# Advancing Sustainable Wastewater Treatment Using Enhanced Membrane Oil Flux and Separation Efficiency through Experimental-Based Chemometric Learning

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## Abstract

**:**

^{2}, MSE, R, and RMSE) and graphical visualizations. For oil flux, the results show that the most effective simulation was achieved in SVR-M2 and the statistical criteria for the testing phase were R

^{2}= 0.9847, R = 0.9923, RMSE = 0.0333, and MSE = 0.0011. Similarly, SVR-M2 was superior to other modeling techniques for the separation efficiency in the testing phase (R

^{2}= 0.9945, R = 0.9972, RMSE = 0.0282, MSE = 0.0008). Reliability outcomes promise to revolutionize how we model and optimize membrane-based oil–water separation processes, with implications for various industries seeking sustainable and efficient solutions.

## 1. Introduction

_{2}nanoparticles and fluorosilanizing using H,1H,2H,2H-perfluorododecyltrichlorosilane for membrane distillation.

## 2. Experimental Methodology

_{r}) from the initial solution (m

_{t}) by the membrane. It is expressed in the following manner:

## 3. Proposed AI Models

#### 3.1. Support Vector Regression

_{i}is the input vector, d

_{i}is the actual value, and N is the total number of data patterns):

_{i}). The regression parameters b and w can be found by providing positive values to the slack parameters ξ and ξ*, minimizing the objective function, as shown in Equation (5):

_{i}and α

_{i}*:

_{i}, x

_{j}); the Gaussian radial basis function, which can be written as follows, is the most well-liked kernel function:

#### 3.2. Robust Linear Regression (RLR)

_{0}+ b

_{1}x

_{1}+ b

_{2}x

_{2}+ … b

_{i}x

_{i}

_{1}signifies the value of the ith predictor, b

_{0}represents the regression constant, and bi stands for the coefficient of the ith predictor.

#### 3.3. Multilinear Regression Analysis (MLR)

_{0}represents the regression constant, X

_{1}stands for the value of the ith predictor, and B

_{i}is the coefficient of the ith predictor.

#### 3.4. Evaluation Criteria

^{2}) and correlation coefficient (CC). Prior to the final development of the model in the simulation phase, a thorough external validation process was thoroughly conducted. This validation procedure relied on the precise 10-fold cross-validation method, strategically designed to fine-tune model performance, improve model integrity, and minimize potential errors in modeling oil flux and separation efficiency. This process partitioned the dataset into ten equal subsets, consecutively utilizing one subset for validation while training the model on the remaining nine, repeating this process ten times to ensure a comprehensive assessment of model generalization. The application of 10-fold cross-validation served a dual purpose: to guard against overfitting, ensuring that models learned meaningful patterns instead of memorizing training data, and to identify potential issues with model robustness and consistency. Consequently, this systematic approach enabled the optimization of model parameters and features in models with superior predictive capabilities, well-suited for real-world applications during the subsequent simulation phase of oil flux and separation efficiency. Additionally, the model’s effectiveness was evaluated using two statistical errors: the root mean square error (RMSE) and the mean square error (MSE). These parameters were assessed using Equations (12)–(15).

^{2}(−∞ < R

^{2}< 1), CC (−1 < CC < 1), MAE (0 < MAE < ∞), RMSE (0 < RMSE < ∞) are expressed as:

- I.
- Coefficient of Determinacy$$\mathrm{R}2=1-\left[\frac{\sum _{i=1}^{N}({J}_{com,i}-{J}_{pre,i}{)}^{2}}{\sum _{i=1}^{N}({{J}_{com,i}-\overline{{J}_{com}})}^{2}}\right]$$
- II.
- Correlation Coefficient$$CC=\frac{\sum _{\mathrm{i}=1}^{\mathrm{N}}\left({J}_{com,i}-\overline{{J}_{com}}\right)\left({J}_{pre,i}-\overline{{J}_{pre}}\right)}{\sqrt{\sum _{\mathrm{i}=1}^{\mathrm{N}}({{J}_{com,i}-\overline{{J}_{com}})}^{2}\sum _{\mathrm{i}=1}^{\mathrm{N}}({{J}_{pre,i}-\overline{{J}_{pre}})}^{2}}}$$
- III.
- Mean Square Error$$MSE=\frac{1}{N}{\sum}_{i=1}^{N}({J}_{com,i}-{J}_{pre,i}{)}^{2}$$
- IV.
- Root Mean Square Error$$RMSE=\sqrt{\frac{1}{N}{\sum}_{i=1}^{N}({J}_{com,i}-{J}_{pre,i}{)}^{2}}$$

^{2}and CC and lowest MSE and RMSE proposed models were also put forth for better prediction within the research domain.

