## 4 Results and Discussion
### A Short Fault of a Faulty Line at the Terminal Block  
The ANN with TFDR results were applied to detect a short fault at the terminal block. Short faults were applied to one of the two terminal blocks (15 m) at lines red-blue, red-black, red-grey, blue-red, black-red, and grey-red) from those of normal line pairs (Lines blue-black, blue-grey, black-blue, black-grey, grey-blue, grey-black). 3 and 4. Figure 7 shows the fault detection and classification results with Line 3 as the generation line. We refer to the reflected signal of each line pair using the number of the generation line followed by the number of the victim line. For instance, Line 3-4 points to the TFDR results with Line 3 as the generator line and Line 4 as the victim line. TFCC and ANN results indicate that the terminal block at 8 m was balanced and thus not defective, whereas the faulty terminal block at 15 m was unbalanced with the cable endpoint due to dissimilarities between the faulty line pair and the normal line pair data, as illustrated in Figure 7. The clustering results at the unbalanced terminal block are illustrated in Figure 7. By clustering at the terminal block, the multi-core diagnostic data was classified into two clusters. One corresponds to line pairs where a short fault occurred (Lines 3-4, 4-3), and the other contains the rest. Normal lines can be discerned from short faulty line pairs through the energy differences of the reflected signals. In addition, clustering results reveal that the pair data of only short fault lines can be distinguished from the pair data of other lines which possess features different from an open fault case.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Fault**} & \multirow{2}{*}{**Cluster**} & \multicolumn{3}{c}{**Fault Location**} & \multicolumn{3}{c}{**Centroid**} & \multirow{2}{*}{**Average**} \\ \cline{3-3} \cline{5-8}  & & **Actual Location (m)** & & & & & **Error (\%)** & TFCC** \\ \hline Automotive lines & Faulty lines & \(9\) & \(8.525\) & \(5.28\) & \(0.842\) & \(-0.580\) & \(0.984\) \\ (Open fault) & Normal lines & \(9\) & \(9.561\) & \(6.23\) & \(0.538\) & \(2.627\) & \(0.938\) \\ Four-core C\& cable & Faulty lines & \(8\) & \(7.818\) & \(2.28\) & \(0.973\) & \(-2.831\) & \(0.999\) \\ (Short fault) & Normal lines & \(7.901\) & \(1.24\) & \(0.357\) & \(-1.886\) & \(1.000\) \\ Seven-core C\& cable & Open fault lines & \(129.1\) & \(0.69\) & \(0.900\) & \(-0.532\) & \(0.856\) \\ (Open/Short fault) & Short fault lines & \(130\) & \(129.8\) & \(0.15\) & \(0.973\) & \(3.186\) & \(0.998\) \\  & Normal lines & \(132.6\) & \(2.00\) & \(0.173\) & \(-0.975\) & \(0.875\) \\ Seven-core & First floor & Faulty lines & \(380\) & \(381.2\) & \(0.32\) & \(0.635\) & \(0.040\) & \(0.968\) \\ C\&I cable & (Lines 3 and 4) & Normal lines & \(.\) & \(.\) & \(0.033\) & \(-1.358\) & \(0.937\) \\ (Open fault) & First and second floor & Faulty lines & \(380.5\) & \(0.13\) & \(0.761\) & \(-0.128\) & \(0.957\) \\ Lines 1, 2, 3, 4 and 5) & Normal lines & \(.\) & \(.\) & \(0.028\) & \(1.639\) & \(0.995\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Fault location and clustering results.