Expectation–Maximization Framework for Fault Diagnosis in Branched Cable Networks via Time–Frequency Domain Reflectometry

Time–frequency domain reflectometry (TFDR) has been widely used in industrial cable diagnostics for its high resolution and accurate fault localization. While TFDR is effective for localizing single faults or terminals of industrial cables, its performance is not guaranteed when applied to branched cable networks, where overlapping reflections from multiple terminations occur frequently. In particular, the diagnostic function of TFDR often interprets overlapping reflections as a single response, which complicates the estimation of terminal or fault locations. To address this challenge, we present a signal-level decomposition algorithm based on an enhanced expectation-maximization (EM) framework that directly separates measured waveforms. By decomposing the closely-spaced waveforms, the method preserves waveform-level characteristics, enabling more detailed analysis of reflections. The method is experimentally validated on a branched cable testbed with comparable branch lengths, designed to emulate realistic diagnostic challenges. Experimental results demonstrate that the proposed algorithm improves reflection location accuracy compared to the state-of-the-art approach and reliably identifies the faulty branch under severe overlapped conditions.