optimal removal rate. The interaction between contact time and temperature indicated that there is an optimal NH

_{4}

^{+}removal area, that is, the area with a contact time of 700~900 min and temperature of 25~35 °C, and the NH

_{4}

^{+}removal rate is above 62%. It can also be seen from the figure that contact time has a greater influence on NH

_{4}

^{+}removal rate than temperature.

#### 3.3.3. Determination of Optimal Conditions for RSM

_{4}

^{+}removal by CB-GAC: Contact time = 911.42 min, initial concentration = 13.49 mg/L, temperature = 18.22 °C, pH = 7.28, removal rate = 62.83%.

#### 3.4. BP-ANN

#### 3.4.1. Determination of the Number of Hidden Neurons

_{4}

^{+}removal rate was depicted in Figure 9. It is observed that the lowest MSE is obtained with 8 neurons for the NH

_{4}

^{+}removal rate. Therefore, the best network structure of 4-8-1 is used for process optimization, which represents 4 inputs in the first layer, followed by 8 neurons in the hidden layer and one output in the last layer.

#### 3.4.2. Evaluation of Model

^{2}values for training, validation, and test and all data, which evaluate the relationship between experimental and predicted values, have been shown in Figure 10. It is seen that approximately the whole values have located around the 45° line with R

^{2}values of 0.99738, 0.99965, 0.99584, and 0.9951 for training, validation, test, and all data. This indicated excellent compatibility between the experimental and predicted results by the ANN model. As shown in Figure 11, after the first iteration, the MSE of the system reaches the preset value, and the system stops training. The trained neural network was tested by the experimental data, and the R

^{2}between the predicted and actual data was 0.99589 (Figure 12), which indicated that the BP-ANN model has good predictive ability.

#### 3.4.3. Sensitivity Analysis

_{4}

^{+}. This result is not completely consistent with the RSM result. They agreed that contact time was the most important factor of the four variables, and initial concentration was the least important. The difference is that the quadratic equation in RSM considers that the influence of temperature is greater than the influence of pH. In addition, the results of sensitivity analysis can concretize the proportion of relative influence degree, but the quadratic equation can reflect the positive and negative correlation of factors. Combining these two results, increasing the contact time, lowering the temperature, and keeping the pH near 7 can effectively improve the adsorption removal rate of NH

_{4}

^{+}.

#### 3.5. Genetic Algorithm (GA)

_{4}

^{+}adsorbed in the adsorption procedure. The optimization objective was determined via searching for the optimum points of the process variables between lower and upper bounds. Variables ranges was set as follows: Contact time 300–900 min, initial concentration 10–20 mg/L, temperature 15–35 °C, pH 5–9. The number of iterations of the genetic algorithm is set to 500. As shown in Figure 13, the system has shown a good convergence effect after about 70 iterations, while after 327 iterations, the system does not change, indicating the optimal results has been found. The results showed that the maximum removal rate was 63.74% under the optimal conditions of contact time = 899.41 min, initial concentration = 17.35 mg/L, temperature = 15 °C, pH = 6.98. The higher prediction accuracy of the ANN-GA model is attributed to the general ability of ANN-GA to estimate the nonlinear behavior of the system, while the response surface model is limited by second-order polynomial regression [44]. Therefore, these results confirm the advantages of ANN-GA model as an alternative to RSM model in prediction.

#### 3.6. Comparison between ANN-GA and RSM

^{2}values between the experimental and predicted values are calculated as 0.9762 and 0.9959 for the RSM and ANN models, respectively, indicating that the predictions resulted by the ANN model are closer to experimental values. The RMSE were found lower values for predictions given by ANN rather than the RSM model, confirming that the less error deviation resulted from the ANN predictions. In comparison, the prediction and statistical metrics for the ANN model were relatively better than the RSM model, and the difference was obvious.

_{4}

^{+}removal rate is 0.87% and 2.46% for ANN-GA and RSM models, respectively. These results suggested greater accuracy and higher reliability of ANN-GA in modelling and optimizing the parameter interaction related to the NH

_{4}

^{+}removal rate.

_{4}

^{+}, and provided graphs to intuitively explain the relationship between independent variables and response values. Additionally, this method only needs a few experiments to produce more information, reducing time and cost. However, the disadvantage is that it can only provide a first or second order polynomial model. Artificial neural network can simulate any form of non-linearity, because it is considered as a black box model, which does not need experimental design to achieve a clear relationship. Therefore, it overcomes the difficulty of experimental design and is a more unlimited method. Finally, according to the excellent results obtained from both modeling processes, the modeling approaches in real-scale stormwater treatment systems can be developed to benefit from their application in modeling, optimizing, and recognizing the relationship among variables.

