# Prediction of Uranium Adsorption Capacity in Radioactive Wastewater Treatment with Biochar

^{*}

## Abstract

**:**

^{2}), error rate and CEC test set are used to judge the accuracy of the model based on the BP neural network. The results show that the Fick’s Law Algorithm (FLA) has a better search ability and convergence speed than the other algorithms. The importance of the input parameters is quantitatively assessed and ranked using XGBoost in order to analyze which parameters have a greater impact on the predictions of the model, which indicates that the parameters with the greatest impact are the initial concentration of uranium (C

_{0}, mg/L) and the mass percentage of total carbon (C, %). To sum up, four prediction models can be applied to study the adsorption of uranium by biochar materials during actual experiments, and the advantage of Fick’s Law Algorithm (FLA) is more obvious. The method of model prediction can significantly reduce the radiation risk caused by uranium to human health during the actual experiment and provide some reference for the efficient treatment of uranium wastewater by biochar.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Collection and Preprocessing

_{i}represents the original data to be normalized, X* is the normalized value, X

_{max}represents the maximum value of the initial data, and X

_{min}is the minimum value. The normalization process scales the data so that the data are uniformly mapped to the [0, 1] interval and the original data distribution pattern can be maintained [30].

^{2}/g), average pore size (Dav, nm), and total pore volume (VTot, cm

^{3}/g) of biochar. Chemical properties included the mass percentage of total carbon (C, %), the molar ratio of oxygen to carbon (O/C), and the molar ratio of oxygen to nitrogen ((O+N)/C). Experimental conditions included pH, temperature (T, K), initial concentration of uranium (C

_{0}, mg/L) and solid–liquid ratio (SLR, g/L) [31].

#### 2.2. Meta-Heuristic Algorithms

#### 2.2.1. Particle Swarm Optimization Algorithm (PSO)

_{i}= (X

_{i1}, X

_{i2}… X

_{iN}) that changes as the number of iterations grows, corresponding to possible solutions to the question. At the same time, particle i also has a velocity vector V

_{i}= (V

_{i1}, V

_{i2}… V

_{iN}) of the same dimension as X that changes continuously as the iteration number becomes higher, which is used to determine which direction particle i moves from the current position and how far it moves, and the speed of all dimensions have an upper limit V

_{max}[33]. The particle’s velocity as well as position update formulas are as in (2) and (3):

_{1}and c

_{2}are learning factors that regulate the maximum step length of learning. r

_{1}and r

_{2}are random functions taking values in the scope of [0, 1] to increase the randomness. pbest represents the individual optimal position of the second particle, while gbest represents the optimal position search of the population. The inertia weight w indicates the effect of the previous speed vector on a new one. Referring to the parameter settings in many literatures, the parameter settings in this paper are as follows: inertia weight = 0.8, learning factor c

_{1}= 0 for the self-knowledge part, and learning factor c

_{2}= 0 for the social experience part. The maximum number of iterations is 100 and the algorithm terminates when it reaches the preset maximum number of iterations.

#### 2.2.2. Differential Evolutionary Algorithm (DE)

_{i}denotes the ith solution, X

_{i}= (X

_{i,1}, X

_{i,2}… X

_{i,D}). After initialization, the individuals of each parent obtain their offspring through a mutation strategy, and for each solution vector X

_{i}, the corresponding mutation vector V is denoted as Equation (4):

_{0}, r

_{1}and r

_{2}are three dissimilar stochastic numbers belonging to [1, …, NP]. F is the variation operator, which takes the value in the range of [0, 2]. If F is too small, it might be trapped in a local optimum, while if F is too big, it is not prone to convergence. After the mutation is completed, the crossover operation is performed on the generated individuals as follows (5):

#### 2.2.3. Optimization Algorithm (CO)

_{1}, the vector update probability is r

_{2}, and the position update probability is r

_{3}; r

_{1}, r

_{2}and r

_{3}are homogeneous arbitrary numbers from [0, 1]. If r

_{2}≥ r

_{3}, the cheetah chooses the motionless waiting strategy; otherwise, it chooses the find or offensive strategy.

_{1}= 0.8, r

_{2}= 0.5, r

_{3}= 0.9. The maximum number of iterations is 100. When the algorithm reaches the preset maximum number of iterations, the algorithm terminates.

#### 2.2.4. Fick’s Law Algorithm

#### 2.3. BP Neural Network

_{1}, X

_{2}, …, X

_{n}are the input samples of the BP neural network and y

_{1}, y

_{2}, …, y

_{m}are the output variables of the BP neural network [38].

#### 2.4. Model Construction

#### 2.5. Performance Assessment Measures

^{2}) and the error rate. The error rate includes the mean square error (MSE), mean absolute error (MAE) and mean bias error (MBE) [39]. The specific formulas are shown in (8)–(11):

_{1}, y

_{2}, …, y

_{n}are the true values, $\overline{\mathrm{y}}$ is the average of all the true values, ${\widehat{\mathrm{y}}}_{1},{\widehat{\mathrm{y}}}_{2}\dots {\widehat{\mathrm{y}}}_{\mathrm{n}}$ are the predicted values, and ${\mathrm{y}}_{\mathrm{i}}-\widehat{{\mathrm{y}}_{1}}$ are the residuals of the ith sample, which indicate the difference between predicted and valid values, and provide a greater reflection of the reality of the error in the predicted value.

