Data-Driven Optimization of Plant-Derived Bio-Coagulants for TDS Removal from Paint Wastewater: Comparative RSM and ANN Modeling

2.1. Equipment, Reagents, and Bio-Coagulant Preparation

The research was conducted using standard laboratory equipment, including a magnetic stirrer, an electronic balance, a graduated cylinder, beakers, a mortar and pestle, a pH meter, an oven, Whatman No. 1 filter paper, and a stopwatch. Avocado pear seeds (PS) and Moringa oleifera seeds (MOS) served as the bio-coagulants, alongside paint wastewater (PWW) and distilled water, while the reagents used included sodium hydroxide, hydrochloric acid, ethylenediaminetetraacetic acid (EDTA), and buffer solutions. PS and MOS were prepared separately following the methods described in [4,25]—washing, sun-drying, and grinding to a fine powder—after which the active ingredients were extracted by suspending 5 g of each powdered bio-coagulant in 100 mL of distilled water, stirring the mixture for 15 min at room temperature, and filtering it through Whatman No. 1 filter paper. Fresh bio-coagulant solutions were prepared before each experiment to ensure consistent results.

2.2. Paint Wastewater Sampling

Wastewater from paint production was collected, with permission from Legacy Paints Limited, at the final effluent disposal point of the company’s facility in Emene Industrial Layout, Enugu State, Nigeria, during peak production in February 2024. Samples were collected in pre-washed, acid-rinsed polyethylene containers to prevent contamination and preserve their physicochemical properties, stored at 4 °C, and analyzed within 24 h according to the procedure described in [4]. Initial TDS concentration was measured prior to treatment.

2.3. Coagulation-Flocculation (Jar Test) Experiments

TDS removal was evaluated using a six-paddle jar test setup as described by [4]. Paint wastewater samples were rapidly mixed at 100 rpm for 5 min to ensure adequate coagulant dispersion, then mixed slowly at 40 rpm for 25 min to promote floc formation, and then allowed to settle for 55 min. The filtered clear supernatant was then tested for TDS, and removal efficiency was estimated using Equation (1) [4]:

where $C_0$ is the initial TDS concentration of the paint wastewater sample and $C_t$ is the final TDS concentration after coagulation-flocculation treatment.

2.4. Bio-Coagulant and Wastewater Characterization

The functional groups in PS and MOS associated with coagulation were identified using Fourier Transform Infrared (FTIR) spectroscopy. TDS, the primary focus of this study, was measured gravimetrically in accordance with standard methods [26], while other wastewater characteristics were noted but not analyzed further in this work.

2.5. Experimental Design and Optimization Using RSM

A Central Composite Design (CCD) within the Response Surface Methodology (RSM) framework was used to optimize TDS removal across three coded factors: dosage (A), pH (B), and settling time (C). A face-centered CCD (α = 1) was chosen to avoid extreme axial points [27]. Experimental design, regression analysis, analysis of variance (ANOVA), response surface generation, determination of optimum TDS removal values for both bio-coagulants, and numerical optimization were all performed using Design-Expert software (Version 9.0.1). The resulting design was a three-factor, three-level face-centered central composite design comprising 20 experimental runs (Table 1), each conducted as described in Section 2.3.

2.6. Artificial Neural Network (ANN) Modeling

Artificial Neural Network (ANN) modeling was performed to predict TDS removal efficiency using the MATLAB Neural Network Fitting Tool (nftool, MathWorks Inc., USA), using dosage, pH, and settling time as inputs and TDS removal efficiency as the output. The dataset was randomly split into training (70%), validation (20%), and testing (10%) subsets: the training data established the relationship between process variables and TDS removal efficiency, the validation data assessed model performance during training and guarded against overfitting, and the testing data evaluated the predictive capability of the resulting network. A feed-forward backpropagation neural network comprising an input layer, one hidden layer, and an output layer was developed, with the Levenberg-Marquardt algorithm adopted as the training function for its suitability to nonlinear prediction problems [18,19]. The output layer used a linear transfer function (purelin), while the hidden layer used a tangent sigmoid (tansig) function; the number of hidden neurons was optimized by trial and error to minimize the mean square error (MSE), and the architecture yielding the lowest prediction error was ultimately selected. Predictive performance was then evaluated through regression analysis and the coefficient of determination (R²), root mean square error (RMSE), and standard error of prediction (SEP) [18-20].

