An Adaptive Joint Operating Parameters Optimization Approach for Active Direct Methanol Fuel Cells

Abstract

The operating parameters of the active direct methanol fuel cell (DMFC) are essential factors that affect cell performance. However, it is challenging to maintain the optimal maximum output power density due to the system’s complexity, the operating conditions variation, and the correlations between those parameters. This paper proposes an adaptive joint optimization method for fuel cell operating parameters. The methods include the adaptive numerical simulation of the operation parameters and the optimization for fuel cell performance. Based on orthogonal tests, a BP neural network is used to build a performance evaluation model that can quantify the influence of the operating parameters on fuel cell performance. The optimal combination of operating parameters for the fuel cell is obtained by a whale optimization algorithm (WOA) through the evaluation model. The experimental results show that the evaluation model could respond accurately and adaptively to the cell operating conditions under different operating conditions. The optimization algorithm improves the maximum power density of the fuel cell by 8.71%.

1. Introduction

Under the background of large-scale global decarbonization in recent years, renewable energy technologies have developed rapidly. Fuel cell technologies directly convert chemical energy into electrical energy, avoiding the loss of electrical energy due to combustion and energy storage, and have broader commercial applications prospects [1,2]. Among the fuel cell technologies, the direct methanol fuel cell (DMFC) uses liquid methanol as fuel, which has many advantages such as smaller size, lightweight, high power density, faster start-up, lower pollution, and easy fuel replacement, etc. It has attracted attention in academics and industries in the mobility power field [3,4,5,6].

To improve fuel cell performance, extensive research has been conducted on structural design, material improvement, MEA membrane catalyst preparation, and parameters optimization [7,8], where the operating and structural parameters of DMFC showed significant effects on power density and energy efficiency [9]. The operating parameters mainly include methanol concentration, flow rate, air flow rate, and temperature [10]. The optimal control of the operating parameters of the cell is an effective way to improve the power density and efficiency of the fuel cell [11]. Seo et al. [12] investigated the methanol penetration rate and efficiency of the DMFC under different operating parameters. The results show that increased methanol concentration and methanol flow rate increased the current density. Furthermore, the methanol crossover was increased by high electro-osmotic drag through the membrane from active electrochemical kinetics as the current density increased. Chen et al. [13] investigated the effects of methanol concentration, methanol flow rate, oxygen flow rate, and cell temperature on DMFC performance for DMFC systems with different anode catalysts. Therefore, the methanol concentration, methanol flow rate, air flow rate, and cell temperature in the DMFC significantly impacted the cell performance and brought about problems such as methanol permeation and catalyst poisoning that affects the cell performance.

However, the active DMFC could not perform optimally when a single structural improvement or parameter adjustment existed [14,15]. Moreover, extra verification will increase the experiment costs when multiple parameters ought to be adjusted [16,17]. DMFC performance was directly affected by methanol concentration, methanol flow rate, air flow rate, and temperature, and the development of a model that reflected the relationship between its operating parameters and performance was the focus of this study. The current semi-empirical model [18], response surface methodology (RSM) [19], steady-state one-dimensional non-isothermal semi-empirical model [20], quasi-two-dimensional isothermal model [21], and Euler–Euler model [22] could accurately and rapidly reflect the direct connection between operating parameters and cell performance [23]. Lee et al. [24] used a simulator to analyze the impact of DMFC operating parameters and thermal management on the system to develop active control strategies for DMFC temperature, methanol crossover, and water recovery by optimizing system components and operating conditions. Tang et al. [25] applied a neural network identification approach to model the optimization of a highly nonlinear thermal management system for direct methanol fuel cells based on experimental data for DMFC systems. Guicheng et al. [26] analyzed the mechanism of influence on DMFC performance by studying the operating parameters of a three-electrode system.The three-electrode system not only reflects the cell methanol permeation but also demonstrates that the main factor affecting the optimal flow of methanol and oxygen is the operating temperature. Jiang et al. [27] constructed a two-dimensional, two-phase, steady-state DMFC model that enables radial and axial oxygen transport to carbon nanotubes in the cathode catalyst layer and verifies the model’s accuracy through simulations. Yang et al. [28] proposed a joint operation method for multi-parameter co-design of DMFC systems, which improved DMFC performance. Cao et al. [29] designed an active DMFC control system to achieve high performance and fuel efficiency by controlling the methanol concentration, active DMFC operating temperature, and the methanol rate entering the an and air entering the cathode.

