## 2 Methods and Models for Evaluating Battery SOH Literature Review  
Firstly, an analysis of methods and models for evaluating the health of a vehicle battery was developed based on the current literature. A search was conducted in the ScienceDirect, Springer, and IEEE repositories using the terms (SoH OR \"State of Health\") AND \"Lead-Acid Battery\" AND (automotive OR vehicle). A total of 431 research articles, 161 review articles and 81 book chapters were obtained from ScienceDirect, 31 articles from Springer Link, and 21 articles from IEEE. Subsequently, some terms were considered for the removal of documents: items related to lithium-ion batteries, stationary usage batteries, solar energy applications, or purely electric vehicles batteries. Thus, this work presents the main findings identified in articles published since 2003. [PERSON] et al. [17] reported that electrochemical sparse-impedance spectroscopy has proven to be an effective technique for assessing the SOH of sealed automotive lead-acid batteries, as it enables onboard data collection within the vehicle. They predicted that sparse-impedance spectroscopy could be increasingly applied in future vehicles to monitor the SOH of lead-acid battery systems. A proposal was presented by May [18] for monitoring batteries under stop-start conditions, which included monitoring the SOC, SOH, open circuit voltage, voltage drop during startup, and voltage response to small loads. They concluded that the SOC and SOH are critical for achieving reliability standards. Similarly, [PERSON] et al. [19] used the current and calculation of voltage ripples acquired with an electrochemical impedance spectroscopy meter across different frequency ranges to perform battery prognostics, concluding that impedance measurement is an effective tool for assessing battery states. In the study presented by [PERSON] et al. [20], the focus was on improving the accuracy of SOC inference by utilizing Direct Current Resistance (DCR), thereby enhancing the correlation between the SOC and DCR. [PERSON] et al. [21] monitored the SOH of the battery during engine startup, introducing a new battery model that considered the internal resistance of the battery and the voltage drop during startup. This approach achieved better battery diagnostic performance compared to the conventional method at the time, which was based on resistance. They also suggested the use of detection methods with statistical models for future research. [PERSON] and [PERSON] [22] also focused their study on SOH estimates for lead-acid batteries, specifically by considering the waveforms of voltage and current at the battery terminals during operation. They produced their SOH estimates by analyzing changes in the battery's internal resistance and capacitance. Aware of the limitations of SOH measurement by inference, [PERSON] et al. [23] proposed measuring the SOH and SOC through the electrolyte density, using an optical fiber inserted into the battery. However, a downside of this research, when compared to the study in this dissertation, is that it requires an invasive method to obtain and measure the electrolyte density. [PERSON] et al. [24] proposed an approach for estimating the SOC and SOH using a dynamic data-driven method, applying Symbolic Dynamic Filtering along with a D-Markov machine and a Probabilistic Finite State Automaton. It considered the current and voltage as parameters in a time series, resulting in a dynamic data-driven method as an alternative to traditional battery model-based methods. [PERSON] et al. (2019) also presented a study involving battery current time series alongside voltage, which can be considered a continuation of the previous research presented in [PERSON] et al. (2019). [PERSON] et al. (2019) presented a system for measuring the SOH based on the battery's voltage drop curve during a startup event, monitoring the first two voltage drops over time, along with the battery's temperature and the SOC.