## 4 Modeling and Prediction  
Based on the above-presented analysis, a model is designed that reproduces the behavior of the battery with respect to aging based on the evolution of internal resistance. For this purpose, a black box type model based on an evolutionary algorithm is used. Black box models rely exclusively on computing data to recreate the relationship between the input and output parameters of a problem. They do not require an understanding of the physics that explains the problem, they are simply able to solve it by processing large amounts of data made up by the experience of the problem [21]. Classically, black box models based on neural networks (ANN) [24], support vector machine (SVM) [25], fuzzy logic clustering (FLC), and Bayesian probable models (BPM), are implemented to estimate the variation of a battery's parameters with its aging and state of charge [26]. Evolution algorithms are a family of metaheuristic methods for solving optimization problems, without the use of derivation. Their main characteristic is that they are based on natural behaviors that solve optimization problems such as finding the best way to find food or choosing which are the best genes for the conservation of a species. They are usually systems with large populations where each individual tries to find the best possible solution to the problem and interacts with the rest to approach the optimal solution together [23]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Influential** &
\begin{tabular}{c} **Included in** \\ **Modifications** \\ \end{tabular} & **Comments** \\ \hline Internal resistance & Yes & Yes & Indicator of battery aging. It will be used as center piece in the modelization. \\  & & & Indicator of battery aging. It will not be used in the model as the internal resistance will be used. However, is has been obtained a clear link between parameters. \\ Depth of discharge & Yes & Yes & Is causes a negative effect in aging. It will be used in the modelization. \\ Voltage dispersion between cells & Yes & Yes & Indicator of battery aging. It will be used in the modelization. \\  & & No & No effect found in the battery performance. Therefore, it will not be used in the modelization. \\  & & No & It causes a negative effect in aging. It will be used in the modelization. \\ Storage time & Yes & Yes & It causes a negative effect in aging. It will be used in the modelization. \\ Discharge rate & Yes & Yes & It causes a negative effect in aging. It will be used in the modelization. \\  & & & It may be an indicator of battery aging, but not accurate data to draw clear conclusions. Therefore, it will not be used in the modelization. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Analysis resume. Four of the most used evolution algorithms are particle swarm optimization (PSO), genetic algorithm (GA), ant colony optimization (ACO), and artificial bees algorithm (ABA). PSO is based on the interaction of some animals, such as birds, when they go in the swarm in search of a common goal, such as food sources [27; 28]. GA is inspired by the biological evolution of species by genetic theory so that individuals continuously evolve adapting better to survive, which is the problem to be optimized [29]. ACO is based on the behaviors of ants when they seek the best ways to find food sources [30]. The ABA is inspired by the bees' food search for a hive that tends to optimize the use of its members [31]. Among these optimization algorithms, the two most used in battery estimation are PSO and GA. Adaptation of PSO is observed in various works to estimate the state of charge and the state of health of batteries but it strongly depends on population size and quality of the data selected at the beginning, and its solution takes longer to converge and is voluminous to implement on a real-time basis [32]. Hence, GA is chosen for this model, as its implementation for this problem is simpler and does not require long computation times.