Increasing Output Power of a Microfluidic Fuel Cell Using Fuzzy Modeling and Jellyfish Search Optimization

Abstract

An efficient electrochemical energy conversion system with little to no environmental impact is the fuel cell (FC). FCs have demonstrated encouraging results in various applications and can even run on biofuel, such as bio-glycerol, a by-product of biodiesel. The most effective ways to operate FCs can significantly enhance their effectiveness. Incorporating fuzzy modeling and metaheuristic methods, this work used artificial intelligence to determine the ideal operating parameters for a microfluidic fuel cell (MFC). The concentrations of the following four variables were considered: bio-glycerol concentration, anode electrocatalyst loading, anode electrolyte concentration, and cathode electrolyte concentration. The output power density of the MFC was used to assess its performance. The output power density of the MFC was modeled using fuzzy logic, taking into account the aforementioned operational parameters. A jellyfish search optimizer (JSO) was then used to find the ideal operating conditions. The results were contrasted with response surface methodology (RSM) and experimental datasets to demonstrate the superiority of the proposed integration between fuzzy modeling and the JSO. In comparison with the measured and RSM approaches, the suggested strategy boosted the power density of the MFC by 9.38% and 8.6%, respectively.

1. Introduction

Climate changes oblige researchers to find an alternative to fossil fuel that fluctuates in price and is limited [1]. Researchers have considered several methods to overcome or minimize the reliance on fossil fuel through (i) utilizing eco-friendly renewable energy [2], (ii) enhancing the efficiency of existing energy conversion systems through the recovery of wasted heat [3,4], and finally, (iii) developing new energy conversion devices that are efficient and have low or no environmental impact, such as fuel cells (FCs) [5]. Among the various electrochemical energy conversion/storage devices, i.e., batteries [6], supercapacitors [7], and fuel cells [8], the latter has garnered a great interest because of its high energy density, long lifetime, and ability to use a wide range of fuels from hydrogen to wastewater [9]. Microfluidic fuel cells (MFCs) are devices that mainly depend on microfluidic channels through which the fluid delivery and removal, electrode structure exits, and reactions take place [10]. MFCs are membrane-less FCs as no membrane separates the cathode and anode. Metal or biological base catalysts can be used, and the cell operates under laminar flow conditions. MFCs’ oxidant and laminar flow create a liquid-liquid interface allowing ion migration. These devices have high theoretical efficiencies, long lifetime, are safe, have no moving parts, have no membrane, operate at low temperatures, and have a simple and easy operation [11,12]. MFCs can be employed for portable electronic devices like pacemakers, laptops, camcorders, glucose sensors, and cell phones. Several liquid fuels were investigated in MFCs such as ethanol, methanol, formic acid, and glycerol.

