#
Efficiency of Orange Yellow II Degradation by Synergistic Hydroxylamine with Fe^{2+} to Activate Peroxymonosulfate Oxidation: Machine Learning Prediction and Performance Optimization

^{1}

^{2}

^{*}

## Abstract

**:**

^{2+}activating peroxymonosulfate (PMS). Using HA-enhanced Fe

^{2+}to activate PMS is a cost-effective method to degrade orange II (AO7). We investigated the individual and interactive effects of the concentrations of Fe

^{2+}, HA, and PMS on the degradation of AO7. The R

^{2}of the BPNN model was 0.99852, and the data were distributed around y = x. Sensitivity analysis showed that the relative importance of each factor was as follows: HA > Fe

^{2+}> PMS. The optimized results obtained by the genetic algorithm were as follows: the concentration of Fe

^{2+}was 35.33 μmol·L

^{−1}, HA was 0.46 mmol·L

^{−1}, and PMS was 0.93 mmol·L

^{−1}. Experiments verified that the AO7 degradation effect within 5 min was 95.7%, whereas the predicted value by the BPNN was 96.2%. The difference between predicted and experimental values is 0.5%. This study provides a new tool (machine learning) to accurately predict the concentrations of HA, Fe

^{2+}, and PMS to degrade AO7 under various conditions.

## 1. Introduction

_{4}

^{·−}). The oxidation capacity of sulfate radicals (E

_{0}= 2.5–3.1 V) is obviously higher than that of PS (S

_{2}O

_{8}

^{2}: E

_{0}= 2.1 V; HSO

_{5}: E

_{0}= 1.82 V) [14]. Compared with other activators, iron salts are widely used as transition metal activators because of their abundance and low price, among which Fe

^{2+}salts are more common. However, in the process of Fe

^{2+}activating PS, the generation of sulfate radicals is affected by the slow regeneration of Fe

^{2+}and the large amount of iron mud generated in the reaction [15,16]. In recent years, studies on the technology of synergistic HA enhancement of Fe

^{2+}to activate PS have shown that HA can accelerate the production of Fe

^{2+}, slow down the accumulation of iron mud [17,18,19], and improve the degradation efficiency of pollutants in the system in a wider pH range [20,21].

^{2+}activation of persulfate is very complex, and various influencing factors and their interactions will change the degradation efficiency. At present, research on Fe

^{2+}-activated persulfate is mainly focused on Fe

^{3+}reduction and recycling, the reaction mechanism, and the efficiency of degrading pollutants. There are few studies on Fe

^{2+}activating persulfate by the machine learning method. An artificial neural network (ANN) is a machine learning model constructed according to the basic principles of biological neural networks that establishes a nonlinear mapping relationship of input and output neurons through training samples [22]. ANNs have been widely applied in the pollutant removal field for processes such as adsorption, catalytic degradation, and so on [23,24,25]. An artificial neural model can directly predict the final state of the pollutant treatment system and guide the process of wastewater treatment. By reducing the number of experiments, processing costs can also be reduced by the use of ANN [26]. In addition, the influence degree of input factors and their interactions on degradation efficiency can be determined through the neural network model. Because of the complexity of advanced oxidation technology, it is important to develop a model to analyze the process of synergistic Fe

^{2+}to activate PMS. Establishing a neural network model of the process can provide valuable guidance in order to improve the degradation effect and further understand the degree of influence of each factor and their interactions on the pollutant degradation effect.

^{2+}/PMS system so that the key factors affecting degradation efficiency and the effect of the interaction of various factors on degradation could be determined.

^{2+}to activate PMS for the degradation of AO7. The Garson and PaD2 algorithms were used to analyze the sensitivity of the neural network. A coupled intelligent algorithm of the neural network and genetic algorithm was constructed, with the genetic algorithm embedded into the neural network to optimize the extreme value, and the optimal process conditions of the synergy of HA with Fe

^{2+}to activate PMS for the degradation of AO7 were obtained. The main contributions of this study are as follows: First, we propose an approach to describe the relationship between influencing factors and degradation efficiency by means of modeling. Second, we optimized the combination of reaction conditions with the best degradation rate on the basis of modeling, which can reduce the amount of trial and error. Third, we introduce the Garson and PaD2 algorithms in machine learning theory, which can be used for sensitivity analysis of influencing factors to obtain their importance ranking.

## 2. Materials and Methods

#### 2.1. Reagents and Instruments

_{16}H

_{11}N

_{2}NaO

_{4}S), hydroxylamine sulfate (H

_{6}N

_{2}O

_{2}·H

_{2}SO

_{4}), FeSO

_{4}·7H

_{2}O, potassium bisulfate (KHSO

_{5}·0.5KHSO

_{4}·0.5K

_{2}SO

_{4}), ethanol (C

_{2}H

_{5}OH), and reagents were analytically pure, purchased from Aladdin Pharmaceuticals, Shanghai, China. All water used in the experiment was ultra-pure water.

