2.1.1. Design Considerations

1) A fixed dome cylindrical batch type digester was selected for the study.

2) The substrate used was cow dung using a mixing ratio of 1:1.

3) A 63 Litre High Density PolyEthylene (HDPE) drum was selected for the construction of the digester because HDPE does not corrode. The choice of HDPE was also made because the drum will be easy to drill in order to insert sensors for the process monitoring (Figure 1Figure 1).

4) Total Solids of cow dung = 17535.55 mg/L (60.1%) and Volatile Solids (VS) = 20058.12 mg/L (68.6%) was obtained from a previous study by Olugasa et al. [30]

5) Hydraulic Retention Time (HRT) of 21 days was selected since the digester operating temperature was about 40˚C, which is slightly above mesophilic conditions. Mesophilic, with operating temperature of 30˚C - 37˚C usually utilizes HRT of 30 - 60 days; while Thermophilic, 50˚C - 55˚C operating temperature utilises HRT of 15 - 30 days [31].

2.1.2. Determination of Digester Volume

The volume of the digester has been selected as 63 Litres going by the nature of the study, which was to model biogas yield. The size of the digester is therefore adequate for the study.

The volume of the digester was estimated using Equation (1):

Volume of a batch type digester is equal to the volume of the slurry V_sl

Volume of Digester ( m 3 ) = V s l = W S l ρ (1) [32]

W_sl = Weight of slurry;

ρ = Density of water ≈ 1000 kg/m³.

Working volume of digester, V_d = 0.040 m³ = 40 Litres.

Since most digesters operate at 75% of the maximum capacity of the digester [33]. Therefore,

V_Total = V_d/0.75 = 53.33 litres

2.1.3. Estimation of Total Solids

The Total Solids (TS) was calculated using Equation (2)

where W_cw = Weight of wet cow dung;

TS% = Percentage of Total solids = 60.1%;

TS = 20 × 60.1/100 = 12.2 kg.

According to Kusmiyati et al. [34], 1 kg of cow dung will generate 30 - 36 L (0.03 - 0.036 m³) of biogas. It is expected that 20 kg of cow dung will generate 20 × 0.036 m³ of biogas = 720 Litres of biogas. A tyre tube which served as a gas bag was therefore attached to the digester as an additional storage space.

2.1.4. Estimation of Volatile Solids (VS)

The volatile solids added in one batch VS_batch can be estimated by Equation (3).

VS_batch = TS × f_VS(3) [35]

where f_VS = Volatile fraction;

F_vs = TS/VS = 17535.55 mg/20058.12 = 0.8742;

VS_batch = 12.2 × 0.8742 = 10.67 kg.

2.1.5. Determination of the Organic Load (OL)

The organic load of a batch digester is expressed per batch volume. This is expressed in Equation (4)

2.1.6. Design of Stirrer

A stirrer made from a network of PVC pipes of 2 cm diameter was used to agitate the slurry in the digester. The length of the stirrer was estimated to be at a distance H/25 from the base of the digester as prescribed by Olugasa et al.[36], where H is the height of the digester. The diameter was determined using Equation (5)

here D_s is the diameter of the stirrer and D is the diameter of the digester [37].

2.1.7. Auxiliary Parts

Slurry Influent and Effluent pipes

The influent and effluent pipes were made of PVC since they are not susceptible to corrosion due to the moisture and alkaline conditions in the digester [34]. The diameter of the influent pipe was 11.5 cm so that it is wide enough to prevent clogging of the pipe when the substrate is being loaded into the digester. However, the diameter of the effluent PVC pipe was 10.5 cm which was slightly smaller than that of the influent pipe. This diameter is adequate because the effluent is composed of materials that have been broken down already by the methanogens.

PVC Ball valve

A PVC ball valve was attached to a brass connector at the top of the digester, which served as the gas outlet. A flexible hose was in turn attached to the valve and connected to a tyre tube. The PVC ball valve and the brass connector are corrosion resistant.

Digester stand/wheels

The digester was mounted on a mild steel stand fitted with four wheels to make it portable.

2.1.8. Fabrication of Digester

The drawings of the designed biogas digester were produced (Figure 1Figure 1 and Figure 2) and subsequently fabricated using a 63 Litre drum, pipes and pipe fittings, valves. Holes were drilled in the drum to allow the insertion of pressure, temperature, pressure, PH and biogas yield sensors (Figure 3Figure 3). The wheels of the portable digester were fabricated from steel and painted to prevent corrosion.

(a) (b)

Figure 1. Views of the digester.

Figure 2. 3D diagram of the digester.

Figure 3. Biodigester fabrication in progress.

