The biological aeration unit consumes the highest energy (67.3%) in wastewater treatment compared with physical (18.8%) and chemical (13.9%) treatment processes. The high energy consumption is caused by the supply of oxygen using air pumps/blowers and temperature that controls microorganisms' growth. The purpose of this study was to model and optimize energy consumption in the biological aeration unit. The multilayer perceptron (MLP) artificial neural network (ANN) algorithm was used to model energy consumption. The particle swarm optimization (PSO) algorithm was used to optimize the energy consumption model. Sensitivity analysis was performed to determine the percentage contribution of input variables towards energy consumption. The MLP ANN algorithm modelled energy consumption successfully and produced R², RMSE, and MSE of 0.89, 0.0265, and 0.00070, respectively, during the testing phase. The PSO algorithm optimized energy consumption successfully and produced a global solution of 0.993 kWh/m³. The percentage reduction between the lowest measured and optimized energy consumption was 38.4%. Aeration period (81%) and temperature (10.7%) contributed the highest towards energy consumption. In conclusion, temperature played a significant role in energy consumption compared with airflow rate (4.2%). When the temperature is conducive to allowing the growth of microorganisms, the removal of COD and ammonia will be rapid resulting in low energy consumption.

  • Temperature is the driver of energy consumption compared with airflow rate in the biological aeration unit.

  • Temperature contributes 6.5% more than airflow rate towards energy consumption in the biological aeration unit.

  • Biological aeration unit should be operated at high temperatures (35 °C) in order to achieve low energy consumption.

  • A total of 38.4% reduction in energy consumption was achieved using the PSO algorithm.

Graphical Abstract

Graphical Abstract
Graphical Abstract

Wastewater treatment plants (WWTPs) are used all over the world including South Africa (SA). WWTPs are responsible for treating domestic and industrial wastewater to an acceptable effluent quality before being discharged into the environment (Żyłka et al. 2021). Treatment of wastewater is achieved using different treatment processes such as physical, biological, and chemical (Crini & Lichtfouse 2019). The physical treatment process is mainly responsible for removing large objects using physical methods such as screens and sedimentation tanks (Saleh et al. 2020). The biological treatment process is responsible for decomposing organic matter and oxidizing inorganic matter using microorganisms (Kanaujiya et al. 2019). The chemical treatment process is usually the final step responsible for chemical stabilization and disinfection of the wastewater before it is discharged into the environment (Singh 2022). WWTPs consume energy during each of the treatment processes in attempting to meet the desired effluent discharge quality (Musvoto & Ikumi 2016).

In SA, physical treatment processes consume on average 0.148 kWh/m³, which is about 18.8% of the total energy consumed by a WWTP (Winter 2011; Van Vuuren 2013; Musvoto & Ikumi 2016). In Italy and Australia, energy consumption was reported to be 0.113 and 0.37 kWh/m³ for the physical treatment process, respectively (Panepinto et al. 2016; Wakeel et al. 2016). The biological treatment process consumes the highest energy in a WWTP (Baquero-Rodríguez et al. 2022). In SA, the biological treatment process consumes 0.53 kWh/m³, which amounts to 67.3% of the total energy consumed in a WWTP (Winter 2011; Van Vuuren 2013; Musvoto & Ikumi 2016). In Spain and Saudi Arabia, the biological treatment process consumes 0.8 and 1.6 kWh/m³, respectively. The chemical treatment process amounts to 13.9% of the total energy consumed in a WWTP. In the United States of America (USA) and Japan, the chemical treatment process consumes on average 0.23 and 0.39 kWh/m³, respectively (Stasinakis et al. 2022).

Research has shown that the biggest driver of energy consumption in the biological aeration unit is the airflow supply (Wakeel et al. 2016; Li et al. 2017; Singh & Kansal 2018; Christoforidou et al. 2020; Siatou et al. 2020). Airflow supplies the oxygen required by microorganisms for respiration in the biological aeration unit (Vogelaar et al. 2000). High airflow rates produce sufficient dissolved oxygen (DO) required by microorganisms, however high airflow rates consume high energy due to large air pumps/blowers utilized (Chiavola et al. 2017). Because of the impact of high airflow supply in the biological aeration unit, different scholars were encouraged to develop optimization models that were focused on optimizing the airflow supply since it was reported to be the biggest driver of energy consumption (Kusiak & Wei 2013; Ozturk et al. 2016; Asadi et al. 2017; Chiavola et al. 2017; Han et al. 2018; Huang et al. 2019; Lu et al. 2021).

Ozturk et al. (2016) optimized energy consumption by minimizing the aeration rate in the biological aeration unit. The results reduced the airflow rate by 72%, resulting in less energy consumption. Asadi et al. (2017) optimized the biological aeration unit by developing a model that minimizes DO concentration. The results showed that the airflow rate was optimized by 31%, resulting in low energy consumption. Chiavola et al. (2017) optimized the biological aeration unit energy consumption by reducing DO concentration to 2 mg/l. The results of the study achieved a 13% reduction in energy consumption. Kusiak & Wei (2013) applied the PSO algorithm in attempts to optimize energy consumption in the activated sludge process. The results of the study showed that a 15% airflow rate reduction minimized energy consumption. The literature detailed above shows that all authors focused on reducing airflow supply into the biological aeration unit. This allowed for a reduction in energy consumption in the biological aeration unit.