Environmental glycerol is an appropriate fuel due to being non-toxic, a byproduct of biodiesel, and cheap and having a higher energy density than methanol and ethanol [13,14]. It is essential to nominate the proper electrocatalyst and the operating conditions to achieve the best MFC performance, as the molecular structure of glycerol is complex. The glycerol electrooxidation showed better reaction kinetics in an alkaline medium than in an acidic one [15]. Various platinum and platinum-free electrocatalysts were examined in MFC [16,17]. Pd was tested for anodic oxidation of glycerol using different morphologies of carbon, such as carbon nano-powder (Pd/C) or MWCNT (Pd/MWCNT) as supporting material in a Y-shape MFC. Pd/MWCNT displayed superior performance as it achieved a high power density of 0.7 mW/cm² in an alkaline medium (0.3 M KOH) containing 0.1 M glycerol [18]. Pd-Pt/C anodes were synthesized via an impregnation reduction approach where the bi-metallic Pd:Pt electrocatalysts were supported with different ratios (by weight) of 16:4, 10:10, 4:16 and Pd on acetylene black carbon [19]. The activity of these anodes towards glycerol oxidation was investigated at 35 °C in an air breathing MFC. Pd-Pt/C of 16:4 (wt.%) revealed the highest catalytic activity for glycerol oxidation among different anodes. Moreover, an increased temperature from 35 °C to 75 °C significantly enhanced the cell performance as the maximum power density (MPD) increased more than 45%. Cu@Pd/C and Cu@Pt/C were tested as anodes at room temperature for the electrooxidation of crude and analytical glycerol in an air-breathing nanofluidic FC under alkaline conditions [20]. Both electrodes showed high tolerance towards the impurities in the crude glycerol with 17.6 mW/ cm² (Cu@Pd/C) and 21.8 mW/cm² (Cu@Pt/C) for crude and analytical glycerol. Low dissolved oxygen concentration in the inlet, low diffusivity, and low mass transfer rate negatively affect the MFC’s performance. A T-shaped air-breathing MFC was designed to conquer these challenges. The T-shaped air cathode is simple and operates more easily than a Y shape [21]. Also, in the T-shaped configuration, the cathode is exposed to higher oxygen concentrations from the air. The oxygen diffusivity is 10,000 times greater than the diffusivity of dissolved oxygen of (using) liquid oxidant [20,22]. Allocating the optimum operating conditions of T-shaped air-breathing MFC fueled with glycerol is essential to achieve the highest fuel cell performance. Hence in this study, different controlling parameters, including electrolyte concentration of both anode and cathode, the concentration of glycerol, and the loading of an anode electrocatalyst, were scrutinized to define the optimum values that realize the highest power output.

Artificial intelligence (AI) has been used in numerous applications, especially in complex or uncertain situations. AI algorithms analyze large amounts of data, identify patterns, and make predictions and recommendations. Some common areas where AI has been successfully applied include image and speech recognition, natural language processing, virtual assistants, autonomous vehicles, fraud detection, and medical diagnosis. In all these areas, AI has demonstrated the ability to handle vast amounts of complex and heterogeneous data, identify relevant features and patterns, and provide useful insights and predictions. In this direction, Huang et. al. produced an artificial neural network to simulate the pulsating Green’s function [23]. Li et. al. suggested a machine learning (ML) approach for the prediction of the singular integrals using the boundary element method. Five ML techniques were examined in [24]. In the same stream, Abidou et. al. constructed a radial basis function model for simulating the removal of material in laser drilling [25]. Fuzzy modeling has been proven a superior predicting method in various engineering applications [26].

The current research aims to suggest a methodology to increase the power density of microfluidic FC. Firstly, an effective fuzzy model is built to simulate microfluidic FC. The considered controlling parameter variables are the concentration of glycerol, the loading of the anode electrocatalyst, the concentration of anode electrolyte, and the concentration of the cathode electrolyte. Next, the best rates of the input variables that increase the power density of the microfluidic FC are estimated by applying the jellyfish search optimizer (JSO). The algorithm mimics the collective behavior of jellyfish, including their following of ocean currents, active and passive motions within a swarm, and converging into a jellyfish bloom. The contributions of this paper are drawn as follows:

• A reliable fuzzy model is constructed to model the microfluidic FC.
• A new application of the jellyfish search optimizer is finding the optimal operating parameters of microfluidic FC operated with environmental glycerol.
• The power density of microfluidic FC is increased.
• The results are compared with those obtained by Ref. [21].

2. Methodology

In this paper, the suggested strategy involves two stages. Based on the measured data, a power density model using fuzzy logic will be established in the first stage. Whereas in the second step, the parameter identification process will be done by JSO to determine the optimal values of glycerol concentration, the loading of the anode electrocatalyst, the concentration of anode electrolyte, and the concentration of the cathode electrolyte for maximization of the power output of the MFC. Finally, the results are compared with those obtained by Ref. [21].

