Predictive modelling of tetracycline removal by I-Bi/Bi₂WO₆/MWCNTs photocatalyst using RSM and ANN-PSO hybrid machine learning approach

Abstract

A visible-light responsive heterostructure photocatalyst (I-Bi/Bi₂WO₆/MWCNTs) was successfully synthesized using an ethylene glycol-assisted hydrothermal method for the photodegradation of the tetracycline (TC) antibiotic. To analyze and streamline the process performance, a hybrid machine learning model that incorporated artificial neural networks (ANN) with particle swarm optimization (PSO) and response surface methodology (RSM) was applied to forecast and optimize key operating parameters, such as solution pH, initial TC concentration, contact time, and photocatalyst dosage. The 4-8-1 topology of ANN-PSO was found to be the optimal network, and the prediction model of TC removal was demonstrated as a matrix of explicit equations. The R² of randomized training (0.98), testing (0.99), and validation (0.96) at the optimized topology confirms the efficiency of the developed ANN-PSO model. The ANN-PSO model showed a better predictive performance in comparison with the RSM model (R² = 0.960, RMSE = 5.379), with the correlation coefficient (0.981) being higher and the RMSE (4.712) lower. A 96.8% TC removal was achieved at solution pH 8, initial TC concentration of 20 mg/L, contact time of 160 min, and photocatalyst dosage of 25 mg.

Introduction

Antibiotics are essential pharmaceuticals often prescribed for the treatment of bacterial infections^1–3. Tetracycline (TC) is a popular broad-spectrum antibiotic that may be present in aquatic environments due to its incomplete metabolism and eventual release into human and animal excreta^4–6. This has resulted in the occurrence of ample amounts of antibiotic-resistant bacteria (ARBs) and antibiotic-resistant genes (ARGs) in aquatic environments^7,8. Globally, ARBs and ARGs are the leading causes of several health effects in humans and animals⁹. Conventional water purification methods are less efficient in removing TC from contaminated water; therefore, there is an urgent need to develop a sustainable and cost-effective treatment method for the complete elimination of antibiotics¹⁰.

In recent years, visible-light-driven photocatalysis has been considered a green technology for water and wastewater treatment owing to its extraordinary efficiency and lower operating cost^5,11–13. The photodegradation of antibiotics in water using the photocatalyst (Bi₂WO₆) demonstrates promising activity under visible-light^14,15. However, owing to certain limitations, such as fast charge-recombination rates and poor light-utilization ability, they require further improvements. In addition, the open-layered structure of bismuth-based photocatalysts results in ion-exchange reactions that affect the overall photodegradation performance^16,17. To overcome these limitations, several modifications have been made to Bi₂WO₆-based photocatalysts, such as metal and non-metallic doping, heterostructure composite formation, and morphology engineering^18,19.

Heterostructure composite formation is one of the various synthesis strategies that has the potential to be a promising approach for developing photocatalysts with enhanced photodegradation²⁰. Recently, multiwalled carbon nanotubes (MWCNTs) coupled with Bi₂WO₆-based photocatalysts have been considered as efficient composites with improved photocatalytic properties²¹. The outstanding properties of MWCNTs, such as their high surface area, high tensile strength, and outstanding electron-transmission ability, provide excellent photocatalytic properties, such as a low charge-recombination rate, high light-utilization capability, and a low energy bandgap^22–24. The MWCNTs with greater surface area provide sufficient space for the semiconducting material to be well distributed, which reduces the energy bandgap and enhances the light-utilization capability²⁵. In addition, the adsorption capability of the synthesized photocatalysts was enhanced owing to the greater surface area of MWCNTs, which led to improved photocatalytic performance^26,27. Moreover, MWCNTs in composite photocatalysts function as electron acceptors and often trap electrons, facilitating photoelectron transmission, resulting in improved photodegradation performance of the as-synthesized photocatalyst²⁸.