Although the reduction of energy consumption was achieved by reducing airflow supply into the biological aeration unit, the current study will show that temperature plays a vital role in reducing energy consumption in the biological aeration unit. This is because microorganisms require a conducive environment for survival, and if the environment is not conducive, longer aeration periods will be required (Loutfi et al. 2020). Temperature controls the environment that allows the growth of microorganisms and enhances the metabolic rate in the biological aeration unit (Chapra et al. 2021). Microorganisms commonly found in wastewater are classified as mesophilic and they grow in the temperature range between 10 and 45 °C, with an optimum of 32.5 °C (Brandam et al. 2008; Zeraik & Nitschke 2012; Haberl-Meglič et al. 2016; Menegol et al. 2017; Balku 2018; Pawlita-Posmyk et al. 2018; Brehar et al. 2019; Shen et al. 2020). For example, Balku (2018) reported that biomass concentrations of 1,550.1; 1,474.4; 1,346.9; 1,188.2 g/m³ were measured at temperatures of 30, 20, 10, and 0 °C, respectively. Shen et al. (2020), reported that a temperature of 33 °C produced a biomass concentration of 0.6 g/l, and a temperature of 25 °C produced biomass of 0.2 g/l. Therefore, low temperatures (18–22 °C) will slow down the growth of microorganisms, and as a result extended aeration period will be required, which results in high energy consumption (Drewnowski et al. 2019). However, if the temperature in the biological aeration unit is maintained at 32.5 °C, the growth of microorganisms will be at an optimum, resulting in rapid removal of chemical oxygen demand (COD) and ammonia. This means that less airflow supply and aeration period will be required, resulting in low energy consumption. The current research will close this existing research gap. The aim of the study was to apply artificial neural network (ANN) and particle swarm optimization (PSO) algorithms in attempts to model and optimize energy consumption in the biological aeration unit. The optimization model will in cooperate for the first time temperature and airflow supply because they are the biggest drivers of energy consumption in the biological aeration unit.

Laboratory experiments

Laboratory experiments were carried out to simulate energy consumption during COD and ammonia removal at different airflow rates and wastewater temperatures. The airflow rates used were 5, 10, 15, 20, 25, and 30 l/min. The temperatures used were 15, 17.5, 20, 22.5, 25, 27.5, 30, 32.5, and 35 °C. Aeration was performed for 4 h nonstop and samples were taken every 2 h. Samples taken were initial concentration, 2-h mark concentration, and 4-h mark concentration, which resulted in three samples per event. Each sample was examined twice in order to check the consistency of the results. The total data points collected were 324. Laboratory data were analyzed using a correlation matrix and linear regression. The biological aeration unit components and the schematic diagram are detailed in Table 1 and Figure 1, respectively.
Table 1

Components of the aeration unit

ComponentsTypeRemarks
Aeration tank Circular aeration tank. (acrylic material) 10–15 mm thick Acrylic material. Dimensions 570 × 300 mm. Total volume is 40 l. Working volume is 30 l 
Dissolved oxygen meter and probe Hanna HI98196 multi-parameter water proof meter Measures DO, pH, and ORP 
Thermostat Local manufacturer Controls temperature in the range 0–40 °C 
Air pump Waterfall Resun LP100 Can supply air between 0 and 140 l/min 
Airflow meter MF5712 200 l/min digital gas air nitrogen oxygen mass flow meter Can measure airflow rate between 0 and 200 l/min 
Air stone disc bubble diffuser Growneer micro pore bubble diffuser Diffuser is 20 cm in diameter 
Digital wattmeter Geewiz (Kill a watt) Measures power between 0 and 3,600 W 
ComponentsTypeRemarks
Aeration tank Circular aeration tank. (acrylic material) 10–15 mm thick Acrylic material. Dimensions 570 × 300 mm. Total volume is 40 l. Working volume is 30 l 
Dissolved oxygen meter and probe Hanna HI98196 multi-parameter water proof meter Measures DO, pH, and ORP 
Thermostat Local manufacturer Controls temperature in the range 0–40 °C 
Air pump Waterfall Resun LP100 Can supply air between 0 and 140 l/min 
Airflow meter MF5712 200 l/min digital gas air nitrogen oxygen mass flow meter Can measure airflow rate between 0 and 200 l/min 
Air stone disc bubble diffuser Growneer micro pore bubble diffuser Diffuser is 20 cm in diameter 
Digital wattmeter Geewiz (Kill a watt) Measures power between 0 and 3,600 W 
Figure 1

Laboratory aeration unit.

Figure 1

Laboratory aeration unit.

