Abstract:The main objective of this study was to create a mathematical tool that could be used with experimental data to predict the rheological flow behavior of functionalized xanthan gum according to the types of chemical groups grafted onto its backbone. Different rheological and physicochemical analyses were applied to assess six derivatives synthesized via the etherification of xanthan gum by hydrophobic benzylation with benzyl chloride and carboxymethylation with monochloroacetic acid at three (regent/polymer) ra… Show more
“…These measures included the correlation coefficient (R), coefficient of determination (R 2 ), adjusted coefficient of determination (R 2 adj), root mean square error (RMSE), and Error Prediction of Model (EPM). The formulas used to calculate these criteria were as follows [26][27][28][29][30][31][32]: In order to assess the performance of the models and select the optimal one, statistical measures were used. These measures included the correlation coefficient (R), coefficient of determination (R 2 ), adjusted coefficient of determination (R 2 adj ), root mean square error (RMSE), and Error Prediction of Model (EPM).…”
Section: Modeling Methodsmentioning
confidence: 99%
“…These measures included the correlation coefficient (R), coefficient of determination (R 2 ), adjusted coefficient of determination (R 2 adj ), root mean square error (RMSE), and Error Prediction of Model (EPM). The formulas used to calculate these criteria were as follows [26][27][28][29][30][31][32]:…”
Monitoring stations have been established to combat water pollution, improve the ecosystem, promote human health, and facilitate drinking water production. However, continuous and extensive monitoring of water is costly and time-consuming, resulting in limited datasets and hindering water management research. This study focuses on developing an optimized K-nearest neighbor (KNN) model using the improved grey wolf optimization (I-GWO) algorithm to predict dry residue quantities. The model incorporates 20 physical and chemical parameters derived from a dataset of 400 samples. Cross-validation is employed to assess model performance, optimize parameters, and mitigate the risk of overfitting. Four folds are created, and each fold is optimized using 11 distance metrics and their corresponding weighting functions to determine the best model configuration. Among the evaluated models, the Jaccard distance metric with inverse squared weighting function consistently demonstrates the best performance in terms of statistical errors and coefficients for each fold. By averaging predictions from the models in the four folds, an estimation of the overall model performance is obtained. The resulting model exhibits high efficiency, with remarkably low errors reflected in the values of R, R2, R2ADJ, RMSE, and EPM, which are reported as 0.9979, 0.9958, 0.9956, 41.2639, and 3.1061, respectively. This study reveals a compelling non-linear correlation between physico-chemical water attributes and the content of dry tailings, indicating the ability to accurately predict dry tailing quantities. By employing the proposed methodology to enhance water quality models, it becomes possible to overcome limitations in water quality management and significantly improve the precision of predictions regarding critical water parameters.
“…These measures included the correlation coefficient (R), coefficient of determination (R 2 ), adjusted coefficient of determination (R 2 adj), root mean square error (RMSE), and Error Prediction of Model (EPM). The formulas used to calculate these criteria were as follows [26][27][28][29][30][31][32]: In order to assess the performance of the models and select the optimal one, statistical measures were used. These measures included the correlation coefficient (R), coefficient of determination (R 2 ), adjusted coefficient of determination (R 2 adj ), root mean square error (RMSE), and Error Prediction of Model (EPM).…”
Section: Modeling Methodsmentioning
confidence: 99%
“…These measures included the correlation coefficient (R), coefficient of determination (R 2 ), adjusted coefficient of determination (R 2 adj ), root mean square error (RMSE), and Error Prediction of Model (EPM). The formulas used to calculate these criteria were as follows [26][27][28][29][30][31][32]:…”
Monitoring stations have been established to combat water pollution, improve the ecosystem, promote human health, and facilitate drinking water production. However, continuous and extensive monitoring of water is costly and time-consuming, resulting in limited datasets and hindering water management research. This study focuses on developing an optimized K-nearest neighbor (KNN) model using the improved grey wolf optimization (I-GWO) algorithm to predict dry residue quantities. The model incorporates 20 physical and chemical parameters derived from a dataset of 400 samples. Cross-validation is employed to assess model performance, optimize parameters, and mitigate the risk of overfitting. Four folds are created, and each fold is optimized using 11 distance metrics and their corresponding weighting functions to determine the best model configuration. Among the evaluated models, the Jaccard distance metric with inverse squared weighting function consistently demonstrates the best performance in terms of statistical errors and coefficients for each fold. By averaging predictions from the models in the four folds, an estimation of the overall model performance is obtained. The resulting model exhibits high efficiency, with remarkably low errors reflected in the values of R, R2, R2ADJ, RMSE, and EPM, which are reported as 0.9979, 0.9958, 0.9956, 41.2639, and 3.1061, respectively. This study reveals a compelling non-linear correlation between physico-chemical water attributes and the content of dry tailings, indicating the ability to accurately predict dry tailing quantities. By employing the proposed methodology to enhance water quality models, it becomes possible to overcome limitations in water quality management and significantly improve the precision of predictions regarding critical water parameters.