Employing data-driven models such as Response Surface Methodology (RSM) and Artificial Neural Network–Particle Swarm Optimization (ANN-PSO) in the analysis and optimization of tetracycline removal presents several important benefits^29,30. RSM is a statistical technique that efficiently evaluates the individual and interactive effects of process variables with a minimum number of experimental runs required to identify optimum operating conditions³¹. In contrast, ANN-PSO integrates the nonlinear predictive capability of Artificial Neural Networks (ANN) with the global optimization ability of Particle Swarm Optimization (PSO), enabling the accurate modeling of complex nonlinear relationships between process variables and response³². Therefore, comparing RSM and ANN-PSO provides valuable insights into the strengths and limitations of both approaches, where RSM offers statistical interpretation and process understanding, whereas ANN-PSO enhances predictive accuracy and optimization performance³³. Such a comparative analysis contributes to the selection of an appropriate modeling technique for the efficient optimization of tetracycline photodegradation under visible-light irradiation.

In this study, the primary objective was to synthesize a novel visible-light-responsive MWCNT-based heterostructure composite (I-Bi/Bi₂WO₆/MWCNTs) photocatalyst for the efficient removal of TC. The second objective was to develop a data-driven predictive model using RSM and a hybrid ANN combined with a PSO machine learning approach for TC removal through as-synthesized I-Bi/Bi₂WO₆/MWCNTs photocatalysts. In this regard, a series of photocatalysts was developed using the ethylene glycol-assisted hydrothermal method; detailed characterization results demonstrating the excellent physicochemical and photocatalytic properties and experimental photodegradation mechanism of TC under visible-light irradiation were published in our previous literature²⁸. The current research focuses on the photodegradation of TC by as-synthesized photocatalysts and optimization of process parameters through RSM and a hybrid ANN-PSO machine learning model. The predictive performance of the developed RSM and ANN-PSO models for the photocatalytic removal of TC was analyzed and compared in detail.

Materials and methods

Materials

The surface-modified multiwalled carbon nanotubes (MWCNTs) used in this study were acquired from a previous study³⁴. Tetracycline (TC), sodium tungstate (Na₂WO₄·2H₂O), Bismuth nitrate pentahydrate (Bi(NO₃)₃·5H₂O), ethylene glycol (EG), sodium hydroxide (NaOH), and potassium iodide (KI) were obtained from Sigma-Aldrich. Sulfuric Acid and Ethanol were purchased from Dae-Jung, Korea. All chemicals used for the synthesis of the photocatalyst were of analytical grade and used without further purification.

Description of photocatalyst synthesis

The composite photocatalysts were synthesized as described in our previous study²⁸. In brief, Solution A was prepared by dissolving 0.97 gm of Bi(NO₃)₃·5H₂O in 50 mL of ethylene glycol under continuous stirring for 20 min. Solution B was obtained by dissolving 0.264 gm Na₂WO₄·2H₂O and 0.12 gm KI in deionized water. Subsequently, Solution B was added dropwise to Solution A under constant stirring for 1 h, yielding Solution C, which was stirred for an additional 30 min. MWCNTs were introduced into Solution C at varying weight ratios (2%, 3%, 5%, and 7%), followed by 20 min of continuous stirring. The resulting suspension was transferred into a Teflon-lined autoclave and heated at 180 °C for 14 h. After hydrothermal treatment, the product was centrifuged to separate the composite photocatalysts (I-Bi/Bi₂WO₆/MWCNTs), washed several times with deionized water and ethanol, followed by drying at 60 °C overnight.

Photocatalytic studies

The photodegradation of TC by the as-synthesized photocatalysts was evaluated as a function of different process parameters, including solution pH, initial TC concentration, contact time, and photocatalyst dosage under visible-light irradiation, within the ranges summarized in Table 1. Design-Expert ^® software (version 12.0.12) was used to design a set of experiments, as presented in Table 2. Each TC removal experiment was conducted in a 250 mL conical flask positioned 25 cm from the light source. Visible-light irradiation was provided by 90 W/m² LED lamps with an emission wavelength range of 440–830 nm. After each photodegradation experiment, the photocatalyst was separated from the mixture through centrifugation, and the TC concentration in the supernatant was analyzed at 356 nm using a UV-vis spectrophotometer (Shimadzu UV-1900i). The percentage of TC removal in each photocatalytic experiment was calculated using Eq. (1).

1

Table 1.

Experimental ranges of independent variables studied in the present work.

Code Variable	Parameter	Parameter Level
		Low (-1)	Centre (O)	High (+ 1)
A	Solution pH	6	8	10
B	TC Concentration (mg/L)	20	30	40
C	Contact time (min)	20	90	160
D	Photocatalyst dose (mg)	10	20	30

Table 2.