2.1. Dataset

The Pd-Pt electrocatalysts with weight ratios of 16:4 were synthesized using PdCl₂ and H₂PtCl₆·6H₂O as precursors, as mentioned in [21]. A definite amount of the synthesized electrocatalyst was mixed with isopropanol, PTFE dispersion, Nafion@dispersion, and activated carbon/acetylene black carbon (C_AB) to form the catalyst ink. Then the catalyst ink was painted on the surface of carbon paper (gas diffusion layer). Finally, the Ni mesh (current collector), the carbon paper, and the catalyst layer were hot-pressed (at 70 °C and 10 kg/cm² for 30 s), as can be seen in Figure 1. The prepared anode was dried and activated to open the blocked pores and examined as in the T-shaped air-breathing MFC [21,27]. A four-layered cathode composed of Pt catalyst (40 wt.%), carbon paper, Ni mesh (current collector),t and PTFE named Pt_HSA was fabricated similarly [27]. The dimension of both the anode and cathode was (3 mm × 30 mm). The loading of the anodic catalyst ranged from 0.5 to 1.5 mg/cm²; glycerol fuel concentration ranged from 0.5 to 2 M; and the concentration of anode and cathode electrolytes varied from 1 to 2 M and from 0.25 to 0.27 M, respectively. The loading of the cathodic catalyst was maintained at 1 mg/cm² for all experiments. All experiments were performed at 1 atm and 35 °C using cathode catalyst loading of 1 mg/cm²; more experimental details were allocated in [21].

2.2. Fuzzy Model of MFC

As explained in Figure 2, there are three main stages during the building the fuzzy model [28]. (1) Fuzzyfication: In this stage, the crisp input variables are converted into fuzzy variables using membership functions. The choice of membership function depends on the nature of the input variables and the problem being addressed. (2) Fuzzy inference: In this stage, fuzzy logic rules are defined to determine how the input variables relate to the output variables. Fuzzy inference uses the fuzzy rules and the fuzzy variables to produce a crisp output value. (3) Defuzzyfication: In this stage, the crisp output value obtained from the fuzzy inference stage is converted back to a fuzzy variable using a defuzzyfication method. The most commonly used method for defuzzyfication is the centroid method, which calculates the center of gravity of the fuzzy output variable to represent the crisp output value. Other defuzzyfication methods include the height method, mean of maximum method, and weighted average method.

Fuzzy models use various shapes of input membership functions (MFs) to represent the degree of membership of an input value to a particular fuzzy set. Some commonly used MF shapes include: (1) triangular, the most used shape for input MFs, where the curve rises linearly to a maximum value and then falls linearly back to zero; (2) trapezoidal, in which the curve rises linearly to a maximum value and then stays constant for a while before falling back to zero; (3) Gaussian, characterized by a bell-shaped curve with a single peak; (4) bell-shaped, which like Gaussian, also has a bell shape, but is not necessarily symmetrical; and (5) sigmoidal, characterized by an S-shape and used to represent gradual or abrupt changes in membership degree. The choice of MF shape depends on the nature of the input variable and the requirements of the application. As an example, the disadvantages of triangular and trapezoidal MFs include the following. (1) Lack of smoothness: Triangular and trapezoidal MF shapes are not as smooth as Gaussian MFs, which can lead to abrupt changes in the output of the system as the input changes. This can be an issue in certain applications, such as control systems, where smoothness is desirable. (2) Limited flexibility: The shape of the triangular and trapezoidal MFs is fixed, which limits the flexibility of the system to adjust to different datasets. (3) Difficulty with complex datasets: Triangular and trapezoidal MFs may not be able to accurately represent complex datasets where the input data have multiple peaks or irregular shapes. This can lead to inaccurate predictions or suboptimal performance of the system. Therefore, Gaussian is adopted to model the MFC.

