# Application of Dynamic Time Warping (DTW) in Comparing MRT Signals of Steel Ropes
## 1 Introduction
To reduce the risk of Type II errors, users apply safety factors (e.g., K \(>\) 5 in mining), frequent MRT inspections, and conservative discard rules. Still, unnecessary rope replacements remain common, contributing to excessive material loss and carbon emissions, especially in large-diameter ropes. Although standards like ISO 4309:2017 and EN 12927:2019 recommend minimum scan resolution (\(\leq\)1 mm), signal-to-noise thresholds (SNR \(>\) 2.0), and baseline comparisons, they do not address how to compensate for rope elongation over time. This directly impacts the consistency of magnetic signatures and undermines comparisons across inspections--particularly in polymer-impregnated ropes. Recent advances in structural health monitoring (SHM) have increasingly leveraged optical fiber sensing and data-driven modeling techniques for deformation assessment in infrastructure. Ref. [30] developed a distributed optical fiber monitoring system based on BOTDA and fiber Bragg grating (FBG) sensors, enabling 3D tracking of pipeline and soil deformation under lateral displacement and demonstrating effectiveness in recovering strain distribution even under environmental noise. Furthermore, [31] implemented a long-gauge FBG sensing system integrated with STOA-Bi-LSTM-GAN to recover missing data and reconstruct deformation fields with \(<\)10% error under data loss conditions. These studies exemplify the increasing capability of advanced SHM methods to detect gradual, distributed damage--insight that directly aligns with our DTW-enhanced MRT approach for early fault detection in wire ropes. The originality of this work lies in the novel application of the Dynamic Time Warping (DTW) algorithm to the synchronization and differential analysis of low-frequency (LF) magnetic signals obtained during magnetic rope testing (MRT). While DTW is widely used in speech processing, bioinformatics, and time-series clustering, its deployment in rope diagnostics, particularly for compensating signal distortion due to elongation and scan variability, remains unexplored. The research addresses a key gap in MRT-based diagnostics: the limited ability of traditional signal processing to adapt to resolution degradation, mechanical strain evolution, and internal changes in polymer-impregnated wire ropes. Existing MRT algorithms focus primarily on localized discontinuities such as wire breaks or corrosion pits, whereas our approach enables the detection of broader spectrum shifts and synchronization challenges across repeated scans. This contribution is especially relevant for steel ropes used in safety-critical applications (e.g., mining, transport, offshore), where long-term signal stability and resolution adaptation are crucial. The method also offers compatibility with standard MRT equipment and is applicable across various software platforms (e.g., R 4.4.2, Python 3.9.21, MATLAB R2024b), enhancing its potential for industry adoption. The structure of the article includes the following: (1) an introduction and literature review, (2) a theoretical section on MRT signal modeling and DTW implementation, (3) the characterization of rope samples and measurement conditions, and (4) experimental validation using active and archival MRT data, followed by a discussion of the results and practical implications.