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Wastewater collection, disposal, and analysis

The APHA (2012) method was used for the collection of wastewater from the WWTP. Wastewater was collected at the Daspoort WWTP, Pretoria, Gauteng Province, South Africa, coordinates (−25.733857, 28.177894). The Daspoort WWTP consists of three bioreactors, and the samples were collected from reactor number two. Non-sterile powder-free nitrile gloves were used to handle all equipment. A 25-l jerry was used to collect the raw wastewater. An additional 2 l of activated sludge was collected from the return activated sludge. Wastewater samples were collected and aerated within 8 h after collection. After the completion of the aeration process, wastewater was disposed by flushing at the laboratory toilet. The disposal method allowed the wastewater to go back to the WWTP. Two wastewater characteristics were measured, namely COD and ammonia (NH3). The method used for analyzing wastewater characteristics was the Standard Methods for the Examination of water and wastewater (APHA 2012). Table 2 provides the details on the wastewater characteristics analysis.

Table 2

Analysis of wastewater characteristics

ParameterEquipmentMethod
COD Spectrophotometer closed reflux colorimetric, Digestion vessels, Block heater, Microburet, and Ampule sealer. DR3900 APHA (2012) method 5220 
Ammonia Spectrophotometer and reagents were used. DR3900 APHA (2012) method 4500 
ParameterEquipmentMethod
COD Spectrophotometer closed reflux colorimetric, Digestion vessels, Block heater, Microburet, and Ampule sealer. DR3900 APHA (2012) method 5220 
Ammonia Spectrophotometer and reagents were used. DR3900 APHA (2012) method 4500 

Energy consumption

Energy consumption was measured in kilowatt-hour (kWh), and then later expressed in terms of the total energy consumed per volume of wastewater treated (kWh/m³). The power output of the air pump was measured using a digital plug-and-play wattmeter as described in Table 1. The digital wattmeter is also equipped with a timer, which was used to monitor the aeration period. Energy consumption was analyzed using the correlation coefficient. The correlation coefficient was conducted on Statistical Package for the Social Sciences Software (SPSS) version 27.

Application of ANN

A regression model was developed using the multilayer perceptron (MLP) ANN algorithm on MATLAB programming software. Continuous data collected from laboratory experiments were used to develop the energy consumption model. Eight steps were followed to model energy consumption using the MLP ANN algorithm.

  • The first step was to select input variables from the data collected during laboratory experiments.

  • The second step was to split the data into 70% training, 15% validation, and 15% testing.

  • The third step was to transform data into input variables using the normalization technique defined by Equation (1).
    formula
    (1)
    where is the scaled sample data point, x is the sample data point, minx is the minimum value in the training dataset, maxx is the maximum value in the training dataset.
  • The fourth step was to select the MLP ANN architecture with one hidden layer and two neurons.

  • The fifth step was to initialize the weights and bias between values of 0 and 1.

  • The sixth step was to use the sigmoid activation function as a transfer function. The sigmoid function is defined by Equation (2) and Figure 2.
    formula
    (2)
  • The seventh step was to use the supervised gradient descent backpropagation learning algorithm to correct the weights and bias.

  • The eighth step was to evaluate the performance of the energy consumption model using MSE, R², and RMSE defined by Equations (3)–(5),respectively.
    formula
    (3)
    formula
    (4)
    formula
    (5)
    where MSE is the mean squared error, is the predicted value, yi is the observed value, N is the number of data points, R2 is the coefficient of determination, SSE is the sum of squared error, and SST is the total sum of squares.

Application of the PSO algorithm

Ten steps were followed to apply the PSO algorithm.
  • Step 1 was to initialize the number of particles to 30.

  • Step 2 was to initialize the random numbers to 1.

  • Step 3 was to initialize the acceleration constants to 1.

  • Step 4 was to initialize the initial velocity of each particle to 0.

  • Step 5 was to initialize the initial position of each particle randomly in the search space.

  • Step 6 was to update each particle's velocity, personal best position of each particle, and global best of the population using Equations (6) and (7).
    formula
    (6)
    formula
    (7)
  • Step 7 was to select the personal best position of each particle by comparing it with the new position at which the particle has landed on/travelled to.

  • Step 8 was to select the global best position from the personal best position of each particle.

  • Step 9 was to repeat steps 6, 7, and 8 until convergence has been reached in the search space. The pseudo code used is shown in Table 3.

  • Step 10 was to conduct sensitivity analysis on the decision variables that contribute most to the optimization results. A one-factor-at-a-time method was used. Each decision variable was individually adjusted by ±10, ±20, and ±50%, while keeping the others unchanged. In addition, decision variables were checked for their direct, inverse, major, or minor changes in energy consumption. The observed versus the optimized energy consumption data were analyzed using the ANOVA test.

Figure 2

Sigmoid function.

Figure 2

Sigmoid function.