“…The accuracy of each model is evaluated using the following essential performance measures: the correlation coefficient (R), root mean square error (RMSE), and mean absolute error (MAE). These individual metrics are computed by applying the following mathematical expressions [40][41][42][43][44]:…”
This study conducts a comprehensive investigation to optimize the degradation of crystal violet (CV) dye using the Fenton process. The main objective is to improve the efficiency of the Fenton process by optimizing various physicochemical factors such as the Fe2+ concentration, H2O2 concentration, and pH of the solution. The results obtained show that the optimal dosages of Fe2+ and H2O2 giving a maximum CV degradation (99%) are 0.2 and 3.13 mM, respectively. The optimal solution pH for CV degradation is 3. The investigation of the type of acid for pH adjustment revealed that sulfuric acid is the most effective one, providing 100% yield, followed by phosphoric acid, hydrochloric acid, and nitric acid. Furthermore, the examination of sulfuric acid concentration shows that an optimal concentration of 0.1 M is the most effective for CV degradation. On the other hand, an increase in the initial concentration of the dye leads to a reduction in the hydroxyl radicals formed (HO•), which negatively impacts CV degradation. A concentration of 10 mg/L of CV gives complete degradation of dye within 30 min following the reaction. Increasing the solution temperature and stirring speed have a negative effect on dye degradation. Moreover, the combination of ultrasound with the Fenton process resulted in a slight enhancement in the CV degradation, with an optimal stirring speed of 300 rpm. Notably, the study incorporates the use of Gaussian process regression (GPR) modeling in conjunction with the Improved Grey Wolf Optimization (IGWO) algorithm to accurately predict the optimal degradation conditions. This research, through its rigorous investigation and advanced modeling techniques, offers invaluable insights and guidelines for optimizing the Fenton process in the context of CV degradation, thereby achieving the twin goals of cost reduction and environmental impact minimization.
“…The quality of the developed models was examined using statistical analysis and ANOVA at a 95% confidence level. Various model quality measures, such as the p-value, F-value, degree of freedom (DF), coefficient of determination (R 2 ), adjusted determination of coefficient (R adj 2 ), and Root Mean Square Error (RMSE), were used to evaluate the statistical adequacy of the models [15,25,[27][28][29][30][31][32][33][34][35]. The F-value describes the variation in the responses, which can be evaluated using a regression equation, whereas the p-value indicates the statistical adequacy of the developed model.…”
This research aimed to study the effects of individual components on the physicochemical properties of systems composed of surfactants, polymers, oils, and electrolytes in order to maximize the recovery efficiency of kerosene while minimizing the impact on the environment and human health. Four independent factors, namely anionic surfactant sodium dodecylbenzene sulfonate (X1) (SDBS), oil (X2) (kerosene), water-soluble polymer poly(ethylene glycol) (X3) (PEG), and sodium chloride (X4) (NaCl), were studied using the full factorial design (FFD) model. Four output variables, namely conductivity (Y1), turbidity (Y2), viscosity (Y3), and interfacial tension (IFT) (Y4), were taken as the response variables. All four FFD models have high coefficients of determination and low errors. The developed models were used in a multi-objective optimization (MOO) framework to determine the optimal conditions. The obtained optimal conditions are X1 = 0.01, X2 = 50, X3 = 5, and X4 = 0.1, with an error of 0.9414 between the predicted and experimental objective function values. This result shows the efficiency of the model developed and the system used for the recovery of kerosene, while also having a positive effect on the protection of the environment.
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