## 1 Introduction  
In various industrial fields, control and instrumentation (C&I) cables assure the stability and reliability of system operations through controlling systems, transmitting signals, and monitoring networks. Likewise, in nuclear power plants (NPP), ensuring the integrity of electrical cables, which is highly relevant with the coolant system, safety injection system, and the containment spray system, is essential for plant operation [1]. The multi-core C&I cables in NPPs are generally installed to minimize both space and cost as well as prevent wiring labor in limited areas. Moreover, C&I cables are often installed in containment areas under the conditions of high temperature and high radiation, thus exposing their polymeric insulation materials to chemical/physical changes. Consequently, faults resulting from various external stresses inflict errors in the C&I signals, signal leakages, and interference noises in the multi-core cables, which pose serious threats to the operation of the NPP. Therefore, it is of paramount importance to accurately distinguish the faulty line among others and to instantaneously detect the fault upon its occurrence to prevent any accidents which may lead to severe health problems and economic losses. Safety measures should also be established for multi-wires inside automotive electronics of vehicles. In automotive electronics, cables and connectors are usually installed near vibration motors and wheels. Thus, the wires subjected to vibration and heat damage are highly susceptible of causing failures during operation [2; 3]. Wiring failures causing the detrimental situations of uncontrollable vehicles or sudden breakdowns endanger both the driver and the pedestrians, leading to secondary damages. The reflectometry technique, a non-invasive electrical cable diagnosis method, possesses the capacity of detecting faults and assessing cable conditions [4]. When an impedance change is caused by a fault or degradation due to operations in a C&I cable, a propagated signal is reflected and transmitted at the local impedance discontinuity point depending on the reflection coefficient [5]. Reflectometry can be divided into two categories depending on its domain of analysis: the time domain reflectometry (TDR) and frequency domain reflectometry (FDR) [6; 7]. Both methods are easy to implement and need not require high voltages. Unfortunately, the diagnostic results of both the TDR and FDR method are highly susceptible to electric noise and crosstalk [8; 9]. Moreover, signal attenuation, distortion, and dispersion, which are all likely to occur in the measured reflected signal during signal propagation, diminish the accuracy and reliability of the diagnostic results. Conversely, the time-frequency domain reflectometry (TFDR) method simultaneously analyzes the reflected signal in both the time and frequency domains, which compensates for the drawbacks of the conventional methods [9]. Herein, the incident signal can be designed in the time and frequency domains according to the characteristics of the cable, and the impedance discontinuity points in the cable can be detected using the time-frequency distribution similarities between the incident signal and the reflected signal. Therefore, reflected signals are less likely to be affected by the cable propagation characteristics or external noises. However, existing reflectometry methods focus on diagnosing a single or pair core cable and is thereby unsuitable for multi-core cables or wired networks. When reflectometry is applied to a multi-core cable, the reflected signal generated at an actual fault point of a defective line is introduced to a normal line and can be measured due to crosstalk [10]. This paper presents a multi-core cable diagnosis method which detects faults and distinguishes faulty lines using the machine learning-based TFDR. First, the location and type of cable fault are detected using a regression-based artificial neural network (ANN) of the TFDR results [11; 12].