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Table 3

Pseudo code for single objective problem

PSO algorithm
1. Initialize the particles’ position (xi), velocity (vi), previous best position (pi), and the number of particles N 
2. While (t < maximum number of iterations (T)) do 
3. For all particles (i) do 
4. Calculate the fitness function for the current position xi of the ith particle (F(xi)) 
5. If (F(xi) < F(pi)) then 
6. Pi = xi end if 
7. If (F(xi) < F(G)) then 
8. G = xi 
9. End if 
10. Adjust the velocity and positions of all particles according to Equations (1) and (2). 
11. End for 
12. Stop the algorithm if a sufficiently good fitness function is met 
13. End while 
PSO algorithm
1. Initialize the particles’ position (xi), velocity (vi), previous best position (pi), and the number of particles N 
2. While (t < maximum number of iterations (T)) do 
3. For all particles (i) do 
4. Calculate the fitness function for the current position xi of the ith particle (F(xi)) 
5. If (F(xi) < F(pi)) then 
6. Pi = xi end if 
7. If (F(xi) < F(G)) then 
8. G = xi 
9. End if 
10. Adjust the velocity and positions of all particles according to Equations (1) and (2). 
11. End for 
12. Stop the algorithm if a sufficiently good fitness function is met 
13. End while 

Analysis of laboratory results

Table 4 and Figures 3(a)–(e) present correlation matrix results and the graphic relationship between energy consumption and input parameters, respectively. The relationship between energy consumption and the aeration period produced a positive correlation of 0.920**. This means that when the aeration period was extended by 2 h, energy consumption also increased because the air pumps/blowers continued operating for longer periods of time. Most studies have recommended an aeration period of 4 h depending on the design of the WWTP (Bhargava 2016; Murillo 2018; Jasim 2020). The 4-h aeration period allows for the complete removal of COD and ammonia in wastewater. Hence, the correlation of COD (−0.860**) and ammonia (−0.759**) with the aeration period was negative as shown in Table 4. Figure 3(a) shows the graphic relationship between energy consumption and the aeration period. Figure 3(a) shows that at aeration period zero, energy consumption was also zero because there was no airflow supply. After 2 h of aeration, energy consumption was recorded to be in the range between 0.0435 and 0.086 kWh. After 4 h of aeration, energy consumption was recorded in the range between 0.087 and 0.172 kWh. This shows that extending the aeration period will result in high energy consumption because the airflow supply will continue in the biological aeration unit.
Table 4

Correlation matrix between energy consumption and parameters

Correlations
ECAPT (°C)NH3CODAR
EC PC      
Time PC 0.920**     
T (°C) PC 0.000 0.000    
NH3 PC −0.689** −0.759** −0.392**   
COD PC −0.781** −0.860** −0.123** 0.712**  
AR PC 0.337** 0.000 0.000 0.020 0.008 
Correlations
ECAPT (°C)NH3CODAR
EC PC      
Time PC 0.920**     
T (°C) PC 0.000 0.000    
NH3 PC −0.689** −0.759** −0.392**   
COD PC −0.781** −0.860** −0.123** 0.712**  
AR PC 0.337** 0.000 0.000 0.020 0.008 

**Correlation is significant at the 0.01 level (two-tailed).

PC, Pearson correlation; EC, energy consumption; T, temperature; NH3, ammonia; AR, airflow rate; AP, aeration period.

Figure 3

Relationship between energy consumption and input variables: (a) Aeration period, (b) COD concentration, (c) ammonia concentration, (d) airflow rate, and (e) temperature.

Figure 3

Relationship between energy consumption and input variables: (a) Aeration period, (b) COD concentration, (c) ammonia concentration, (d) airflow rate, and (e) temperature.

Close modal

Similar to the aeration period, the relationship between energy consumption and airflow rate produced a positive correlation of 0.337**. This indicates that when the airflow rate increased, energy consumption also increased because a higher demand of power was required from the air pumps/blowers. Energy consumption was expressed in terms of the air pump/blower power for every aeration period that the air pump/blower is utilized (kW h) (Guerrini et al. 2017; Singh & Kansal 2018). This means that when there is an increase in power demand (kW), energy consumption will increase in the biological aeration unit. Figure 3(d) shows the graphic relationship between energy consumption and airflow rate. In Figure 3(d), an airflow rate of 5 l/min resulted in an energy consumption of 0.087 kWh, and an airflow rate of 30 l/min resulted in energy consumption of 0.172 kWh. This implies that increasing the power demand will result in high energy consumption in the biological aeration unit.

The relationship between energy consumption and COD produced a negative correlation of −0.781** as shown in Table 4. This means that when COD is reduced to acceptable discharge standards, energy consumption increases. Energy consumption during COD removal is consumed indirectly. During COD removal, oxygen is essential for the respiration of microorganisms, and the oxygen is supplied using air pumps/blowers. Hence COD removal results in high energy consumption because air pumps/blowers supply oxygen (Dai et al. 2019; Siatou et al. 2020; Marlina et al. 2021). In addition, when COD removal takes time, the aeration period will increase resulting in high energy consumption. This can be justified by the relationship between COD and the aeration period which produced a negative correlation of −0.860**. This means that when there is an increase in the rapid removal of COD, less aeration period will be required, resulting in less energy consumption because air pumps/blowers will be utilized for a shorter period of time (Alisawi 2020; Amiri et al. 2020; Chakawa & Aziz 2021). Figure 3(b) shows the graphic relationship between energy consumption and COD removal. It can be observed in Figure 3(b) that high energy consumption was recorded at a low COD concentration, at the end of the aeration process. This means that in order to achieve low COD concentrations, large quantities of energy will be consumed.

