## 3 Data Analysis
### Internal Resistance  
The internal resistance is a fundamental parameter in the analysis of batteries since their increase is one of the most accepted indicators of aging [11]. It is one of the measurements that is conventionally used to indicate the end of life of batteries, along with the fall in capacity and the increase in relaxation voltage drop [10].  
The internal resistance measurement was not foreseen initially due to the great variability of the values obtained and the low accuracy of the meter. However, they were noted at certain moments, only when they were consolidated changes in the values obtained, that is, when all the lithium cells were stabilized at a higher internal resistance value. Despite this, the number and accuracy of measurements are considered sufficient to study their evolution. The icharger [8] was used to take the measurements, as it allows to obtain the internal resistance value of each cell. The battery pack internal resistance was registered, as the sum of the cells' values.  
Finally, the internal resistance will be the parameter on which the prediction models will be focused. To study its evolution, its percentage increase in reference to its factory value, 35 m\(\Omega\)h (100%) will be considered.  
Figure 3 presents the evolution of the internal resistance in the nine Hacker Topfuel Eco-x batteries that were studied. The points indicate the internal resistance measurements taken at different moments of battery life. The lines are connected by polynomial for easier reading. Three different groups of batteries can be distinguished: for batteries 1, 2, 5, and 6, the internal resistance stays practically constant at the beginning of life, preceding an exponentially increasing growth. The growth of internal resistance can be linked to a deep discharge, such as for battery 1 in cycle 64, where a 4905 mAh discharge resulted in a 23% increase in internal resistance. Generally, the increase of internal resistance is mainly caused by contact loss, including the binder decomposition, current collector corrosion, the oxidation of conductive agent, and eventual loss of ionic concentration in electrolytes [12]. Some batteries (B3 and B4) encounter even a slight decrease of internal resistance during the beginning of life. The internal resistance of battery 4 dropped to 91.5% and remained stable for several cycles; one explanation is the good use of the cells. These batteries also happened to have the longest lifetime. This phenomenon is called passive electrode effect and is linked to [13].  
It is also interesting to study the case of battery 7, whose internal resistance began to grow considerably and early in use, presenting a different evolution from the rest. This was due to the poor use of this battery in the first few months and indicates poor battery health. This is the battery of the group with the shortest life (42 cycles) and it also ended up particularly swollen.  
Comparing the evolutions of all cells in the same battery, it can be seen that during much of the battery life, the resistances of the 10 evolve in approximately the same way. However, at the end of life, the cells that are located at the ends of the serial connections experience much greater rises than the cells located in the middle of the battery, because they are more in demand. Despite this phenomenon, no differences were identified inthe performance of these cells compared to the others, although it is not ruled out that they exist.  
Finally, the comparison of the evolution of internal resistance in all batteries shows, despite the comparable evolution of resistance increases, a clear link between the early increase of internal resistance and battery life. Hence, the slope of the internal resistance will be one of the parameters that will be used to compare aging, together with the number of cycles.