## 4 Results and Discussion  
### An Open Fault in an Automotive Line  
Among four lines with different colors (red, grey, black blue), the red line was opened at the UEC connector while others intact. In these lines, 12 reflected signals were measured. Figure 6 shows the fault detection and classification results with the blue line as the generation line. Figure 6a,b represent the reflected signals in the time domain and the phase estimation results, respectively. Since the reflected signals are much smaller than that of the incident signal, time-domain results are incapable of determining neither the fault location nor the faulty line. The phase at the UEC connector with a faulty line pair is zero whereas that of normal line pairs are not. The TFCC results amplify the value at the impedance discontinuity point, as illustrated in Figure 6c. TFCC results show that the UEC connector is commonly detectable in every line pair data with differing degrees depending on the victim line. Since line blue-red showed the highest value of all possible line pairs as shown in Figure 6c, the TFCC results can be utilized in deciphering fault occurrence and location. The line classification results of the reflected signals obtained via the ANN are shown as an image under the plot of Figure 6c. The line classification results are expressed as the sum of \(F(t)\) and \(U(t)\) to intuitively interpret the results. The maximum value indicates a partial fault occurring at the cable junction. In addition, a value of 1 indicates that the entire cable is defective due to external stress or the case of a reflected signal measured at the cable junction point in a normal cable. The results show that the faulty UEC connector is detected at 7 m except the input mismatch at 4 m.  
Figure 5: C&I cable cross section. (**a**) four-core C&I cable and (**b**) seven-core C&I cableThe heat-map was used to identify the clustering results between each signal data. The heat-map shows the normalized Euclidean distance of each 2D data (TFCC results and phase synchrony index) according to its similarity. Therefore, as the distance increases the irrelevance between the data grows as well. In addition, the actual fault wire can be distinguished from the normal wire in the multi-core cable. The number of clusters was set to the number of sudden jumps in the dendrogram which was set to 0.5241 of maximum distance. The clustering results showed that the reflected signal at the UEC connector can be classified into two groups which is illustrated in Figure 6d. The clustering results revealed that the entire data set from the first group included the red line in the generation line or the victim line. Therefore, when an open fault occurs in a multi-core cable, all pairs of the connected lines are clustered into the same group. The first group possessed a high TFCC value and centered around the phase value of zero. On the other hand, the feature data in the second group showed lower TFCC values but had higher phase values. The centroid and the variance of each cluster are summarized in Figure 6d. The clustering results showed that the clustering results are consistent with the clustering results. Figure 6: Fault detection and classification results with the blue line as the generator line. (**a**) TFDR reflected signals, (**b**) phase estimation results, (**c**) TFCC and ANN results and (**d**) heat-map representation and hierarchy clustering results on TFDR results. in Table 1. All silhouette indexes for the clustering results are more than 0.9 which indicate that the line pair data was well clustered using the time-frequency features. The total line pair data classified as a faulty line contained a red line as the generation line or the victim line.