#### 2.2. Experimental Methods

^{2+}, and HA were evenly mixed, and then the specified amount of PMS was added to start the reaction. The initial volume of the mixture was kept at 50 mL. At the fifth minute of reaction, 1 mL of reaction solution was extracted and quenched with 1 mL of ethanol. The concentration of the solution was measured using a UV spectrophotometer. The experiments were carried out against the background pH of the mixed solution. All experiments were repeated in triplicate. The methods of determining the concentrations of AO7 and Fe

^{2+}are described in previous studies [20,21]. Based on the results of the single-factor experiment, the concentration range of each influencing factor was determined. The initial concentration of AO7 was 100 mg/L, and the initial pH of the solution was 4.7. The reaction time of all experiments was set at 5 min.

#### 2.3. BP Neural Network Model

^{2+}, and PMS were the input variables, and the degradation efficiency of AO7 was the output variable. Based on the single-factor experiment, the experimental variables and coding levels were obtained, as shown in Table 1 [20,21], and the Box–Behnken design (BBD) method was adopted to design the experiment, as shown in Table 2. In order to avoid the impact of data dimension, the data were processed without dimension. The Premnmx function in MATLAB was used to normalize the data. The experimental data were randomly allocated according to the following proportions: training set 70%, verification set 15%, and test set 15%. The influence of different hidden layer node numbers, training function, and excitation function on the BPNN was investigated by trial and error to determine the optimal structure of the BPNN. The root mean square error (RMSE) was used as the performance evaluation index for the neural network; the lower the RMSE value, the better the performance of the neural network.

#### 2.4. Garson and PaD2 Algorithms

_{i}is the ith factor value of the model), and it determines the degree of influence of each factor on the response value of the model when the range changes. The sensitivity coefficient represents the factor’s influence degree. The larger the sensitivity coefficient, the greater the influence of the factor on the response value of the model. Based on different analysis objects, sensitivity analysis can be divided into local and global sensitivity analysis. Local sensitivity analysis examines the influence of a single factor on the response value of the model, while global sensitivity analysis examines the impact of multiple factors on the response value of the model at the same time, as well as the impact of the interaction between factors [29]. The Garson algorithm is a local sensitivity analysis method based on the connection weights of a neural network. Through the connection weights, the degree of influence of a single factor on the response value of the model is calculated [30]. The PaD2 algorithm is used to analyze the influence of the interaction of two factors on the response value of the model. It is assumed that the topological relationship of the BPNN is M-N-1, and the network output form is $y=f\left({x}_{1},{x}_{2},\cdots ,{x}_{n}\right)$. By solving the second partial derivative of the equation, the degree of influence of the interaction between the two factors on the response value of the model can be analyzed [31]. In this study, the Garson algorithm (Equation (1)) was used to analyze local sensitivity, and the PaD2 algorithm (Equation (2)) was used to analyze global sensitivity.

_{ik}is the sensitivity coefficient of the ith input variable to the kth output variable, M is the number of neurons in the input layer, N is the number of hidden layer neurons, L is the number of neurons in the output layer, w

_{ij}is the weight of the connection between the ith neuron in the input layer and the jth neuron in the hidden layer, and v

_{jk}is the weight of the connection between the jth neuron of the hidden layer and the kth neuron of the output layer.

_{ik}

^{t}is the sensitivity coefficient of factors x

_{i}and x

_{k}of the tth sample to response value y, N is the number of hidden layer neurons, w

_{ij}is the weight of the connection between the ith neuron in the input layer and the jth neuron in the hidden layer, w

_{kj}is the weight of the connection between the kth neuron in the input layer and the jth neuron in the hidden layer, v

_{j}is the weight of the connection between the jth neuron in the hidden layer and the neuron in the output layer, f ′(net

^{t}) is the first partial derivative of the excitation function of the neurons in the output layer, f ′(net

_{j}

^{t}) is the first partial derivative of the excitation function of the hidden layer neuron, and f ″(net

_{j}

^{t}) is the second partial derivative of the excitation function of the hidden layer neuron.

_{i}and x

_{k}to response value y is shown in Equation (3):

_{ik}is the overall sensitivity coefficient of x

_{i}and x

_{k}to the response value y and m is the total number of samples.

## 3. Results and Discussion

#### 3.1. Determination of the BPNN Structure

#### 3.2. Performance Evaluation of the BPNN

^{2}, the better the BPNN fits. The R

^{2}of the training set is 0.99985, indicating that the model can explain 99.985% of the response value changes. The R

^{2}of the verification set is 0.99628, that of the test set is 0.99660, and that of all sets is 0.99852. The data are distributed near the line y = x, indicating that the error between measured and predicted value is small. The BP neural network has good predictive ability and a nonlinear mapping relationship.

