A quantitative evaluation method for broken wires in bridge cables using 3D spatially sampled magnetic flux leakage signals

Bridge cables, which serve as critical load-bearing components in cable-supported bridges, are highly susceptible to broken wires caused by corrosion and fatigue. Accurate quantitative evaluation of this type of damage is essential to ensure structural safety. This study presents a novel quantitative evaluation method for identifying the number of broken wires by employing the magnetic flux leakage (MFL) signal in three-dimensional (3D) space. The method first acquires the 3D spatial magnetic leakage field and generates 3D arrays of MFL signals for computational analysis. It then extracts two categories of features. The first is the global feature, defined as the L1 norm distance (L1D) between the measured 3D spatial MFL signal and the defect-free reference signal. The second is the local feature, consisting of multi-scale waveform features organized as a feature array. The multi-scale waveform feature arrays are compressed using Multilinear Principal Component Analysis (MPCA) to reduce computational redundancy. The compressed feature arrays are then introduced into the Elastic Net-Constrained Regression (ENCR) model to predict defect width. The number of broken wires is ultimately calculated as the ratio of the total L1D value to the L1D value corresponding to the predicted width of a single wire. For a given broken wire width, the L1D demonstrates linear superposition with respect to the number of broken wires, with goodness-of-fit values exceeding 0.999, enabling proportional quantification. Validation through simulations and experiments on PES7-127 cables (127 wires of 7 mm diameter) confirms the method's effectiveness. The simulations achieved 100 % accuracy in counting broken wires across varying widths and distributions, while experimental results verified 100 % quantification accuracy (within a tolerance of ±1 wire) for defects involving ≤4 broken wires. This performance is obtained using a training dataset of only 30 samples. This study provides a practical and efficient approach for bridge cable assessment.