A New Approach for Improving Microbial Fuel Cell Performance Using Artificial Intelligence

Abstract

Microbial fuel cells have recently received considerable attention as a potential source of renewable energy. Due to its complex and hybrid nature, it has significant nonlinear features and substantial hysteresis behavior, making it hard to optimize and control its power generation directly. This study modeled power density and COD removal using random forest regression and gradient boost regression trees. System inputs are three key parameters that affect performance and commercialization. There is a range of 0.1–0.5 mg/cm² of Pt, a degree of sulfonation of sulfonated polyether-etherketone varying from 20% to 80%, and a cathode aeration rate of 10–150 mL/min. Based on the model’s accuracies, gradient boost regression was selected for power density prediction and random forest for COD removal prediction. Particle swarm optimization was used as the optimization algorithm after selecting the best models to maximize COD removal and power density. It was found that DS was the most critical parameter for COD removal, and Pt was the most critical parameter for power density. There is a different optimal input value for each model. In order to maximize power density, DS (%) must be 67.7087, Pt (mg/cm²) must be 0.3943, and Aeration (mL/min) must be 117.7192. To maximize COD removal, the DS (%) must be 75.8816, the Pt (mg/cm²) must be 0.3322, and the Aeration (mL/min) must be 75.1933.

1. Introduction

Many countries worldwide have turned their attention to renewable energy options such as wind, solar, and water as a solution to the energy crisis [1]. A fuel cell (FC) is an alternative energy source that uses high-value metal catalysts (in the traditional version) to generate energy. FC has several advantages over other energy generator types, such as no emissions of environmentally harmful gases (such as NOx, SOx, CO, and CO₂), higher efficiency, no mobile devices, and no sonic pollution [2]. A disadvantage of these new energy sources is their high cost and mass production [3]. There are different types of fuel cells such as direct methanol fuel cells (DMFCs), proton exchange membrane fuel cells (PEMFCs), and so on. The main difference between the fuel cells is the working style and output of the fuel cells. For example, DMFCs utilize methanol and convert the chemical energy to electricity. There are various means by which a fuel cell can convert a pollutant fuel to green energy [1,2,3].

Microbial fuel cells (MFCs) have recently received substantial interest as a new renewable energy technology. Direct bio-electrochemical reactors, such as MFCs, convert the chemical energy of microorganisms into electricity, use the organism as a substrate, and generate electricity directly from the redox reactions of microbes [4,5]. In MFCs, microorganisms oxidize the substrate to generate energy. Microorganism growth rate, pH, operating temperature, external load, and substrate concentration affect MFC performance. MFCs can be divided into indirect MFCs (mediator-based) and direct MFCs (conduction-based) based on how electrons are supplied to the anode [6,7].

The proton exchange membrane (PEM) distinguishes two-chamber MFCs from single-chamber MFCs [8]. Using wastewater as the substrate and simultaneously generating electrical power, MFCs have the potential to replace traditional fossil fuels while reducing the impact on the environment.

Furthermore, wastewater can be used as the substrate for generating electricity power simultaneously [9]. It is challenging to optimize and control the power generation of MFCs directly due to their complex and hybrid nature, which involves several coupling reactions. This results in robust nonlinear performance and substantial hysteresis behavior [10]. Bacterial inoculation and performance measurement via experiments are inefficient and time-consuming [11].

Artificial intelligence (AI) algorithms have become increasingly popular in MFC applications as predictive models, as they are reliable and efficient tools for modeling MFC problems. Using an ANFIS model, Ghasemi et al. [12] predicted COD removal and power density, then optimized both these parameters using single-object optimization and multi-object optimization. ANN models were used to predict the voltage of MFCs and compared with experimental results by Ahmed et al. [13]. A correlation coefficient of 0.999 was obtained for the constructed ANN model. Lesnik and Liu [14] modeled 33 MFCs using ANN, including eight substrates and three wastewaters. Based on these values, the mean percent prediction error values were 1.77 ± 0.57%, 16.01 ± 4.35%, and 4.07 ± 1.06% for coulombic efficiency, PD, and COD removal, respectively. Tsompanas et al. [15] used ANN to simulate the polarization curves with various membrane materials and electrode configurations.