^{2+}to activate PMS.

#### 3.3. Sensitivity Analysis of the BPNN

^{2+}(32.4%) > PMS (28%). According to the PaD2 algorithm, the order of influence of the interaction of two factors on the degradation effect is as follows: concentration of Fe

^{2+}and PMS (7.54) > concentration of HA and PMS (5.97) > concentration of Fe

^{2+}and HA (2.21).

#### 3.4. Influence of Concentrations of Fe^{2+}, HA, and PMS on Degradation of AO7

^{2+}, HA, and PMS and the degradation of AO7 were obtained. Origin 2018 software was used to make a three-dimensional surface map, and the results are shown in Figure 6. Each surface map shows the interaction of only two factors on the response value of the model, with the other factors remaining at the central level.

^{3+}to Fe

^{2+}, so that there will be a sufficient amount of Fe

^{2+}in the system to activate PMS and produce SO

_{4}

^{•−}to degrade AO7 [33]. Similarly, it can be seen from Figure 6a,c that the efficiency of degrading AO7 increased with increased concentration of Fe

^{2+}. Increasing the concentration of Fe

^{2+}can activate PMS to produce more SO

_{4}

^{•−}, thus improving the degradation effect.

_{4}

^{•−}, reducing the amount of SO

_{4}

^{•−}in the system [34,35], and thus reducing the degradation effect. When the concentration of HA is high, increasing the concentration of PMS could improve the degradation of AO7. These results further show that there was an obvious interaction between the concentrations of HA and PMS.

_{4}

^{•−}is shown in Equation (5):

_{5}

^{−}+ SO

_{4}

^{•−}→SO

_{4}

^{2−}+ SO

_{5}

^{•−}+ H

^{+}

^{2+}is low, increasing the concentration of PMS would reduce the degradation of AO7. When the concentration of Fe

^{2+}is high, increasing the concentration of PMS would improve the degradation effect. These results further show that the interaction between the concentration of Fe

^{2+}and the concentration of PMS was significant.

#### 3.5. Optimization of Process Parameters

^{2+}, HA, and PMS can be obtained by combining BPNN with the genetic algorithm. Using this combination, the ideal AO7 degradation rate can be obtained, and the error is small. Therefore, BPNN combined with the genetic algorithm can be used to optimize the parameters of AO7 degradation in the HA/Fe

^{2+}/PMS system.

## 4. Conclusions

^{2+}/PS advanced oxidation system. At the beginning of the study, we obtained the level of each reaction condition based on the results of a single-factor experiment, and we designed the experimental scheme according to the Box–Behnken design. Then we obtained the degradation rate of AO7 according to each experimental scheme, trained the BP neural network, and established the neural network model. In order to obtain the sensitivity of each reaction condition to the degradation rate, Garson and PaD2 algorithms were innovatively introduced, showing the novelty of this study. Finally, we carried out three verification experiments based on the optimized reaction conditions. The experimental results show the advantages of modeling and optimization in this study. The conclusions are as follows:

- (1)
- The final BPNN topology was 3-11-1. The excitation functions used in the hidden and output layers were tansig and purelin, respectively, and the training function was trainlm. The R
^{2}of the established BPNN model was 0.99852, and the data were distributed near the line y = x. The results show that the predicted value based on the BP neural network model was in good agreement with the measured value, and that there was a good fit of the model for the process of synergistic hydroxylamine with Fe^{2+}to activate PMS. - (2)
- Using the Garson and PaD2 algorithms based on the neural network weights, the order of influence of factors and factor pairs on the degradation of AO7 was calculated as follows: concentration of HA > Fe
^{2+}> PMS, and concentrations of Fe^{2+}and PMS > concentrations of HA and PMS > concentrations of Fe^{2+}and HA. - (3)
- The optimization result obtained by the genetic algorithm was as follows: the concentration of Fe
^{2+}was 35.33 μmol·L^{−1}, HA was 0.46 mmol·L^{−1}, and PMS was 0.93 mmol·L^{−1}. According to the verification experiment, the degradation of AO7 was 95.7%, which was only 0.5% lower than the model’s predicted value, 96.2%.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Influence of number of hidden layer neurons and excitation function; (

**b**) training function on performance of BPNN.

**Figure 5.**BPNN model training results: (

**a**) comparison of predicted and measured values; (

**b**) histogram of residuals.

**Figure 6.**Effects on degradation of AO7. Interaction between concentrations of (

**a**) HA and Fe

^{2+}, (

**b**) HA and PMS, and (

**c**) PMS and Fe

^{2+}.