The relationship between energy consumption and ammonia produced a negative correlation of −0.689**. Similar to COD removal, ammonia removal consumes energy indirectly. Energy consumption during ammonia removal is consumed similar to COD removal since ammonia removal relies on microorganisms (Jiang et al. 2018; Zou et al. 2019). Figure 3(c) shows the graphic relationship between energy consumption and ammonia removal. Similar to COD removal, high energy consumption was recorded at low ammonia concentration, at the end of the aeration process. This means that in order to achieve low ammonia concentrations, large quantities of energy will be consumed. The temperature was neither positively nor negatively correlated to energy consumption. However, temperature affects energy consumption indirectly because it controls the removal efficiency of COD and ammonia (Zhang et al. 2019; Alisawi 2020). At low temperatures, the growth and metabolic rate of microorganisms are low which results in a slow removal of COD and ammonia in wastewater. Alisawi (2020) reported COD removal of 40 and 70% were measured at temperatures of 10 and 30 °C, respectively. Zhang et al. (2019) reported the highest and lowest ammonia removal of 98 and 78% at temperatures of 18 and 13 °C, respectively. This indicates that when low temperatures are applied, a longer aeration period will be required in order to achieve acceptable discharge standards, which will result in high energy consumption. This can also be justified by the correlation of COD (−0.123**), and ammonia (−0.392**) on temperature shown in Table 4. The relationship between temperature, COD, and ammonia indicates that high temperatures will accelerate the removal of COD and ammonia, resulting in less aeration period required. Less aeration period means that less airflow supply will be required, therefore less energy will be consumed. Figure 3(e) presents the relationship between energy consumption and temperature.

Modelling energy consumption

The general form of the MLP ANN algorithm is shown in Equation (8). Where X is the jth nodal value for the previous layer. Y is the ith nodal value in the current layer. f is the activation function. Wij is the weighting factor, and b is the bias of the ith node.
formula
(8)
A total of five input variables were used as inputs to model energy consumption using MLP ANN algorithm. The input variables used were aeration period (AP), COD, ammonia, airflow rate (AR), and temperature (T °C). A total of 324 data points were used to train, validate, and test the model. The data were split into 70% training (226), 15% validation (49), and 15% testing (49). The MLP ANN network architecture is shown in Figure 4.
Figure 4

MLP ANN energy consumption architecture.

Figure 4

MLP ANN energy consumption architecture.

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Figure 5 shows the 226 observed energy consumption data that were used as input data during the training phase and the predicted energy consumption data from the MLP ANN energy consumption model during the training phase. The predicted data were close to the observed data, therefore MLP ANN algorithm was able to predict the energy consumption data during the training phase. Although the energy consumption model showed signs that it struggled to predict the high values, the overall performance of the model was acceptable.
Figure 5

Observed vs. predicted values during the training phase.

Figure 5

Observed vs. predicted values during the training phase.

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Figures 6 and 7 show the 49 observed data that were determined during the experiments and the predicted data from the MLP ANN algorithm during the validation and testing phase of the energy consumption model, respectively. During the validation phase, the model predicted the minimum, middle, and maximum values accurately compared with the training phase. This means that the model generalized the data accurately as shown in Figure 6. Similarly, the model was able to predict the observed data during the testing phase.
Figure 6

Observed vs. predicted values during the validation phase.

Figure 6

Observed vs. predicted values during the validation phase.

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Figure 7

Observed vs. predicted values during the testing phase.

Figure 7

Observed vs. predicted values during the testing phase.

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The prediction accuracy of the MLP ANN energy consumption model was evaluated using R², RMSE, and MSE as shown in Table 5. The optimum MSE of 0.00026596 was determined during the validation phase of the energy consumption model. The highest MSE of 0.00070446 was determined during the testing phase of the model. Although the testing phase produced the lowest performance, the model performance was still acceptable. This means that the distance between the data points and the regression line is close to each other. The difference between the highest and lowest MSE was 62.25%, which was a significant difference. The MLP ANN energy consumption model performed well in all learning phases (training, validation, and testing).

Table 5

MLP ANN energy consumption model performance

MSERMSER²
Training 0.00040857 0.02 0.93 
Validation 0.00026596 0.016 0.95 
Testing 0.00070446 0.0265 0.89 
MSERMSER²
Training 0.00040857 0.02 0.93 
Validation 0.00026596 0.016 0.95 
Testing 0.00070446 0.0265 0.89 

The RMSE during training, validation, and testing phase results were 0.2, 0.016, and 0.0265, respectively, as shown in Table 5. The optimum RMSE was determined during the validation phase, which justifies that the optimum MSE was obtained during the validation phase. The difference between the highest and lowest RMSE was 39.6%, which was a significant difference. The R² also showed good performance during the training, validation, and testing phases. The training phase of the model produced R² value of 93.38% as shown in Figure 8(a). This means that 93.38% of the data points fit the model perfectly. Outlies are visible in Figure 8(a), which means that some of the data points did not fit the model perfectly during the training phase.
Figure 8

(a) R² during the training phase, (b) validation phase, and (c) testing phase.

Figure 8

(a) R² during the training phase, (b) validation phase, and (c) testing phase.

Close modal

The validation phase produced R² value of 95.8% as shown in Figure 8(b). This means that 95.8% of the data points fit the model perfectly. Outliers were visible which means that some of the data points did not fit the model perfectly. The testing phase produced R² value of 89.1% as shown in Figure 8(c). This was a slight drop from the validation R². In other words, the model generalized the training dataset perfectly. There are fewer outliers compared with the validation phase, which shows that the model learned the training data perfectly.