During the experimental procedure for obtaining the dataset used to construct the ANN model, two membrane types with two unique electrode structures were examined. The model correlation coefficient was 0.996. Esfandyari et al. [16] used both ANFIS and ANN. The medium nitrogen concentration, ionic strength, temperature, and pH were input parameters, and columbic efficiency and PD were output parameters. Both ANFIS and ANN models achieved suitable correlation coefficients greater than 0.99. Ismail et al. [17] trained an ANN to determine the effectiveness of MFCs based on an experimental dataset. The investigation considered different particle sizes and concentrations of giant reed. MFC PD was defined as the neural network’s output, whereas the duration, concentration of giant reed, and particle size were utilized as input parameters. Based on the results, the optimal result was achieved at 12 hidden layers and the coefficient of determination was 0.9993.

MFC performance was assessed by Islam et al. [18] using RSM to control co-culture composition, substrate concentration, time, and pH. Optimal results occurred at 1:1, 15.50 days, 7.21, and 26.690 mg/L for inoculum composition, time, pH, and initial COD, respectively. To optimize the cell’s PD and COD, Sedighi et al. [19] utilized RSM. A value of 58.19 mW/m² was optimal for PD and 94.8% for COD removal. To optimize the effectiveness of MFC using RSM, Muaz et al. [20] utilized three input parameters: moisture content (% vol/wt), electrode distance (cm), and temperature (°C). MFC reached a maximum output voltage of 927.7 mV, while COD removal increased to 170.8 mg/L.

In regression and classification tasks, a random forest algorithm (RF) has been extensively applied by combining aggregation and bootstrapping techniques to build numerous regression and classification trees (CARTs) [21,22]. In regression problems using RF, output variables are fitted by using samples of input variables. At each divided point, the sum of square error (SSE) is determined for predicted and actual values for each input variable. The minimum SSE value is then determined for this node. Furthermore, the variable importance can be determined by rearranging all the input variables and comparing their prediction accuracy in the out-of-bag samples [23].

Gradient boosting is an optimization algorithm based on error functions. The gradient boosting technique is a machine learning technology applied to identify classification and regression problems. Weak prediction models, such as decision trees, generate a strong prediction model. Friedman developed the GBRT algorithm later [24]. A basic model performs each calculation, and the next calculation is undertaken to reduce the residual, creating a new basic model in the gradient direction with reduced residuals [25]. Therefore, it is possible to minimize and optimize the loss function by constantly adjusting the weights of weak learners.

The main objective of this research is to determine the best magnitudes for input parameters that maximize power density and COD removal. This study used MFC datasets to make models that use DS, Pt, and Aeration as inputs and power density or COD removal as outputs. To build the microbial FC machine learning model for power density and COD removal prediction, random forest regression and gradient boost regression tree algorithms were utilized. Using particle swarm optimization as a single object optimizer, we found the optimal input parameters that maximized the power density or COD removal after preparing the models with high accuracy.

2. Materials and Methods

In many cases, all the experiments to cover all the control parameters cannot be conducted. It is impossible to experiment with many operating parameters in such cases because it is either expensive or takes a long time. In the absence of certain operating point data, one of these statistical methods can be used to build an acceptable model. Several AI techniques, including random forest regression and gradient boost regression, have been proven to be efficient and accurate modeling tools. After the accurate model has been established, the spatial layout for determining the input–output relationship can also be determined. Maximal/minimal parameters can be predicted using well-established optimization approaches.

2.1. Dataset

In this study, MFC data were utilized. A real dataset consists of 226 examples of data (80% training, 20% testing) with 5 attributes (3 inputs, 2 outputs); the inputs are Pt, Aeration, and DS, and the outputs are power density or COD removal. In

Table 1. Data summary.

