BOTDR Monitoring of Tensile State in Three-Core Fiber-Optic Composite Submarine Cables with a Three-Layer Mechanical Structure and Dual-Threshold Sensing Model

Abstract

Submarine cables are critical components for power transmission in offshore wind farms, making their condition monitoring paramount for ensuring operational reliability. Addressing unclear strain transfer and underdeveloped Brillouin optical time-domain reflectometry (BOTDR) sensing models for three-core fiber-optic composite submarine cables, this study investigated a 66 kV cable and clarified a BOTDR monitoring principle based on the three-layer mechanical structure. Using the external optical unit’s average Brillouin shift for temperature compensation, four characteristic parameters ($\Delta v_{\mathrm{y}}$, $\Delta v_{\mathrm{p}}$, $v_{\mathrm{m}}$, $v_{\mathrm{F}}$) were analyzed. The results show the optical unit’s tensile strain-induced Brillouin shift exhibits periodic distribution along the cable. The stable average peak $v_{\mathrm{F}}$ achieved a correlation coefficient of 0.98 with tensile load F_i. A dual-threshold sensing model was established: no shift response below F₀ = 90 kN (7.84% Rated Tensile Strength (RTS)); strong linear correlation between $v_{\mathrm{F}}$ and F_i beyond F_m = 110 kN (9.58% RTS) with a tensile sensitivity coefficient of 0.03788 MHz/kN. This study provides key BOTDR technical support for submarine cable tensile monitoring in complex marine environments.

1. Introduction

Submarine cables serve as crucial power transmission channels connecting offshore wind farms, and their long-term operational reliability is essential for power supply security. In complex marine environments, mechanical tensile loads from laying traction, anchor dragging, ocean current scouring, and tidal changes can lead to structural damage, insulation aging, and even fracture failure of submarine cables [1,2]. The traction tension during the laying process can reach about 120 kN, approximately 10∼20% of the submarine cable’s Rated Tensile Strength (RTS) [3,4]. The tensile effect caused by anchor impact can even exceed 1000 με [5]. Accurately monitoring mechanical states such as tension, bending, and torsion during laying and operation is therefore essential [6]. Moreover, the inherently harsh marine environment accelerates the accumulation of fatigue in mechanical components [7], leading to increased focus on structural integrity monitoring for mechanical degradation and stress concentration. Brillouin optical time-domain reflectometry (BOTDR), with its capabilities for distributed strain sensing, offers a promising solution for such monitoring.

For submarine cable monitoring, Rayleigh scattering-based Distributed Acoustic Sensing (DAS) offers advantages like high spatiotemporal resolution and full-link coverage for vibration/impact detection. However, it is susceptible to environmental noise from sea waves and vessel traffic, and cannot quantitatively characterize tensile loads. In contrast, BOTDR boasts full-range sensing, strong anti-interference capability, and a dual role as a communication fiber [8,9]. In recent years, it has been applied to civil engineering infrastructure condition monitoring [10] and transmission line icing monitoring [11], enabling real-time, continuous strain distribution along the entire cable length, accurate load assessment, and localization of local overload sections. It holds unique advantages for distributed monitoring of submarine cables’ mechanical states [12,13], though related research remains in the exploratory stage.

Despite this promise, research on BOTDR-based mechanical monitoring for submarine cables, especially for the increasingly common three-core fiber-optic composite designs, remains in its infancy. Existing studies primarily focus on temperature monitoring [14] or vibration detection using phase-sensitive OTDR [15]. While valuable, these do not address the core need for quantitative tensile load sensing. Previous mechanical investigations (such as tensile tests on single-core cables) have revealed the phenomenon of low-load “blind zones” arising from design fiber redundancy lengths [16], yet these studies remained confined to descriptive observations without establishing the critical load or quantitative criteria for the termination of such blind zones. Other studies, including armored cable testing [17] and field deployments for seismic strain detection [18], have demonstrated the feasibility of integrated optical fibers within cables for strain monitoring applications. However, none have established a quantitative load-strain correlation model, nor have they addressed the impact of helical structures on coupling efficiency. Similar studies based on finite element analysis have revealed the mechanical properties of cables [19,20,21] and internal fiber strain [22,23,24,25]. Further research has explored the potential engineering applications of fiber optic monitoring for submarine cable burial depth [26,27] and vortex-induced vibration [28,29]. However, existing research lacks clear criteria for the complete coupling of the optical fiber–optical unit–cable system. No experimentally validated model has been established for the complex layered structure of submarine cables. Furthermore, the approach of directly correlating distributed BOTDR strain characteristics with the macro-tensile load state of three-core submarine cables cannot be applied to practical engineering scenarios.