2.7. Comparative Analysis of RSM and ANN

The predictive performance of the RSM and ANN models was compared using Equations (2)–(4) [19,20]:

Root Mean Square Error (RMSE):

Coefficient of Determination (R²):

Standard Error of Prediction (SEP):

where ${\mathrm{Y}}_{\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{d}}$ is the predicted TDS removal, ${\mathrm{Y}}_{\mathrm{e}\mathrm{x}\mathrm{p}}$ is the experimental TDS removal, ${\mathrm{Y}}_{\mathrm{e}\mathrm{x}\mathrm{p},\mathrm{a}\mathrm{v}\mathrm{e}}$ is the average experimental TDS removal, and n is the number of data points; ${\mathrm{Y}}_{\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{d}}$ , ${\mathrm{Y}}_{\mathrm{e}\mathrm{x}\mathrm{p}}$ , and ${\mathrm{Y}}_{\mathrm{e}\mathrm{x}\mathrm{p},\mathrm{a}\mathrm{v}\mathrm{e}}$ are all expressed as percentages.

3.1. Characterization of Bio-Coagulants and Paint Wastewater Sample

The characterization results for the bio-coagulants—functional groups and proximate analysis—along with the wastewater sample before and after treatment are presented in Table 2, Table 3 and Table 4. Table 2 summarizes the functional groups identified in PS and MOS bio-coagulants by FTIR analysis, with their proposed roles in coagulation-flocculation interpreted according to established mechanisms reported in the literature [4,7]. This analysis revealed key functional groups—amines (N-H), carbonyls (C=O), alcohols (C-O), and alkyl/alkane groups (C-H)—that are associated with proteins and polysaccharides and that may promote coagulation primarily through charge neutralization and particle bridging, thereby supporting floc formation and improving TDS removal [3,4]. Together, these results point to both PS and MOS as suitable, environmentally friendly, and sustainable options for treating industrial wastewater.

The proximate analysis results in Table 3 highlight the components that most influence bio-coagulant performance. Moringa oleifera seed (MOS) had a higher yield (30.52%) and a markedly higher protein content (37.5%) than avocado pear seed (PS), which had a yield of 25.63% and a protein content of 18.5%, whereas PS had a higher carbohydrate content (53.08% versus 44.63% for MOS). The high protein content of MOS enhances charge neutralization and thus strengthens floc formation, while the higher carbohydrate content of PS improves particle bridging and provides structural support during floc aggregation [4,7]—explaining why the two bio-coagulants differ in TDS removal efficiency.

Table 4 shows that the untreated paint wastewater sample had an initial TDS concentration of 2524.43 mg/L. Post-treatment TDS values dropped considerably with both bio-coagulants, falling to 165.54 mg/L with PS and 100.13 mg/L with MOS, corresponding to removal efficiencies of approximately 93.5% and 97.2%, respectively. This confirms that both bio-coagulants effectively promoted flocculation and sedimentation, improving overall water quality; the superior performance of MOS, in particular, can be linked to its higher protein content and favorable functional groups, which enhance charge neutralization and floc formation and thereby improve dissolved solids removal [4].

