The HNT/Al₂O₃-GO nanocomposite was synthesized following a standard operating procedure. Initially, a solution was generated through the continuous agitation of 25 mg of GO in 100 mL of distilled water at 25 °C. It was agitated for 1 hour after adding 1.5 g of HNT to this solution. A stirring-conditioned solution of 0.625 g of aluminum nitrate (Al(NO₃)₂) in 50 mL of water was added to the HNT and GO solution. Following the addition of a 12 mL dropwise solution of ammonium hydroxide (NH₄OH) after 30 min, the reaction mixture was agitated at 25 °C for 24 h. The obtained precipitate underwent filtration and was meticulously rinsed using acetone and distilled water. The HNT/Al₂O₃-GO composite was desiccated in an oven for 12 h at 105 °C. The identical synthetic methodology was utilized to generate Al₂O₃ without GO and HNT.

Membranes were fabricated using PSF and varying concentrations of HNT/Al₂O₃-GO, as outlined in Table 1. To incorporate HNT/Al₂O₃-GO nanoparticles into the PSF membranes, a phase inversion method was employed. In order to distribute varying amounts of HNT/Al₂O₃-GO, ultrasonication was employed in a specific quantity of N-Methyl-2-pyrrolidone (NMP) following the preparation of the casting solution. A fixed quantity of Polyvinylpyrrolidone (PVP) and Silk Fibroin (SF) was quickly blended into the mixture to eliminate trapped air bubbles. The solution was evenly distributed on a glass plate using a glass stick to maintain a width of 100 μm. The plate was promptly placed into a coagulation water bath. The membrane underwent testing on the glass plate surface following a phase transition. Following that, the membrane was transferred from the coagulation bath to a separate water bath and allowed to sit for 24 h. This step was necessary to eliminate any lingering solvents and facilitate the separation process. Following that, deionized water was utilized to ensure the membrane’s safety. Various solutions were prepared using different concentrations of HNT/Al₂O₃-GO, including 0.5%, 0.75%, and 1%.

To eliminate moisture from the HNT/Al₂O₃-GO nanoparticles, a vacuum desiccator was employed for 2 days, after which an oven at 60 °C was utilized for 2 h. X-ray diffraction (XRD) spectrum analysis was utilized to determine the crystal state of the nanotubes. The analysis was performed using the D/max-rB 12 kW Rigaku instrument from Japan. We used a Shimadzu X-ray diffractometer to analyze HNT/Al₂O₃-GO and HNT crystal properties and obtained XRD patterns. With the help of an IMC-159D contact angle measurement instrument by IMOTO Machinery, the contact angle was measured at five locations on the same membrane using the sticky drop method. A 2-h soak in deionized water followed by drying with filter paper was used to determine the porosity of the membranes. We measured the weight difference between the membrane before and after water absorption, and we used the following Equation 1 to determine the membrane’s porosity (Aldrees et al., 2024; Sutariya et al., 2025). ε = W w − W d ρ H 2 O × A × L × 100 (1)

Where, A is the effective area of the membrane, L is the thickness of the membrane, ρ is the water density, and W w and W d are the weight of the wet and dry membranes. Each sample was averaged by taking three measurements.

BSA rejection and pure water flux were measured to evaluate membrane performance. A rotary filtration system with an effective membrane surface area of 14 c m 2 with the flow of 2 l / ⁡ min was used to study the performance. Water flow was measured at 1–5 atm pressures with 1 atm increments. The water flux j w was calculated using the following Equation 2 (Lu et al., 2025). j w = v A ∆ t (2)

Where, v is the weight of permeated pure water, A is the effective area of the membrane, and ∆ t is the permeation time. Filtering tests were performed at 20 °C. An evaluation of the performance was conducted by examining the inhibition of BSA.

Nutritional BSA solution at 200 mg/L was prepared for use in aqueous medium. Rejection is defined according to the following Equation 3 (Manouchehr et al., 2017). R = 1 − c p c f × 100 (3)

Penetrant concentration is c p , and feed concentration is c f . At 280 nm, a UV spectrophotometer measured BSA concentration.