To date, existing research has shown the potential of long-distance distributed BOTDR for submarine cable monitoring. Current studies focus on scenarios like temperature monitoring and vibration, with limited research into mechanical load monitoring and sensing models. Revealing strain transfer in the cable’s multi-layer mechanical structure (optical fiber, optical unit, filling layer, armor wires, cable core), considering the optical unit’s helical stranding, and establishing an optical fiber excess-length strain sensing model are fundamental for assessing the mechanical state of submarine cables during offshore wind farm cable laying, operation, and maintenance. This paper clarified the BOTDR monitoring principle based on a three-layer mechanical structure, established a tensile test monitoring platform, and investigated the distributed optical fiber monitoring characteristics and dual-threshold sensing model for a 66 kV three-core fiber-optic composite submarine cable under tensile conditions. The proposed sensing model defines dual thresholds F₀ (90 kN, fiber excess-length exhausted) and F_m (110 kN, full coupling), partitioning the sensing process into three intervals: blind zone—transition zone—stable zone. This establishes a linear relationship between the stable average peak $v_{\mathrm{m}}$ and load (R² = 0.98), achieving quantitative load inversion from strain sensing. Furthermore, while prior studies overlooked temperature–strain cross-sensitivity issues, this research proposes a laboratory method of “external optical unit mean compensation” and recommends Raman Optical Time-Domain Reflectometry (ROTDR)collaborative compensation for engineering applications.

2. Three-Layer Mechanical Structure BOTDR Monitoring Principle

To construct a mechanical transfer model, it is necessary to understand the structure of the three-core submarine cable and the mechanical coupling relationships between fiber strain, optical unit strain, and submarine cable strain.

2.1. Three-Layer Mechanical Structure of Submarine Cable, Optical Unit, and Optical Fiber

The three-core fiber-optic composite submarine cable tested in this paper is model HYJQF41-F-38/66, as shown in Figure 1. The filling layer contains two optical units. Each optical unit contains 48 B1 single-mode fibers.

The fiber grease in the optical unit provides protection for the fibers and also serves a lubricating function, allowing the fibers to slide axially to a certain degree within the optical unit. This enhances the fiber’s adaptability to external mechanical disturbances.

To ensure that the fibers maintain low-loss, stable transmission performance under complex environmental conditions such as mechanical stress and temperature changes, the fiber length within the optical unit is slightly longer than the optical unit itself. The percentage ratio of this difference to the optical unit length is called the fiber excess length δ [30], see Equation (1). The design value for submarine cable excess length δ₀ is generally controlled between 0.6 and 0.7% [31].

$$\delta ={\displaystyle \frac{L_{\mathrm{fiber}}-L_{\mathrm{unit}}}{L_{\mathrm{unit}}}}\times 100\%$$

(1)

2.2. Strain Relationships in Three-Layer Structure of Submarine Cable, Optical Unit, and Optical Fiber

2.2.1. Strain of Submarine Cable, Optical Unit, and Optical Fiber

The optical unit is helically wound within the submarine cable as shown in Figure 2a. A planar diagram of the axial elongation during stretching is shown in Figure 2b [32].

In Figure 2b, L is the lay length (pitch) of the optical unit winding, which is much larger than the outer diameter d of the optical unit (L > 10d); Lu is the length of the optical unit corresponding to one pitch. If the submarine cable undergoes axial elongation Δl under axial tension, the corresponding elongation of the optical unit is Δl_u. The following relationships exist:

$${\theta }_1=\arctan ({\displaystyle \frac{\pi d}{L}})$$

(2)

$${\theta }_2\arctan ({\displaystyle \frac{\pi d}{L+\Delta l}})$$

(3)

$$L_{\mathrm{u}}={\displaystyle \frac{L}{\cos {\theta }_1}}$$

(4)

$$L_{\mathrm{u}}+\Delta l_{\mathrm{u}}={\displaystyle \frac{L+\Delta l}{\cos {\theta }_2}}$$

(5)

where θ₁ and θ₂ are the helical winding angles of the optical unit. Since L >> d, $cos{\theta }_1\approx cos{\theta }_2\approx 1$; therefore, L_u ≈ L, Δl_u ≈ Δl.