3.2. RSM and ANN Results of TDS Removal Using Avocado Pear and Moringa oleifera Seed Bio-Coagulants

Table 5a,b present the combined RSM and ANN results for TDS removal using avocado pear and Moringa oleifera seed bio-coagulants. Both materials performed effectively across the design space, with removal efficiencies ranging from 57–93% for avocado pear seed (PS) and 61–97% for Moringa oleifera seed (MOS); in both cases, the highest and most consistent removal efficiencies occurred at the center-point conditions of 4 mg/L dose, pH 4-, and 40-min settling time, pointing to a consistent and effective coagulation range. Predicted values for PS agreed well with the experimental results, with only minor discrepancies at the extreme factorial points—an unsurprising outcome, since particle destabilization and floc formation can vary considerably under very high or low pH and dosage levels [19]. ANN predictions for MOS, by contrast, tracked the experimental data even more closely, underscoring the stronger predictive capability of the machine learning approach. Overall, these results indicate that both bio-coagulants are promising for TDS removal, with optimum performance concentrated at the middle values of the experimental parameters.

3.3. Model Fit Summary for TDS Removal

The model fit summary in Table 6 shows that the quadratic model provided the best fit for TDS removal efficiency with both coagulants: PS yielded an adjusted R² of 0.9874 and a predicted R² of 0.9416, while MOS yielded correspondingly high values of 0.9837 and 0.9194, indicating strong agreement between predicted and experimental responses. By comparison, the linear and two-factor interaction (2FI) models performed poorly, reflected in their low or negative predicted R² values, while the cubic models were aliased and could not be estimated or interpreted reliably [19].

3.4. Analysis of Variance for TDS Removal

The analysis of variance (ANOVA) results, presented in Table 7a,b, further confirm the suitability of the quadratic model for both bio-coagulants. In both tables, the linear (A, B, C), interactive (AB, AC, BC), and quadratic (A², B², C²) terms were all statistically significant (p < 0.05) [19], showing that TDS removal depends on both individual factors and their interactions. The relatively high F-values for dosage, pH, and settling time in both models likewise confirm that these process factors significantly shape the coagulation-flocculation process. The predicted R² values of 0.9416 and 0.9194 for PS and MOS, respectively, align reasonably well with their adjusted R² values of 0.9874 and 0.9837, with differences under 0.1 in each case, while Adequate Precision ratios of 41.9060 (PS) and 35.9382 (MOS)—both well above the desirable threshold of 4—indicate adequate signal-to-noise ratios for navigating the design space [19,27]. Taken together, the Model Fit Summary (Section 3.3) and these ANOVA results confirm that the quadratic RSM model fits the data well and captures both the nonlinear and interaction effects governing TDS removal, providing a reliable basis for numerical optimization, response surface generation, and comparison against the ANN models.

3.5. Mathematical Model Equations for TDS Removal Using Avocado Pear Seed (PS) and Moringa oleifera Seed (MOS)

Building on the significant model terms identified through the quadratic ANOVA analysis (Section 3.4), mathematical models were developed relating dosage (A), pH (B), and settling time (C) to the TDS removal efficiencies of PS ( ${\mathrm{T}\mathrm{D}\mathrm{S}}_{\mathrm{P}\mathrm{S}}$ ) and MOS ( ${\mathrm{T}\mathrm{D}\mathrm{S}}_{\mathrm{M}\mathrm{O}\mathrm{S}}$ ). Equations (5) and (6) present the fitted second-order polynomials—including linear, interaction, and quadratic terms—generated from the CCD experimental design, serving as predictive tools for estimating TDS removal within the studied factor ranges; both final empirical models are expressed here in terms of coded factors.

3.6. Graphical Analysis of TDS Removal Using Avocado Pear Seed and Moringa oleifera Seed

3.6.1. Predicted vs. Experimental Plots

Figure 1a,b present the predicted versus experimental TDS removal values for PS and MOS, respectively. In both cases, the data points cluster closely around the 45° line representing perfect agreement between predicted and experimental values [27], indicating a close fit between the RSM predictions and observed responses [27], with the resulting linear plots clustering closely along the lines of best fit—evidence that the generated models can adequately predict the TDS removal efficiency of both PS and MOS [27].

