# Application of Dynamic Time Warping (DTW) in Comparing MRT Signals of Steel Ropes
## 1 Introduction  
Steel wire ropes are essential components in vertical and horizontal transport systems including cranes, mine hoists, offshore structures, aircraft arresting systems, and cable-ways [1]. Their operational reliability directly affects human safety, equipment durability, and economic performance. Among various non-destructive testing (NDT) methods, magnetic rope testing (MRT) remains the most widely adopted diagnostic technique due to its ability to detect internal and external defects without dismantling the rope. Unlike visual inspection, which covers only surface-level damage and ~20% of the rope cross-section, MRT offers a full-profile magnetic assessment and is standardized under several international norms (e.g., ISO 4309:2017 [2], EN 12927:2019 [3]). MRT is relatively cost-effective, robust, and applicable to ropes in a wide range of industrial environments. gaDespite technological advancements, MRT still suffers from diagnostic uncertainty due to signal degradation caused by rope elongation, external wire abrasion, corrosion, and inconsistent data acquisition settings. Steel wire ropes consist of multiple outer and inner strands, whose surface wear manifests over time through visible damage such as strand flattening or broken wires. The number of broken outer wires is directly correlated with the rope's consumption level relative to its expected service life [4; 5; 6]. Figure 1 shows different levels of corrosion observed in ropes exposed to harsh environments. Corrosion risk is minimized through protective measures such as galvanized coatings with zinc, aluminum, and magnesium (e.g., BEZINAL(r) 3000) or zinc, aluminum, and sodium (e.g., ZINCAL(r)); factory lubrication with in-service reubrication; polymer-impregnated strand fills; and polymer sheathing [1; 10]. In aggressive conditions, ropes made of corrosion-resistant high-alloy steels (e.g., X5 CrNiMo17-12-2, X1 CrNiMoCuN20-18-7, X1 CrNi25-21) are preferred [EN 10088-1:2005 [11]; EN 10088-5:2009 [12]]. However, these austenitic steels are paramagnetic and therefore not suitable for MRT. Wear and fatigue are also influenced by structural design, such as the contact type between wires (Figure 2a), compacted strand geometry (Figure 2b), and outer surface construction (Figure 2c). Additional factors include strand core type (Figure 2d-e), motion parameters, and interacting element geometry. These factors help minimize contact stresses, protect against galvanic layer wear, and reduce crack initiation. Figure 1: Steel wire rope corrosion: (**a**) after less than 12 months of service in offshore marine conditions [7; 8]; (**b**) after 18 months of low-load operation during shaft deepening in a mining environment [9]. During operation, steel wires are subjected to complex stress states caused by repeated bending, torsion, and axial loads. These forces lead to localized strain hardening, fatigue-induced microstructural degradation, and progressive mechanical softening. As the fatigue process evolves, the average tensile strength of the wires decreases--a phenomenon particularly evident in ropes with polymer cores such as the 6 \(\times\) 36 construction [17]. This mechanical degradation is accompanied by alterations in magnetic properties, including shifts in magnetic permeability and remanence, which further complicate the interpretation of magnetic rope testing (MRT) signals. These combined magneto-mechanical effects reduce the clarity of diagnostic features, especially in advanced rope designs where internal damage may not produce a strong magnetic response. Laboratory-based empirical formulas (Equation (1)) describe the fatigue life of steel wire ropes under bending in controlled conditions [1]. The rope is described by a MISO (Multi-Input Single-Output) model considering only a single mechanical parameter. However, real-world degradation progresses faster due to variable loads, environmental exposure, and human factors. The adjusted fatigue life considering exploitation quality is given in Equation (2).