Factors | Levels | ||
---|---|---|---|

−1 | 0 | +1 | |

Concentration of Fe^{2+} (μmol·L^{−1}) | 10 | 25 | 40 |

Concentration of HA (mmol·L^{−1}) | 0.1 | 0.3 | 0.5 |

Concentration of PMS (mmol·L^{−1}) | 0.5 | 0.75 | 1 |

Runs | Fe^{2+}(μmol·L ^{−1}) | HA (mmol·L ^{−1}) | PMS (mmol·L ^{−1}) | R_{AO7} (%) | |
---|---|---|---|---|---|

Actual | Predicted | ||||

1 | 40 | 0.1 | 0.75 | 66.9 | 66.9 |

2 | 10 | 0.5 | 0.75 | 73.8 | 73.8 |

3 | 25 | 0.3 | 0.75 | 86.1 | 86.1 |

4 | 25 | 0.3 | 0.75 | 86.1 | 86.1 |

5 | 10 | 0.3 | 1 | 58.7 | 58.7 |

6 | 40 | 0.5 | 0.75 | 94.9 | 94.9 |

7 | 25 | 0.3 | 0.75 | 85.7 | 86.1 |

8 | 10 | 0.3 | 0.5 | 69.5 | 69.5 |

9 | 25 | 0.5 | 1 | 91.8 | 91.8 |

10 | 25 | 0.5 | 0.5 | 83.5 | 83.5 |

11 | 40 | 0.3 | 1 | 92.8 | 92.8 |

12 | 25 | 0.1 | 0.5 | 63.7 | 63.7 |

13 | 25 | 0.3 | 0.75 | 86.4 | 86.1 |

14 | 10 | 0.1 | 0.75 | 43.1 | 44.9 |

15 | 25 | 0.3 | 0.75 | 85.7 | 86.1 |

16 | 40 | 0.3 | 0.5 | 80.5 | 80.5 |

17 | 25 | 0.1 | 1 | 55.1 | 56.4 |

Hidden Layer Neuron | Weight between Input and Hidden Layers | Threshold of Hidden Layer | Weight between Hidden and Output Layers | Threshold of Output Layer | ||
---|---|---|---|---|---|---|

Fe^{2+} | HA | PMS | ||||

1 | 2.8783 | −0.7327 | −1.1964 | −3.0276 | −0.1574 | −0.2901 |

2 | −2.1334 | −2.3543 | −0.2061 | 2.3871 | −0.0495 | |

3 | −1.8180 | 2.3485 | −0.3131 | 2.0163 | −0.1829 | |

4 | −0.1180 | 2.9386 | −0.7082 | 1.4494 | 0.5138 | |

5 | −2.9141 | −0.9853 | 0.4082 | 0.6374 | −0.0003 | |

6 | 1.6788 | 1.6654 | 2.0006 | 0.1730 | 0.2882 | |

7 | −1.1376 | −2.5627 | −1.2200 | −0.8487 | 0.0315 | |

8 | 3.0577 | 0.2525 | −0.3583 | 1.2881 | 0.2380 | |

9 | −0.7018 | 2.0271 | −2.2731 | −1.8713 | −0.0537 | |

10 | 1.0895 | 0.7200 | −2.6689 | 2.7863 | 0.3428 | |

11 | −2.4593 | −1.3092 | −1.6007 | −2.9865 | 0.0662 |

No. | Optimized Conditions | Predicted Degradation Rate | Actual Degradation Rate | Mean; Error |
---|---|---|---|---|

1 | Fe^{2+}: 35.33 μmol·L^{−1}, HA: 0.46 mmol·L^{−1}, PMS: 0.93 mmol·L^{−1} | 96.2% | 96.0% | 95.7%; −0.5% |

2 | 95.4% | |||

3 | 95.6% |

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Zhou, R.; Zhang, K.; Zhang, M.
Efficiency of Orange Yellow II Degradation by Synergistic Hydroxylamine with Fe^{2+} to Activate Peroxymonosulfate Oxidation: Machine Learning Prediction and Performance Optimization. *Water* **2023**, *15*, 1931.
https://doi.org/10.3390/w15101931

**AMA Style**

Zhou R, Zhang K, Zhang M.
Efficiency of Orange Yellow II Degradation by Synergistic Hydroxylamine with Fe^{2+} to Activate Peroxymonosulfate Oxidation: Machine Learning Prediction and Performance Optimization. *Water*. 2023; 15(10):1931.
https://doi.org/10.3390/w15101931

**Chicago/Turabian Style**

Zhou, Runjuan, Kuo Zhang, and Ming Zhang.
2023. "Efficiency of Orange Yellow II Degradation by Synergistic Hydroxylamine with Fe^{2+} to Activate Peroxymonosulfate Oxidation: Machine Learning Prediction and Performance Optimization" *Water* 15, no. 10: 1931.
https://doi.org/10.3390/w15101931