# Detecting Arcing Faults in Switchgear by Using Deep Learning Techniques
## 3 Performance Metrics  
The effectiveness of the proposed models was evaluated using a confusion matrix, as presented in Table 4. In this matrix, arcing and non-arcing situations were represented by 0 and 1, respectively. The model's performance was assessed using various indices, including categorization, reliability, dependability, sensitivity, and F1 measure, as determined by Equations (8)-(11). Recall represents the ratio of relevant samples that were accurately identified from all relevant samples, while precision refers to the percentage of relevant samples that were correctly identified from the retrieved data. Additionally, the cross-entropy loss was employed to evaluate the model's performance by measuring the closeness of the model's predictions to the target data as given in Equation (12). One important performance requirement is the minimization of the gap between the arcing and non-arcing  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**1D-CNN** & **LSTM** & **1D-CNN-LSTM** \\ \hline
1 DConv(16-RELU) & LSTM(64) & 1 DConv(64-RELU) \\ Drop-out & Drop-out & MaxPooling \\ MaxPooling & LSTM(32) & Drop-out \\
1 DConv(32-RELU) & Drop-out & 1 DConv(128-RELU) \\ Drop-out & Flatten & MaxPooling \\ MaxPooling & Dense(32-RELU) & Drop-out \\ Dense(2) (SoftMax) & & LSTM(32) \\  & & Dense(2) (SoftMax) \\ Total Parameters & & \\ \hline \hline
11,922 & 35,298 & 217,986 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The deep learning algorithm designs for time domain.  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**1D-CNN** & **LSTM** & **1D-CNN-LSTM** \\ \hline
1D Conv(16-RELU) & LSTM(64) & 1D Conv (64) (RELU) \\ Drop-out & Drop-out & MaxPooling \\ MaxPooling & LSTM(64) & Drop-out \\
1D Conv(32-RELU) & Drop-out & 1D Conv(128-RELU) \\ Dropout & Flatten & MaxPooling \\ Max-Pooling & Dense(32-RELU) & Drop-out \\ Flatten & Dense(2) (SoftMax) & LSTM(128) \\ Dense(32-RELU) & & Dropout \\ Dense(2) (SoftMax) & & LSTM(32) \\  & & Dense(2) (SoftMax) \\ Total Parameters & & \\ Total Parameters & & \\
5650 & 84,578 & 184,706 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The deep learning algorithm designs for Frequency Domain.  
states of two probability distributions, which is frequently addressed in binary classification problems. For a perfect model, the loss value would be 0.  
\[\text{Classification Accuracy}(\%)=100\times\frac{\text{TP}+\text{TN}}{\text{TP}+ \text{FP}+\text{FN}+\text{TN}} \tag{10}\]  
\[\text{Recall}(\text{Sensitivity})(\%)=100\times\frac{\text{TP}}{\text{TP}+ \text{FN}} \tag{11}\]  
\[\text{Precision}(\text{Dependability})(\%)=100\times\frac{\text{TP}}{\text{TP}+ \text{FP}} \tag{12}\]  
\[\text{F1 measure}(\%)=100\times 2\times\frac{(\text{Precision}\times\text{ Recall})}{(\text{Precision}+\text{Recall})} \tag{13}\]  
\[\text{Loss}(\text{L})=-\frac{1}{N}\times\sum_{l=1}^{M}T_{i}\text{log}(x_{i}) \tag{14}\]  
\(x_{i}\) is the projected answer, \(N\) is the number of observations overall in \(x\), and \(M\) is the total number of expected replies in \(x\) (all findings and categories combined). The goal value is \(T_{i}\). The binary crossentropy loss is normalised by the total number of instances after adding up all the categories and observations.  
False Positive (FP) and False Negative (FN) stand for inaccurate forecasts, while True Positive (TP) and True Negative (TN) stand for accurate predictions (TN).