Sedimentation experiments were carried out using the transverse flow smoothing unit in 1 bar, which was prepared in a laboratory. After filtering the pure water for 65 min, the feeding was started, and the measurement of the permeate solution began 10 min later. After filtering the BSA for 75 min, 30 min of distilled water washing without pressure was followed. A filtration test was performed, and the overall time was 200 min. The membranes that have nanoparticles show a nodal arrangement on the surface of the membrane. Different orientations of feed flow states are studied with this nodal arrangement. A parallel flow of feed flowed to the nodal arrangement. This filtration experiment used a perpendicular feed flow and a perpendicular membrane rotation at 90 °C. As shown in Figure 1, the cross-flow smoothing unit can operate in several modes.

The FRR is formulated as Equation 4 (An et al., 2023). F R R = 1 − J w , 2 J w , 1 × 100 (4)

Where, J w , 1 and J w , 2 are the pure water flux after 65 and 145 min of filtering.

Filter membranes with a high FRR have better antifouling properties. To calculate fouling ratios ( R t ), reversible fouling ratios ( R r e v ), and irreversible fouling ratios ( R i r ), the following Equations 5–7 are used (Manouchehr et al., 2017; Yang et al., 2019). R t = 1 − J P J w , 1 (5) R r e v = J w , 2 − J p J w , 1 × 100 (6) R i r = R t − R r e v = J w , 1 − J w , 2 J w , 1 × 100 (7)

Where, J p is the permeate flux at 135 min of filtering when the feed is a BSA solution.

Water flux is affected by the hydrophilic property. Figure 3a shows the flux for all membranes. It has been found that the water flux increases according to the hydrophilicity property. The tendency to increase in Pure Water Flux (PWF) is consistent with improving the hydrophilicity property according to the HNT/Al₂O₃-GO concentration. The membrane flux increases with more HNT/Al₂O₃-GO concentration (Li et al., 2012; Vadhva et al., 2021). The results show that it reaches its highest value when the amount of HNT/Al₂O₃-GO is 1 wt%. During the phase transformation process, Al₂O₃-GO increases water flux due to its hydrophilic properties. Improved water permeability results from increased membrane porosity.

Figure 3b shows the change in BSA removal and permeation flux in filtration. The PSF and HNT/Al₂O₃-GO -0.5 composite membrane flux often remains constant after 40 min, and the BSA removal after 40 min is close to 100%. On the other hand, the fluxes of the HNT/Al₂O₃-GO -0.75 and HNT/Al₂O₃-GO -1 composite membranes gradually decrease, and the BSA removal increases over time. Finally, after 140 min from the time of filtration, the BSA removal is close to 100% and 95%, respectively. As a result, BSA molecules gradually close the large pores in the last two layers of the skin. While 140 min have passed, the fluxes of HNT/Al₂O₃-GO -0.75 and HNT/Al₂O₃-GO -1 composite membranes are still much higher than PSF and HNT/Al₂O₃-GO -0.5.

Membrane reproducibility in liquid filtration is strongly dependent on membrane sedimentation. An excellent membrane has a low sedimentation and high selectivity and flux over time. Cake layer (mold) formation and concentration polarization hole closure reduce flux. During sedimentation, membrane surface behavior plays a crucial role. Hydrophobic membrane surfaces explain the weak antifouling property. It has been suggested that polymer composition materials and surface modification can be modified to improve membrane permeability and antifouling properties (Li et al., 2012; Vadhva et al., 2021; Mirzaei et al., 2021).

You can combine hydrophilic additives with the above methods to improve the anti-deposition property. The membrane was installed perpendicular to the flow direction, and 200 ppm of BSA solution was applied. Figure 3C depicts the permeation flux. Switching to BSA solution decreases the fluxes of pure PSF and HNT/Al₂O₃-GO -0.5 membranes. After the flux goes back to pure water, it is not completely recovered.

On the other hand, according to HNT/Al₂O₃-GO -0.75 and HNT/Al₂O₃-GO -1 composite membranes, when the feeding of BSA solution starts, the flux decreases drastically. After approximately 12 min from the infiltration of pure water, the recovery begins.

The FRR is shown in Table 3. A higher FRR enhances membrane antifouling properties. Clean PSFs have a lower FRR (58.59%) than membranes containing nanotubes embedded inside. The HNT/Al₂O₃-GO -0.5 composite membrane shows approximately an FRR of 72.5%, while both 0.75% and 1% membranes show an FRR of 90%.