In Figure 2c, L_f is the fiber length within one pitch. The blue solid line represents the fiber in a loose state within the optical unit, and the blue dashed line represents the fiber in a just-tightened state within the optical unit. When the submarine cable is not subjected to tensile load, the fiber length is the sum of the optical unit length and the initial fiber excess length, i.e., $L_{\mathrm{f}}=L_{\mathrm{u}}+L_{\mathrm{u}}\cdot {\delta }_0$.

2.2.2. Critical Sensing Tensile Load F₀

This paper defined the tensile load at which the fiber excess length in the submarine cable is exhausted (i.e., the optical unit length equals the fiber length) as the critical sensing tensile load F₀.

When the tensile load is below the critical sensing tensile load F₀, the optical unit length is less than the fiber length (Figure 2c). The fiber maintains its initial length $L_{\mathrm{f}}=L_{\mathrm{u}}+L_{\mathrm{u}}\cdot {\delta }_0$, and the fiber elongation Δl_f = 0. Correspondingly, the fiber strain ${\epsilon }_{\mathrm{f}}=0$. At this point, the fiber cannot sense the mechanical state of the submarine cable.

When the tensile load reaches the critical sensing threshold F₀, the optical unit elongates to the fiber’s original length, the fiber becomes perfectly taut, and the fiber’s slack is exhausted, i.e., $\delta =0$, $L_{\mathrm{u}}=L_{\mathrm{f}}$, yet the fiber exhibits no elongation and remains incapable of sensing the stress applied to the submarine cable.

2.2.3. Minimum Sensing Tensile Load F_m

When the tensile load exceeds the critical sensing tensile load F₀, the fiber begins to be stretched, as shown in Figure 2d. The fiber length becomes the sum of its original length and the elongation, i.e., $L_{\mathrm{f}}+\Delta l_{\mathrm{f}}=L_{\mathrm{u}}+L_{\mathrm{u}}\cdot {\delta }_0+\Delta l_{\mathrm{f}}$. Under axial tension, the submarine cable’s filling layer gradually compacts. The helically twisted armor wires undergo slight adjustment relative to the cable core to eliminate initial interlayer gaps, whilst the relative movement between the optical unit and the filling layer remains not yet fully constrained.

This paper defined the minimum sensing tensile load F_m as the transition point where the optical unit and the submarine cable shift from incomplete coupling to complete coupling. When the tensile load continues to increase and reaches F_m, the entire composite cross-section of the submarine cable achieves full engagement and compaction, and the optical unit and the submarine cable are in a state of complete coupling. Thereafter, the fiber elongation equals the optical unit elongation, i.e., $\Delta l_{\mathrm{f}}=\Delta l_{\mathrm{u}}$. Because the fiber excess length δ₀ is extremely small and can be neglected, the fiber strain is as shown in Equation (6):

$${\epsilon }_{\mathrm{f}}={\displaystyle \frac{\Delta l_{\mathrm{f}}}{L_{\mathrm{f}}}}={\displaystyle \frac{\Delta l_{\mathrm{u}}}{L_{\mathrm{u}}+L_{\mathrm{u}}\cdot {\delta }_0+\Delta l_{\mathrm{f}}}}\approx {\displaystyle \frac{\Delta l_{\mathrm{u}}}{L_{\mathrm{u}}+\Delta l_{\mathrm{f}}}}={\displaystyle \frac{\Delta l_{\mathrm{u}}}{L_{\mathrm{u}}+\Delta l_{\mathrm{u}}}}\approx {\displaystyle \frac{\Delta l}{L+\Delta l}}={\epsilon }_{\mathrm{c}}$$

(6)

where ${\epsilon }_{\mathrm{f}}$ is the strain of the submarine cable fiber, and ${\epsilon }_{\mathrm{c}}$ is the axial strain of the submarine cable. Although the helical winding structure of the optical unit and the fiber excess length design cause the actual fiber path to be slightly longer than the axial length of the submarine cable, within one winding pitch, the fiber strain is nearly equal to the axial strain of the submarine cable.