In a fuzzy model, the IF-THEN rules define the relationships between the input variables and the output variable(s) in a linguistic and interpretable way. Each rule typically consists of two parts: the antecedent (IF) and the consequent (THEN). The antecedent specifies the conditions under which the rule is valid, typically by defining a fuzzy set or combination of fuzzy sets for one or more input variables. The consequent specifies the consequence or output of the rule, typically by defining a fuzzy set or combination of fuzzy sets for the output variable(s).

Here is an example of an IF-THEN rule in a fuzzy model:

IF x is X and y is Y THEN z = f(x, y)

(1)

where, x and y denote the inputs.

z is the output.

X and Y are the MFs of x and y.

f value is defined as follows.

$$f={\tilde{\omega }}_1{f}_1+{\tilde{\omega }}_2{f}_2$$

(2)

$${\tilde{\omega }}_1=\frac{{\omega }_1}{{\omega }_1+{\omega }_2} and {\tilde{\omega }}_2=\frac{{\omega }_2}{{\omega }_1+{\omega }_2}$$

(3)

$${\omega }_1={\mu }_{A_1}\times {\mu }_{B_1} and {\omega }_2={\mu }_{A_2}\times {\mu }_{B_2}$$

$${\mu }_{A_1}, {\mu }_{A_2},{\mu }_{B_1} and {\mu }_{B_2} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{M}\mathrm{F} \mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{w}\mathrm{o} \mathrm{i}\mathrm{n}\mathrm{p}\mathrm{u}\mathrm{t}\mathrm{s}$$

2.3. Jellyfish Search Optimizer

In comparison with conventional optimization techniques that use a limited number of computational parameters, jellyfish search optimization (JSO) offers several benefits. JSO has been seen to converge more quickly and have better searching abilities. Additionally, compared to previous algorithms, it achieves a better balance between exploitation and exploration. To successfully explore the issue space and exploit potential regions for the best solutions, this balance is essential. These characteristics are what make JSO a desirable option for optimization jobs [29]. The fundamental concept behind JSO was inspired by the ways in which jellyfish behave in order to survive in the ocean. The movement of jellyfish is either determined by the current of the ocean or takes place within the swarm [29,30]. A time control process governs the transition between different types of movement.

The current ocean path ($\stackrel{⃑}{co}$) can be described by taking the average of all the vectors that travel from each jellyfish in the ocean to the jellyfish that has the best-obtained position.

$$\overrightarrow{d}=\frac{1}{n}{\displaystyle \sum {\overrightarrow{d}}_i}=\frac{1}{n}{\displaystyle \sum ({\mathrm{X}}_{\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}}-{\mathrm{e}}_{\mathrm{c}}{\mathrm{X}}_i)}={\mathrm{X}}_{\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}}-{\mathrm{e}}_{\mathrm{c}}\frac{{\displaystyle \sum X_i}}{n}={\mathrm{X}}_{\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}}-{\mathrm{e}}_{\mathrm{c}}\mu ={\mathrm{X}}_{\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}}-df$$

(4)

where n donates the number of populations, X_best donates the optimal location, e_c denotes the convergence rate, and μ is the average of the jellyfish locations. The new location is determined as mentioned in (4).

$$X_i(\mathrm{t}+1)=X_i(\mathrm{t})+r(X_{\mathrm{best}}-\beta \cdot r)\mu$$

(5)

where r is an arbitrary number and β is a distribution factor.

Jellyfish swarm: Jellyfish display both passive (Form A) and active (Form B) movement at this stage. Initially, the swarm starts with Form A movement and then gradually transitions to Form B movement. Form A movement can be defined by the following relationship.

$$X_i(\mathrm{t}+1)=X_i(\mathrm{t})+\gamma \cdot r(Ub-Lb)$$

(6)

where Ub and Lb are the max and min boundaries, and γ is a movement coefficient.