This shows that the fouling resistance increases with the participation of HNT/Al₂O₃-GO. In Table 4, FRR is observed to be hydrophilic. In addition to absorbing water molecules, the hydrophilic surface can delay precipitation and absorb protein molecules. Graphene oxide, multiwalled carbon nanotubes, and silica exhibit lower FRRs than other carbon nanofillers.

There are two kinds of membrane fouling: fixable and non-fixable. Reverse hydraulic contamination involves the facile removal of materials via water washing. Conversely, fouling comprises substances that adhere very firmly to the membrane surface and are not removable.

In this case, the reverse washing process makes the membrane less valuable and raises the cost of running it. Chemical cleaning can remove irreversible fouling, but the membrane’s lifespan is reduced. Table 4 demonstrates different types of fouling. Modified membranes have lower resistance coefficients but higher flux recovery ratios. It is concluded that the modified membranes are more susceptible to fouling. The membrane’s irreversible resistance decreased dramatically from 22.5% to 3%. Also, Atomic Force Microscopy (AFM) imaging of the surface of the membrane revealed improved fouling of the embedded HNT/Al₂O₃-GO membranes and improved surface characteristics.

In this section, we propose a high-accuracy empirical correlation to predict the removal percentage of BSA, flux, and permeation flux. Our correlation models are developed based on the key parameters of pressure, time, and HNT/Al₂O₃-GO concentration, which have been identified as crucial factors affecting the mentioned parameters. We want to have a thorough grasp of the process of pollution removal by considering these aspects.

Equation 8 presents a multivariate polynomial correlation used to predict BSA removal percentage, pure water flux, and permeation flux as functions of three key parameters: HNT/Al₂O₃-GO concentration (C, wt%), operating pressure (P, bar), and filtration time (t, min). These variables were selected due to their strong influence on membrane behavior: nanomaterial concentration affects hydrophilicity and pore structure, pressure drives water transport through the membrane, and time reflects the duration of fouling exposure. Each term in the polynomial captures linear, interaction, and higher-order effects among these variables. Despite its complexity, this structure is essential to represent the nonlinear dependencies observed experimentally. Y = C 1 + C 2 x + C 3 y + C 4 x 2 + C 5 x y + C 6 y 2 + C 7 x 2 y + C 8 x y 2 + C 9 y 3 (8)

Furthermore, it is important to note that our correlation models have been validated and demonstrate high accuracy (Chai et al., 2020; Alkhouzaam and Qiblawey, 2021). This guarantees that our suggested strategy is reliable and resilient. Researchers and practitioners may better use operating circumstances and water treatment system efficiency by using these correlations to learn more about the pollutant removal process. Table 5 displays the valued constants that have been optimized.

A time limit of more than 100 min is needed to get the best rate of BSA removal, as shown in Figure 4a. Additionally, keeping the HNT/Al₂O₃-GO mixture between 0.6% and 0.9% seems to be the best choice. On the other hand, things go badly when both time and HNT/Al₂O₃-GO levels are low.

There is a clear trend in the data showing that the removal of BSA is significantly better when the treatment lasts 120 min. Also, the clearance rate increases noticeably when the amount of HNT/Al₂O₃-GO goes above a certain level of about 0.7%.

As shown in Figure 4b, there is a clear link between the rise in flow and the rise in pressure. The effect of the HNT/Al₂O₃-GO concentration also aligns with this trend. So, the highest flow is reached when the pressure is 6 bar, and the concentration of HNT/Al₂O₃-GO is 1%. While looking at the information in Figure 4b, we can see that the flux goes up in the same way that the pressure on the system goes up. In the same way, a higher quantity of HNT/Al₂O₃-GO leads to a higher flux level. The best flux is at 6 bar and 1% HNT/Al₂O₃-GO. The results suggest that achieving optimal control over the flow in the membrane separation process requires meticulous regulation of the pressure and amount of HNT/Al₂O₃-GO. Specialists and researchers may enhance the efficiency of water purification systems by adjusting the settings of these components based on different flow rates.

