The Blockauss pumping station, located in Cocody near Saint Peter’s Catholic Church, provides the pumping of wastewater originating primarily from Félix Houphouët-Boigny University, the Cocody University Hospital (CHU), and the Cocody Ambassade district, before conveying it to the Treichville Market trunk sewer through a sub-lagoon crossing (Figure 1).

Wastewater samples were collected at the Blockauss pumping station, located in the municipality of Cocody within the Abidjan District, using an automatic sampler equipped with an adiabatic enclosure (Figure 2). Sampling was carried out at the Blockauss station and at the Digue pre-treatment station using the automatic sampler. The sampler was programmed to operate on 24-h sampling cycles. Accordingly, six (06) 24-h sampling campaigns were conducted at each site from February 2024 to December 2024, covering both dry and rainy seasons, with one campaign conducted every two months. The automatic sampler was programmed to collect 1-h integrated samples by collecting 200 mL of wastewater every 12 min. Five sampling series were performed over 1 h to constitute a 1-L sample. Samples were collected at the raw wastewater inlet of the respective stations. Thus, twenty-four (24) daily samples were obtained per site and transported to the laboratory for analysis.

Figure 1. Blockauss pumping station.

Figure 2.Hourly wastewater sampling at the Blokauss station.

In the laboratory, all wastewater samples were analyzed for physical parameters (turbidity and TSS) and a chemical parameter (COD) in accordance with the French standard [3] and the methods developed by the Centre of Expertise in Environmental Analysis of Québec (CEAEQ) [4]. All methods are summarized in Table 1.

Table 1.Analytical methods for the physical and chemical parameters.

Modeling of total suspended solids (TSS) and chemical oxygen demand (COD) from turbidity was performed using an artificial neural network (ANN) implemented in Matlab R2014 (MathWorks Inc., USA). The backpropagation algorithm used made it possible to establish an empirical model of the general form:

where:

Y is the TSS or COD concentration value, i.e., the network output (response);

λ i is the weighting coefficient assigned to the hidden-layer neurons;

y i is the summation of the values resulting from the different activation functions; and b is the bias, i.e., the error made by the network.

The experimental data (200 observations) were normalized to the interval [−1; +1] according to Equation (2):

where:

y i ∘ = is the normalized experimental value;

y i = is the experimental value;

y min = is the minimum experimental value;

y max = is the maximum experimental value.

The data were then randomly divided into three sets: training (50%), validation (25%), and testing (25%).

The architecture selected was a multilayer perceptron comprising an input layer (turbidity), an output layer (TSS or COD), and a hidden layer whose number of neurons (k = 1 to 15) was optimized. A hyperbolic tangent sigmoid transfer function was adopted as the activation function, expressed as follows:

where:

tanh is the hyperbolic tangent function, used as the activation (transfer) function;

Y : is the value resulting from the activation function;

λ i : is the new (normalized) transformed value;

y i : is the weight of the element (observation) in the network, which determines the network’s output response; and

b : is the bias, i.e., the error made by each neuron.

Validation of the optimized neural model was carried out using the correlation coefficient (R) and the mean square error (MSE). In accordance with Yeh [5] and Hsu [6], a model is considered acceptable when R² ≥ 0.5, i.e., R ≥ 0.71. The mean square error (MSE) is expressed as follows (4),

where y e and y c represent, respectively, the experimental values and the values calculated by the network for i = 1 , ⋯ , N ; y e ¯ and y c ¯ are the respective means of the experimental values and the values calculated by the network.

N represents the number of observations.

where:

y c and y e are, respectively, the values calculated by the network and the experimental values for i = 1 , ⋯ , N , with

N: the number of input variables.

This stage evaluates the relevance of the connection weights and their ability to explain the phenomenon under study, using the 25% of samples reserved for testing. Model performance is assessed through the coefficient of determination (R²) and the mean relative deviation (MRD). A model is considered satisfactory when R² tends toward 1, reflecting a good fit, and when the MRD remains below 10%. The MRD is calculated as follows:

where:

y e and y p r e d represent, respectively, the experimental and calculated values for i = 1 , ⋯ , N , and corresponds to the mean value of the measured or experimental data.

where:

y e = is the normalized experimental value for i = 1 , ⋯ , N ;

y c = is the normalized value calculated by the network for i = 1 , ⋯ , N ; and N is the number of observations.