## 3. Results and Discussion

#### 3.1. Model Prediction Results

#### 3.2. Comparative Analysis of Model Performance

^{2}explains the variance score of the regression model. According to Table 1, the R

^{2}after optimization of the Fick’s Law Optimization Algorithm (FLA) is 0.90. The R

^{2}after the Cheetah Optimization Algorithm (CO) is 0.85. An R

^{2}closer to 1 indicates that the independent variable explains the variance change in the dependent variable better. It can be concluded from Figure 4 that the models of the Fick’s Law Optimization Algorithm (FLA) and the Cheetah Optimization Algorithm (CO) outperform the Particle Swarm Optimization Algorithm (PSO) model and the Differential Evolutionary Algorithm (DE) model. But when predictive models are in pursuit of higher accuracy, they often encounter some tradeoffs or limitations. For example, overfitting can reduce a model’s ability to generalize because it makes the model too dependent on specific details in the training data.

#### 3.3. Performance Analysis in CEC Tests

#### 3.4. Important Feature Visualization

_{0}, mg/L), which has a value of 1968, and the adsorption rises with the preliminary concentration of uranium. It begins to slow down when the initial concentration of uranium is too large. The second most influential is pH, with a value of 424. pH indicates the acidity or alkalinity of the solution in the environment. Under different pH conditions, the charge state of the biochar surface changes. When the pH is low (acidic environment), the surface of biochar is positively charged and attracted to the negative charge of uranium. In contrast, at a higher pH (alkaline environment), the surface of the biochar is negatively charged and repelled by the negative charge of uranium, resulting in lower adsorption capacity. In practical applications, selecting appropriate pH conditions can enhance the adsorption effect of biochar on uranium.

^{2}/g) of the biochar, with a value of 299, whose magnitude visually indicates the magnitude of the adsorption capacity of the adsorbent, and a greater specific surface area implies more reactive adsorption sites, which can increase the contact area between the biochar and the uranium, and thus enhance the adsorption effect. Next is the total pore volume (VTot), which has a value of 80. A larger total pore volume means more adsorption space, providing more sites to accommodate uranium ions. This makes the biochar more effective in adsorbing uranium. Therefore, a larger specific surface area and total pore volume can improve the adsorption ability of biochar for uranium when manufacturing adsorbents. These properties make biochar an effective adsorbent material with many applications in water treatment and environmental remediation.

## 4. Conclusions

- A prediction model of the uranium adsorption capacity is constructed using Python 3.10. Four meta-heuristic optimization algorithms for model searching based on the BP neural network, namely Particle Swarm Optimization (PSO), Differential Evolution (DE), Cheetah Optimization (CO) and Fick’s Law Algorithm (FLA), are used to establish four prediction models: PSO-BP, DE-BP, CO-BP and FLA-BP. Predictive models are available to foresee the uranium adsorption capacity of biochar in actual situations, significantly reducing the experimental effort and safety risks associated with radioactivity;
- The accuracy of the four models is verified by the coefficient of determination (R
^{2}) and error rate. After training and validation, the Fick’s Law Algorithm (FLA) is optimized with R^{2}of 0.90, showing more obvious advantages and a strong generalization performance. This algorithm is more robust than the other three regarding its robustness, generalization, and ability to go beyond the local optimum. When predictive models are in pursuit of higher accuracy, there are often trade-offs or limitations that require continued research; - The influence of the input performance parameters in the prediction model on the adsorption capacity is analyzed using XGBoost to search for the optimal performance parameters. The analysis showed that the most influential experimental conditions on the ability of biochar to adsorb uranium are the initial concentration of uranium (C
_{0}, mg/L) and pH; the most influential chemical properties are the mass percentage of total carbon (C, %) and the molar ratio of oxygen to carbon (O/C); and the most influential physical properties are the specific surface area of biochar (SA, m^{2}/g) and the total pore volume (VTot), providing some important lessons for the study of the uranium adsorption capacity of biochar.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Training set fitting results of biochar for predicting the uranium adsorption capacity: (

**a**) PSO-BP; (

**b**) DE-BP; (

**c**) CO-BP; (

**d**) FLA-BP.

**Figure 3.**Test set fitting results for predicting uranium adsorption capacity of biochar: (

**a**) PSO-BP; (

**b**) DE-BP; (

**c**) CO-BP; (

**d**) FLA-BP.

MSE | MBE | MAE | R^{2} | |
---|---|---|---|---|

PSO-BP | 0.01106 | 0.00097 | 0.07655 | 0.59230 |

DE-BP | 0.01348 | 0.00172 | 0.08292 | 0.50359 |

CO-BP | 0.00555 | 0.00098 | 0.05355 | 0.79556 |

FLA-BP | 0.00424 | 0.00082 | 0.04816 | 0.90125 |

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**MDPI and ACS Style**

Qu, Z.; Wang, W.; He, Y.
Prediction of Uranium Adsorption Capacity in Radioactive Wastewater Treatment with Biochar. *Toxics* **2024**, *12*, 118.
https://doi.org/10.3390/toxics12020118

**AMA Style**

Qu Z, Wang W, He Y.
Prediction of Uranium Adsorption Capacity in Radioactive Wastewater Treatment with Biochar. *Toxics*. 2024; 12(2):118.
https://doi.org/10.3390/toxics12020118

**Chicago/Turabian Style**

Qu, Zening, Wei Wang, and Yan He.
2024. "Prediction of Uranium Adsorption Capacity in Radioactive Wastewater Treatment with Biochar" *Toxics* 12, no. 2: 118.
https://doi.org/10.3390/toxics12020118