Cable is crucial to the control and instrumentation of machines and facilities. Therefore, early diagnosis of cable faults is the most effective approach to prevent system downtime and maximize productivity. We focused on a "soft fault state", which is a transient state that eventually becomes a permanent fault -open-circuit and short-circuit. However, the issue of soft fault diagnosis has not been considered enough in previous research, which could not provide crucial information, such as fault severity, to support maintenance. In this study, we focused on solving soft fault problem by estimating fault severity to diagnose early-stage faults. The proposed diagnosis method comprised a novelty detection and severity estimation network. The novelty detection part is specially designed to deal with varying operating conditions of industrial applications. First, an autoencoder calculates anomaly scores to detect faults using three-phase currents. If a fault is detected, a fault severity estimation network, wherein long short-term memory and attention mechanisms are integrated, estimates the fault severity based on the time-dependent information of the input. Accordingly, no additional equipment, such as voltage sensors and signal generators, is required. The conducted experiments demonstrated that the proposed method successfully distinguishes seven different soft fault degrees.