3.1.1. Artificial Neural Network Architecture

Table 2 presents the correlation coefficients (R) obtained during the respective training and validation phases for TSS concentrations. This coefficient ranges from 0.870 to 0.923 during the training phase and from −0.185 to 0.928 during the validation phase. A hidden-layer neuron count of 1 gives the highest correlation simultaneously in both the training phase (R training = 0.923) and the validation phase (R validation = 0.928). Accordingly, the selected neural architecture is 1-1-1. This neural topology comprises 1 neuron in the input layer (turbidity), 1 neuron in the hidden layer, and 1 neuron in the output layer (TSS).

Table 2.Correlation coefficients of the training and validation sets of the ANN (TSS).

3.1.2. Determination of the Linear Model of the Optimized Neural Architecture

The linear model for the 1-1-1 (Figure 3) neural architecture was constructed first from the weights and bias associated with the input variable, and then from the linear weights connecting the hidden layer to the output layer. The resulting model is:

Figure 3.Schematic representation of the optimized neural network architecture (1-1-1).

3.1.3. Neural Model Validation

The neural model is validated since the correlation coefficient in the validation phase (R validation = 0.928 ≈ 0.93) is very high and close to 1 (R ≥ 0.93). According to Yeh [5] and Hsu [6], the minimum acceptable threshold is R² = 0.5, whose square root is R ≈ 0.71. Furthermore, the mean-squared errors generated by these neural models are low and tend virtually toward zero (Figure 4).

Figure 4.Evolution of the mean squared errors of TSS concentrations generated by the ANN.

3.1.4. Prediction Model Performance

The suspended solids (TSS) prediction model demonstrated good performance, with a coefficient of determination (R²) of 0.80, an RMSE of 0.127, and a mean relative deviation (MRD) of 7.46% (Table 3). These results indicate good agreement between the experimental concentrations and those estimated by the artificial neural network (ANN). The R² value indicates that turbidity accounts for approximately 80% of the variability in TSS concentrations, while the MRD below 10% reflects an overall low relative prediction error.

Table 3. TSS prediction performance criteria.

The testing phase further confirmed these performances, with a correlation coefficient of R = 0.88 between the experimental and predicted values (Table 3). The good agreement between the trends observed (Figure 5) in confirms the model’s ability to reproduce overall variations in TSS concentrations. These results are consistent with the findings of Zare Abyaneh [7], who demonstrated the usefulness of artificial neural networks for predicting wastewater quality parameters, particularly TSS and COD. In that study, conducted at the Ekbatan wastewater treatment plant in Tehran, ANN model performance was assessed using, among other criteria, the correlation coefficient and RMSE.

Figure 5.Comparison of the trends in experimental TSS concentrations and those predicted by the artificial neural network.

The good performance obtained in the present study can be primarily explained by the close relationship between turbidity and TSS [8], particularly when measurements are performed at 860 nm in the infrared range. Turbidity is an optical indicator directly influenced by the presence of suspended particles and can therefore be used as an indirect variable to estimate TSS concentrations in sewer systems. Bertrand-Krajewski [9] demonstrated that a site-specific empirical relationship could be established between continuously measured turbidity and TSS concentrations determined from samples, thereby allowing TSS concentrations to be estimated from turbidity measurements. This relationship was also investigated by Bertrand-Krajewski et al. [10], who showed that turbidity could be used to continuously estimate TSS concentrations and, under certain conditions, COD concentrations in sewer systems. However, the authors emphasized that the quality of the turbidity-TSS relationship depends on wastewater characteristics, flow conditions, and sensor calibration.

The differences observed between the experimental and ANN-predicted concentrations (Figure 5) may therefore be attributed to variations in the physical characteristics of suspended particles. The relationship between turbidity and TSS is not universal, since the optical response depends, in particular, on the size, shape, nature, concentration, and optical properties of the particles. Experimental studies have shown that different sensors may produce different turbidity readings for the same suspended solids concentration, although site-specific turbidity TSS relationships may nevertheless exhibit high coefficients of determination.