Form B movement may be defined by the following relationship.

$$\begin{array}{l}{X}_i(\mathrm{t}+1)=X_i(\mathrm{t})+r\cdot \overrightarrow{D}\\ \overrightarrow{D}=\left\{\begin{array}{l}{X}_j(\mathrm{t})-X_i(\mathrm{t})\hspace{0.17em}\hspace{0.17em}\mathrm{i}\mathrm{f}\hspace{0.17em}\hspace{0.17em}\mathrm{f}\mathrm{i}\mathrm{t}(X_i)\ge fit(X_j)\\ X_i(\mathrm{t})-X_j(\mathrm{t})\hspace{0.17em}\hspace{0.17em}\mathrm{i}\mathrm{f}\hspace{0.17em}\hspace{0.17em}\mathrm{f}\mathrm{i}\mathrm{t}(X_i)<\mathrm{f}\mathrm{i}\mathrm{t}(X_j)\end{array}\right.\end{array}$$

(7)

where fit is the fitness function, and j is selected arbitrarily.

The time control process (C) changes the type of movement between a swarm of jellyfish and an ocean current. The following equation can be used to figure out what its value is:

$$c(\mathrm{t})=\left|(1-\frac{t}{T_{\max }})\cdot (2\cdot r-1)\right|$$

(8)

where T_max is the maximum iterations. The procedure of JSO may be summarized as presented in Figure 3.

3. Results and Discussion

The considered data contain 28 data points,

Table 1. Effect of the different operating factors on the power output of the MFC [21].

Run	Catalyst Load at Anode/mg cm−2	Glycerol Conc./M	Conc. Anodic Electrolyte/M	Conc. Cathodic Electrolyte/M	Power Output/mW cm−2
1	0.5	0.5	1.5	0.5	1
2	0.5	1	2	0.5	1.1
3	0.5	1	1.5	0.25	2.2
4	0.5	1	1.5	0.75	1.1
5	0.5	1	1	0.5	0.95
6	0.5	1.5	1.5	0.5	0.96
7	1	0.5	1.5	0.25	1.95
8	1	0.5	1	0.5	1.48
9	1	0.5	2	0.5	1.65
10	1	1	1	0.75	1.9
11	1	1	2	0.25	2.44
12	1	1	1.5	0.5	2.65
13	1	1	1.5	0.5	2.6
14	1	1	2	0.75	2.43
15	1	1	1.5	0.5	2.77
16	1	1	1.5	0.5	2.77
17	1	1	1	0.25	2.1
18	1	1	1.5	0.5	2.77
19	1	1.5	2	0.5	2.1
20	1	1.5	1.5	0.75	2.32
21	1	1.5	1	0.5	1.4
22	1	1.5	1.5	0.25	1.64
23	1.5	0.5	1.5	0.5	0.8
24	1.5	1	1	0.5	1.38
25	1.5	1	1.5	0.75	2.2
26	1.5	1	1.5	0.25	1.4
27	1.5	1	2	0.5	1.3
28	1.5	1.5	1.5	0.5	1.7

. Twenty points are employed for training the model, and eight points are employed for testing it. The Mamdani model assigns input variables to output variables using fuzzy rules, and the result is a fuzzy set represented by membership functions. This is very helpful when language variables are used to characterize the system. The number of rules was 18 as illustrated in Figure 4. Next, the model was trained to meet a minor MSE, as illustrated in

Table 2. Numerical estimation of the constructed fuzzy model of MFC.

MSE			RMSE			R-Squared
Training	Testing	All	Training	Testing	All	Training	Testing	All
4.8 × 10−4	0.0260	0.0084	0.0219	0.1613	0.0917	0.9988	0.8706	0.9798

.

Referring to Table 2, the values of RMSE are 0.0219 and 0.1613, respectively, for training and testing. The R-squared values are 0.9988 and 0.8706, respectively. Compared with ANOVA, the RMSE decreased from 0.86 to 0.0917. Using fuzzy logic, the R-squared is raised from 0.93 to 0.9988 and from 0.8 to 0.8706, respectively, for both stages.