Figure 4c shows the permeation flux in a very useful way. Following our findings, it is clear that the concentration of HNT/Al₂O₃-GO is more important than time, as the trend shows. Interestingly, the highest diffusion flux is seen in the 0.75%–1% concentration range for HNT/Al₂O₃-GO. The biggest absorption flow happens at the start and end of the process considering the time factor. On the other hand, when the HNT/Al₂O₃-GO content is 0.2%, the penetration flow is the lowest.

In this study, three machine learning algorithms ANN, RF, and SVR were employed to predict the BSA removal efficiency and permeation flux of nanocomposite membranes. Contact angle, viscosity, porosity, and HNT/Al₂O₃-GO concentration were selected as input features based on strong correlations with BSA removal and permeation flux. These factors influence membrane hydrophilicity, pore structure, and transport behavior. The HNT/Al₂O₃-GO concentration ranged from 0% to 1.0%, contact angle from 58° to 70°, and porosity from 72% to 80%, with viscosity varying accordingly. These ranges ensured meaningful variation while avoiding issues like nanoparticle agglomeration or high casting viscosity. Limitations included non-linear interactions and fabrication challenges at high concentrations, which justify the use of machine learning for robust modeling. These variables were selected as inputs based on Pearson correlation analysis, which confirmed their strong influence on the target outputs. The machine learning models were developed using a dataset consisting of 40 data points, representing variations in membrane composition and performance characteristics. Prior to training, all input features were normalized using MinMax scaling. The dataset was randomly divided into 70% training (28 samples) and 30% testing (12 samples) sets to evaluate model generalization. To ensure robustness and mitigate overfitting, 5-fold cross-validation was applied during hyperparameter tuning for each algorithm. All machine learning models were implemented using the Python programming language (version 3.10.12). The Random Forest and SVR models were developed using the scikit-learn library (version 1.3.2), while the ANN model was built using TensorFlow (version 2.14.0) with the Keras API (integrated with TensorFlow). The dataset was preprocessed using MinMaxScaler from scikit-learn for normalization, ensuring that all input features were scaled to a uniform numerical range (Kallem et al., 2022; Jia et al., 2019; Hashemi et al., 2022; Karakurt and Kartal, 2023; Alayande et al., 2022).

The ANN model was designed as a multilayer feedforward network consisting of an input layer, two hidden layers, and a single output layer. Each neuron in the network computes a weighted sum of its inputs and applies a non-linear activation function. The mathematical formulation for the output of an ANN can be written as Equation 9: y ^ = f ∑ j = 1 n w j . g ∑ i = 1 m x i . v i j + b j + b (9) where x i are the input variables, v i j ​ are the weights connecting the input and hidden layers, w j ​ are the weights from the hidden to output layer, b j ​ and b are bias terms, and g · and f · represent activation functions. The rectified linear unit (ReLU) function was used in the hidden layers, while a linear activation was applied to the output layer. The network was trained using the Adam optimization algorithm with a learning rate of 0.001, and the loss function minimized during training was the mean squared error (MSE), expressed as Equation 10. M S E = 1 n ∑ i = 1 n y i − y i ^ 2 (10)

Model parameters such as the number of neurons per layer, batch size, and number of epochs were optimized using a grid search. The model was trained for 100 epochs with early stopping to prevent overfitting. Among all tested models, the ANN achieved the highest accuracy in terms of both coefficient of determination (R²) and mean absolute error (MAE) (Khosravi et al., 2022).

RF regression was also applied as a robust ensemble method that constructs a collection of decision trees during training and outputs the average prediction from all trees. The prediction function in RF is given by Equation 11: y = 1 T ∑ t = 1 T h t x (11) where T is the total number of trees in the forest, and h t x denotes the prediction of the t-th tree. Each decision tree is trained on a random subset of the data and features, a process known as bootstrap aggregating or bagging. The algorithm uses the reduction in impurity (typically measured by mean squared error for regression tasks) to decide on feature splits at each node. Important hyperparameters, including the number of trees, the maximum tree depth, and the minimum number of samples required for a split, were tuned through grid search. In addition to its accuracy, the RF model provided insights into feature importance, helping to quantify the relative contribution of each input variable to the predicted outputs (Lu and Elimelech, 2021).

