# Application of Dynamic Time Warping (DTW) in Comparing MRT Signals of Steel Ropes
## 3 Results
### Passive Experiment
Reliable alignment with a single wire break anomaly is limited to a window of approximately 1.5 m.  
Based on the analysis of MRT data from 2019 to 2023 for over 680 m NRHD24 steel wire ropes from the copper mine shaft, the effectiveness of LF1 and LF2 time-series synchronization was confirmed for ropes with a multi-strand Warrington steel core despite observed changes in signal characteristics between subsequent experiments. Upon analyzing the signals, distinct differences are observed in the following:  
Figure 18: MRT data analysis of a round-stranded steel rope from the Guido shaft (ENCODER mode, 1.0 mm resolution): FFT spectra of LF1 (**a**) and LF2 signals (**b**) from 2020 and 2023 show reduced structural noise and consistent lay pitch peak; (**c**) DTW-based synchronization of LF1 time series (2020 vs. 2024) within a 9 m window; (**d**) resulting differential signal after alignment. * The spectrum of the signal that can be visually seen in the time series imaged in the MD121 View software (Figure 19);
* Color noise, which increases in the subsequent years of operation of the NRHD24 rope as opposed to the noise of the round-strand rope (Figure 20);
* Amplitude modulation parameters of harmonic components of signals (Figure 20). In the residual DTW signal, the following symptoms occur: a broken single wire per 183 m of rope, increasing corrosion of the wires, and processes of cyclic fatigue of the material (Figure 21). A characteristic feature of the operation of polymer-impregnated steel ropes, e.g., STRATOPLAST MF, is the extended time of strand laying and the accompanying significant change in the LF signal spectrum. The spectrum includes characteristic frequencies (TIMER mode) or characteristic orders related to the reference length of the rope (ENCODER mode, apparent frequency), which reflect both the structural features of the rope (number of strands, number of strand layers and the distances between them) as well as the vibration  
Figure 19: Analysis of NRHD-24 steel rope degradation from a copper mine using MD121 View software: (**a**) full signal recording of LF1, LF2, and I(LF1) from 2019 and 2023 showing amplitude growth and the appearance of a single wire break in 2023 at 183 m; (**b**) zoomed signal comparison near the defect zone reveals desynchronization between years and changes in the time-domain spectral characteristics. components of the rope (dynamic conditions of the rope system and modal properties of the rope) (Figure 22). For all the analyzed steel ropes, it was found that after synchronizing the LF time series with the DTW algorithm, it is possible to diagnose the progressive degradation of the rope's technical condition more precisely, especially in the initial phase of degradation preceding the appearance of  
* the first break of the wire,
* excessive abrasion of the wire,
* developed corrosion  
and exceeding the signal-to-ratio SNR > 2 (linear scale) criterion for a reliable diagnostic symptom required by EN 12927:2019. Figure 20: Analysis of LF signal features of the NRHD-24 steel rope based on MRT data: (**a**) 2019; (**b**) 2023. The PSD of the LF1 signal exhibits harmonic components modulated by rope vibrations. In 2023, a more than tenfold increase in the second harmonic amplitude of the outer strands is observed. The accuracy of synchronization between two time series was assessed based on the quality of stitching synchronized fragments of reference data along the entire rope length. It was found that the highest synchronization errors occurred for polymer-impregnated ropes and did not exceed 5.0% in ENCODER mode at a measurement discretization resolution of 2.5 mm (400 points per meter of rope). The synchronization quality was affected by significant changes in the PSD spectrum. For steel wire ropes, with a sampling resolution of 1.0 mm (1000 points per meter of rope) and relatively stable PSD characteristics, the synchronization error level did not exceed 1.5%.