## 4. Conclusions

_{4}

^{+}removal from stormwater by CB-GAC was carried out using BBD-RSM and GA-ANN. In terms of prediction, neural network had better prediction accuracy than response surface method, with R

^{2}of 0.9959 and 0.9762, respectively. The ANOVA and response surface plots in RSM confirmed that contact time was the most significant parameter of NH

_{4}

^{+}removal, and the relative influence order of the factors according to the coefficients of the code equation is as follows: Contact time > temperature > pH > initial concentration. The best network structure of 4-8-1 was utilized in BP-ANN modeling. The results of sensitivity analysis showed that the factors of NH

_{4}

^{+}removal rate were in the order of: Contact time (31.23%) > pH (24.68%) > temperature (22.93%) > initial concentration (21.16%). The process input factors were optimized by GA-ANN and BBD-RSM for the optimum NH

_{4}

^{+}removal rate. The predicted results were verified by experiments. According to the results, the predicted values of GA-ANN were in better agreement with the experimental values. The optimum level of contact time, initial concentration, temperature, pH is 899.41 min, 17.35 mg/L, 15 °C, 6.98, respectively, under which condition, the maximum NH

_{4}

^{+}removal rate is achieved 63.74%. The proposed method is effective for optimizing the process parameters of NH

_{4}

^{+}removal from stormwater by CB-GAC, and is helpful to reduce the time and cost of experiments. In the future research, this method can be applied to the parameter optimization and efficiency prediction of the actual stormwater treatment process.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Flow chart of back-propagation artificial neural network (BP-ANN) coupled with genetic algorithms (GA).

**Figure 3.**The characteristics of coal-based granular activated carbon (CB-GAC): (

**a**) SEM image 1000×; (

**b**) SEM image 5000×; (

**c**) X-ray diffraction patterns; (

**d**) N

_{2}adsorption desorption isotherm and pore size distribution.

**Figure 4.**Langmuir, Freundlich, and Temkin isotherms for the adsorption of NH

_{4}

^{+}onto CB-GAC. (Experimental conditions: Initial pH: 7; CB-GAC dose: 10 g/100 mL; temperature: 25 °C; contact time: 24 h).

**Figure 5.**Pseudo-first-order, pseudo-second-order kinetics and removal rate for the adsorption of NH

_{4}

^{+}onto CB-GAC. (Experimental conditions: Initial pH: 7; CB-GAC dose: 10 g/100 mL; temperature: 25 °C; initial concentration: 15 mg/L).

**Figure 6.**The relationship between the predicted and actual values for the Box-Behnken design, R

^{2}= 0.9762.

**Figure 7.**2D contour plot (

**a**) and 3D response surface plot (

**b**) showing the effect of contact time and pH on the removal rate of NH

_{4}

^{+}.

**Figure 8.**2D contour plot (

**a**) and 3D response surface plot (

**b**) showing the effect of contact time and temperature on the removal rate of NH

_{4}

^{+}.

**Figure 9.**MSE (mean square error) plot for different numbers of neurons in the hidden layer (1–14) for the response of NH

_{4}

^{+}removal rate.

Type | Models | Equations |
---|---|---|

Isotherm models | Langmuir | $\frac{{\mathrm{C}}_{\mathrm{e}}}{{\mathrm{Q}}_{\mathrm{e}}}=\frac{{\mathrm{C}}_{\mathrm{e}}}{{\mathrm{Q}}_{\mathrm{max}}}+\frac{1}{{\mathrm{K}}_{\mathrm{L}}{\mathrm{Q}}_{\mathrm{max}}}$ |

Freundlich | $\mathrm{lg}{\mathrm{Q}}_{\mathrm{e}}=\frac{1}{\mathrm{n}}\mathrm{lg}{\mathrm{C}}_{\mathrm{e}}+\mathrm{lg}{\mathrm{K}}_{\mathrm{F}}$ | |

Temkin | ${\mathrm{Q}}_{\mathrm{e}}=\frac{\mathrm{RT}}{{\mathrm{b}}_{\mathrm{T}}}{\mathrm{lnK}}_{\mathrm{T}}+\frac{\mathrm{RT}}{{\mathrm{b}}_{\mathrm{T}}}{\mathrm{lnC}}_{\mathrm{e}}$ | |

Kinetic models | Pseudo-first-order | $\mathrm{ln}\left({\mathrm{Q}}_{\mathrm{e}}-{\mathrm{Q}}_{\mathrm{t}}\right)=\mathrm{ln}{\mathrm{Q}}_{\mathrm{e}}-{\mathrm{k}}_{1}\mathrm{t}$ |