3.6.2. 3D Response Surface Plots for TDS Removal

A 3D response surface was generated to estimate how combinations of the independent variables affect TDS removal efficiency for both coagulants; the resulting plots appear in Figure 2a–f. For both coagulants, increasing dosage improved TDS removal, whereas pH and settling time each showed nonlinear effects. Figure 2a–d show that pH has a more prominent effect at moderate to high dosage levels, pointing to a specific pH range where TDS removal is most effective, while Figure 2b–f show that longer settling times improved removal efficiency, particularly in combination with higher dosages. Overall, the response surfaces exhibit distinct maxima rather than flat trends, confirming that specific combinations of these variables yield optimal TDS removal.

3.6.3. Artificial Neural Network Regression Plots

Figure 3a,b present the artificial neural network (ANN) regression plots for TDS removal from paint wastewater, based on data divided into training (70%), validation (20%), and testing (10%) subsets. In both figures, the training regression plots show near-perfect correlation (R = 1) between predicted outputs and experimental targets, the validation regressions show high correlation coefficients (R ≈ 0.969 in Figure 3a and R ≈ 0.9698 in Figure 3b) with data points closely distributed around the best-fit line, again reach R=1, although the test subset contains only two observations and does not conclusively demonstrate model generalization. Combined with the very low RMSE and SEP values reported in Section 3.7, these results further confirm the ANN model’s superior predictive performance over RSM in capturing nonlinear interactions [19].

3.7. Predictive Performance Metrics (R2, RMSE, SEP) of RSM and ANN for Avocado Pear Seed and Moringa oleifera Seed

Table 8 summarizes the predictive performance of the RSM and ANN models for TDS removal using PS and MOS bio-coagulants. The reported root mean square error (RMSE), standard error of prediction (SEP), and coefficient of determination (R²) are a quantitative basis for evaluating the accuracy of each modeling approach.

3.8. Comparative RSM and ANN Modeling

The predictive performance of the RSM and ANN models, developed using Design-Expert and MATLAB respectively, was compared using RMSE, SEP, and the coefficient of determination (R²). R² reflects the percentage of variation in TDS removal efficiency explained by the model, with values close to unity indicating strong agreement between experimental and predicted results [18-19, 27]; RMSE and SEP were also examined, however, Since R² alone does not fully capture model accuracy, and lower values of both indicate reduced prediction error and greater model reliability [18,21]. For PS, the ANN model achieved an R² of 0.9998 against 0.990407 for RSM, while RMSE and SEP fell from 0.86902 and 1.048711 to 0.12 and 0.144813, respectively. For MOS, the ANN R² similarly approached unity (1.0000), with RMSE and SEP dropping sharply from 1.009331 and 1.171387 under RSM to 5.3 × 10⁻⁵ and 6.15 × 10⁻⁵. This improved accuracy suggests within the present dataset that the ANN model captured the nonlinear relationships among dosage, pH, settling time, and TDS removal efficiency more closely than the quadratic RSM model, suggesting that the coagulation-flocculation process involves complex nonlinear relationships not fully represented by the second-order polynomial structure of the RSM model [16]. Nevertheless, the exceptionally high R² and extremely low prediction errors obtained for MOS warrant caution, since the relatively small experimental dataset available for model development may have contributed to this unusually strong predictive performance. While these results demonstrate ANN’s strong predictive capability for this system, future studies should therefore employ larger datasets and cross-validation approaches to further assess model generalization and robustness across broader operating conditions.

3.9. Optimum Parameters for TDS Removal from Paint Wastewater Using Avocado Pear and Moringa oleifera Seed Bio–Coagulants