		Inputs		Outputs
	DS (%)	Pt (mg/cm2)	Aeration (mL/min)	Power Density (mW/m2)	COD Removal (%)
mean	49.823	0.292	73.637	40.646	61.957
Std.	19.865427	0.141063	39.796273	11.624616	16.819326
Min.	20	0.1	10	12.54	10.68
25%	30	0.2	40	31.975	53.2575
50%	50	0.3	72.5	43.37	63.475
75%	70	0.4	104.5	50.74	73.475
Max.	80	0.5	150	56.95	90.56

, the mean value (mean), maximum (max.), minimum (min.), standard deviation (std.), sample numbers (count), median (50%), first quartile (25%), and third quartile (75%) are listed.

2.2. Random Forest Regression (RFR)

Random forest (RF) is a robust multi-class learning algorithm based on classification and regression trees. Ho [26] developed the first random decision forest algorithm, and Breiman [22] extended it. Both classification and regression have demonstrated satisfactory performance in many aspects. RF models a decision tree for each bootstrap sample and then averages the predictions of all the decision trees as a statistical learning theory. By putting back samples and randomly changing predictor combinations in different tree evolutions, the model increases the diversity of decision trees.

The most important step in this investigation is the determination of the regression. Therefore, only regression trees (RT) are discussed. At each branching of RT, the sample mean and mean square error (MSE) were calculated between samples. Regression trees will stop growing when there are no more features available or when the overall MSE is optimal when following the minimum leaf MSE as a branching condition. The regression tree number (N estimators) and the number of random variables of nodes (Max depth) are two important custom parameters [27,28]. Optimization of these parameters can reduce data processing errors. Bootstrap sampling in the RF algorithm extracts training sets from the original dataset for N estimators. There are about two-thirds as many training sets as the original datasets. Each bootstrap sample will exclude about one-third of the data during training. Out-of-bag data refer to this part of the data. Each bootstrap training set is analyzed using a regression tree. A “forest” is formed by combining regression trees of N estimators, but they are not pruned. In every tree, the optimal attribute is not necessarily chosen as the internal node. A random selection of Max depth attributes is used to select the optimal attribute. An RF algorithm improves extrapolation prediction by increasing the difference between regression models by various training sets. As a result of n-time model training, a regression sequence $\left\{t_1(x),t_2(x),\dots ,t_k(x)\right\}$ is achieved, which is then utilized to build a multi-regression model (forest). To calculate the value of the new sample, we take the prediction results from the N estimators’ regression tree and use a straightforward standard approach. As a result of the regression, the following formula is used:

$$f_{rf}^K(x)=\frac{1}{K}{\displaystyle \sum _{k=1}^K{t}_i(x)}$$

(1)

The combined regression model is represented by $f_{rf}^K(x)$, the decision tree regression model by $t_i$, and the number of regression trees (N estimators) by K. Figure 1 illustrates the random forest algorithm modeling process.

2.3. Gradient Boost Regression Tree (GBRT)

Friedman [29] introduced the gradient-boosting machine learning model. To increase the precision and robustness of the final model, gradient boosting utilizes multiple weak learners. Gradient boosting models are built by using a single leaf and constructing regression trees. Regression trees are decision trees that estimate continuous real-valued functions instead of classifiers. The regression tree is constructed in an iterative process by splitting the data into smaller groups or nodes. Initially, all observations are grouped. The data are then divided into two partitions based on every available predictor. The predictor that splits the tree is the one that separates the observations most clearly and minimizes residual errors, which are measured by the Friedman MSE [29]. Gradient boosting creates new trees based on the error in the previous tree, and it makes more trees until the fit or number cannot be enhanced any further. Gradient boosting scales the new tree’s contribution based on a learning rate to avoid overfitting. For the input data, s, and a differentiable loss function, $L(y_i,F(x))$, which in this study is a squared regression, Friedman’s gradient boosting algorithm takes the following steps.

