## 2 Methods and Models for Evaluating Battery SOH Literature Review
They used a driving cycle called the Worldwide Light Duty Driving Test Cycle in the laboratory to perform acquisitions simulating real-world usage. Indicators obtained through time and frequency domain measurements of the voltage and current over defined time intervals were used, allowing for real-time investigation of battery SOH degradation. [PERSON] et al. [35] presented an article on a battery management system based on cloud processing, utilizing a Digital Twin for the SOH and SOC of the battery. The study considered a context where battery data would be available via the Internet of Things, making this initiative feasible. For this work, equivalent circuit models, electromechanical models, and machine learning models were used, with the pros and cons of each model being considered. [PERSON] et al. [36] introduced a new approach using Electrochemical Impedance Spectroscopy to predict the lifespan of battery cells under specific aging conditions. Fluctuations were monitored during charge and discharge sequences at two SOC levels. By studying the resonance frequencies of the batteries during the aging process, a trend in the battery's SOH was identified. [PERSON] et al. [37] proposed the ERMES algorithm which offers a robust and computationally efficient method for real-time estimation of a battery's SOC and SOH, addressing the challenges posed by complex and time-varying battery dynamics. A key feature of ERMES is its ability to capture sudden SOH variations based on a simple battery model, with potential for extension to other parameters. The algorithm also provides a figure of merit, called the SOU, which measures the accuracy of its estimates, allowing for real-time monitoring of its robustness. If prediction uncertainty exceeds a certain threshold, the system can dynamically adjust the model composition, such as by fine-tuning parameters or adding models close to the current SOH estimate. In summary, there are several algorithms used for the estimation of the SOC and SOH of batteries. The voltage method for estimating the SOC involves measuring the open-circuit voltage of the battery and then comparing it to either a lookup table or a mathematical model. Although this approach is noninvasive, it is susceptible to fluctuations in temperature and the evolving nature of battery aging [29; 38; 29]. The Coulomb counting method estimates the SOC by integrating the current flowing in and out of the battery. Although this method is simple to implement, it is vulnerable to cumulative errors stemming from inaccuracies in measurements, parasitic currents, and variations in battery capacity due to temperature and aging fluctuations [40; 41; 42]. The KF approach utilizes a recursive filter algorithm along with a comprehensive mathematical model of the battery. While offering a more precise estimation of the SOC when compared to other methods such as Coulomb counting and voltage estimation [43], this approach requires substantial computational resources, constraining its practicality in resource-limited applications, especially in the automotive sector [33; 44]. The Neural Network method involves training a neural network using a dataset of batteries measurements to establish a correlation between input parameters (such as the ampere, temperature, and voltage) and the SOC. Subsequently, the neural network is employed to forecast the SOC or SOH based on real-time or historical battery data [45; 46]. However, the effective deployment of this algorithm heavily depends on the presence of a sizable and varied dataset for training the neural network, along with a remarkable computational resources for both training and inference tasks [47]. [PERSON] and [PERSON] ([46]) provided an extensive evaluation and comparison of different methods for analyzing the SOH of batteries. An ideal SOH estimation method that can be applied in any charging or discharging situation, and can be used quickly, accurately, and economically, does not exist yet.