## 4 Results and Discussion
### Performance Prediction and Analysis  
The cell voltage uniformity (\(U_{cell}\)) (14) and _range_ (15) are parameters used for evaluating the stack voltage consistency. The cell voltage uniformity shows the dispersion of the voltages in cells, and it can be expressed as the following:  
\[U_{cell}=\sqrt{\frac{1}{N}\sum_{i=1}^{N}\left(V_{i}-\overline{V}\right)^{2}} \tag{14}\]  
The _range_ is the difference between the maximum and minimum cell voltages, illustrating the magnitude of the fluctuation in cell voltages. The _range_ is calculated as the following:  
\[Range=V_{max}-V_{\min} \tag{15}\]  
The tested voltage distributions and model predicted outputs of 100 cells with the same current density but different assembly torques are shown in Figure 6. All of the subgraphs have a longitudinal span of 0.02 V. The more significant the fluctuation within the same variation range of the longitudinal axis, the worse the cell's consistency. Figure 6(a2,b2,c2) compares the model's predicted outputs to the tested results of the 50 groups with two cells. Under different assembly torques, all of the model predictions match the experimental results closely, and the predicted outputs are always higher than the tested. The model predicts accurately when the assembly torque is 14 N.m. When the assembly torques are 12 N.m or 15 N.m, a voltage deviation about 2 mV is observed around the 95 th cell between the model and experiment results. When the assembly torque is 12 N.m, the graph has the lowest fluctuation amplitude, indicating that this is the best cell voltage consistency of the fuel cell stack. The comparisons of predicted and tested outputs in the 100 and 50 groups are shown in Figure 6(a1,a2,b1,b2,c1,c2). The model's predictions of the cell voltage distributions fit well with those of the experimental results and provide detailed information of individual cell voltages. Figure 6(a3,b3,c3) presents a comparison of the predicted outputs and experimental results of the 20 groups of cells each with 5 cells. As  
Figure 5: Predicted results with different fuel cell grouping strategies. (**a**) \(R^{2}\) for D1 (6-8-5-5); (**b**) \(R^{2}\) for D2 (6-8-5-10); (**c**) \(R^{2}\) for D3 (6-8-5-20); (**d**) \(R^{2}\) for D4 (6-8-5-50); (**e**) \(R^{2}\) for D5 (6-8-5-100); (**f**) \(MSE\) and _training time_ of the models. the number of the group (output dimension) is reduced, the predicted results lose detailed cell voltage information but retain the distribution trends of the stack for potential status evaluation of the fuel cell. The comparisons within Figure 6(a4,a5,b4,b5,c4,c5) show that more details of cell voltage distribution are lost as the number of groups decreases. The diagram should be a straight line parallel to the \(x\)-axis when there is only one group, showing only the average voltage of the 100 cells and missing the cell voltage distribution information. Figure 7 shows the cell voltages of model predictions and experiment findings with a constant assembly torque of 14 N.m but with varied grouping strategies and load cur  
Figure 6: Comparison between the model and experiment results of cell voltage distributions under the load current density of 1.5 A/cm\({}^{2}\) with different assembly torques: (**a1**,**a2**,**a3**,**a4**,**a5**) 12 N.m; (**b1**,**b2**,**b3**,**b4**,**b5**) 14 N.m; (**c1**,**c2**,**c3**,**c4**,**c5**) 15 N.m.  
rents. Under varying assembly torques, all predictions match the experimental results closely, and the predicted outputs are generally slightly greater than the tested ones. The cell voltage consistency decreases across all groups as the load current increases, and the fluctuation becomes more pronounced in the groups with more data groups. Furthermore, as the load current grows, the prediction accuracy improves. The detail losses in D3 (6-8-5-20), D2 (6-8-5-10), and D1 (6-8-5-5) described in Figure 6 persist.