## 3 Materials and Method  
### Data Acquisition and Vehicle Setup  
For data acquisition, a PicoScope 2204A digital oscilloscope from the 2000 series was used, with a bandwidth of 10 MHz and 8-bit resolution at 100 MS/s, connected to a laptop running the PicoScope 6 application, version 6.14.23.5207. The probe tip was positioned directly on the battery terminals for voltage acquisition. The setup used for acquisitions was \(+/-\) 20 V and 100 ms/div, with a trigger for voltage drops below 10 V. The sampling rate in the BMS-BCM system available in vehicles was adjusted to 1 ms per point.  
Following the instrumentation, a Vehicle Start and Stop procedure was performed. At this stage, battery rest was preconditioned for at least 12 h with the vehicle at rest after use. During this stage, the voltage time series data to be evaluated were collected. All data were collected at the same time of day, on a single day in an indoor environment, ensuring conditions without significant changes in equipment temperature. The collected data were filtered to display only the area of interest, keeping the initial point of all measurements aligned at the same moment, i.e., the zero point before voltage drops, allowing monitoring of each millisecond of the measurements while maintaining the same length of the time series. It is important to define the length of the time series, because a finite number of records can introduce unacceptable fluctuations and bias in statistical calculations. To ensure reliable analysis, our final dataset consists of 1193 points per vehicle, which provides a sufficient number of data points to capture the voltage behavior up to a stable reference point in the graph.  
The tested vehicles were as follows:  
* Y1.1 = Subcompact car, 1.5 L engine, with 1 month of battery usage
* Y1.2 = Subcompact car, 1.5 L engine, with 6 months of battery usage
* Y1.3 = Subcompact car, 1.5 L engine, with 32 months of battery usage
* Y2.1 = Compact car, 2.0 L engine, with 15 months of battery usage
* Y2.2 = SUV car, 2.0 L engine, with deteriorated SOH
* Y2.3 = SUV car, 2.0 L engine, where the original battery was replaced by an aftermarket battery. Aftermarket battery with 6 months of usage
* Y2.4 = SUV car, 2.0 L engine, with deteriorated SOH. The battery received a new charge before the measurement  
The starter motor system and engine are the same for the Compact (Y2.1) and SUV (Y2.2, Y2.3, and Y2.4) vehicles. During the data acquisition and subsequent filtering of voltage time series, it was possible to obtain the set of curves presented in Figure 1. A voltage drop can be observed at the moment of starting, which is particularly pronounced in batteries with deteriorated SOH. In vehicles Y2.2 and Y2.4, the initial voltage dip was not only deeper but also took longer to recover, indicating a reduced capacity to supply the necessary current. Comparatively, vehicles Y1.1 and Y2.1, which served as baselines, exhibited a more stable voltage profile, with a faster recovery to nominal voltage values. This suggests that the ability of a battery to maintain voltage under load conditions is directly correlated with its SOH. Additionally, the oscillations observed in the voltage time series for vehicles with degraded batteries may indicate increased internal resistance and reduced charge retention capacity. As the engine starts, the voltage tends to increase until the voltage returns above 12 volts. which is characteristic of a functioning combustion engine.