Moreover, introducing intelligent optimization algorithms may reduce the uncertainty caused by experiments [30,31] and improve the accuracy of the optimization of operating parameters [32,33]. Therefore, this study proposes an evaluation model for active DMFC operating parameters based on the BP neural network model. A novel optimization algorithm verifies the accuracy of the result, which could further improve the cell performance.

2. Methodology

2.1. Data Acquisition

The active DMFC test platform consists of five parts: DMFC single cell, methanol supply system, air supply system, temperature control system, and measurement system, as shown in Figure 1. A single cell structure consists of 5 cm × 5 cm transparent PMMA endplates, PTFE gaskets, flow field plates, and an MEA is shown in Figure 2.

The cell is fed with methanol of different concentrations and flow rates through a peristaltic pump (LM60, flow rate 0∼1420 ml/min). The air is supplied through a gas compressor (OTS-550-8L) and an airflow meter (MF-4003). A hot air box (101-OA) is used to heat the cell to a constant operating temperature. An electronic load (IT8510) is used to perform the controllable discharge tests. This work focuses on the parameters tuning for methanol concentration $C_{me}$, flow rate $F_{me}$, air flow rate $F_{air}$, and fuel cell operating temperature T. The parameters initialization is shown in

Table 1. Parameters initialization.

Parameter	Lower Limit	Upper Limit
$C_{me}$	$0.25$ mol/L	2 mol/L
$F_{me}$	$0.5$ ccm	$4.5$ ccm
$F_{air}$	200 ccm	1000 ccm
T	30 °C	70 °C

.

The MEA is activated under constant current discharge conditions to restore sufficient hydration. Wetting activation is performed by passing distilled water (1 ccm) and air (200 ccm) to the anode and the cathode, respectively. The cell temperature is maintained at 70 °C in the thermostatic drying oven for three hours. Then, the discharge activation is performed by feeding the anode and the cathode with methanol solution (1 mol/L at 2 ccm) and air (300 ccm), respectively. After one hour of constant discharge, the methanol solution is exhausted, the auxiliary system is turned off, and the cell is left to relax for eight hours.

The flow plate is made of 5 cm × 5 cm 304 stainless steel, and the flow field is a serpentine flow channel. The opening rate of the flow field is 53.92%, the width of the flow channel is 0.8 mm, the depth of the flow channel is 20 mm, the total length of the flow channel is 20 mm, and there are 13 flow channels. Its structure is shown in Figure 3.

2.2. Orthogonal Test

A comprehensive parameters coupling experiment is conducted by varying the operating parameters and using an orthogonal test. A total of 20 sets of experiments are conducted on the effect of single-parameter characteristics on the cell performance by varying the operating parameters. The orthogonal experiments are performed according to the parameter work range set in Table 1, which includes four operating parameters with five gradients (for each parameter), as shown in

Table 2. Operating parameter candidates for orthogonal tests.

Parameters	Values
$C_{me}$ (mol/L)	0.50	0.75	1.00	1.25	1.50
$F_{me}$ (ccm)	0.5	1.5	2.5	3.5	4.5
$F_{air}$ (ccm)	200	400	600	800	1000
T (°C)	30	40	50	60	70

and

Table 3. Orthogonal array for 25 experiments with four variables and five levels.

No.	${\mathit{C}}_{\mathit{me}}$ (mol/L)	${\mathit{F}}_{\mathit{me}}$ $\left(\mathbf{ccm}\right)$	${\mathit{F}}_{\mathit{air}}$ $\left(\mathbf{ccm}\right)$	T (°C)	No.	${\mathit{C}}_{\mathit{me}}$ $(\mathbf{mol}/\mathbf{L})$	${\mathit{F}}_{\mathit{me}}$ $\left(\mathbf{ccm}\right)$	${\mathit{F}}_{\mathit{air}}$ $\left(\mathbf{ccm}\right)$	T (°C)
1	0.25	0.5	200	30	14	0.75	3.5	200	70
2	0.25	1.5	800	50	15	0.75	4.5	800	40
3	0.25	2.5	400	70	16	1.00	0.5	1000	50
4	0.25	3.5	1000	40	17	1.00	1.5	600	70
5	0.25	4.5	600	60	18	1.00	2.5	200	40
6	0.50	0.5	800	70	19	1.00	3.5	800	60
7	0.50	1.5	400	40	20	1.00	4.5	400	30
8	0.50	2.5	1000	60	21	1.50	0.5	600	40
9	0.50	3.5	600	30	22	1.50	1.5	200	60
10	0.50	4.5	200	50	23	1.50	2.5	800	30
11	0.75	0.5	400	70	24	1.50	3.5	400	50
12	0.75	1.5	1000	30	25	1.50	4.5	1000	70
13	0.75	2.5	600	50

.