Table 9 presents the optimum operating conditions identified through numerical optimization, together with their corresponding desirability values. For PS, the optimization predicted a maximum TDS removal of 93.53% at a dosage of 4.00 mg/L, pH 6.00, and a settling time of 40 min, with a desirability of 0.99. Although the highest experimental removal efficiency occurred at the center-point condition of pH 4, dosage 4 mg/L, and settling time 40 min, the RSM optimization identified pH 6 as the mathematical optimum; the small gap between the experimental maximum (93.16%) and the optimized prediction (93.53%) suggests that PS removal efficiency remained relatively stable across the pH range studied, with several operating conditions capable of achieving similarly high removal [18,19]. For MOS, the optimal conditions were estimated at a dosage of 4.28 mg/L, pH 3.71, and a settling time of 37.97 min, yielding a TDS removal efficiency of 97.24% and a desirability of 1.00. These optimal MOS conditions sat close to the center of the design space but shifted slightly toward acidic pH and shorter settling time, implying that MOS can achieve strong treatment performance under mildly acidic conditions without requiring extended settling periods. The high desirability values obtained for both bio-coagulants confirm that the optimized solutions effectively meet the objective of maximizing TDS removal [18,19].

3.10. Validation of Optimal Parameter Results

Validation studies were conducted using the identified optimum process parameters for both PS and MOS bio-coagulants to confirm the reliability of the developed models and the predicted optimum operating conditions. Experiments were run in triplicate under these optimal conditions, and the resulting mean values were compared against the model predictions. As shown in Table 10, the average experimental TDS removal efficiencies were 93.53 ± 0.65% for PS and 97.24 ± 0.39% for MOS, closely matching the predicted removals of 92.87% and 96.49%, respectively, with percentage deviations of only 0.71% and 0.78%—confirming that the models predict treatment performance effectively. The low standard deviations further indicate good repeatability of the coagulation-flocculation process under optimal conditions, and the combination of low experimental variability with sub-1% prediction deviations indicates close agreement between the validation results and predictions of the optimized parameters for TDS removal from paint wastewater, consistent with validation criteria applied in similar optimization studies [18-19, 27].

3.11. Practical Implications, Techno-Economic Considerations, Sustainability and Future Scale-Up Perspectives

Avocado pear and Moringa oleifera seeds are abundant agricultural materials in many tropical countries, often discarded as underutilized biomass waste. Using these bio-coagulants could therefore reduce dependence on commercially produced chemical coagulants, lowering treatment costs while adding value to agricultural waste streams. Although a full techno-economic analysis fell outside the scope of this study, the use of locally available biomass suggests strong economic potential for decentralized, small-scale wastewater treatment systems, consistent with similar studies highlighting the economic attractiveness of plant-derived treatment materials owing to their low acquisition costs, renewability, and reduced environmental burden relative to synthetic treatment chemicals [11-13]. Beyond its economic relevance, this study directly supports several United Nations Sustainable Development Goals (SDGs): effective paint wastewater treatment contributes to SDG 6 (Clean Water and Sanitation) by improving water quality management [11,12]; the use of plant-based waste materials as bio-coagulants aligns with SDG 12 (Responsible Consumption and Production) through resource recovery and waste valorization [28]; replacing conventional chemical coagulants with biodegradable alternatives supports SDG 13 (Climate Action) by reducing the environmental impact of chemical production and disposal [16]; and data-driven optimization methods such as RSM and ANN advance SDG 9 (Industry, Innovation and Infrastructure) by encouraging new, sustainable wastewater treatment solutions [9,12]. This data-driven modeling approach could offer a broader framework for process design, operational control, and performance prediction, supporting future scale-up efforts—though pilot-scale studies will still be needed to evaluate process stability under continuous flow and varying wastewater compositions. Several limitations nonetheless remain: this study did not examine the potential for bio-coagulant regeneration or reuse after treatment, nor the properties or management of the resulting sludge. Future work should therefore evaluate coagulant reuse cycles, treatment efficiency after repeated use, sludge formation rates, and the potential for sludge valorization as a soil amendment or other beneficial application.

4.1. Limitations and Future Research

One limitation of this study is the relatively small dataset used to develop the ANN model, a consequence of the experimental design matrix. Although the resulting ANN models achieved high predictive accuracy, future studies should draw on larger experimental datasets and more advanced validation procedures—such as k-fold cross-validation and external validation datasets—to further test model robustness and generalizability. Doing so would strengthen confidence in applying ANN models to large-scale industrial wastewater treatment optimization.