# A Multinomial DGA Classifier for Incipient Fault Detection in Oil-Impregnated Power Transformers
## 3 Methods and Modeling
### The Data Set  
An exhaustive analysis of the data was carried through data exploration. Exploratory Data Analysis (EDA) is a preprocessing procedure used on raw data to obtain additional insight about the data before engaging in model building and training. During the EDA, the investigator is interested in knowing the shape of the data, the number of features it contains and the types of variables therein. EDA techniques are ran on raw data to extract its essential characteristics, define feature variables and obtain guidance on the selection of machine-learning algorithms [44; 45; 46]. To understand the data fully, multiple exploratory \begin{table}
\begin{tabular}{l l} \hline \hline
**Type** & **Fault** \\ \hline
**PTD** & Partial Discharge \\
**DLE** & Discharge of Low Energy \\
**DHE** & Discharge of High Energy \\
**TF1** & Thermal Fault 1 (for t \(<\) 300 \({}^{\circ}\)C) \\
**TF2** & Thermal Fault 2 (for 300 \({}^{\circ}\)C \(<\) t \(<\) 700 \({}^{\circ}\)C) \\
**TF3** & Thermal Fault 3 (t \(>\) 700) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Fault Code for Classic faults in oil-immersed transformers [12; 40; 41]. Figure 3: Comparative proportion of dissolved gas concentrations in mineral oil as a function of temperature and fault type [12]. techniques are used, and the results aggregated. Figure 4 shows the contemporary methods employed in EDA and which have been used in this work. Univariate visualization provides statistics for each parameter and is visualized in a one-dimensional space. Bivariate visualization determines the relationship that exist between each variable in the dataset and the dependent variable. Multivariate visualization aids in the identification of existing interactions between different fields in the dataset and examines the variables for correlation. Dimensionality reduction is a technique used to identify the most critical predictors so that the model is built using the minimum number of predictors required to maintain high accuracy [44; 45; 46]. Figure 5 shows the type and number of variables in the dataset. The variable \"Status\" is the dependent variable and is of a categorical type while the rest are integers. The total number of observations for each were 2912 entries. Primarily, the data was investigated for missing values. Figure 6 shows that there are no missing values. Whenever missing values exist, the columns affected show discontinuous gaps. In this case, the columns are continuous indicating that there are no missing values. Next, a box-and-whisker plot was created as shown in Figure 7. It suggests that the variables, acetylene and ethylene, have several outlying points above the outer whisker while hydrogen (H\({}_{2}\)), and carbon monoxide (CO) have no outliers. Outliers are normally handled by prediction or imputation (using the mean, mode and median) but by looking at the data, it is difficult to conclude that the outliers are as a result of human or mechanical error [47; 48; 49]. Therefore, the outliers were left as they were. It becomes  
Figure 4: Major steps of Exploratory Data Analysis. Figure 5: The Independent and Dependent Variables. imperative to handle outliers when it is evident that they result from errors committed during data collection or entry. The correlation matrix or heat-map shown in Figure 8 establishes the correlation between the various pairs of variables from where it is determined that the correlation between the two variables, acetylene and ethylene, is high. A keen consideration of Figure 3 reveals that this correlation occurs in a coincidental manner because as the temperature rises there is a parallel increased production of both gases in slightly differing quantities. It is, therefore, concluded that this correlation does not imply causality [50]. Figure 9 investigates the probability distribution of the variables. The variables hydrogen, methane, ethylene, ethane, and carbon monoxide appear to have a Gaussian distribution. Figure 6: Checking for missing values. Figure 7: Box-and-whisker plot.