The set of experiments designed through central composite design (CCD) (photocatalytic conditions: temperature 25 ± 1 °C; shaking rate 120 rpm).

S. No.	Solution pH	TC Concentration (mg/L)	Contact Time (min)	Photocatalyst Dose (mg)
1	8	30	90	30
2	10	20	20	10
3	8	30	160	20
4	6	40	20	30
5	10	20	160	10
6	10	40	160	30
7	6	30	90	20
8	10	30	90	20
9	10	40	160	10
10	8	30	90	20
11	8	20	90	20
12	8	30	90	20
13	6	20	160	30
14	8	40	90	20
15	10	30	90	20
16	8	30	90	10
17	6	40	160	30
18	6	20	160	10
19	6	30	90	20
20	8	40	90	20
21	6	20	20	10
22	10	20	20	30
23	8	30	20	20
24	8	30	90	20
25	10	40	20	10
26	6	20	20	30
27	10	40	20	30
28	8	30	90	30
29	8	30	90	10
30	6	40	160	10
31	8	30	90	20
32	8	30	20	20
33	8	30	160	20
34	6	40	20	10
35	8	30	90	20
36	8	30	90	20
37	8	20	90	20
38	10	20	160	30

Where, is the initial TC concentration and is the equilibrium TC concentration.

Response surface methodology

Several process parameters significantly influence the efficiency of the photocatalytic process, each of which can significantly affect the overall TC removal efficiency. To systematically evaluate and optimize these effects, Response Surface Methodology (RSM) was employed^35,36. RSM is a statistical and mathematical tool that facilitates the design of experiments, the development of empirical models, and the assessment of the interactive effects of multiple operating variables. The purpose of RSM is to develop an appropriate polynomial model that accurately represents the data obtained through experiments and identifies the optimal operating conditions by analyzing the relationship between variables and their interactions.

2

Where Y is the model-predicted response, is the constant coefficient, , and are the linear coefficient, interaction coefficient, and quadratic parameter, respectively. Here, k denotes the number of independent variables, and describes the individual input variable³⁷. A Central Composite Design (CCD) was employed within the framework of Response Surface Methodology (RSM) to develop a mathematical model for predicting the TC removal% by the synthesized photocatalyst under visible light at varying performance parameters. The coefficient of determination (R²) and adjusted coefficient of determination (R_adj² were used to evaluate the accuracy of the developed RSM model, which determined the fitting quality of the developed model. Model selection and validation were further based on the significance of the regression terms, determined by p-values at a confidence level of 95%.

ANN-PSO hybrid machine learning model

Artificial Neural Networks (ANNs) are computationally inspired models that mimic the information-processing mechanisms of the human brain and are widely employed for prediction, classification, and regression applications. Their layered architecture, comprising an input layer, hidden layer, and output layer, facilitates the modeling of complex nonlinear relationships between input and output variables. Training is performed through feed-forward propagation, where input data are sequentially processed to generate outputs, followed by backpropagation, which adjusts the network weights based on error gradients. This iterative learning process progressively minimizes errors and enhances predictive accuracy, making ANNs powerful tools for representing nonlinear systems.

To further improve predictive performance, it is necessary to optimize ANN parameters, particularly weights and biases. Particle Swarm Optimization (PSO) provides an efficient approach for this purpose. PSO is a population-based optimization algorithm inspired by the collective behavior of bird flocks and fish schools. In this framework, each particle represents a candidate solution, and the swarm collectively explores the solution space to identify optimal outcomes. A particle is defined by its position and velocity, which govern its trajectory in the search space. During the optimization process, each particle retains its best historical position (pBest) and simultaneously considers the best solution identified by the entire swarm (gBest). The velocity and position of each particle were iteratively updated based on both pBest and gBest, thereby balancing global exploration with local exploitation. These update mechanisms are mathematically expressed in Eqs. 3 and 4, respectively²⁹.

3

4

Where, represents the velocity of particle in dimension at time t;  w is the inertia weight; and are the acceleration co-efficient; and demonstrate the random numbers evenly spread between 0 and 1; pBest is the best position previously achieved by the particle in the dimension; gBest is the best position found by the entire swarm in the dimension; is the current position of the particle in the dimension at time t; n represents the population size.

