# Online Model Adaption for Energy Management in Fuel Cell Electric Vehicles (FCEVs)
## 3 Results and Discussion
Employing a higher \(R\), it is expected that the algorithm slowly adapts the map, thus attributing higher reliability to the map previously implemented in  
Figure 11: Left plot: Evolution of the FC power signal for the 3 maps in the last cycle. Right plot: Histogram of the operating conditions of the fuel cell power in the driving cycle. Figure 10: Relative and cumulative H2 consumption comparing the Actual map to the Learning map. the EMS. On the contrary, for a lower \(R\), the higher the Kalman gain, so the EMS relies more on measuring the fuel cell output power. For this reason, it provides fast adaptation of the map. Figure 12 presents a parametric study of the proposed method using three different learning rates (\(1\times 10^{5}\), \(7.75\times 10^{4}\), and \(2.25\times 10^{4}\)), ranging from slow to fast learning rates, respectively. It is noticed that the proposed method can reduce the error in estimating the fuel cell power, presenting reductions close to 86% in some cycles. For all the learning rates, the proposed method generates strong adaptations to the map in the first 4 h of operation. Then, after this period, the medium and fast learning rates present better accuracy in the map adaptations. In addition, results with faster learning rates prove to be limited, as the algorithm is no longer able to reduce the error, but rather, it generates higher errors due to the dynamic operating conditions of the fuel cell, especially at higher loads. These limitations can be assigned to conditions wherein a sequence of measurements quickly adapt the map, but regardless, the algorithm is not capable of perfectly tracking all the deviations of the model due to the nonlinearity and complexity of the fuel cell system. The learning rate also impacted hydrogen consumption, Figure 13 shows the hydrogen consumption for each cycle and also the cumulative hydrogen consumption of all 15 cycles for the slow to fast learning rates. A similar pattern to the reduction in the estimation error in Figure 12 is observed. Furthermore, analysing the consumption cycle to cycle, it is observed that in some cycles, the fast learning rate can overcome the fuel consumption reduction of the medium and slow learning rates, e.g., cycle 3. However, it can also increase hydrogen consumption in some conditions, as observed in cycle 14. However, when comparing the cumulative consumption, the medium learning rate shows slight improvements compared to the other two. Figure 12: Reduction in the absolute error in the estimation of fuel cell power comparing three learning rates to the Biased map. Figure 13: Relative and cumulative H\({}_{2}\) consumption compared with the that of the Biased map for three learning rates. Finally, regarding the map adaptations with the three learning rates, it is demonstrated that the proposed method can guarantee improvements in map calibration up to a certain limit, constrained by the dynamic behaviour of the fuel cell. Furthermore, when comparing the overall performance of different learning rates using the BM as the reference, it becomes evident that in the case of the medium learning rate, the proposed method achieves slight improvements in estimation error and fuel savings considering the set of driving cycles compared to the cases of fast and slow learning rates. The evolution of map adaptations with three different learning rates is depicted in Figure 14, spanning from the initial operation to the fourth cycle. For all the LM cases, the initial calibration employed is the BM, followed by an ongoing map adaptation as the FCEV operates. All three cases demonstrate the ability to rapidly update the map to match the current output power provided by the FC in the first minutes of operation. In the cases of medium and fast learning rates, the algorithm can adapt the maps quickly, applying stronger corrections to the map for any changes in fuel cell conditions. Conversely, the algorithm applies smoother corrections when employing the low learning rate.