Through the orthogonal experimental table, it is found that 25 experiments are required for five gradients of four parameters. After completing 25 experiments, the methanol concentration settings are first changed to obtain 25 sets of experimental data by setting five gradients from 0.6 mol/L at 0.3 mol/L intervals. Next, the methanol flow rate setting is changed, and 25 sets of experimental data are obtained by setting five gradients from 1 ccm to 0.5 ccm intervals. Finally, the air flow rate is changed and 25 sets of experimental data are obtained by setting five gradients from 100 ccm to 200 ccm intervals. Therefore, a total of 100 sets of experiments are conducted as the data base for building the BP neural network model.

We use a radial basis function (RBF) model for evaluating the performance of DMFC based on the orthogonal experiments [34]. Different physical quantities are involved in each studied parameter and vary significantly in order of magnitude from each other. For example, the airflow rate can reach 1000, while the methanol concentration is only 0.5. Therefore, to prevent numerical problems (physical quantities with low values are swamped in the calculation) and improve the model convergence, it is necessary to preprocess the sample data by normalization [35]. The following surrogate model described by Equation (1) is developed based on RBF interpolation:

$$\widehat{y}\left(x\right)=\sum _{i=1}^N{\alpha }_i\phi \left(∥x-x_i∥\right)$$

(1)

where $\phi \left(∥x-x_i∥\right)$ is the basis function, the training data point $x_i$ is the center of the basis function $\phi \left(∥x-x_i∥\right),∥x-x_i∥$ is the distance in space between x and the ith sample $x_i$, and ${\alpha }_i$ is the weigh factor. The characteristics of the RBF model are determined according to the basis function (Gaussian):

$$\phi \left(r\right)=exp\left(-\frac{r^2}{2{\delta }^2}\right)$$

(2)

where $r^2$ is the distance from the sample point to the center point and ${\delta }^2$ is the variance.

2.3. Experimental Analysis

Twenty sets of single-parameter characterization experiments and 100 sets of orthogonal experiments are performed according to each set of determined operation parameters ($C_{me}$, $F_{me}$, $F_{air}$, T). The cell is discharged with constant current, and the current is gradually increased at intervals of 5 mA within 20 s. The polarization and power density curves are shown in Figure 4.

Figure 4a shows the cell performances of different methanol concentrations. The results show that the performance increases gradually as the methanol concentration increases from 0.25 mol/L to 0.75 mol/L. It decreases sharply at 1 mol/L, then recovers when the concentration increases to 1.5 mol/L. The maximum power is inferior to that at 0.75 mol/L because when the methanol concentration increases, intensifies the methanol permeation and causes irreversible poisoning of the cathode catalyst, limiting the cell power output under a medium flow rate. The performances at different methanol flow rates are shown in Figure 4b. It can be seen that the cell power density increases as the flow rate increases from 0.5 ccm to 2.5 ccm and decreases from 3.5 ccm to 4.5 ccm. A specific methanol flow rate reduces the bubbles generated in the flow channel, preventing the methanol from contacting the MEA film and reducing the cell performance. The cell reaction generates heat, and the increase in temperature enhances the catalyst activity and thus improves cell performance.

On the other hand, when the methanol flow rate reaches a threshold, the flow takes out the heat inside the cell, reducing the catalyst activity and decreasing the cell performance. Figure 4c shows the performance comparison at different air flow rates. The cell performance decreases as the airflow rate increases. The results in Figure 4d show that the cell performance stability increases with the fuel cell operating temperature thanks to the catalyst activity. However, the cell performance decreases to 70 °C. The reason is that the methanol evaporates faster under high temperatures, which rapidly generates air bubbles in the flow channel to obstruct the methanol flow. On the other hand, it increases the methanol concentration to produce methanol permeation to decrease the stability.

It can be seen in Figure 4 that different parameters impact the cell performance of the active DMFC, and those parameters affect each other. Therefore, orthogonal experiments are employed with multi-parameter coupling and adaptive optimization to find the optimal parameter combinations.