## 4. Results of AI-Based Models

^{2}, MSE, root MSE (RMSE), and R. Table 1 and Table 2 show the computed results for these statistical indicators of training and testing datasets. Additionally, this table shows the multistate performance of the model depending on various input variables. The outcomes indicated that the various predictive modeling strategies had varying degrees of accuracy. Furthermore, SVR-M2 was the superior prediction accuracy for both the training (R

^{2}= 0.9477, R = 0.9735, RSME = 0.0520, MSE = 0.0027) and testing phases (R

^{2}= 0.9847, R = 0.9923, RMSE = 0.0333, MSE = 0.0011). The worst performing regression method for the prediction of oil flux was MLR-M1, with the computed values of the indicators as training (R

^{2}= 0.7936, MSE = 0.0107, RMSE = 0.01033, R = 0.8908) and testing (R

^{2}= 0.7931, MSE = 0.0150, RMSE = 0.1223, R = 0.8906). Similarly, for the separation efficiency, SVR-M2 was superior to other modeling techniques with training stage training (R

^{2}= 0.9891, MSE = 0.0010, RSME = 0.0313, R = 0.9946) and the testing phase (R

^{2}= 0.9945, MSE = 0.0008, RMSE = 0.0282, R = 0.9972); whereas, MLR-M1 had the worst performance with training (R

^{2}= 0.9760, MSE = 0.0022, RMSE = 0.0466, R = 0.9879) and testing (R = 0.9815, MSE = 0.0027, RMSE = 0.0516, R = 0.9907). When both responses were simultaneously modeled using the different studied modeling techniques, it was observed that, for training and testing phases, MLR-1 and MLR-2 outdo other techniques in adequately predicting the combination of the responses. This is attributed to the high values of R and R

^{2}and low values of MSE and RMSE (Table 1 and Table 2). It was also observed that MLR-2 faintly outdid MLR-1 in terms of these statistical indicators. It is important to note that SVR-M2 is superior to other modelling techniques; this can be attributed to several factors. SVR excels in capturing nonlinear relationships within data, making it effective for modeling complex patterns. It also demonstrates robustness by being less sensitive to outliers, thus accommodating noisy datasets. SVR’s flexibility, enabled by customizable kernel functions, ensures adaptability to diverse data structures and its propensity for generalization aids in reliable predictions for unseen data. Moreover, SVR handles high-dimensional data efficiently and can be fine-tuned through parameter optimization, enhancing its predictive accuracy. The choice of SVR-M2 as superior to other techniques likely depends on the specific dataset, modelling objectives, and performance metrics in the given context.

## 5. Conclusions

^{2}= 0.9477, MSE = 0.0027, RSME = 0.0520, R = 0.9735) and testing phases (R

^{2}= 0.9847, MSE = 0.0011, RMSE = 0.0333, R = 0.9923) while the worst performing regression method for the prediction of oil flux was MLR-M1 with computed values of the indicators of training (R

^{2}= 0.7936, MSE = 0.0107, RMSE = 0.01033, R = 0.8908) and testing (R

^{2}= 0.7931, MSE = 0.0150, RMSE = 0.1223, R = 0.8906). Similarly, for the separation efficiency, SVR-M2 was superior to other modeling techniques with training stage training (R

^{2}= 0.9891, MSE = 0.0010, RSME = 0.0313, R = 0.9946) and the testing phase (R

^{2}= 0.9945, MSE = 0.0008, RMSE = 0.0282, R = 0.9972); whereas, MLR-M1 had the worst performance with training (R

^{2}= 0.9760, MSE = 0.0022, RMSE = 0.0466, R = 0.9879) and testing (R = 0.9815, MSE = 0.0027, RMSE = 0.0516, R = 0.9907). When both responses are simultaneously modeled using the different studied modeling techniques, in the training and testing phases, MLR-1 and MLR-2 outdo other techniques in adequately predicting the combination of the responses corresponding to a value of R

^{2}higher than 0.9266. MLR-2 faintly outdid MLR-1 in terms of these statistical indicators. This shows that the SVR, RLR, and MLR techniques are promising tools in the prediction of both oil flux and separation efficiency. The results also suggested that hybrid models, emerging algorithms, and optimization methods can be used to enhance filtration performance. The successful integration of AI with membrane-based oil–water separation promises enhanced operational efficiency, cost savings, and superior environmental protection for industries. By optimizing separation processes, industries can achieve faster, more cost-effective results while minimizing environmental impacts. Future research and applications may focus on expanding datasets, refining AI models, real-time monitoring, and tailoring solutions to specific industry needs. Such advancements, combined with the IoT and collaborative efforts, position AI-driven oil–water separation as a pivotal solution for sustainable industrial practices and environmental conservation.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The schematic demonstration of the spinning process of the ceramic membrane fabrication process.