Figure 5 displays the 3D surface of the fuzzy model of the MFC. Figure 5 demonstrates the relations between the different input parameters, i.e., the concentration of glycerol, the loading of the anode electrocatalyst, the concentration of anode electrolyte, and the concentration of cathode electrolyte, on the power output of the glycerol MFC. As depicted from Figure 5, with the increase in the anode electrolyte concentration, the cell’s power increased and then decreased when boosting the concentration. This is clear at the different glycerol concentrations, cathode electrolyte concentrations, and anode catalyst loading. The highest power was recorded at intermediate values of anode catalyst loading of 1 mg/cm², cathode electrolyte concentration of 0.5 M, and glycerol concentration of 1 M. The growth in the anode catalyst loading followed by boosting the power output, but the further growth in loading beyond 1 mg/cm² resulted in decreasing the power output. The maximum power output was clear at 1 M of glycerol, 0.5 M of cathode electrolyte, and 1.5 M of anode electrolyte. Similarly, the cathode electrolyte demonstrated the best performance at an intermediate value of 0.5 M at the intermediate values of the other controlling factors. Glycerol also exhibited the best performance at an intermediate value of 1 M using the intermediate values of the other controlling factors.

When the anode electrolyte concentration increases, the performance increases because there are more OH⁻ groups at the anode surface, which are needed for the electrochemical oxidation of glycerol. This is shown by the following equation:

$${\mathrm{C}}_3{\mathrm{H}}_5(\mathrm{O}\mathrm{H}{)}_3+20 \mathrm{O}{\mathrm{H}}^{-}\stackrel{ }{\to }3 \mathrm{C}{\mathrm{O}}_3^{2-}+14 {\mathrm{H}}_2\mathrm{O}+14 {\mathrm{e}}^{-}$$

(9)

Therefore, the initial increase in the anode electrolyte concentration increased the performance; however, after 1.5 M KOH concentration, the performance decreased, which could be related to the unbalance between the available molecules of the OH⁻ and glycerol molecules on the catalyst surface [21,31]. Regarding the increase and reduction in the performance with boosting the cathode electrolyte concentration, the initial improvement in the performance would be related to the improved ionic conductivity of the cathode side; however, the increase in the concentration of the KOH would result in increasing the viscosity of the electrolyte [32], which in turn will hinder the mass transfer of the oxygen in the electrolyte. The power increases when increasing the glycerol (fuel) concentration to 1 M as the available glycerol molecules at the anode catalyst surface increase; thus, more power is obtained. However, at higher glycerol concentrations, catalyst poisoning can occur, and thus, the performance decreases [33]. Also, the increase in the anode catalyst loading improved the performance as more active sites become available for performing the electrochemical oxidation of glycerol; however, at higher catalyst loading a thick catalyst layer will be formed, and limited access to the active sites can occur; therefore, performance decreases.

In this work Gaussian MFs are adopted. The advantages of Gaussian MFs include the following three factors. (1) Smoothness: Gaussian MFs lead to smooth and continuous membership functions, which can be desirable in certain applications such as control systems. (2) Flexibility: Gaussian MFs can be easily adjusted to fit different datasets by changing the mean and variance parameters. (3) Suitability for modeling bell-shaped distributions: Gaussian MFs are ideal for modeling input data that follow a bell-shaped distribution (e.g., normal distribution). The fuzzy model’s input membership function (MF) shapes are demonstrated in Figure 6. It is operated on the domain of all possible values. In a Gaussian MF, the peak of the Gaussian function is often given a high intensity color, such as red, to represent a high degree of membership. This color gradually fades as the input value moves away from the peak, indicating a lower degree of membership. This allows for a quick visual understanding of the input-output relationship of the system and can be useful for interpreting the behavior of a fuzzy inference system. The predicted versus measured data of fuzzy model are given in Figure 7. The good matching between the estimated and measured data demonstrates the consistency of the constructed model. Figure 8 illustrates that the fuzzy model predictions are spread around the diagonal line with 100% precision. If the plotted predictions of the fuzzy model for both training and testing data are closely spread around the diagonal line that represents 100 percent accuracy, it suggests that the model is performing well and accurately predicting the output for the input data. The closeness of the plot points to the diagonal line indicates that the model has a high level of precision and is able to closely match the target values. However, it is important to note that achieving 100% accuracy is unlikely in practice, and it is possible that there may be some degree of error or variability in the predicted values even if they are closely clustered around the diagonal line. In addition, the model’s performance should also be evaluated using appropriate statistical measures such as the MSE and/or RMSE to provide a quantitative assessment of its accuracy. The values of MSE and RMSE are presented in Table 2.

