“…These neurons work together to form the network, and the functionality of the network is primarily determined by the connections between the neurons [ 16 , 17 ]. The neurons in an ANN are divided into three separate layers: the input layer, the output layer, and the hidden layer [ 18 , 19 ]. The input layer contains the same number of neurons as there are input variables, while the output layer has a corresponding number of neurons to the output variables [ 18 ].…”
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) ratios R equal to 2.4 and 6. Results from the FTIR study verified that xanthan gum had been modified. The degree of substitution (DS) values varying between 0.2 and 2.9 for carboxymethylxanthan gum derivatives were found to be higher than that of hydrophobically modified benzyl xanthan gum for which the DS ranged from 0.5 to 1. The molecular weights of all the derivatives were found to be less than that of xanthan gum for the two types of derivatives, decreasing further as the degree of substitution (DS) increased. However, the benzyl xanthan gum derivatives presented higher molecular weights varying between 1,373,146 (g/mol) and 1,262,227 (g/mol) than carboxymethylxanthan gum derivatives (1,326,722–1,015,544) (g/mol). A shear-thinning behavior was observed in the derivatives, and the derivatives’ viscosity was found to decrease with increasing DS. The second objective of this research was to create an ANN model to predict one of the rheological properties (the apparent viscosity). The significance of the ANN model (R2 = 0.99998 and MSE = 5.95 × 10−3) was validated by comparing experimental results with the predicted ones. The results showed that the model was an efficient tool for predicting rheological flow behavior.
“…These neurons work together to form the network, and the functionality of the network is primarily determined by the connections between the neurons [ 16 , 17 ]. The neurons in an ANN are divided into three separate layers: the input layer, the output layer, and the hidden layer [ 18 , 19 ]. The input layer contains the same number of neurons as there are input variables, while the output layer has a corresponding number of neurons to the output variables [ 18 ].…”
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) ratios R equal to 2.4 and 6. Results from the FTIR study verified that xanthan gum had been modified. The degree of substitution (DS) values varying between 0.2 and 2.9 for carboxymethylxanthan gum derivatives were found to be higher than that of hydrophobically modified benzyl xanthan gum for which the DS ranged from 0.5 to 1. The molecular weights of all the derivatives were found to be less than that of xanthan gum for the two types of derivatives, decreasing further as the degree of substitution (DS) increased. However, the benzyl xanthan gum derivatives presented higher molecular weights varying between 1,373,146 (g/mol) and 1,262,227 (g/mol) than carboxymethylxanthan gum derivatives (1,326,722–1,015,544) (g/mol). A shear-thinning behavior was observed in the derivatives, and the derivatives’ viscosity was found to decrease with increasing DS. The second objective of this research was to create an ANN model to predict one of the rheological properties (the apparent viscosity). The significance of the ANN model (R2 = 0.99998 and MSE = 5.95 × 10−3) was validated by comparing experimental results with the predicted ones. The results showed that the model was an efficient tool for predicting rheological flow behavior.
“…Any finite range of those random variables has a joint Gaussian distribution. The probabilistic illustration of a goal function can be used for regression and classification (Tahraoui et al 2022b;Tahraoui et al 2022c).…”
Section: Gaussian Process Regression Coupled With the Dragonfly Algor...mentioning
confidence: 99%
“…where x stands for the measurements of input variables, f is the unknown functional dependence and is a Gaussian noise with variance 2 n . GPR uses GP as a prior to describe the distribution on the target function fx (Park et al 2017;Tahraoui et al 2022b). In GPR, the function values…”
Section: Gaussian Process Regression Coupled With the Dragonfly Algor...mentioning
confidence: 99%
“…are treated as random variables, where Park et al 2017;Tahraoui et al 2022b). GP is defined as a collection of random variables (stochastic process), any finite number of which is assumed to be jointly Gaussian distributed (Park et al 2017;Tahraoui et al 2022b). GP can fully describe the distribution over an unknown function…”
Section: Gaussian Process Regression Coupled With the Dragonfly Algor...mentioning
“…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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