# An Intelligent Approach for Contact Pressure Optimization of PEM Fuel Cell Gas Diffusion Layers
## 4 Results and Discussion
### Optimization of Packing  
Compromise should be made between the contact resistance and the porosity by means of varying the clamping force on the fuel cell on the premise of no leakage. The optimal clamping force depends on the structure, the material of BPP, GDL, and MEA, as well as the target operating voltage. In this study, 0.5 MPa is set as the object contact pressure for SGL-10-BB GDL to achieve optimum current density under 0.5-0.6 V operating voltage [11]. The optimization problem is defined as  
Find:  
\[X=(F_{1},F_{2},F_{3},F_{4},L_{1},L_{2},L_{3})\]  
Minimize:  
\[P(X)=\frac{\sum_{i=1}^{30}\left|P_{i}(X)-0.5\right|}{30}\]  
Subject to  
\[\left\{\begin{array}{l}0\ \leq\ F_{1},\ F_{2},\ F_{3},\ F_{4}\ \leq\ 3000\ \mathrm{N}\\ (91,\ 0)\ \leq\ L_{1}(x,\ y)\ \leq\ (135,\ 0)\ \mathrm{mm}\\ (32,\ 0)\ \leq\ L_{2}(x,\ y)\ \leq\ (77,\ 0)\ \mathrm{mm}\\ (8,\ 0)\ \leq\ L_{3}(x,\ y)\ \leq\ (18,\ 0)\ \mathrm{mm}\ \mathrm{or}\ (0,\ 8)\ \leq\ L_{3}(x,\ y)\ \leq\ (0,\ 36)\ \mathrm{mm}\end{array}\right.\]  
where \(X\) is the set of design variables. Since the objective contact pressure on the GDL is set as 0.5 MPa, the corresponding pressure on the gasket, which is much stiffer than the GDL, should be high enough to avoid leakage so there is no need to consider the seal problem in this optimization, neither as a constraint nor as the lower limit of clamping force. The RBFNN-based agent model is used in the fitness function of GA. The population size is 40, the probability of crossover is 0.7, the probability of mutation is 0.01, the maximum generation number is 100, and the generation gap is 0.9. The convergence process of optimization and final optimal results are given in Figure 12.  
The optimum combination of design parameters obtained is \(X=(2146.63,1750.73,325.51,2524.93,107.47,44.62,35.85)\), as shown in Figure 13 in red. It can be seen that the positions of Bolts 1 and 2 are moved towards the right side, and Bolt 3 is moved to the central line. The clamping force of Bolt 4 is the largest, followed by Bolt 1 and Bolt 2. The clamping force of Bolt 3 is far smaller. Additionally, the optimized position of Bolt 3 is very close to Bolt 4. For the sake of engineering practice, Bolt 3 was removed from the packing, which can also lower the cost and lighten the weight of the fuel cell (in total, 4 bolts were removed for a full fuel cell).  
The final optimum packing design was fed back to the FE model, and the corresponding contact pressure on GDL was calculated. For comparison, the clamping force of origin design was also adjusted to reach a comparable level of the mean contact pressure to the optimized design. The contours of contact pressure of the original and optimized packing designs are given in Figure 14. As we can see, the high contact pressure at the four corners is significantly reduced by 24% from 2.12 to 1.61 MPa in the optimized case. At a similar mean contact pressure level, the maximum value decreases and the minimum value increases. The standard deviation of contact pressure decreases from 0.071 to  
Figure 11: Error contour of contact pressure prediction on the gas diffusion layer (GDL).  
0.049 MPa by 31%. The apparent border between solid-contact and loose-contact areas is merged and the bad-contact area is eliminated. In other words, the uniformity of contact pressure on the GDL is greatly improved, with a well-designed equivalent pressure magnitude.  
Figure 12: Objective function values of (**a**) iterations and (**b**) individuals.  
Figure 13: Optimal packing design with 2.5-bolts in a 1/8 fuel cell.