Step 1: Set the model with a constant value:

$$F_0(x)=\arg {\max }_{\gamma }{\displaystyle \sum _{i=1}^{n}L(y_i,\gamma )}$$

(2)

$\gamma$ is a predicted value, $F_0(x)$ is the average of the observed values, and $y_i$ is an observed value.

Step 2: For m = 1 to M:

(A)

Calculate

$${\gamma }_{im}=-{\left[\frac{\partial L(y_i,F(x_i))}{\partial F(x_i)}\right]}_{F(x)=F_{m-1}(x)}fori=1,\dots ,n$$

(3)

Fit a regression tree to the ${\gamma }_{im}$ values and create terminal regions $R_{jm}$ for j = 1 … $j_m$.

(B)

For j = 1 … $j_m$, determine

$${\gamma }_{jm}=\arg {\max }_{\gamma }{\displaystyle {\sum }_{x_i\in R_{ij}}L(y_i,F_{m-1}(x_i)+\gamma )}$$

(4)

Update

$$F_m(x)=F_{m-1}(x)+\upsilon {\displaystyle \sum _{j=1}^{j_m}{\gamma }_{m}I(x\in R_{jm})}$$

(5)

ν is the learning rate. It is possible to customize the loss functions by changing the learning rate. This feature enhances flexibility and minimizes the overfitting problem through slower iterations [30].

Step 3: Output:

$$\widehat{F}(x)=F_M(x)$$

(6)

2.4. Particle Swarm Optimization Algorithm

Particle swarm optimization is an algorithm that simulates the behavior of a flock of birds [31]. For applications involving real decision variables, PSO emerged as a widely used optimization tool [32]. A particle moves in a multidimensional search space to find a possible response to a problem. Each particle alters its position depending on its experience and neighbors. The ith particle in n-dimensional search space is presented as follows [33]:

$$X_i=(x_{i1},x_{i2},\dots ,x_{iN})$$

(7)

The best among all the particles in the population $(P_g)$, the best previous location of each particle $(P_i)$, the velocity $(V_i)$, and the maximum velocity $(V_{\max -i})$ of each particle are expressed as [33]

$$P_i=(p_{i1},p_{i2},\dots ,p_{iN})$$

(8)

$$P_g=(p_{g1},p_{g2},\dots ,p_{gN})$$

(9)

$$V_i=(v_{i1},v_{i2},\dots ,v_{iN})$$

(10)

$$V_{\max -i}=(v_{\max -i1},v_{\max -}{}_{i2},\dots ,v_{\max -}{}_{iN})$$

(11)

Particles are limited by the maximum velocity set by the user. A maximum velocity encourages global exploration, while a low maximum velocity encourages local exploration [32]. An appropriate value must be specified to achieve a balance between these two states. The following relations [33] can be utilized to determine the new particle’s velocity and position:

$$v_{i,n}=w.v_{i,n}+c_1.r_1.(p_{i,n}-x_{i,n})+c_2.r_2.(p_{g,n}-x_{g,n})$$

(12)

$$x_{i,n}=x_{i,n}+v_{i,n}$$

(13)

Acceleration constants c₁ and c₂ are used in the above relations. Particles are driven toward their best positions based on these values. Furthermore, r₁ and r₂ are uniformly generated random numbers between 0 and 1 [33]. Current velocity is influenced by previous velocity history through the inertia weight [34]. A constriction parameter is defined in some problems to enhance PSO performance and its ability to control particle velocity [33,35]:

$$K=\frac{2}{\left|2-\phi -\sqrt{{\phi }^2-4\phi }\right|}$$

(14)

Therefore,

$$\phi ={\phi }_1+{\phi }_2(\phi >4)$$

(15)