2.4. Surrogate Models Prediction Performance

Based on the standard operating conditions set in Table 2 and Table 3, orthogonal experiments are performed with 100 valid sets of results, and we count the maximum power densities measured in each set of experiments. Then, the four input parameters ($C_{me}$, $F_{me}$, $F_{air}$, T) and one output parameter (the maximum power density p corresponding to each set of experiments) are taken as a new set of data. Finally, a total of 100 data items are obtained. These 100 data items are randomly divided into a training set and a test set at a ratio of 3:1, namely the training data items correspond to 75 and the test data items correspond to 25, which are used for training and verification of the ensemble models.

Figure 5 shows the predict set and test set of the model. Good fitting results can be viewed from the Figure, the $R^2$ values are 0.9892 and 0.9802, respectively. Such high correlations between the predicted and simulated data show the accurate prediction performance of the surrogate models.

Three sets of experimental designs and corresponding results are randomly selected from the experimental results, as shown in

Table 4. Selected operating parameters for performance evaluation.

${\mathit{C}}_{\mathbf{me}}$ (mol/L)	${\mathit{F}}_{\mathbf{me}}$ (ccm)	${\mathit{F}}_{\mathbf{air}}$ (ccm)	T (°C)
1.00	2.5	600	30
0.75	0.5	200	30
2.00	3.5	400	50

.

The simulated polarization curves are compared with the experimentally obtained ones, as shown in Figure 6. The black curves in the figure are the polarization curves based on three sets of experiments by taking 15 current density values from 5 mA/cm² to 75 mA/cm². The red ones are the polarization curves simulated by the RBF model based on the same input values. The results show that the adaptive simulation model can well adapt and define different values of multiple parameters in the design space.

3. Experiment

3.1. Operating Parameters Optimization

In this study, we use a DMFC performance evaluation model based on orthogonal tests with methanol concentration $C_{me}$, methanol flow rate $F_{me}$, air flow rate $F_{air}$, fuel cell operating temperature T as the input, and the power density P as output. Moreover, the RBF model is developed to take into account the correlations among the input quantities to find the optimal solution to a four-dimensional problem. The whale optimization algorithm (WOA) is introduced for model construction to find the maximum power density under the optimal DMFC operating parameters combination [36]. An RBF model is built as the objective function of WOA. The process is illustrated in Figure 7.

3.2. Whale Optimization Algorithm and Joint Optimization

WOA is used to solve the continuum optimization problem built from the RBF model. In this study, since the optimal design is not known prior, in the first generation, when the algorithm starts, the optimal or near-optimal solution is first searched randomly in the global solution space within the range of parameter values. During the subsequent iterations, depending on the parameter settings, the choice is made to continue searching for feasible optimal solutions in the global solution space or approach the optimal candidates in the previous generation to find feasible solutions around. At the end of the iteration, the output is used to update the RBF model, and the current optimal result is recorded. The WOA search process is repeated sequentially and terminated if the preset number of executions is reached. The RBF model and WOA are used to find the four optimal input parameters and their corresponding output power P.

The whale optimization algorithm (WOA) was proposed by Mirjalili [37]. The first mechanism of the local search phase is encircling predation. Its position-update is described by:

$$\left\{\begin{array}{c}X\left(t_{iter}+1\right)=X^{*}\left(t_{iter}\right)-A·D\hfill \\ D=\left|C·X^{*}\left(t_{iter}\right)-X\left(t_{iter}\right)\right|\hfill \\ A=2a·r_1-a\hfill \\ C=2r_1\hfill \\ a=2\left(1-\frac{t_{iter}}{T_{max}}\right)\hfill \end{array}\right.$$

(3)

where $X^{*}\left(t_{iter}\right)$ is the optimal individual of the current population, namely the location of the optimal candidate solution; $x(t_{iter}+1)$ is the location of the next generation population individual, and $x\left(t_{iter}\right)$ is the location of the current population individual. D denotes the distance between the current population optimal individual and other individuals, A is the convergence factor, C is the oscillation factor, $r_1$ is a random number within (0,1), and a is the wandering factor.

In addition to encircling predation, the local search phase can also use spiral bubble search.

$$\left\{\begin{array}{c}X\left(t_{iter}+1\right)=D^{\prime }·e^{b{r}_2}·cos\left(2\pi r_2\right)+X^{*}\left(t_{iter}\right)\hfill \\ D^{\prime }=\left|X^{*}\left(t_{iter}\right)-X\left(t_{iter}\right)\right|\hfill \end{array}\right.$$

(4)

where $D^{\prime }$ denotes the distance between the optimal individual of the current population and the other individuals; b is the logarithmic spiral shape coefficient, usually taken as 1; and $r_2$ is a random number within $[-1,1]$.