Pseudo-second-order | $\frac{\mathrm{t}}{{\mathrm{Q}}_{\mathrm{t}}}=\frac{1}{{\mathrm{k}}_{2}\times {\mathrm{Q}}_{\mathrm{e}}^{2}}+\frac{\mathrm{t}}{{\mathrm{Q}}_{\mathrm{e}}}$ |

Factors | Variables | Unit | Level | ||
---|---|---|---|---|---|

Low (−1) | Middle (0) | High (+1) | |||

A | Contact time | min | 300 | 600 | 900 |

B | Initial concentration | mg/L | 10 | 15 | 20 |

C | Temperature | °C | 15 | 25 | 35 |

D | pH | / | 5 | 7 | 9 |

Type | Description |
---|---|

Input layer | 4 neurons (contact time, initial concentration, temperature, pH) |

Hidden layer | 1 layer; 8 neurons |

Output layer | 1 neuron (NH_{4}^{+} removal rate) |

Learning rate | 0.01 |

Epoch | 1000 |

MSE goal | 0.001 |

Algorithms | Levenberg-Marquardt (trainlm) |

Function | Sigmoid (tansig): Between input and hidden layers Linear: Between hidden and output layers |

Parameters | BET Surface Area (m^{2}/g) | Langmuir Surface Area (m^{2}/g) | t-Plot Micropore Area (m^{2}/g) | t-Plot External Surface Area (m^{2}/g) | Total Pore Volume of Pores (cm^{3}/g) | t-Plot Micropore Volume (cm^{3}/g) | Average Pore Diameter (nm) |
---|---|---|---|---|---|---|---|

CB-GAC | 32.2108 | 59.304 | 12.9979 | 19.2129 | 0.063856 | 0.006107 | 7.92976 |

Model | Parameters | Values |
---|---|---|

Langmuir | ${\mathrm{Q}}_{\mathrm{max}}$ (mg/g) | 0.2821 |

${\mathrm{K}}_{\mathrm{L}}$ (L/mg) | 0.0481 | |

R^{2} | 0.9951 | |

RSS (×10^{−4}) | 2.9047 | |

Freundlich | 1/n | 0.7165 |

${\mathrm{K}}_{\mathrm{F}}$ (L/mg) | 0.0171 | |

R^{2} | 0.9843 | |

RSS (×10^{−4}) | 9.2406 | |

Temkin | ${\mathrm{b}}_{\mathrm{T}}$ | 48,263.81 |

${\mathrm{K}}_{\mathrm{T}}$ | 0.6299 | |

R^{2} | 0.9925 | |

RSS (×10^{−4}) | 4.3932 |

Model | Parameters | Values |
---|---|---|

Pseudo-first-order | ${\mathrm{k}}_{1}$ | 0.5682 |

${\mathrm{Q}}_{\mathrm{e}}$ (mg/g) | 0.0893 | |

R^{2} | 0.9535 | |

RSS (×10^{−4}) | 5.2933 | |

Pseudo-second-order | ${\mathrm{k}}_{2}$ | 9.1682 |

${\mathrm{Q}}_{\mathrm{e}}$ (mg/g) | 0.0956 | |

R^{2} | 0.9868 | |

RSS (×10^{−4}) | 1.5052 |

**Table 7.**RSM (response surface methodology) and ANN (artificial neural network) predicted results and errors, along with experimental values of the response.

Run | Variables | NH_{4}^{+} Removal Rate | |||||||
---|---|---|---|---|---|---|---|---|---|