SVR was employed to construct a regression model that finds a function with at most ε deviation from the actual outputs while maintaining model complexity as low as possible. The regression function is expressed as Equation 12: f x = w , x + b (12) where w and b are the weight vector and bias term, respectively. The optimization problem seeks to minimize Equation 13: min w , b , ξ , ξ * 1 2 w 2 + C ∑ i = 1 n ξ i + ξ i * (13) subject to the constraints of Equation 14. y i − w , x i − b ≤ ε + ξ i , w , x i + b ‐ y i ≤ ε + ξ i * , ξ i , ξ i * ≥ 0 (14)

Here, C is a regularization parameter that controls the trade-off between flatness and error tolerance, while ε defines the width of the margin in which no penalty is given for prediction errors (El Jery et al., 2023a; El Jery et al., 2023b; Chandrashekar and Sahin, 2014; Chaurasia and Pal, 2021; Bagherzadeh et al., 2021; Chang and Gupta, 2024). To model non-linear relationships between input and output variables, the SVR implementation used a radial basis function (RBF) kernel (Batool et al., 2024), defined as Equation 15: K x i , x j = exp − γ x i − x j 2 (15) where γ is the kernel coefficient. The SVR model’s hyperparameters, including C, ε, and γ, were optimized using a grid search with cross-validation.

All three models were trained on 80% of the dataset, with the remaining 20% used for testing. Model performance was evaluated using the MAE and R² (Eskandari et al., 2022; Zhao et al., 2020; Alimoradi et al., 2020), where using Equations 16, 17, respectively. M A E = 1 n ∑ i = 1 n y i − y i ^ (16) R 2 = 1 − ∑ y i − y i ^ 2 ∑ y i − y i ¯ 2 (17)

Selecting appropriate input parameters is critical for effective data analysis (Alimoradi and Shams, 2017; Chen et al., 2024; Ismail et al., 2024; Abba et al., 2024). Heat maps are a widely used tool for visualizing the strength and direction of correlations between variables. Each cell in a heat map represents the correlation coefficient between two parameters, with color gradients indicating the degree of association. This visual representation helps identify strongly related features, redundant variables, and underlying patterns in the data (Gbadamosi et al., 2024; Tao et al., 2024).

Figure 5 presents the heat map of the Pearson correlation of contributing parameters for both desired features. The results show the parameters’ independence and how each affects the output parameter. Therefore, the selected parameters as the input of the machine learning algorithms are contact angle, viscosity, concentration of HNT/Al₂O₃-GO, and porosity.

The results of the predictive models for BSA removal percentage are presented in Figure 6. Figure 6a displays the outcomes obtained from the ANN model, demonstrating remarkable accuracy with an MAE of 1.04% and an R² value of 0.99. Furthermore, the figure includes a linear regression plot that aligns closely with the ideal case ( y = x ), indicating the model’s high precision. Moving on to Figure 6b, it showcases the results of the RF algorithm, which exhibits a notably low MAE of 1.98% and an R² value of 0.97. Although the linear regression slightly deviates from the accurate case, it is worth noting that the intercept of this model is higher than that of the ANN model. Finally, Figure 6c presents the SVR model, which demonstrates comparatively lower accuracy than the other two models. This is evident from the relatively lower R² value of 0.96 and a higher MAE of 2.84%. Additionally, the linear regression plot in this model showcases even more deviation from the accurate case.

Figure 7 shows a similar study that was conducted on permeation flux. Figure 7a shows that the ANN model has a very high R² value of 1 and an MAE of 1.35. The regression line lines up perfectly with the y = x line, which shows how accurate the model is. The deep structure of the ANN models lets them make such accurate predictions. This is the second most accurate model, with an MAE of 2.12% and a R² value of 0.98. The RF model for permeation flow is shown in Figure 7b. The regression line, on the other hand, seems to diverge a little more than the ANN model. The SVR model in Figure 7c has an R² value of 0.97, which can predict what will happen. It has a relatively low MAE of 2.87%, even though it is the least reliable model compared to the other two. It is worth highlighting that the SVR model exhibits high predictive capabilities for both output parameters despite its lower accuracy when compared to the other models.

The ANN emerged as the most accurate model for both parameters. A big reason for this is that deep learning models use the backpropagation method. The ANN changes its weights and biases every epoch, which makes it more accurate. This important trait is why ANN is used so much and is a good choice in many areas.