The random search mechanism takes the value of the convergence factor A as the judgment criterion. When $\left|A\right|\ge 1$, the whale individual will deviate from the candidate solution position for the global search of the algorithm, to improve the search capability of the WOA and stop the algorithm from falling into the local optimum.

$$\left\{\begin{array}{c}X\left(t_{iter}+1\right)=X_{rand}\left(t_{iter}\right)-A·D^{″}\hfill \\ D^{″}=\left|C·X_{rand}\left(t_{iter}\right)-X\left(t_{iter}\right)\right|\hfill \end{array}\right.$$

(5)

where $X_{rand}\left(t_{iter}\right)$ is the location of a random whale individual in the current population, and $D^{″}$ denotes the distance between a random individual and other individuals in the current population.

Each of the two mechanisms in the WOA local search phase have a 50% probability of occurring during the search. Therefore, let p be a random number within (0,1), add a judgment criterion into Equations (3) and (4), and synthesize Equation (5) to obtain the overall WOA location update formula, as shown in Equation (6a–c).

$$X\left(t_{iter}+1\right)=\left\{\begin{array}{ll}{X}^{*}\left(t_{iter}\right)-A·D,p<0.5,\left|A\right|<1& \mathrm{(6a)}\\ X_{rand}\left(t_{iter}\right)-A·D^{″},p<0.5,\left|A\right|\ge 1& \mathrm{(6b)}\\ D^{\prime }·e^{b{r}_2}·cos\left(2\pi r_2\right)+X^{*}\left(t_{iter}\right),p\ge \mathrm{0.5}& \mathrm{(6c)}\end{array}\right.$$

Within the set number of iterations, based on the changes in the values of p and A, the WOA uses the above three mechanisms to update the individual positions continuously, and find the position of the feasible optimal solution to complete the optimization goal and end the algorithm cycle, as summarized in Algorithm 1.

Algorithm 1 WOA algorithm

1: Initializing the RBF model 2: X* the best position 3: P* = the best output of RBF 4: k = 1 5: while$k<$ Maximum number of executions do 6:  Initialize the whales population $X_i(i=1,2,3\dots 50)$ 7:  Calculate the fitness of each search agent 8:  Update $X^{*}$ and $P^{*}$ if there is a better solution 9:  $t=1$ 10:  while $t<$ maxmum numer of iterations do 11:   for each search agent do 12:    Update a, A, C, $r_1$, $r_2$ and p 13:    if  $p<0.5$  then 14:     if  $\left|A\right|<1$  then 15:      Update the position of search agent by Equation (6a) 16:      else if  $\left|A\right|\ge 1$  then 17:      Update the position of search agent by Equation (6b) 18:      end if 19:    else if  $p>0.5$  then 20:      Update the position of the search agent by Equation (6c) 21:    end if 22:   end for 23:   Check if any search agent goes beyond the search space and amend it 24:   Update $X^{*}$ and $P^{*}$ if there is a better solution 25:   $t=t+1$ 26:  end while 27:  Find 10 best outputs of final iteration 28:  Replace 10 worst outputs of original data 29:  Pbest = the best output of all 100 data 30:  Update RBF model return Pbest 31:  $k=k+1$ 32: end while 33: Select all Pbest in turn to plot the output curve

The details on the optimal design of multi-type parameters in DMFCs are explained as follows.

• A total of 100 sets from the orthogonal tests are sorted in descending order in terms of output power (normalized).
• We select the data from these 100 initial tests and build the RBF model. The model serves as the objective function of the WOA. We set the output of 100 data sets as P and the input as X=$\{C_{me},F_{me},F_{air},T\}$. The range of each input quantity is shown in Table 1. We set the global maximum output power as $P^{*}$ and its input as $X^{*}$.
• Based on the RBF model, the WOA is used to find the best input values. According to the range of input parameters, in the first generation of the WOA, we use one set of RBF model data as one WOA individual. Then, we randomly generate 100 individuals as the initial population by the WOA and screen out an individual with the highest output from those individuals. We assume that the output power of this individual is better than the original $P^{*}$. In that case, the original $P^{*}$ will be replaced by the output power of this individual, and the input position of $P^{*}$ is used as the current WOA global optimal position $X^{*}$.
• We generate the next generation population of WOA according to the overall WOA location update formula, continue to find the individual with the highest output power, and then update the global optimization position $X^{*}$ and the maximum output power $P^{*}$. We set the algorithm to run 50 iterations. When the algorithm loop ends, we screen out 20 individuals from the final 100 individuals of the WOA with the highest output power.
• We screen 20 datasets from the original 100 datasets with the lowest output power and replace them with the 20 WOA individuals obtained in Step 4. We note the highest output power in those 100 datasets as Pbest.
• We update the RBF model with newly obtained 100 datasets and repeat Step 3. The procedure is repeated sequentially 150 times.