PSO offers distinct advantages over traditional optimization techniques, such as Simulated Annealing (SA) and Genetic Algorithms (GA), owing to its straightforward implementation, few control parameters, and strong adaptability across a wide range of optimization problems. When coupled with ANNs, PSO effectively tunes network weights and biases, thereby minimizing prediction errors and enhancing model accuracy. The optimization process was further streamlined by constraining the feasible solution space within the permissible parameter ranges to ensure computational efficiency. Consequently, the ANN–PSO framework represents a robust empirical modeling strategy capable of managing incomplete datasets and accurately capturing complex, nonlinear system dynamics. The algorithmic structure of the ANN–PSO model used in this study is illustrated in Fig. 1.

Fig. 1.

Schematic representation of ANN-PSO model algorithm²⁹.

Results and discussion

Outcomes of RSM model

RSM was performed to optimize the process conditions for the maximum photodegradation of TC using the as-synthesized photocatalysts under a visible-light source. Based on the design obtained by the Design of Experiments (DOE), 38 sets of experiments were performed with varying process variables. The perturbation graphs obtained via RSM allow us to investigate and compare the operating process parameters with reference to the special point in a designed space³⁸. The influence of each operating parameter on the deviation from the reference point is shown in Fig. 2 (a). A similar effect on TC removal was observed for the as-synthesized composite photocatalyst. The sharp curves in the perturbation graphs for all the independent variables, namely solution pH (A), TC concentration (B), contact time (C), and photocatalyst dosage (D), suggest that the photocatalytic removal of TC is extremely sensitive to all four independent variables.

Fig. 2.

(a) The perturbation plot demonstrates the effect of solution pH (A), initial TC concentration (B), contact time (C), and photocatalyst dose (D), (b) Optimization graphs for maximum TC removal.

The numerical optimization of process parameters for maximum TC removal was successfully evaluated through RSM modelling, as illustrated in Fig. 2 (b). The obtained results show that the maximum 96.85% TC removal was achieved at the optimized process parameters of solution pH of approximately 8, initial TC concentration of 28 mg/L, contact time of 159.6 min, and photocatalyst dose of 25.3 mg. The estimated TC removal efficiency followed the maximum desirability function of 1³⁹. The experimental result of TC removal was 96.6%, which is in close agreement with the model prediction, confirming the efficacy of the RSM model.

The statistical significance of the results obtained through RSM was further investigated through Analysis of Variance (ANOVA), and the obtained results are presented in Table 3. The coded quadratic equation for TC removal (Eq. 5) was developed based on the dependent and independent process variables, including solution pH (A), TC initial concentration (B), contact time (C), and photocatalyst dosage (D).

5

Table 3.

Summary of the quadratic outcomes (ANOVA) for TC removal under visible-light irradiation.

Source	Sum of Squares	df	Mean Square	F-value	P-value
Model	11128.9	14	794.93	48.05	< 0.0001	Significant
A- Solution pH	98.70	1	98.70	5.97	0.0227
B-Concentration	25.42	1	25.42	1.54	0.02277
C-Contact time	6679.59	1	6679.59	403.74	< 0.0001
D- dose	451.54	1	451.54	27.29	< 0.0001
AB	17.59	1	17.59	1.06	0.3133
AC	7.39	1	7.39	0.4467	0.5106
AD	7.25	1	7.25	0.4382	0.5146
BC	0.0072	1	0.0072	0.0004	0.9835
BD	8.35	1	8.35	0.5045	0.4847
CD	229.70	1	229.70	13.88	0.0011
A²	102.63	1	102.63	6.20	0.0204
B²	104.21	1	104.21	6.30	0.0196
C²	363.42	1	363.42	21.97	0.0001
D²	180.21	1	180.21	10.89	0.0031
Residual	380.52	23	16.54
Lack of Fit	247.48	10	24.75	2.42	0.0690	Insignificant
Pure Error	133.04	13	10.23
Cor Total	11509.4	37