Thus, the differences observed in the present study do not undermine the usefulness of the model but rather reflect the inherent limitations associated with the use of an indirect optical measurement to estimate TSS. Nevertheless, the developed model demonstrated satisfactory performance (R² = 0.80; R = 0.88; RMSE = 0.127; MRD = 7.46%) and may therefore constitute a complementary tool for the rapid estimation of TSS concentrations in wastewater from the Blokauss treatment plant. However, in accordance with the recommendations of Bertrand-Krajewski et al. [10], its application to other wastewater treatment plants would require site-specific validation and calibration, given the variability in particle and wastewater characteristics.

3.2.1. Artificial Neural Network Architecture

According to Table 4, the correlation coefficients obtained range from 0.794 to 0.861 during the training phase and from 0.006 to 0.844 during the validation phase. The best correlation during training is achieved with 14 neurons, whereas during validation, it is achieved with 2 neurons. Several architectures (1-1-1, 1-2-1, 1-3-1, 1-4-1, 1-5-1, 1-7-1) appear to offer good compromises.

The best neural model was determined by comparing the error indicators and correlation coefficients between the experimental and predicted COD concentrations. The final analysis thus identifies the 1-2-1 architecture as the most efficient, with 1 input neuron (turbidity), 2 hidden neurons, and 1 output neuron (COD) (Table 5).

Table 4.Correlation coefficients of the training and validation sets of the ANN (COD).

Table 5. Error indicators and correlation coefficients of the tested architectures (COD).

3.2.2. Determination of the Linear Model of the Neural Architecture

The linear model of the 1-2-1 (Figure 6) neural architecture was established in two steps: first from the weights and bias associated with the input variable, and then from the weights connecting the hidden layer to the output and the associated bias. The resulting model is:

Figure 6.Schematic representation of the optimized neural network architecture (1-2-1).

3.2.3. Neural Model Validation

The 1-2-1 neural model is validated, with a correlation coefficient in the validation phase of Rvalidation = 0.84, close to 1. The mean-squared-error curves for the training, validation, and test phases are decreasing, and tend toward zero (Figure 7). This result is confirmed by the studies of Yeh [5] and Hsu [6].

Figure 7.Evolution of the mean squared errors of COD concentrations generated by the ANN.

3.2.4. Prediction Model Performance

The COD prediction model developed using turbidity as the sole input variable yielded a coefficient of determination (R²) of 0.66, an RMSE of 0.246, and a mean relative deviation (MRD) of 12.83% (Table 6). Thus, turbidity accounted for approximately 66% of the variability in the total COD measured experimentally in the wastewater from the Blockauss treatment plant. These results indicate moderate predictive performance but demonstrate that turbidity can provide useful indirect information for estimating COD concentrations. This relationship has also been reported in previous studies, which highlighted associations between turbidity, total suspended solids (TSS), and COD [11][12].

The testing phase yielded a correlation coefficient of approximately 0.80 between the experimental and predicted concentrations (Table 6), with an overall agreement in the observed trends (Figure 8). Bersinger et al. [12] reported a positive relationship between turbidity and COD in a sewer system, confirming the potential of turbidity as an indirect indicator of organic load. However, the strength of this relationship depends on wastewater characteristics as well as hydrodynamic and seasonal conditions.

Table 6.COD prediction performance criteria.

Figure 8.Comparison of the trends in experimental COD concentrations and those predicted by the artificial neural network.

The performance obtained is consistent with previous studies on COD modelling using artificial neural networks (ANNs). Matheri et al. [13] demonstrated that ANNs can effectively predict COD concentrations in wastewater, while emphasizing the importance of input variables in determining model performance. Similarly, Abba and Elkiran [14] achieved improved predictive performance by using several physicochemical parameters as explanatory variables. Aghdam et al. [15] also demonstrated that COD prediction could be improved by incorporating multiple wastewater quality parameters, particularly TSS.

The relatively lower performance of the COD model compared with that developed for TSS may therefore be attributed, at least in part, to the use of turbidity as the sole explanatory variable and to the intrinsic complexity of COD. Incorporating additional parameters, such as pH, temperature, electrical conductivity, TSS, and dissolved oxygen, could improve predictive performance. However, such an approach would require additional data and independent validation to minimize the risk of overfitting and assess the model’s generalization capability. Finally, given the specificity of the model to wastewater from the Blockauss treatment plant, its application to other treatment plants should be preceded by validation and, where necessary, recalibration using site-specific data.