## 5 Information Processing Module (IPM) Design
### Exploratory Data Analysis (EDA)
Therefore, based on the analysis of the preceding figure, the following features have been identified as redundant:  
* The features \(\mathrm{i_{inAC}}\) and \(\mathrm{P_{inAC}}\) have been identified as redundant due to their high correlation (r \(\geq\) 0.95);
* The features \(\mathrm{i_{inDC}}\), \(\mathrm{i_{outDC}}\), \(\mathrm{P_{inDC}}\), and \(\mathrm{P_{outDC}}\) have been identified as redundant due to their high correlation (r \(\geq\) 0.95);
* The features \(\mathrm{v_{outDC}}\) and \(\mathrm{D}\) have been identified as redundant due to their high correlation (r \(\geq\) 0.95);  
Once the redundant features have been identified, it is crucial to remove those that are less relevant and redundant. To achieve this, two feature selection methods will be employed. Feature selection methods are commonly classified into the following: filters, wrappers, and embedded and hybrid methods [61]. In this study, two filter-based methods will be applied, as they enable feature selection independently of the ML model. Filter-type methods can be categorized into two types: univariate and multivariate approaches. The former evaluates each feature individually, allowing the creation of a ranking of the most important features (Figures 10 and 11), while multivariate approaches evaluate subsets of features collectively. This article employs two univariate techniques commonly used in classification tasks: mutual information gain and the Fisher score [61]. Mutual information (MI) is a statistical metric used to quantify the dependency between two variables (X and Y), capturing both linear and non-linear relationships. It can be computed as follows [64; 65]:  
\[MI(X;Y)=\sum_{x,y}p(x,y)\ log\bigg{(}\frac{p(x,y)}{p(x)p(y)}\bigg{)} \tag{2}\]  
where the joint probability distribution of X and Y is represented by \(p(x,y)\), while \(p(x)\) and \(p(y)\) indicate the marginal probability distribution of X and Y, respectively. In this case, the goal is to assess the strength of dependence between each feature (X) and the target (Y). Figure 10 presents the features ranked by their relevance, which is based on the mutual information (MI) values. Figure 9: Correlation among all features. Figure 10 reveals that \(\mathrm{v_{outAC}}\), \(\mathrm{i_{outAC}}\), and \(\mathrm{P_{outAC}}\) demonstrate the highest mutual information values with respect to the target variable (capacitor status or class), whereas D and \(\mathrm{i_{outDC}}\) exhibit the lowest values. Although certain features show reduced MI values, this reduction is not substantially pronounced. Therefore, the Fisher score (FS) was employed for further analysis, and the features were ranked by their relevance (Figure 11). The FS of feature \(f^{j}\) can be computed as follows [64; 65]:  
\[FS\left(f^{j}\right)=\frac{\sum_{l=1}^{c}n_{l}\left(\mu_{l}^{j}-\mu^{j}\right)^ {2}}{\sum_{l=1}^{c}n_{l}\left(\sigma_{l}^{j}\right)^{2}} \tag{3}\]  
where \(\mu_{l}^{j}\) and \(\sigma_{l}^{j}\) represent the mean and standard deviation of the \(l\) class corresponding to feature \(f^{j}\), \(\mu^{j}\) denotes the mean of \(f^{j}\), c represents the number of classes, and \(n_{l}\) the number of samples for label \(l\). Since the features \(\mathrm{i_{outAC}}\), \(\mathrm{v_{outAC}}\), \(\mathrm{P_{outAC}}\), and R exhibit correlation values below the predetermined threshold (r < 0.95) with all other features, they are retained for three primary reasons. Firstly, aging induces an increase in the capacitor impedance, which consequently affects the output current, voltage, and power; secondly, \(\mathrm{v_{outAC}}\), \(\mathrm{i_{outAC}}\), and \(\mathrm{P_{outAC}}\) demonstrate the highest mutual information (MI) values and Fisher scores (FS) relative to the target variable. Third, the R feature plays a crucial role in accurately determining the power converter operational status. Figure 11: Fisher score by feature regarding each class (ranked by their relevance). Figure 10: Mutual information between the features and the target (ranked by their relevance).