The results obtained in this study were similar to results obtained from other studies (Güçlü & Dursun 2010; Hamada et al. 2018; Bekkari & Zeddouri 2019; Hassen & Asmare 2019; Sharghi et al. 2019; Struk-Sokołowska et al. 2019; Demir 2020; Newhart et al. 2020). Bekkari & Zeddouri (2019) reported that the ANN algorithm was successful with modelling the effluent COD, and produced R² value of 89, 96, and 87% during training, validation, and testing phases, respectively. MSE values of 0.007, 0.002, and 0.0045, respectively, and the results were similar to the results obtained in the current study. Güçlü & Dursun (2010) reported that the ANN algorithm produced R² value of 87 and 85% during training and testing phases, respectively, and the results were similar to the results obtained in the current study. Sharghi et al. (2019) reported that the ANN algorithm produced R² value of 74, 70, and 67% during training, validation, and testing phases. The results were in agreement with the results obtained in the current study.

Similarly, Hamada et al. (2018) reported that the ANN algorithm produced R² value of 82, 71, and 81% during training, validation, and testing phases, and the results were in agreement with the results obtained in the current study. Similarly, Demir (2020) reported that the ANN algorithm produced R² value of 98% and MSE of 0.000302, which were similar to results obtained in the current study. Struk-Sokołowska et al. (2019) reported that the ANN algorithm produced R² value of 97%, which was in agreement with the results obtained in the current study. Hassen & Asmare (2019) reported that the ANN algorithm produced R² value of 98.2 and 88.5% for training and testing phases MSE values of 0.007 and 0.057. The results were similar to the results obtained in the current study. Newhart et al. (2020) conducted a study on the prediction of peracetic acid disinfection for secondary municipal wastewater treatment using the ANN algorithm. Although the R² and MSE values were not revealed, the conclusion of the study was that ANN algorithm was successful in modelling the data. Other studies that reported similar successful results were Vyas & Kulshrestha (2019), Wei et al. (2020), and Bhuvaneswari et al. (2020).

Optimization of the energy consumption model

A single objective optimization function was considered because the only problem to be optimized was energy consumption in the biological aeration unit. The single objective function that has to be minimized is defined in Equation (9).
formula
(9)
where Yi is the energy consumption model, AP is the aeration period, COD is the chemical oxygen demand concentration, NH3 is the ammonia concentration, AR is the airflow rate, and T is the temperature in the biological aeration unit. The decision variables in the optimization model were AP, COD, NH3, AR, and T. The constraints are listed in the following equations:
formula
(10)
formula
(11)
formula
(12)
formula
(13)
formula
(14)
The PSO algorithm was successful in minimizing the objective function in order to find the global optimum solution (lowest energy consumption) subject to constraints. The objective function optimum value results from the PSO algorithm are presented in Figure 9. The PSO algorithm converged after performing 199 iterations. Beyond 199 iterations, the algorithm maintained the same solution until 300 iterations were reached and the algorithm terminated as shown in Figure 9.
Figure 9

Optimum objective function value.

Figure 9

Optimum objective function value.

Close modal

The PSO algorithm produced a global optimum solution (objective function optimum value) of 0.0268 kWh after performing 199 iterations as shown in Figure 9. The volume of wastewater treated per cycle was 27 l (0.027 m³). Therefore, the global optimum solution becomes 0.993 kWh/m³, when expressed in terms of the volume of wastewater treated. The optimum measured energy consumption during COD and ammonia removal in the laboratory experiments was 1.611 kWh/m³. The optimum optimized energy consumption during COD and ammonia removal was 0.993 kWh/m³. The percentage reduction between the optimum observed and the optimum optimized energy consumption during COD and ammonia removal was 38.4%. This is a satisfactory reduction in energy consumption. The results obtained in this study were superior compared with results reported by other scholars (Kusiak & Wei 2013; Asadi et al. 2017; Chiavola et al. 2017; Han et al. 2018; Huang et al. 2019; Lu et al. 2021). Asadi et al. (2017) reported a reduction of 31% in energy consumption. Chiavola et al. (2017) reported a reduction of 13% in energy consumption. Kusiak & Wei (2013) reported a reduction of 15% in energy consumption. Huang et al. (2019) reported a reduction of 17% in energy consumption. Lu et al. (2021) reported a reduction of 7.5% in energy. Han et al. (2018) reported a 10% decrease in energy consumption. This indicates that the addition of temperature as a decision variable leads to superior results.