**Figure 5.**Observed and predicted values of separation efficiency from the models against the time series.

**Figure 6.**Observed and predicted values of separation efficiency and oil flux from the models against the time series.

**Figure 7.**Scatter plots of oil flux for LMH between the observed and predicted values, (

**a**) Normalized predicted SVR-M1(LMH) vs. Normalized observed oil flux (LMH), (

**b**) Normalized predicted SVR-M2(LMH) vs. Normalized observed oil flux (LMH), (

**c**) Normalized predicted RLR-M1(LMH) vs. Normalized observed oil flux (LMH), (

**d**) Normalized predicted RLR-M2(LMH) vs. Normalized observed oil flux (LMH), (

**e**) Normalized predicted MLR-M1(LMH) vs. Normalized observed oil flux (LMH) and (

**f**) Normalized predicted MLR-M2(LMH) vs. Normalized observed oil flux (LMH).

**Figure 8.**Scatter plots of separation efficiency based on observed and predicted values, (

**a**) Normalized predicted SVR-M1(%) vs. Normalized observed separation efficiency (%), (

**b**) Normalized predicted SVR-M2(%) vs. Normalized observed separation efficiency (%), (

**c**) Normalized predicted RLR-M1(%) vs. Normalized observed separation efficiency (%), (

**d**) Normalized predicted RLR-M2(%) vs. Normalized observed separation efficiency (%), (

**e**) Normalized predicted MLR-M1(%) vs. Normalized observed separation efficiency (%) and (

**f**) Normalized predicted MLR-M2(%) vs. Normalized observed separation efficiency (%).

**Figure 9.**Scatter plots of separation efficiency and oil flux (%&LMH), (

**a**) Normalized predicted SVR-M1(%&LMH) vs. Normalized observed separation efficiency and oil flux (%&LMH), (

**b**) Normalized predicted SVR-M2(%&LMH) vs. Normalized observed separation efficiency and oil flux (%&LMH), (

**c**) Normalized predicted RLR-M1(%&LMH) vs. Normalized observed separation efficiency (%&LMH), (

**d**) Normalized predicted RLR-M2(%&LMH) vs. Normalized observed separation efficiency and oil flux (%&LMH), (

**e**) Normalized predicted MLR-M1(%&LMH) vs. Normalized observed separation efficiency and oil flux (%&LMH) and (

**f**) Normalized predicted MLR-M2(%&LMH) vs. Normalized observed separation efficiency and oil flux (%&LMH).

**Figure 10.**Error graph of oil flux (

**a**,

**b**) and separation efficiency (

**c**,

**d**) for comparison, (

**a**) Normalized MSE for oil flux vs. models, (

**b**) Normalized RMSE for oil flux vs. models, (

**c**) Normalized MSE for separation efficiency vs. models, (

**d**) Normalized RMSE for separation efficiency vs. models.

**Figure 11.**Error graph of combined output (oil flux and separation efficiency) for comparison, (

**a**) Normalized MSE for separation efficiency and oil flux vs. models, (

**b**) Normalized RMSE for separation efficiency and oil flux vs. models.

**Table 1.**Performance evaluation of SVR, RLR, and MLR in predicting oil flux, separation efficiency, and both in the training phase.