The obtained F-value of 48.05, as mentioned in Table 3, revealed that the overall model was significant. In addition, a lower p-value indicates that the model terms in the quadratic equations are also significant. Based on the results obtained through ANOVA, it was confirmed that all the process parameters represented in the model were significant. However, based on the obtained p-values, the dominant process parameters responsible for TC photodegradation were contact time (C) and photocatalyst dose (D) as opposed to the solution pH (A) and initial TC concentration (B). Moreover, the obtained determination coefficients R² and adjusted R_adj2 were 0.96 and 0.95, respectively, demonstrating that the obtained model was well aligned with the experimental TC removal results. In addition, the difference between the predicted and adjusted correlation coefficients was quite small (0.1), which further confirms the best agreement between them. The relationship between the experimental TC photodegradation and the model-predicted results is shown in Fig. 3. The relationship between the results obtained through the model and experimental are in close agreement, confirming that the developed model and empirical equation can be used to evaluate the relationship between TC photodegradation process parameters.

Fig. 3.

Graph of actual versus model-predicted photodegradation response of TC.

Effect of process variables on TC removal

The influence of the process variables on the photodegradation of TC under a visible-light source using the as-synthesized I-Bi/Bi₂WO₆/MWCNTs composite photocatalyst is represented as a 3D response surface plot in Fig. 4. For each plot, two independent variables were varied across their respective experimental domains, whereas the other two parameters were maintained at constant values. Figure 4 (a) shows the interactive influence of solution pH and initial TC concentration on the percentage TC removal. TC removal increased with increasing solution pH and decreased with increasing initial TC concentration. A maximum TC removal efficiency of 96.75% was achieved at the optimum solution pH of 8 and an initial TC concentration of 20 mg/L. The enhanced degradation under mildly alkaline conditions can be attributed to the pH-dependent surface charge and speciation of TC, which can influence its interaction with the photocatalyst surface and the availability of reactive sites⁴⁰. Furthermore, alkaline conditions favor the formation and stabilization of superoxide radicals (•O₂⁻), which were identified as the dominant reactive species responsible for TC photodegradation. The enhanced degradation at higher pH may also be associated with the increased susceptibility of TC to direct photolysis. This behavior can be related to the pH-dependent electronic structure of TC and the π–π* transitions between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of its chromophore groups²⁸. Therefore, the improved TC removal under alkaline conditions likely results from the combined contributions of enhanced photocatalytic oxidation by •O₂⁻ and increased direct photolysis of TC.

Fig. 4.

3D plot for a photo-degradation of TC under visible-light irradiation (a) pH vs. concentration (mg/L), (b) pH vs. time (min), (c) pH vs. photocatalyst dose (mg), (d) concentration (mg/L) vs. time (min), (e) concentration (mg/L) vs. dose (mg), (f) time (min) vs. dose (mg).

Figure 4 (b) shows the combined effect of solution pH and contact time on TC photodegradation. The TC removal efficiency was found to be increased by increasing contact time from 0 to 160 min and solution pH from 2 to 8 under visible-light irradiation. The TC removal efficiency increased steadily with varying contact time, indicating that prolonged exposure to light enhanced the photodegradation process. The rapid initial photodegradation might be attributed to the presence of abundant active sites on I-Bi/Bi₂WO₆/MWCNTs photocatalysts and the efficient generation of reactive radicals, including •O₂⁻ and •OH, which readily oxidize the TC. As the reaction proceeded, the TC photodegradation rate decreased gradually owing to the reduced TC concentration and possible accumulation of intermediate products on the surface of photocatalysts⁴¹. Nonetheless, the maximum TC removal was observed at a contact time of 160 min and a solution pH of 8, suggesting that sufficient contact time promotes the generation of reactive radicals, thereby improving the overall TC photodegradation efficiency.

The combined effect of photocatalyst loading and solution pH on photodegradation of TC is shown in Fig. 4 (c). The TC removal percentage was found to be significantly enhanced with increasing I-Bi/Bi₂WO₆/MWCNTs loading from 10 to 20 mg, which can be attributed to the availability of higher active sites on the surface of photocatalysts. The greater number of active sites promotes the light absorption capability and facilitates the separation of photo-generated charges, thereby increasing the photocatalytic degradation rate of TC under visible-light irradiation²⁸. However, further enhancing the I-Bi/Bi₂WO₆/MWCNTs photocatalyst loading from 20 to 30 mg shows no appreciable effect on TC removal. However, further increasing the photocatalyst loading from 20 to 30 mg produced no appreciable improvement in TC removal. At excessive catalyst dosages, particle agglomeration and the light-shielding effect become more pronounced, reducing light penetration into the reaction medium and limiting the effective utilization of photo-catalytically active sites. Consequently, the rate of ROS generation reaches a plateau, resulting in negligible enhancement of degradation efficiency⁴². The optimum photocatalyst loading was 20 mg in solution pH of 8.