Sensitivity analysis

Figure 10 presents the results of the sensitivity analysis of the optimized energy consumption model. Aeration period contributed 81% towards energy consumption in the biological aeration unit. This was because when aeration is maintained for 4 h, air pumps/blowers are kept operating in order to supply oxygen for the respiration of microorganisms. If the aeration period is reduced by 50%, plant managers/operators will achieve low energy consumption in the biological aeration unit. The second highest contributor to energy consumption in the biological aeration unit was temperature (10.7%). Temperature controls COD and ammonia removal efficiency, which means that if the temperature is conducive to allow the growth and improve the metabolic rate of microorganisms, rapid removal of COD and ammonia will take place. This will result in less aeration period and airflow supply being required, therefore low energy consumption will be achieved. The airflow rate (4.2%) was the third highest contributor to energy consumption in the biological aeration unit. Airflow supply consumes energy because of the air pumps/blowers utilized. The air pumps/blowers operate 24 h nonstop in order to maintain DO concentration in the wastewater for the respiration and survival of microorganisms. The air pumps/blowers are forced to operate 24 h nonstop because oxygen is partially soluble in wastewater. The low solubility of oxygen in wastewater is caused by the gas–liquid film that prevents gas from dissolving in a liquid as defined by the two-film theory (Lewis & Whitman 1924).
Figure 10

Sensitivity analysis of the optimized energy consumption model.

Figure 10

Sensitivity analysis of the optimized energy consumption model.

Close modal

Ammonia (3.7%) was the fourth contributor towards energy consumption in the biological aeration unit. Ammonia removal consumes energy consumption indirectly in the biological aeration unit. Ammonia removal relies on microorganisms, and microorganisms require oxygen which is supplied using air pumps/blowers in the biological aeration unit (Ata et al. 2017; Mousavi et al. 2018). Hence, the removal of ammonia contributes to energy consumption. Similarly, COD (0.4%) removal contributed to energy consumption in the biological aeration unit. Energy consumption during COD removal is consumed similar to ammonia removal in the biological aeration unit (Jungles et al. 2017; Fajri et al. 2018). However, ammonia removal contributed 3.3% more to energy consumption than COD removal in the biological aeration unit. This is because the removal of ammonia is slow compared with COD removal due to the dominance that heterotrophic bacteria have on autotrophic bacteria responsible for ammonia removal (Pan et al. 2017). Because of this dominance, ammonia removal will require more airflow supply in order to maintain a high DO concentration that can accommodate autotrophic bacteria. In addition, the dominance of heterotrophic bacteria results in a slow removal of ammonia, therefore longer aeration period will be required, which results in high energy consumption.

The relationship between each decision variable and the energy consumption is presented in Figure 11(a)–11(e). The relationship between decision variables (aeration period, COD, ammonia, and airflow rate) increased with an increase in energy consumption. The decision variable that produced the highest positive linear regression was the aeration period (0.0409 kWh) as shown in Figure 11(a). This justifies the fact that the aeration period contributed 81% of energy consumption in the biological aeration unit. This indicates that when the aeration period was extended by 2 h, energy consumption increased by 0.034 kWh in the biological aeration unit.
Figure 11

(a) Effect of aeration period, (b) COD concentration, (c) ammonia concentration, (d) airflow rate, and (e) temperature on energy consumption.

Figure 11

(a) Effect of aeration period, (b) COD concentration, (c) ammonia concentration, (d) airflow rate, and (e) temperature on energy consumption.

Close modal

COD and ammonia removal produced a positive linear regression of 0.00005 and 0.0017 kWh as shown in Figure 11(b) and 11(c), respectively. The rate of change in energy consumption caused by the change in ammonia removal (0.0017 kWh) was higher compared with COD removal (0.00005 kWh) in the biological aeration unit. This justifies the fact that ammonia removal requires more oxygen compared with COD removal due to the dominance of heterotrophic bacteria on autotrophic bacteria. Hence ammonia removal consumes high energy compared with COD removal. In addition, high concentrations of ammonia contain high concentrations of free ammonia (Qian et al. 2017; Liu et al. 2019). Free Ammonia is caused by the presence of ammonia in wastewater, in alkaline conditions. Ammonia concentration of 30 mg/l contains free ammonia in the range between 0.14 and 1.38 mg/l, which slows down the removal of ammonia, resulting in high energy consumption (McCarty 2018).

The relationship between energy consumption and airflow rate produced a positive linear regression of 0.0012 kWh as shown in Figure 11(d). This was lower compared with the aeration period (0.0409 kWh), which justifies the fact that the aeration period contributes more towards energy consumption. Increasing the aeration period by 2 h increases energy consumption by 0.034 kWh, whereas increasing the airflow rate by 5 l/min increased energy consumption by 0.027 kWh. This indicates that low energy consumption can be achieved by reducing the aeration period rather than optimizing airflow rates (Huang et al. 2019; Lu et al. 2021). Temperature was the only decision variable that produced a negative linear regression of 0.0005 kWh. This means that 0.0425 kWh of energy is reduced when the temperature is increased by 5 °C. This means that energy consumption can be reduced by increasing the temperature of wastewater. Increasing the temperature in the biological aeration unit increases the removal efficiency of COD and ammonia, resulting in less aeration period, therefore low energy will be consumed. Optimization of the biological aeration unit should be performed at optimum temperatures in order to achieve optimum results (low energy consumption).