2.2.1. Problem Specification

The problem to be solved by the model was identified and the degree of accuracy required was determined. The model was set to predict the outcomes of anaerobic digestion of substrate using full-scale plant experimental data. The degree of accuracy of the model was evaluated using the Mean Squared Error (MSE) and the Correlation coefficient (R).

2.2.2. Data Preparation

Cow dung, which was mixed with water in ratio 1:1 was used as the substrate and fed into the digester for biogas production (Figure 2). The data used for developing the ANN models was collected from a data logger attached on the designed biogas digester which was situated at the Dairy Unit of the University of Ibadan Teaching and Research Farm (UITRF) and downloaded on the mobile phone set aside for this study. The data required for the neural network models were the input data and output (or target) data. The input sets were: mass of substrate (S), Total Solid (TS), Temperature (T), pH and feedstock (FS). The target data was the volume of biogas produced.

The physical quantities of the biogas system such as temperature, pressure and pH level were measured with electrical sensors and were recorded by a microcontroller, which stored the data on an SD card.

List and description of sensors/components used:

1) LM75: It is a temperature sensor module which converts analog to digital readings. It is cost-effective, consumes less power and is highly precise. It operates at a temperature range of −55˚C - 125˚C. It is effective in taking the temperature of the biogas system (Figure 4Figure 4).

2) Analog Pressure Sensor: Internally the pressure sensor uses a piezo resistive semiconducting element. With a maximum pressure of 50 psi, the analog pressure sensor is capable of recording the pressure of the biogas system which does have a pressure slightly above atmospheric pressure ~14 - 15 psi (Figure 5Figure 5).

Figure 4. LM75 temperature sensor.

Figure 5. Pressure sensor.

3) pH sensor:The pH sensor comprises a probe and a PCB board (Figure 6Figure 6). The probe, when dipped in a solution, measures the voltage or potential difference of the solution. The hydrogen ion concentration is obtained from the potential difference using the Nernst equation. The pH sensor has a range of 0 - 14 pH.

Figure 6. pH sensor.

4) SIM800L: The SIM800L GSM/GPRS module is a miniature GSM modem that was integrated into the biogas digester. It is an IoT network device which communicates with the microcontroller over UART (Universal Asynchronous Receiver-Transmitter) using AT commands. It ensures real-time data is received on a mobile device. It makes a phone call to alert the users when the battery voltage of the system is low.

5) SD card/SD card module: The SD card module is used to connect the SD card to the microcontroller, which is used to store the data read from the sensors, it uses SPI (Serial Peripheral Interface) communication protocol. The SD card has to be supplied with a voltage of 3.3 v.

6) DS1302: The DS1302 trickle-charge timekeeping chip contains a real-time clock/calendar and 31 bytes of static RAM. It communicates with a microprocessor via a simple serial interface. The real-time clock/calendar provides seconds, minutes, hours, days, dates, months, and year information. Interfacing the DS1302 with a microprocessor is simplified by using synchronous serial communication. Only three wires are required to communicate with the clock/RAM: CE, I/O (data line), and SCLK (serial clock). The current time is obtained from the DS1302 which is stored alongside other recorded data.

7) ESP 32: It is a 32-bit microcontroller, that features WiFi and deep sleep which consumes a very low current. The data obtained from the sensors is stored locally on an SD card with the help of an embedded SQLite engine, the stored data is retrieved by downloading a CSV file which is obtained via a mobile phone or PC to the system WiFi, and accessing a webpage on the device web browser at I.P address: “192.168.4.1”. It also features an ADC (Analog to Digital Converter) which is used to convert the analog voltages from the pressure sensor and pH sensor into meaningful numbers.

In this study ANN models were designed using the multi-layered feed-forward architecture. The networks were designed to contain one input layer containing five neurons, one hidden layer, and one output layer containing one neuron. The number of neurons in the hidden layer was determined using trial and error experimentation, which is a standard method for obtaining the optimal number of neurons. The architecture of the neural network models was determined by varying the number of neurons in the hidden layer (from one to ten neurons) for three different trials of data separation (70% of training set: 15% of validation set: 15% of testing set).

2.3.1. Neural Network Training

Neural network training involves the adjustment of the values of the connection weights and biases to generate the outputs with the given inputs. Training is a crucial step which determines the generalisation of the models. Levenberg-Marquardt backpropagation training algorithm (trainlm) was used to train the neural networks in this study.

The input data was normalized prior to the training using the min-max scaling approach. This enhances numerical stability and improves convergence. The mapminmax function was used, which linearly rescales each input variable independently to the interval [−1, 1]. The normalization parameters were estimated from the training dataset and applied consistently to validation and test data. The inverse transformation was used to restore network outputs to their original scale. In order to prevent overfitting, early stopping technique was employed and the number of epochs limited to 1000.