Similarly, Fig. 4 (d) illustrates the interactive effect of initial TC concentration and contact time on TC removal under visible-light irradiation. The TC removal efficiency decreased with increasing initial TC concentration from 20 mg/L to 40 mg/L, while it increased with increasing contact time. The TC removal ranged from 35 to 96.75% over 0–160 min. The highest removal efficiency (96.75%) was achieved at an initial TC concentration of 20 mg/L and a contact time of 160 min. The lower removal at higher TC concentrations can be attributed to the limited availability of active photocatalytic sites and increased light attenuation by TC molecules. Prolonged irradiation enhanced the generation of reactive species, thereby promoting TC degradation. Thus, 20 mg/L TC concentration and 160 min contact time were identified as the optimum conditions.

Figure 4(e) demonstrates the combined effect of photocatalyst dose and initial TC concentration on TC removal. The removal efficiency increased with increasing photocatalyst dose and decreasing initial TC concentration. The enhanced removal at higher photocatalyst doses can be attributed to the greater availability of active sites and increased generation of reactive species under visible-light irradiation. In contrast, the lower removal at higher TC concentrations may result from the saturation of active sites and increased light attenuation within the reaction suspension. The optimum conditions were identified as a photocatalyst dose of 20 mg and an initial TC concentration of 20 mg/L, which resulted in the maximum TC removal. Figure 4 (f) shows the interactive effect of concentration-dose and dose-contact time on TC removal percentage. All the results obtained in 3D plots are in good agreement with the results obtained by performing experiments using conventional methods.

ANN-PSO model development for evaluating prediction performance

The photocatalytic performance parameters, such as solution pH, initial TC concentration, contact time, and photocatalyst dosage, were used as input parameters for the ANN model, and the output of the model was TC removal (%), as shown in Fig. 5. The ANN toolbox in MATLAB v8.30.532 (R2023a) was used with the Levenberg-Marquardt (LM) backpropagation procedure. Purelin and Tansig methodologies were employed in the output and hidden layers.

Fig. 5.

A schematic representation of the ANN-PSO hybrid model.

The results of the CCD-DOE were utilized in ANN modelling for testing, training, and validation data, comprising 70%, 15%, and 15%, respectively. The equation sets were randomly segregated for testing, training, and validation to obtain better ANN model performance. The values of the photocatalytic performance parameters were of different magnitudes; therefore, all independent and dependent variables were normalized within the range of 0.1 to 0.9 to avoid numerical overflow owing to the small or large weight of the data. Normalization makes the model unbiased, as ANN considers all datasets on the same scale. Equation (5) was used to normalize the datasets^43–45.

5

In this study, 38 sets of experiments were performed, which were used in CCD-RSM modelling. All experiments were conducted in triplicate, and the average of the three experimental results was used in the RSM approach. For instance, in ANN modelling, instead of using the average result, all the experimental results (38 × 3 = 114) were utilized because the average value may not pass through the inherent ANN process mechanism³².

The PSO model was embedded in the ANN architecture, and a schematic representation of the ANN-PSO hybrid machine learning model is shown in Fig. 5. The primary objective of embedding PSO into ANN was to optimize the weights, which helped in predicting the optimized learning model. The optimized learning model will help evaluate the TC removal percentage as a function of different process conditions using the as-synthesized photocatalysts. Because the performance of an Artificial Neural Network (ANN) is highly influenced by the number of neurons in the hidden layer, various network topologies with more than one hidden layer were systematically evaluated. To enhance the predictive capability of the ANN, Particle Swarm Optimization (PSO) was employed to optimize the input space (weights) of the ANN, which resulted in improved model accuracy as reflected by lower RMSE and higher R² values.

