# Application of Dynamic Time Warping (DTW) in Comparing MRT Signals of Steel Ropes
## 3 Results
### Passive Experiment  
The aim of this stage of the study was as follows:  
* Optimization of the analysis window width is necessary because, for time series x and x' of length m and n, respectively, and the same ordering, there exist \(O\left(\frac{\left(3+2\sqrt{2}\right)^{n}}{\sqrt{n}}\right)\) different paths in \(A\left(x,x^{\prime}\right)\), which exponentially increases the required memory and data processing time. The length of the ropes tested in actual industrial installations was many times greater than that of the rope used in the active experiment, and due to the available computational power and data processing time, it was necessary to perform DTW analysis on successive segments of the current recording, taking into account the previous alignment results with the reference data. * Verification of the effectiveness of the DTW algorithm in industrial conditions of MRT testing considering that the dynamics of rope operation and its degradation processes are impossible to reproduce in laboratory conditions. To reduce the time required for initial synchronization of the measurement data, only time series recorded in the same rope movement direction were analyzed. The initial offset resulted from the starting position of the transport vessel (upper skip), the periodic manual shortening of the rope by the user, and the natural elongation/shortening of the rope during operation due to load differences and progressive fatigue degradation of the rope material. The maximum offset between the analyzed time series occurred at the final position of the hoisting vessel. Automatic recognition of the two rope scanning directions and synchronization of such time series will be developed in future research. * The research included data from long-term monitoring of wire ropes of various types and two resolutions of rope scanning in the ENCODER mode:
* Not less than 1.0 mm, required by ISO 4309:2017;* Either 2.5 mm or 5.0 mm, used until the introduction of the amendment to the above-mentioned standard in 2017, and the MRT method still found in some users. Examples of research results are illustrated in Figures 17-22. Based on the analysis of MRT data from 2020 to 2024 for an over 170-m round-strand steel rope from the Guido shaft, the following was shown (Figures 17 and 18):
* The possibility of realizing LF time series matching using the Euclidean distance method in a window not exceeding 1.5 m of rope length and the DTW algorithm in a window of about 9 m;
* The need to perform DTW analysis with the use of a movable window (similar to the fast Fourier transform, SEFT) due to the limitation of the required memory volume needed to store the calculation results and the calculation time of a single rope fragment;
* Repeatability of the results of time-series synchronization obtained with the DTW algorithm for LF1 and LF2 signals, with a slight offset between the synchronized LF1 and LF2 signals increasing with the rope's lifetime, probably resulting from the design features of the GP heads and differences in the magnetic field spectrum on the two rays of the search coils;
* The ability to monitor progressive corrosion of wires before reaching the ignition criterion of the current diagnostic rule and with a small impact of cyclic material fatigue (lack of broken wires) and abrasions;
* The desirability of analyzing harmonic components and noise in the LF signal in the aspect of rope system diagnostics, including longitudinal and transverse vibrations of the rope. After many years of operation, the rope shows repeatability of the frequency of harmonic signals, reflecting the rope's pitch and the distance between the strands, which are amplitude-modulated along the tested rope--the influence of longitudinal, transverse, and torsional vibrations of the rope. Figure 17: Synchronization of LF1 time series (2020–2024) for a round-stranded steel rope from the Guido shaft using Euclidean distance.