2.2.4. Submarine Cable Strain and Fiber Strain

Considering material coupling effects, the fan-shaped PE filling structure undergoes non-uniform compressive deformation under axial tension, forming a composite stress field at the fiber-filling medium interface. Based on elastic mechanics and fiber sensing theory, this stress transfer process can be expressed as follows:

$${\epsilon }_{\mathrm{f}}=\eta {\epsilon }_{\mathrm{c}}=\eta ({\displaystyle \frac{F_{\mathrm{i}}}{A_{\mathrm{c}}{E}_{\mathrm{c}}}})$$

(7)

where η is the strain transfer efficiency coefficient (0 < η ≤ 1). η characterizes the overall conversion efficiency from macroscopic axial strain in the cable body to axial strain in the optical fiber. As a lumped parameter, η encompasses the mechanical coupling relationship between the optical fiber, optical unit, and cable body, incorporating the combined effect of complex stress states such as lateral pressure on frequency shift. Under the assumption of ideal bonding and the absence of interfacial slip, the theoretical upper limit of strain transfer is determined by the helical path of the optical unit. Calculating the helix angle based on cable structural parameters (rotation diameter d ≈ 75 mm, pitch L = 5 m) yields ${\eta }_{\max }={\cos }^2\theta \approx 0.9978$ under ideal conditions. This value represents an idealized geometric upper bound and does not account for the various loss mechanisms inherently present within η’s definition. F_i is the single-end tensile force applied to the submarine cable, $A_{\mathrm{c}}$ is the cross-sectional area of the submarine cable, and $E_{\mathrm{c}}$ is the equivalent elastic modulus of the submarine cable. Its calculation requires consideration of the combined response of all structural materials transmitting axial tensile forces:

$$E_{\mathrm{c}}={\displaystyle \frac{\sum E_{\mathrm{i}}\cdot A_{\mathrm{i}}\cdot k_{\mathrm{i}}}{\sum A_{\mathrm{i}}}}$$

(8)

where $A_{\mathrm{i}}$ is the cross-sectional area of each structure, $E_{\mathrm{i}}$ is the elastic modulus of each structural material, and k_i denotes the helical structure correction coefficient for each helically twisted configuration, typically approximated as $k_{\mathrm{i}}\approx {\cos }^3{\theta }_{\mathrm{i}}$. This study focuses on the overall mechanical response of submarine cables under axial tension. To simplify calculations, the overall axial stiffness is determined by directly summing the three-phase structures, which results in an E_c value slightly greater than the actual value. The total cross-sectional areas and material elastic moduli of each structure for the submarine cable used in this experiment are shown in

Table 1. Numerical Table of Cross-Sectional Areas for Various Structures of Fiber Optic Composite Submarine Cables and Their Corresponding Material Modulus of Elasticity.

Structure	Material	${\mathit{A}}_{\mathbf{i}}$ (mm2)	${\mathit{E}}_{\mathbf{i}}$ (GPa)
Conductor	Copper	5.6 × 103	110
Insulation layer	XLPE	7.14 × 103	0.3
Inner sheath	PE	2.41 × 103	1.0
Armor layer	Steel wire	3.88 × 103	200
Outer serving	PP	2.72 × 103	1.3
Optical unit (single)	Steel wire	67.3	200

.