The influence of neurons in the hidden layers, swarm size, and PSO parameters such as C₁ and C₂ on statistical performance parameters, including RMSE and R² for both training and testing datasets, is summarized in Table 4. Statistical observations confirmed that 4-8-1 was the best-optimized ANN-LMBP topology. Therefore, further analysis was performed on the 4-8-1 topology, as shown in Fig. 5. The results presented in Table 4 show that the optimal configuration of the model consisted of eight neurons in the hidden layer, a particle swarm size of 100, and C₁ and C₂ values of 1.5 and 2.5, respectively, confirmed from the statistical observations, including a higher correlation coefficient R² and lower RMSE.

Table 4.

Identification of various performance parameters of ANN-PSO and the effect of performance parameters on the datasets used for training and testing.

Neurons	Maximum Iterations	Swarm-size	C1	C2	Training		Testing
					R 2	RMSE	R 2	RMSE
1	300	100	1	3	0.898	0.1360	0.787	0.1486
2	300	100	1	3	0.896	0.1253	0.791	0.1392
3	300	100	1	3	0.902	0.1135	0.799	0.1263
4	300	100	1	3	0.913	0.1041	0.814	0.1162
5	300	100	1	3	0.917	0.1104	0.823	0.1045
6	300	100	1	3	0.919	0.0998	0.829	0.1017
7	300	100	1	3	0.771	0.0987	0.856	0.0989
8	300	100	1	3	0.791	0.0968	0.911	0.0912
9	300	100	1	3	0.801	0.0946	0.918	0.0956
10	300	100	1	3	0.814	0.0934	0.922	0.0962
11	300	100	1	3	0.928	0.0921	0.929	0.0843
12	300	50	1	3	0.936	0.0913	0.938	0.0868
13	400	50	1	3	0.934	0.0893	0.948	0.0871
15	500	25	1	3	0.949	0.0889	0.912	0.0886
20	300	100	1	3	0.956	0.0874	0.929	0.0892
25	300	100	1	3	0.951	0.0862	0.971	0.0796
30	300	100	1	3	0.955	0.0853	0.881	0.0783
8	300	100	1	3	0.964	0.0843	0.895	0.077
8	300	100	1	3	0.962	0.0826	0.899	0.0061
8	100	100	3	2.5	0.971	0.0196	0.921	0.0097
8	250	100	2	1	0.979	0.0098	0.939	0.0091
8	300	100	1.5	2.5	0.982	0.005	0.969	0.0089

The neurons in hidden layers describe the overall performance of the developed ANN models. These neurons in ANN are responsible for learning nonlinear relationships between datasets, extracting patterns, and transforming input data into meaningful outputs 46. Therefore, ANN-PSO was further investigated at varying numbers of neurons from 1 to 24 in the hidden layer at constant PSO parameters. The obtained RMSE and R² results for the different numbers of neurons are shown in Fig. 6. The higher correlation coefficient (R²) of 0.9815 with a lower RMSE of 0.005 was observed at 8 neurons in the hidden layer. Hence, the obtained result confirms that the 4-8-1 is the best optimal topology for the ANN-PSO hybrid architecture. The biases and weights of the ANN-PSO model for the 4-8-2 topology are summarized in Table 5.

Fig. 6.

Variation in statistical observations (R² and RMSE) at varying numbers of neurons in hidden layers.

Table 5.

The bias and optimal weight of the ANN-PSO model for the topology of 4-8-1.

Input(4)-Hidden layer (8)			Hidden layer (8)-Output (1)
Weight			bias	Weight	bias
-1.06	0.67	-1.60	-0.67	-0.41	-0.62
0.67	-1.30	0.30	1.50	0.08
-0.23	1.50	0.02	0.31	0.37
-1.60	1.60	1.01	0.24	-1.06
-0.92	-0.18	0.65	1.60	0.49
0.36	-0.89	0.77	0.84	-0.51
1.21	1.43	1.02	0.96	0.62
1.77	1.07	-1.04	-1.40	-0.40

The prediction of the ANN-PSO model for testing, validation, and training at optimized weights (Wi) and bias (bi) is shown in Fig. 7. The scatter plots (Fig. 7) reveal that the ANN-PSO topology produces excellent predictions that are close to the experimental results. The coefficients of determination (R²) for the training, validation, and testing datasets were 0.981, 0.992, and 0.968, respectively, confirming that the ANN models predicted well. Furthermore, all the testing, training, and validation data in combination were also investigated; the results further confirmed the excellent performance of the ANN model with a correlation coefficient of 0.981. Thus, it can be concluded that the predicted response of TC photodegradation by I-Bi/Bi₂WO₆/MWCNTs under visible-light from the ANN-PSO model was close to the experimental results; therefore, it can be used for the prediction of TC photodegradation at different process parameters with minimum error.