2.5. Regression Evaluation Metrics

Regression algorithms are typically evaluated using RMSE, MAE, and R-squared [36]. Three metrics are determined as follows:

$$RMSE=\sqrt{\frac{1}{m}{\displaystyle \sum _{i=1}^m{(y_i-{\widehat{y}}_i)}^2}}$$

(16)

$$MAE=\frac{1}{m}{\displaystyle \sum _{i=1}^m\left|y_i-{\widehat{y}}_i\right|}$$

(17)

Generally, the lower the MAE and RMSE values, the better the fit. An important index to verify the accuracy of a regression algorithm is the R-squared, which has a range between 0 and 1. R-squared is defined as follows:

$$R-squared=1-\frac{{\displaystyle \sum _{i=1}^m{(y_i-{\widehat{y}}_i)}^2}}{{\displaystyle \sum _{i=1}^m{(y_i-{\overline{y}}_i)}^2}}$$

(18)

${\overline{y}}_i$ denotes the mean value of the actual value $y_i$. An R-squared value of 1 represents a regression model that gives accurate predictions. Generally, the higher the R-squared value, the better the fit.

3. Results

This section simulates and validates the proposed prediction models for COD removal and power density. To visualize the interrelationship between inputs and outputs, it is better to have a 3D form of the spatial figure before describing the modeling results. In a 3D figure, the output is shown responding to input changes. Figure 2 shows the plot of MFC outputs versus inputs for every two inputs. Since the input–output relationship is nonlinear, the AI modeling technique was a suitable option because it can analyze such a variety of data efficiently.

3.1. Correlation Analysis

Visualizing the correlation coefficient of multi-source data in a heat map is generally possible, since all parameters can be connected logically and clearly. To compute correlations between each pairwise variable, Spearman’s rank correlation coefficient (r_s) was assigned to the data distribution, followed by generating a heat map containing all correlation coefficients. According to Figure 3, Pt is strongly correlated with power density, whereas power density is moderately correlated with COD removal, while Aeration is almost independent of COD removal.

3.2. Making a Machine Learning Model

Cross-plots of experimental and predicted/estimated COD removal and power density by RFR and GBRT models are shown in Figure 4 and Figure 5, respectively, illustrating the comparison between RFR and GBRT algorithm models on the training and testing dataset using three performance indicators: RMSE, MAE, and R-squared. During both the training and testing phases, precision and efficiency are ensured. According to Figure 6 and Figure 7, the GBRT algorithm model achieves the best performance indicators for power density prediction, while the RFR algorithm model is the best for power COD removal prediction (

Table 2. The model’s precision obtained for power density prediction.

Accuracy	Random Forest Regression	Gradient Boost Regression Tree
	Training Data
R-squared	0.9958	0.9997
RMSE	0.7514	0.1962
MAE	0.5693	0.1287
Accuracy	Random Forest Regression	Gradient Boost Regression Tree
	Testing Data
R-squared	0.9470	0.9540
RMSE	2.5745	2.2696
MAE	1.9209	1.6544

and

Table 3. The model’s precision obtained for COD removal prediction.

Accuracy	Random Forest Regression	Gradient Boost Regression Tree
	Training Data
R-squared	0.9936	0.9997
RMSE	1.3309	0.2631
MAE	0.9736	0.1761
Accuracy	Random Forest Regression	Gradient Boost Regression Tree
	Testing Data
R-squared	0.9813	0.9695
RMSE	2.3046	3.0143
MAE	1.5957	2.2944

).

As shown, the GBRT prediction model for the power density parameter has higher precision (R-squared = 0.9997, RMSE = 0.1962, and MAE = 0.1287; for testing data, R-squared = 0.9540, RMSE = 2.2696, and MAE = 1.6544) than the RFR prediction model (R-squared = 0.9958, RMSE= 0.7514, and MAE = 0.5693; for testing data, R-squared = 0.9570, RMSE = 2.5745, and MAE = 1.9209) on a few training and testing data. Figure 7 also presents precision values obtained for the COD removal parameter, demonstrating that GBRT prediction models perform worse than RFR prediction models (for training data, R-squared = 0.9997, RMSE = 0.2631, MAE = 0.1761; for testing data, R-squared = 0.9695, RMSE = 3.0143, and MAE = 2.2944) (for training data, R-squared = 0.9936, RMSE = 1.3309, and MAE = 0.9736; for testing data, R-squared = 0.9813, RMSE = 2.3046, and MAE = 1.5957).