Model | Training Phase (Oil Flux) | |||
---|---|---|---|---|

R^{2} | MSE | RMSE | R | |

SVR-M1 | 0.9055 | 0.0049 | 0.0699 | 0.9516 |

SVR-M2 | 0.9477 | 0.0027 | 0.052 | 0.9735 |

RLR-M1 | 0.8151 | 0.0096 | 0.0978 | 0.9029 |

RLR-M2 | 0.7889 | 0.0109 | 0.1045 | 0.8882 |

MLR-M1 | 0.7936 | 0.0107 | 0.1033 | 0.8908 |

MLR-M2 | 0.8369 | 0.0084 | 0.0919 | 0.9148 |

Training Phase (S.E) | ||||

R^{2} | MSE | RMSE | R | |

SVR-M1 | 0.9781 | 0.002 | 0.0444 | 0.989 |

SVR-M2 | 0.9891 | 0.001 | 0.0313 | 0.9946 |

RLR-M1 | 0.9752 | 0.0022 | 0.0474 | 0.9875 |

RLR-M2 | 0.9777 | 0.002 | 0.0449 | 0.9888 |

MLR-M1 | 0.976 | 0.0022 | 0.0466 | 0.9879 |

MLR-M2 | 0.9808 | 0.0017 | 0.0416 | 0.9904 |

Training Phase (Oil Flux + S.E) | ||||

R^{2} | MSE | RMSE | R | |

SVR-M1 | 0.6398 | 0.0194 | 0.1394 | 0.7999 |

SVR-M2 | 0.6831 | 0.0171 | 0.1308 | 0.8265 |

RLR-M1 | 0.6459 | 0.0191 | 0.1382 | 0.8037 |

RLR-M2 | 0.6591 | 0.0184 | 0.1356 | 0.8119 |

MLR-M1 | 0.928 | 0.0039 | 0.0623 | 0.9633 |

MLR-M2 | 0.9496 | 0.0027 | 0.0521 | 0.9745 |

**Table 2.**Performance evaluation of SVR, RLR, and MLR in predicting oil flux, separation efficiency, and both in the testing phase.

Model | Testing Phase (Oil Flux) | |||
---|---|---|---|---|

R^{2} | MSE | RMSE | R | |

SVR-M1 | 0.8859 | 0.0083 | 0.0908 | 0.9412 |

SVR-M2 | 0.9847 | 0.0011 | 0.0333 | 0.9923 |

RLR-M1 | 0.8943 | 0.0018 | 0.0427 | 0.9457 |

RLR-M2 | 0.8683 | 0.0095 | 0.0976 | 0.9318 |

MLR-M1 | 0.7931 | 0.015 | 0.1223 | 0.8906 |

MLR-M2 | 0.8427 | 0.0114 | 0.1067 | 0.918 |

Testing Phase (S.E) | ||||

R^{2} | MSE | RMSE | R | |

SVR-M1 | 0.9807 | 0.0028 | 0.0526 | 0.9903 |

SVR-M2 | 0.9945 | 0.0008 | 0.0282 | 0.9972 |

RLR-M1 | 0.9823 | 0.0025 | 0.0505 | 0.9911 |

RLR-M2 | 0.9892 | 0.0016 | 0.0394 | 0.9946 |

MLR-M1 | 0.9815 | 0.0027 | 0.0516 | 0.9907 |

MLR-M2 | 0.9885 | 0.0016 | 0.0406 | 0.9942 |

Testing Phase (Oil Flux + SE) | ||||

R^{2} | MSE | RMSE | R | |

SVR-M1 | 0.7809 | 0.0194 | 0.1394 | 0.8837 |

SVR-M2 | 0.7856 | 0.019 | 0.1378 | 0.8864 |

RLR-M1 | 0.7504 | 0.0221 | 0.1487 | 0.8663 |

RLR-M2 | 0.7653 | 0.0208 | 0.1442 | 0.8748 |

MLR-M1 | 0.9266 | 0.0065 | 0.0807 | 0.9626 |

MLR-M2 | 0.9504 | 0.0044 | 0.0663 | 0.9749 |

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## Share and Cite

**MDPI and ACS Style**

Usman, J.; Abba, S.I.; Muhammed, I.; Abdulazeez, I.; Lawal, D.U.; Yogarathinam, L.T.; Bafaqeer, A.; Baig, N.; Aljundi, I.H.
Advancing Sustainable Wastewater Treatment Using Enhanced Membrane Oil Flux and Separation Efficiency through Experimental-Based Chemometric Learning. *Water* **2023**, *15*, 3611.
https://doi.org/10.3390/w15203611

**AMA Style**

Usman J, Abba SI, Muhammed I, Abdulazeez I, Lawal DU, Yogarathinam LT, Bafaqeer A, Baig N, Aljundi IH.
Advancing Sustainable Wastewater Treatment Using Enhanced Membrane Oil Flux and Separation Efficiency through Experimental-Based Chemometric Learning. *Water*. 2023; 15(20):3611.
https://doi.org/10.3390/w15203611

**Chicago/Turabian Style**

Usman, Jamilu, Sani I. Abba, Ibrahim Muhammed, Ismail Abdulazeez, Dahiru U. Lawal, Lukka Thuyavan Yogarathinam, Abdullah Bafaqeer, Nadeem Baig, and Isam H. Aljundi.
2023. "Advancing Sustainable Wastewater Treatment Using Enhanced Membrane Oil Flux and Separation Efficiency through Experimental-Based Chemometric Learning" *Water* 15, no. 20: 3611.
https://doi.org/10.3390/w15203611