Fig. 7.

The performance of the ANN-PSO model.

Comparison of RSM and ANN-PSO model

The performances of the RSM and ANN-PSO models were further evaluated and compared using multiple statistical tools. The correlation coefficients obtained from the data validation and different nonlinear error functions were used to compare the performance of both models, and the details are summarized in Table 6. From the correlation coefficients (R²), it could be confirmed that the ANN-PSO model was the best, with a higher correlation coefficient of 0.981 compared to RSM, which shows an R² value of 0.96. Furthermore, the values of all the error functions for ANN-PSO were lower than those of RSM, further confirming that ANN-PSO is the best model for predicting TC photodegradation performance.

Table 6.

Non-linear error functions and the efficiency of model prediction^32,47.

Error-functions	Mathematical Equation	RSM output	ANN-PSO output
Coefficient of determination (R2)		0.96	0.981
Sum of Square error (SSE)		59.12	43.61
Sum of absolute error (SAE)		0.538	0.471
Root Mean Square Error (RMSE)		5.379	4.712
Pearson’s Chi-square measure		13.41	6.236
Average relative errors (ARE)		6.145	4.169
Hybrid fractional error function (HYBRID)		47.73	19.45
Absolute average deviation (ADD)		0.9436	0.725
Marquart’s percentage standard deviation (MPSD)		81.36	51.26

p is the number of parameters, and n is the number of experimental runs.

Optimization and validation of models

Based on the ANOVA analysis and numerical optimization results, the optimum operating conditions for achieving maximum TC degradation (96.75%) were determined as a solution pH of 8, an initial TC concentration of 20 mg/L, a contact time of 160 min, and a photocatalyst dosage of 20 mg. These optimized conditions represent the combined effects of the investigated process variables and provide the conditions under which the photocatalytic degradation performance was maximized. To assess the reliability and predictive capability of the developed RSM model, three sets of optimum conditions predicted by the model were experimentally validated. The corresponding experimental results, together with the model-predicted values, are presented in Table 7. A close agreement was observed between the experimental and predicted TC removal efficiencies, with a standard error of less than 2%, demonstrating the satisfactory predictive capability of the model. Furthermore, the ANN-PSO model predictions showed a closer agreement with the experimental observations than the RSM predictions. This improved agreement indicates the superior predictive capability of the ANN-PSO approach for describing the nonlinear relationships between the operating parameters and TC degradation efficiency.

Table 7.

Model validation at optimized conditions for TC removal.

No.	A	B	C	D	TC removal (%)
	pH	Conc. (mg/L)	Contact-time (min.)	Dose (mg)	ANN-PSO Pred.	RSM Pred.	Exp.
1	8.291	28.806	160	29.524	96.713	96.872	96.612
2	8.329	30.139	155	28.630	96.862	96.918	96.712
3	8.232	29.067	152	25.936	96.914	96.975	96.861

Conclusion

In this study, the photocatalytic removal of tetracycline using a novel visible-light-responsive heterostructure composite (I-Bi/Bi₂WO₆/MWCNTs) was modeled using response surface methodology (RSM) and a hybrid artificial neural network–particle swarm optimization (ANN–PSO) approach. The ANN–PSO model exhibited superior predictive performance compared to RSM, yielding closer agreement with the experimental data. Under optimized conditions (pH 8, initial TC concentration 20 mg/L, contact time 160 min, and photocatalyst dosage 25 mg), a maximum TC removal efficiency of 96.8% was achieved, consistent with both model predictions. While both models demonstrated good accuracy, the ANN–PSO framework proved more reliable for high-precision predictions.

Author contributions

Shoaib Ahmed: Writing - original draft, InvestigationYie Hua Tan: Conceptualization, Supervision, Review and EditingNabisab Mujawar Mubarak: Conceptualization, Supervision, Review and EditingMohammad Khalid: Supervision, Review and EditingRama Rao Karri: Methodology, Review and Editing.

Funding

The authors received no financial support for this work.

Data availability

All data generated or analysed during this study are included in this published article.

Declarations

Competing interests

The authors declare no competing interests.