A/min | B/mg·L^{−1} | C/°C | D | Experiment | RSM | Error | ANN | Error | |

1 (Tra.) | 600 | 15 | 35 | 9 | 54.37 | 53.92 | 0.0083 | 54.3700 | 0.0000 |

2 (Tra.) | 300 | 20 | 25 | 7 | 52.65 | 52.6 | 0.0009 | 52.6500 | 0.0000 |

3 (Tra.) | 600 | 15 | 25 | 7 | 59.85 | 59.7 | 0.0025 | 59.6175 | 0.0039 |

4 (Tra.) | 600 | 10 | 15 | 7 | 61.27 | 60.49 | 0.0127 | 61.2700 | 0.0000 |

5 (Tra.) | 900 | 10 | 25 | 7 | 61.44 | 61.97 | 0.0086 | 61.4400 | 0.0000 |

6 (Tra.) | 600 | 10 | 25 | 9 | 56.36 | 56.45 | 0.0016 | 56.3600 | 0.0000 |

7 (Tra.) | 600 | 15 | 25 | 7 | 59.47 | 59.7 | 0.0039 | 59.6175 | 0.0025 |

8 (Tra.) | 600 | 15 | 25 | 7 | 60.27 | 59.7 | 0.0095 | 59.6175 | 0.0108 |

9 (Tra.) | 600 | 20 | 25 | 9 | 56.16 | 55.95 | 0.0037 | 56.1600 | 0.0000 |

10 (Tra.) | 600 | 15 | 25 | 7 | 58.88 | 59.7 | 0.0139 | 59.6175 | 0.0125 |

11 (Tra.) | 300 | 15 | 15 | 7 | 54.67 | 55.02 | 0.0064 | 54.6700 | 0.0000 |

12 (Tra.) | 600 | 10 | 25 | 5 | 53.38 | 54.16 | 0.0146 | 53.3800 | 0.0000 |

13 (Tra.) | 600 | 20 | 35 | 7 | 55.97 | 55.7 | 0.0048 | 55.9700 | 0.0000 |

14 (Tra.) | 900 | 15 | 25 | 5 | 57.47 | 56.69 | 0.0136 | 57.4700 | 0.0000 |

15 (Tra.) | 600 | 15 | 35 | 5 | 51.34 | 50.86 | 0.0093 | 51.3400 | 0.0000 |

16 (Tra.) | 300 | 15 | 25 | 5 | 49.26 | 48.33 | 0.0189 | 49.2600 | 0.0000 |

17 (Val.) | 300 | 15 | 25 | 9 | 50.27 | 56.18 | 0.1176 | 51.0862 | 0.0162 |

18 (Val.) | 900 | 15 | 25 | 9 | 59.62 | 59.61 | 0.0002 | 58.9691 | 0.0109 |

19 (Val.) | 600 | 15 | 25 | 7 | 60.03 | 49.37 | 0.1776 | 59.6175 | 0.0069 |

20 (Val.) | 900 | 15 | 15 | 7 | 63.32 | 60.08 | 0.0512 | 62.2006 | 0.0177 |

21 (Tes.) | 600 | 10 | 35 | 7 | 56.44 | 50 | 0.1141 | 56.4456 | 0.0000 |

22 (Tes.) | 900 | 15 | 35 | 7 | 59.39 | 59.5 | 0.0019 | 59.9995 | 0.0103 |

23 (Tes.) | 300 | 15 | 35 | 7 | 48.12 | 59.7 | 0.2406 | 49.0211 | 0.0187 |

24 (Tes.) | 600 | 20 | 15 | 7 | 60.88 | 62.64 | 0.0289 | 60.2450 | 0.0104 |

25 (Pre.) | 600 | 20 | 25 | 5 | 53.29 | 53.77 | 0.0090 | 53.2720 | 0.0003 |

26 (Pre.) | 300 | 10 | 25 | 7 | 53.19 | 52.84 | 0.0066 | 52.9502 | 0.0045 |

27 (Pre.) | 600 | 15 | 15 | 9 | 56.47 | 57.44 | 0.0172 | 56.3900 | 0.0014 |

28 (Pre.) | 900 | 20 | 25 | 7 | 60.48 | 61.32 | 0.0139 | 61.5586 | 0.0178 |

29 (Pre.) | 600 | 15 | 15 | 5 | 55.08 | 56.02 | 0.0171 | 55.1653 | 0.0015 |

Source | Sum of Squares | Degree of Freedom | Mean Square | F-Value | p-Value | |
---|---|---|---|---|---|---|

Model | 433.70 | 14 | 30.98 | 40.94 | <0.0001 | significant |

A-Contact time | 239.06 | 1 | 239.06 | 315.92 | <0.0001 | |

B-Initial concentration | 0.5852 | 1 | 0.5852 | 0.7734 | 0.3940 | |

C-Temperature | 56.59 | 1 | 56.59 | 74.79 | <0.0001 | |

D-pH | 15.03 | 1 | 15.03 | 19.86 | 0.0005 | |

AB | 0.0441 | 1 | 0.0441 | 0.0583 | 0.8127 | |

AC | 1.72 | 1 | 1.72 | 2.27 | 0.1543 | |

AD | 0.3249 | 1 | 0.3249 | 0.4294 | 0.5229 | |

BC | 0.0016 | 1 | 0.0016 | 0.0021 | 0.9640 | |

BD | 0.0030 | 1 | 0.0030 | 0.0040 | 0.9505 | |

CD | 0.6724 | 1 | 0.6724 | 0.8886 | 0.3618 | |

A² | 25.57 | 1 | 25.57 | 33.79 | <0.0001 | |

B² | 1.83 | 1 | 1.83 | 2.42 | 0.1419 | |

C² | 7.23 | 1 | 7.23 | 9.55 | 0.0080 | |

D² | 108.33 | 1 | 108.33 | 143.16 | <0.0001 | |

Residual | 10.59 | 14 | 0.7567 | |||

Lack of Fit | 9.41 | 10 | 0.9412 | 3.19 | 0.1377 | not significant |

Pure Error | 1.18 | 4 | 0.2954 | |||

Cor Total | 444.30 | 28 |

Std. Dev. | Mean | C.V. % | R² | Adjusted R² | Predicted R² | Adeq Precision |
---|---|---|---|---|---|---|