2.3.2. Model Validation

In this study, Mean Squared Error (MSE) and Regression R-value were calculated to evaluate and validate the performance of the neural network models in order to evaluate its capability to solve the problem.

Artificial Neural Network NS2 of MATLAB R2020a was used to develop the neural network model for the anaerobic digestion process of the substrate. The Neural Network Toolbox, which is a built-in tool in MATLAB has the ability to model complex nonlinear problems (MathWorks, 2020). The procedure for the neural network modelling is summarised in Figure 7Figure 7.

Figure 7. The neural network modelling procedure. (Source: Mathworks, 2020).

The values of the designed portable biogas digester are presented in Table 1.

Table 1. Calculated values in digester design.

The experimental data used for modelling the ANN models ranged as follows: The pH was seen to vary from 6 - 10.9 (slightly acidic-basic), Temperature (22.75 - 49.63)˚C, Pressure (9 - 15) atm, System battery voltage (0 - 4.05) V, Yield (0 - 88) dm³, Cumulative yield (0 - 987847.70) dm³, VS = 77.7% and TS = 36%.

The result of ANN modelling using Levenberg-Marquardt algorithm with 10 neurons in the hidden layer and 15 neuron-hidden layer are presented in Table 2 and Table 3. The MSE for both 10 neuron-hidden layer and 15 neuron-hidden layer was observed to be very low and the R values for both cases were very high (0.99 - 99) for training, testing and validation samples (Figure 9Figure 9). It however converged in 1000 epochs for both the 10 neuron-hidden layer and the 15 neuron-hidden layer as seen in Figure 8Figures 8-10, respectively. It is still acceptable based on the complexity of the relationships to be modelled.

Table 2. Result of artificial neural networks modelling using Levenberg-Marquardt algorithm.

Figure 8. Training of ANN Model with 10 neuron-hidden layer at 1000 Epochs.

Figure 9. Regression Plots of the ANN Model with 10 neuron-hidden layer with Levenberg Marquardt.

Table 3. Artificial Neural Networks Modelling using Levenberg-Marquardt (15 neuron-hidden layer).

The model was trained with Bayesian Regulation algorithm using 10 neurons in the hidden layer and 20 neuron-hidden layer. It was observed that the training converged in 13 epochs and 11 epochs, respectively (Figure 11Figure 11 & Figure 12Figure 12). However, though the computing time was low compared to the Levenberg Marquardt algorithm, the R value was very low as seen in Figure 13Figure 13 and Figure 14Figure 14.

Figure 10. Training of ANN Model using 15 neuron-hidden layer using Levenberg-Marquardt algorithm.

Figure 11. Training of ANN Model with Bayesian Regularisation at 13 Epochs.

Figure 12. Training of ANN Model with 20 neuron-hidden layer using Bayesian Regularization.

Figure 13. Regression Plots of the ANN Model using Bayesian Regularization algorithm with 10 neuron-hidden layer.

Figure 14. Regression Plots of the ANN Model using Bayesian Regularisation with 20 neuron-hidden layer.

SCG algorithm was used to train the ANN Model using 10 neurons in the hidden layer as presented in Figure 15Figure 15 and Figure 16. It was observed that though it converged at 177 epochs (Figure 15Figure 15), a value higher than BR but lower than LM. The R value was very low (Figure 16). However, it was observed as seen in Figure 17Figure 17 and Figure 18Figure 18, that the model with the 20 neuron hidden layer converged in 93 epochs and had a R-value of 0.9987 for all the samples. Showing excellent accuracy and satisfactory computation time.

Figure 15. Training of Artificial Neural Networks (ANNs) Model with SCG algorithm at 177 Epochs.

Figure 16. Regression Plots of the ANN Model using SCG with 10 neuron-hidden layer.

Figure 17. Regression Plots of the ANN Model using SCG Algorithm with 20 neuron-hidden layers.

Figure 18. Regression Plots of the ANN Model using SCG Algorithm with 20 neuron-hidden layer.

The results of the study showed that the ANN model was able to accurately predict the biogas yield from the cow dung substrate. The values of R were very high when both Levenberg-Marquardt and scaled conjugate gradient algorithms were used. While the reported correlation coefficients are high, overfitting is unlikely since comparable performance was observed across the training, validation and test datasets and normalization parameters were derived solely from the training data. In addition to this, the data were strictly partitioned, with no overlaps. The high correlation values are attributed to the strong underlying relationships between the input variables and the output.

On the other hand, the values of R were very low when Bayesian regularization algorithm was used. This could be because Bayesian regularization prioritises generalization over correlation maximization, and can therefore deliberately reduce apparent fit quality, especially when the dataset is relatively small.