4. Results and Discussion

In this study, numerical and experimental tests perform on joint optimization simulation runs to accurately assess the model performance. The terminal condition of multi-type parameters optimization is defined so that more than 10 adjacent samples have similar input and output values. The joint optimization starts with a model built from 100 experimental datasets and ends at 150 cycles.

As shown in Figure 8, the black horizontal line indicates the best power density value of 66.53 mW/cm² obtained in 100 orthogonal tests. One can see the fluctuation during the global optimization search.After 100 oscillations between 45 and 75 mW/cm², the final results are stable and all above 70 mW/cm². The results show that the optimally selected parameters combination by the algorithm can provide higher max power densities than the orthogonal tests. The maximum power density stabilizes when the number of iterations reaches 86. We validate the simulated results by implementing the optimal parameter settings in the test platform for 15 sets of data from 86 to 100 iterations, and the results are listed in

Table 5. Optimization search results and experimental validation results for iterations from 86 to 100.

No.	${\mathit{C}}_{\mathit{Me}}$ (mol/L)	${\mathit{F}}_{\mathit{Me}}$ (ccm)	${\mathit{F}}_{\mathit{Air}}$ (ccm)	T (°C)	Power Density (mW/cm2)
					Simulation	Experiment
86	1.27	2.58	800	62	70.16	68.61
87	1.27	1.64	300	70	71.67	71.91
88	0.94	3.62	300	66	72.32	70.56
89	0.94	3.62	400	70	71.24	71.67
90	1.58	2.58	800	57	71.35	69.09
91	1.58	1.77	200	68	70.87	70.73
92	1.58	3.62	500	62	71.68	69.71
93	1.49	1.66	670	69	71.62	71.09
94	1.49	2.58	300	52	71.68	69.86
95	1.49	2.58	800	70	72.16	72.38
96	1.27	3.11	300	62	71.52	69.72
97	1.27	3.11	400	69	71.75	71.61
98	0.94	1.64	670	70	71.85	70.39
99	0.88	1.64	670	70	71.49	71.90
100	0.88	2.58	300	62	71.35	69.92

.

The maximum power density of the optimization results is 72.32 mW/cm², which is 8.71% higher than the orthogonal test results. The performances are compared in Figure 9.

The maximum deviation of the validation results compared with the optimization search results is 3.17%, the minimum deviation is only 0.21%, and the average deviation is 1.51%. The validation results are higher than 66.53 mW/cm² in the orthogonal experimental test, and the average power density of the validation results is 70.61 mW/cm², which is a significant improvement in fuel cell performance. The results show that the error between the optimization search results and the experimental verification results is small, and WOA accuracy and stability are high. By changing the different coupling cases among the operating parameters, the optimal power density of the active DMFC can be effectively improved, and its operation stability can be guaranteed under the unified MEA film and pole plate parameters. When the methanol concentration is high (above 1 mol/L), methanol permeation can be reduced by selecting a higher methanol flow rate (above 3 ccm). Higher air flow rates (above 800 ccm) reduce the cell operating temperature, but the effect of this factor can be reduced by external temperature supplementation and effectively reduce cathode flooding and polarization.

5. Conclusions

This paper proposes an adaptive joint simulation optimization method based on numerical simulation to achieve the collaborative design of direct methanol fuel cell operation parameters and power density improvement. The results indicate the following:

• Tests were conducted for operating parameters to verify their impacts on cell performance. Based on 100 orthogonal test results, an RBF model was built as the objective function for the WOA, which can reflect the correlations among the following operating parameters: methanol concentration $C_{me}$, methanol flow rate $F_{me}$, air flow rate $F_{Air}$, fuel cell operating temperature T, and the output power density P.
• An adaptive joint optimization method was proposed based on WOA. The optimized parameters were obtained by searching for the best input parameters combination within the inputs variation range. The power density was increased by 8.71%, which indicates that the proposed method could positively improve the performance of the active direct methanol fuel cell.

In future study, we would investigate two more indicators, the cell energy conversion efficiency and methanol permeability under the proposed optimization framework.