0.8699 | 56.53 | 1.54 | 0.9762 | 0.9523 | 0.8738 | 22.87 |

**Table 10.**The weights and biases of BP-ANN in input-hidden layer (${w}_{i}$ and ${b}_{i}$) and hidden-output layer (${w}_{j}$ and ${b}_{j}$).

Number of Neurons | ${\mathit{w}}_{\mathit{i}}$ | ${\mathit{b}}_{\mathit{i}}$ | ${\mathit{w}}_{\mathit{j}}$ | ${\mathit{b}}_{\mathit{j}}$ | |||
---|---|---|---|---|---|---|---|

Contact Time | Initial Concentration | Temperature | pH | ||||

1 | 0.2513 | 0.7242 | 2.6647 | 0.6973 | 2.6315 | 0.3643 | −0.7167 |

2 | 0.5408 | 0.1291 | 0.5256 | 2.2940 | −1.5721 | 0.0955 | |

3 | −0.9756 | −2.1045 | 0.5286 | −1.0694 | 0.1463 | 0.1405 | |

4 | 1.3235 | −0.5437 | 0.8937 | −0.3642 | 0.7363 | 0.7143 | |

5 | 1.2157 | 1.4659 | −0.4634 | −1.3170 | −0.2739 | −0.0235 | |

6 | −1.9242 | 0.6120 | −1.8276 | 1.3909 | −1.2270 | 0.0557 | |

7 | 0.7446 | 1.5502 | −1.9754 | −0.6814 | 1.8150 | 0.2089 | |

8 | −1.1734 | 0.5911 | 2.5940 | −0.6891 | −1.7490 | −0.3516 |

Input Variables | Relative Significance (%) | Ranking |
---|---|---|

Contact time | 31.23 | 1 |

Initial concentration | 21.16 | 4 |

Temperature | 22.93 | 3 |

pH | 24.68 | 2 |

**Table 12.**Comparison of experimental validation results and predicted results of BBD-RSM and BP-ANN-GA.

Variables | BBD-RSM | BP-ANN-GA | ||
---|---|---|---|---|

Predicted Parameters | Experimental Parameters | Predicted Parameters | Experimental Parameters | |

Contact time (min) | 911.42 | 910 | 899.41 | 900 |

Initial concentration (mg/L) | 13.49 | 13.5 | 17.35 | 17.5 |

Temperature (°C) | 18.22 | 18 | 15 | 15 |

pH | 7.28 | 7.3 | 6.98 | 7.0 |

Removal rate (%) | 62.83 | 61.32 | 63.74 | 63.19 |

Relative error (%) | 2.46 | 0.87 | ||

R^{2} | 0.9762 | 0.9959 | ||

RMSE | 3.4509 | 0.4690 |

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## Share and Cite

**MDPI and ACS Style**

Yu, A.; Liu, Y.; Li, X.; Yang, Y.; Zhou, Z.; Liu, H.
Modeling and Optimizing of NH_{4}^{+} Removal from Stormwater by Coal-Based Granular Activated Carbon Using RSM and ANN Coupled with GA. *Water* **2021**, *13*, 608.
https://doi.org/10.3390/w13050608

**AMA Style**

Yu A, Liu Y, Li X, Yang Y, Zhou Z, Liu H.
Modeling and Optimizing of NH_{4}^{+} Removal from Stormwater by Coal-Based Granular Activated Carbon Using RSM and ANN Coupled with GA. *Water*. 2021; 13(5):608.
https://doi.org/10.3390/w13050608

**Chicago/Turabian Style**

Yu, Aixin, Yuankun Liu, Xing Li, Yanling Yang, Zhiwei Zhou, and Hongrun Liu.
2021. "Modeling and Optimizing of NH_{4}^{+} Removal from Stormwater by Coal-Based Granular Activated Carbon Using RSM and ANN Coupled with GA" *Water* 13, no. 5: 608.
https://doi.org/10.3390/w13050608