3.3. Optimization

Power density and COD removal models have been selected as the best models. These models are used to optimize input parameters. Particle swarm optimization (PSO) was used as a meta-heuristic algorithm for its efficiency and simplicity. Despite its many variants, PSO can still be applied to address a diverse range of optimization problems. By considering lower and upper bounds for input parameters (DS, Pt, and Aeration), PSO was used for optimizing the mentioned parameters to find the maximum value for COD removal and power density. Based on trial and error, the number of iterations and particles are set to 1000 and 10, respectively. Self and overall information constants, c₁, c₂, and w, are set to 0.5, 0.3, and 0.9, respectively.

$$Lower-Bound=\left\{Ds(\%)=20,Pt({\mathrm{mg}/\mathrm{cm}}^2)=0.1,Aeration(\mathrm{mL}/\min )=10\right\}$$

(19)

$$Upper-Bound=\left\{Ds(\%)=80,Pt({\mathrm{mg}/\mathrm{cm}}^2)=0.5,Aeration(\mathrm{mL}/\min )=150\right\}$$

(20)

Figure 8 shows the convergence history of the PSO algorithm.

Table 4. Optimized power density and COD removal values.

Parameters	DS (%)	Pt (mg/cm2)	Aeration (mL/min)	Best Cost
The optimum value for power density	67.7087	0.3943	117.7192	55.9069
The optimum value for COD removal	75.8816	0.3322	75.1933	90.6

summarizes the PSO algorithm’s optimized values. Each model has a different optimal input value. To maximize power density, DS (%) must be 67.7087, Pt (mg/cm²) must be 0.3943, and Aeration (mL/min) must be 117.7192. Additionally, to maximize COD removal, DS (%) must be 75.8816, the Pt (mg/cm²) must be 0.3322, and Aeration (mL/min) must be 75.1933. Based on the results, the optimization method can enhance the performance of MFCs and achieve economic benefits.

Table 5. Comparing obtained results with those of recent MFC studies.

Item	Description	Ref.
1	With an ANFIS model, COD removal and power density were predicted, and then optimized using single-object optimization and multi-object optimization.	[12]
2	The voltage of MFCs was predicted using ANN models and compared with experimental results.	[13]
3	ANN was used to model 33 MFCs, including 8 substrates and 3 wastewaters.	[14]
4	ANN was used to simulate polarization curves with various membrane materials and electrode configurations.	[15]
5	The power density and COD removal were modeled using random forest regression and gradient boost regression trees, and the modeled parameters were optimized using particle swarm optimization.	This study

compares the results of this study with those of other recent studies. While most studies have used artificial neural networks (ANN) to model MFC, this study used RFRs and GBRTs to estimate power density and COD removal, and then used the models to optimize the objective functions.

4. Conclusions

A wide range of input data, including DS, Pt, and Aeration, were used to model COD removal and power density using machine learning algorithms, after which the machine learning models were utilized as objective functions. Using the particle swam optimization algorithm, the input parameters were optimized to maximize power density and COD removal, with the following main results:

• All the developed models for MFC prediction of COD removal and power density produced accurate results for both the training and testing stages. According to their accuracy, the proposed techniques can be sorted as follows: power density prediction, GBRT > RFR; COD removal prediction, RFR > GBRT.
• The PSO optimization algorithm can converge in a few iterations, resulting in optimum states.
• In regression problems with low data, RFR and GBRT are accurate algorithms.
• The most important parameter affecting COD removal is DS, while Pt is the most important parameter affecting power density.