Figure 12 shows the results of the observed and optimized energy consumption data points (120) plotted on the same axis. The results in Figure 12 justify the reduction in energy consumption from the optimized energy consumption model. The optimized energy consumption data points were lower than the observed. This indicates that the PSO algorithm was successful in optimizing energy consumption in the biological aeration unit. Table 6 shows the sum of the observed (12.281 kWh) and optimized (10.241 kWh) data. This indicates that the optimized energy consumption data were lower compared with the observed data. The average optimized energy consumption of 0.085 kWh was also lower compared with the average observed energy consumption of 0.102 kWh. The F critical value of 3.881 was lower than the F statistic value of 10.241, which implies that there was a significant difference between the observed and optimized energy consumption. The P-value of 0.0017 was less than the significance level of 0.05, which means that there was a significant difference between the optimized and observed energy consumption data. Therefore, the inclusion of the optimum temperature in the optimization problem benefitted the reduction in energy consumption.
Table 6

The ANOVA test on observed and optimized data set

SUMMARY
GroupsCountSumAverageVariance
Observed energy 120 12.281 0.102 0.002   
Optimized energy 120 10.241 0.085 0.0015   
ANOVA 
Source of variationSSdfMSF statisticP-valueF critical
Between groups 0.017 0.017 10.031 0.0017 3.881 
Within groups 0.411 238 0.002    
Total 0.429 239     
SUMMARY
GroupsCountSumAverageVariance
Observed energy 120 12.281 0.102 0.002   
Optimized energy 120 10.241 0.085 0.0015   
ANOVA 
Source of variationSSdfMSF statisticP-valueF critical
Between groups 0.017 0.017 10.031 0.0017 3.881 
Within groups 0.411 238 0.002    
Total 0.429 239     
Figure 12

Observed and optimized energy consumption data points.

Figure 12

Observed and optimized energy consumption data points.

Close modal

The robustness of the PSO algorithm in wastewater treatment applications has been reported by a number of authors such as (Nassef et al. 2019; Ye et al. 2019; Rafati et al. 2020; Sinwar et al. 2021). Rafati et al. (2020) conducted a study on determining the most effective process control parameter on the activated sludge using the PSO algorithm. The PSO algorithm was successful in optimizing the wastewater parameters in the activated sludge. The control parameters such as COD improved by 1.5%, TSS improved by 1.5%, TN improved by 1.6%, and BOD improved by 2.5%. Ye et al. (2019) conducted a study on multi-agent hybrid PSO for wastewater network planning. The PSO algorithm was successful in the optimization planning. The PSO algorithm achieved a 20.13% improvement from the original wastewater treatment scenario. Nassef et al. (2019) conducted a study to enhance lipid extraction from microalgae in wastewater treatment using the PSO algorithm. The PSO algorithm was successful in maximizing the lipid extraction of microalgae. The PSO algorithm achieved a 22% increase in lipid extraction when compared with the obtained experimental data. Sinwar et al. (2021) conducted a study on the availability and performance optimization of the physical processing unit in a sewage treatment plant using GA and PSO algorithms. The PSO algorithm achieved 99.19% system availability and performance when compared with GA. Yousefi et al. (2017) conducted a study on the conjunctive use of wastewater and groundwater in varamin plain. The PSO algorithm was successful in improving the net benefit of cropping pattern optimization. The PSO algorithm achieved an improvement of 35 and 88% for wastewater withdrawals and fertilizer consumption, respectively. Mosayebi & Bahrami (2018) conducted a study on parameter estimation of a biological system using the PSO algorithm. The PSO algorithm was successful and achieved a net improvement of 54.4 and 26.7%. Asadi et al. (2017) conducted a study on wastewater treatment aeration process optimization using the PSO algorithm. The PSO algorithm was successful and achieved an energy reduction of 31.4%. Other authors that used the PSO algorithm in wastewater treatment were (Sendrescu 2013; Khoja et al. 2018; Faia et al. 2019; Kaddoura & Zayed 2019; Lu et al. 2021).

In conclusion, the PSO algorithm managed to reduce energy consumption in the biological aeration unit. The optimized energy consumption was 0.933 kWh/m³ compared with the measured laboratory energy consumption of 1.611 kWh/m³. The total energy consumption reduction was 38.4%, which was superior compared with what other scholars achieved. The aeration period, airflow rate, ammonia removal, and COD removal increased with an increase in energy consumption. The aeration period was the highest contributor (81%) towards energy consumption in the biological aeration unit. This was because during the aeration process, air pumps/blowers are utilized and if aeration is maintained constantly, energy is continuously consumed. The airflow rate was the second highest contributor (4.2%) towards energy consumption. This was because oxygen is partially soluble in wastewater, hence air pumps/blowers operate 24 h nonstop, to try and force oxygen to dissolve in wastewater for the respiration of microorganisms. Ammonia removal (3.7%) contributed more towards energy consumption compared with COD removal (0.4%). Ammonia removal requires a high airflow supply in order to maintain a high DO concentration for autotrophic bacteria to survive. This was caused by the dominance of heterotrophic bacteria on autotrophic bacteria. Temperature played a vital role in energy consumption reduction in the biological aeration unit. Temperature influences the rapid removal of COD and ammonia, which reduces the aeration period and airflow supply required, resulting in low energy consumption. Input parameters that should be considered in optimizing energy consumption are aeration period, airflow rate, ammonia, and temperature since they contributed more towards energy consumption. COD should be eliminated since it only contributed 0.4% of energy consumption in the biological aeration unit.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.

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