Parameter Identification

To determine the best values of the four controlling parameters of the MFC to boost the power density of the MFC, JSO is applied to do the parameter identification process. Thus, in addition to obtaining a reliable fuzzy model of MFC, JSO is utilized to find the optimum values for controlling input parameters. The statement of the optimization procedure can be expressed as:

$$x=\underset{x\in R}{\arg }\min \left(y\right)$$

(10)

where x represents input variables, and y is the power density.

The JSO must be run several times before its results can be accepted. This is to make sure that the solution does not emerge by accident. So, the JSO was done 30 times, and the results are shown in Figure 9. Figure 9a shows the most important objective function (OF) for each of the 30 runs. The lowest, highest, average, and STD values are 2.9432, 3.0293, 3.0035 and 0.0241, respectively. This shows the accuracy of the JSO. Figure 7b displays the change of the best cost function during 30 runs. The JSO requires about 35 iterations to achieve the optimum solution. The convergence of particles is demonstrated in Figure 9c–f for the concentration of cathode electrolyte, loading of anode electrocatalyst, concentration of anode electrolyte, and glycerol concentration, respectively. Referring to Figure 9c–f, the particles converge to 0.59, 1.6, 1.63 and 1.4, respectively, for the concentration of cathode electrolyte, loading of anode electrocatalyst, concentration of electrolyte, and glycerol concentration.

The optimized result achieved through the proposed fuzzy modeling and the JSO has been compared with measured data and response surface methodology (RSM) as shown in

Table 3. Best values of controlling variables and cost function.

Strategy	Concentration of Glycerol Fuel (M)	Concentration of Anode Electrolyte (M)	Loading of Anodic Electrocatalyst (mg/cm2)	Concentration of Cathode Electrolyte (M)	Power Density (mW/m2)
Experimental [21]	1.0	1.5	1.0	0.5	2.77
RSM [21]	1.07	1.62	1.12	0.69	2.79
JSO and Fuzzy	1.4	1.63	1.16	0.59	3.03

.

Considering Table 2, the JSO and fuzzy modeling increased the power density of the MFC by 9.38% and 8.6%, respectively, compared to the measured data and RSM.

4. Conclusions

The aim of this paper is to enhance the power density of a microfluidic fuel cell (MFC) by integrating fuzzy modeling and the jellyfish search optimizer (JSO). The proposed method consists of two stages. First, a fuzzy model was created using a measured dataset to simulate the power density of the MFC based on the operating parameters. The root mean squared error (RMSE) values for training and testing were 0.0219 and 0.1613, and the R-squared values were 0.9988 and 0.8706. In comparison to ANOVA, the RMSE was reduced from 0.86 to 0.0917. Thanks to fuzzy modeling, the R-squared values were increased from 0.93 to 0.9988 and from 0.8 to 0.8706 for the training and testing phases, respectively. Next, the fuzzy model was integrated with the JSO to identify the optimal levels of glycerol concentration, anode electrocatalyst loading, anode electrolyte concentration, and cathode electrolyte concentration. The combination of fuzzy modeling and the JSO increased the power density of the MFC by 9.38% and 8.6% compared to the experimental and RSM, respectively.