# Online Model Adaption for Energy Management in Fuel Cell Electric Vehicles (FCEVs)
## 3 Results and Discussion
Figure 9 presents the reduction in the mean absolute error (MAE) for fuel cell power estimation in the AM and LM compared to the BM under identical driving conditions. This approach allows a statistical comparison of how the three maps correlate with the actual fuel cell output power. The MAE is calculated by determining the absolute difference between the predicted FC power estimated by the maps and the measured FC output power for all the data in one cycle. Remarkably, within just 1 h of operation, the LM achieves substantially lower estimation errors, obtaining an error reduction of 85% compared with the BM. In contrast, the AM reduces the error by around 81%. These results highlight that the BM does not provide an acceptably accurate estimation of fuel cell power and propagates errors that can affect powertrain control and overall vehicle performance. However, even though the AM achieves a similar error reduction to the LM, it relies on a complex calibration process that maps the aged FC model under steady-state conditions. This calibration process involves substantial effort to determine the actual level of ageing in the fuel cell, making it impractical for real-time control applications, suggesting the need for adaptation algorithms to improve calibration accuracy. As expected, by increasing the fuel cell power estimation accuracy, the EMS can also generate better control actions for the fuel cell, thus ensuring fuel savings. Moreover, Figure 10 shows the relative H2 consumption compared with that of the BM for each cycle and for the cumulative results of the 15 cycles. Due to the higher estimated error the BM provides, its poor estimation also affects the H2 consumption. When examining the LM, a reduction of 1.6% was observed in cycle 11 compared to the BM reference case, with a cumulative decrease of 1.2% across all cycles. Similarly, the AM exhibited a reduction of close to 1.7% in cycle 3 and a reduction of 1.3% for the cumulative consumption. It is important to note that the initial fuel consumption difference in the first cycle is influenced by variations in the battery state of charge that each of the three cycles reaches at the end of  
Figure 9: Reduction in the absolute error for the estimation of fuel cell power employing the Actual map and the Learning map compared to the Biased map. the cycle. In this context, AM significantly reduced hydrogen consumption due to higher battery energy depletion. However, considering long-term vehicle operation, it is possible to observe that after 45 h of vehicle use, the battery state of charge variation tends to be minimized, and the LM can overcome the cumulated H2 consumption and start to save fuel compared to the AM. Figure 11 illustrates the impact of the three different maps on EMS control actions for the fuel cell. The left chart shows the evolution of fuel cell output power during the last cycle. In contrast, the right chart depicts the histogram of operation conditions at various fuel cell output power levels. When using the BM, the EMS predominantly controls the fuel cell to operate at medium to low power levels. In contrast, both the AM and the LM guide the EMS to distribute fuel cell operation at mid-range power levels. The high frequency of fuel cell operation at low power with the BM can be attributed to the map's lower accuracy, as seen in Figure 8. Consequently, the EMS assesses that the BM can provide more power at low and medium current densities for the same current density and hydrogen consumption compared to the other two maps. The importance of fuel model accuracy is highlighted when comparing the histograms of the control action decisions provided by the EMS for each calibration. As the FC model accuracy increases, the EMS can improve the control actions, leading to an expected reduction in fuel consumption. An important parameter implemented in the algorithm is \(R\) (Equation (15b)). This parameter can regulate the Kalman gain of the adapter algorithm. In this case, the higher this value, the lower the gain.