2.3. BOTDR Monitoring Principle for Fiber Strain

Brillouin scattering is a nonlinear scattering effect arising from the interaction between light waves and acoustic waves in a medium. Microscopic inhomogeneities in material properties such as density and refractive index cause scattering of light propagating in the optical fiber. Environmental temperature and tensile load (strain) influence the speed of sound and the refractive index of light in the fiber, causing a linear change in the Brillouin frequency shift. Their relationship [33] is as follows:

$$v_{\mathrm{B}}(t,\epsilon )=v_{\mathrm{B}}(t_0,{\epsilon }_0)+C_{\mathrm{t}}(t-t_0)+C_{\mathsf{\epsilon }}(\epsilon -{\epsilon }_0)$$

(9)

where $v_{\mathrm{B}}(t,\epsilon )$ is the Brillouin frequency shift of the fiber under the combined effect of temperature t (°C) and strain ε (με); $v_{\mathrm{B}}(t_0,{\epsilon }_0)$ is the Brillouin frequency shift of the fiber at the initial temperature t₀ (°C) and initial strain ε₀ (με); $C_{\mathrm{t}}$ (MHz/°C) and $C_{\mathsf{\epsilon }}$ (MHz/με) are the temperature sensitivity coefficient and strain sensitivity coefficient of the Brillouin frequency shift, respectively.

When environmental temperature changes, after temperature compensation of the fiber Brillouin frequency shift (i.e., knowing $C_{\mathrm{t}}(t-t_0)$ in Equation (9)), a linear relationship between the Brillouin frequency shift difference and the strain difference can be established:

$$\Delta v_{\mathrm{B}}=C_{\mathsf{\epsilon }0}\Delta {\epsilon }_{\mathrm{c}}$$

(10)

where $C_{\mathsf{\epsilon }0}$ is the relative strain sensitivity coefficient, representing the change in Brillouin frequency shift relative to the initial strain ε₀ (με) caused by a unit change in strain. Its typical value is 0.0483 MHz/με [34].

The direct physical quantity monitored by BOTDR is fiber strain. This paper establishes the theoretical formula from submarine cable strain sensing to mechanical load sensing as follows:

$$\Delta v_{\mathrm{B}}=C_{\mathsf{\epsilon }0}\Delta {\epsilon }_{\mathrm{c}}$$

(11)

This paper defined the change in Brillouin frequency shift per unit tensile load, $C_{\mathrm{vF}}={\displaystyle \frac{C_{\mathsf{\epsilon }0}}{A_{\mathrm{c}}{E}_{\mathrm{c}}}}$, as the tensile sensitivity coefficient. Its value is determined by the fiber strain sensitivity coefficient and the equivalent axial stiffness of the submarine cable.

3. Experiment

To verify the aforementioned monitoring principle, this paper, referencing CIGRE TB623 [35,36], established a submarine cable tensile test BOTDR monitoring platform at South Sea Submarine Cables Co., Ltd., Shanwei, China. The platform includes a horizontal tension machine, BOTDR, fiber optic patch cords, a 66 kV three-core fiber-optic composite submarine cable, and fixing devices at both ends of the cable, as shown in Figure 3a.

BOTDR with a temperature measurement accuracy of ±1 °C, a strain measurement accuracy of ±20 με, and a spatial resolution better than 1 m was used in the experiment. The experimental environment temperature in this study was 21 ± 0.6 °C, with overall temperature fluctuation not exceeding 1 °C.

The test cable sample length was 45 m. For convenient connection to BOTDR, a section of the optical unit approximately 15 m long was stripped out near the monitoring end. This optical unit retains the original submarine cable optical unit structure, consisting sequentially from inside to out of fiber, water-blocking grease, stainless steel tube, HDPE sheath, etc. It serves as the external optical unit section, as shown in Figure 1b. The external optical unit section was mechanically separated from the stressed submarine cable section, arranged in a slack configuration without being embedded in loading fixtures. It retains its complete protective structure, free from lateral constraints that could cause bending. It is unaffected by tensile loads and is influenced solely by ambient temperature.

The experimental setup is shown in Figure 3b. BOTDR is connected to the external optical unit via a 510 m fiber optic patch cord, which shares the same optical path as the submarine cable’s optical unit. Both ends of the submarine cable are fixed using fixtures to maintain structural stability, as shown in Figure 3c. The galvanized low-carbon steel wires of the armor layer and the three-phase copper conductors are embedded and locked into the fixtures. The near-end fixture is fixed to a rigid base and remains stationary. The far-end fixture is connected to the horizontal tension testing machine via a traction device for applying tensile load.

The host system controls the horizontal tension machine with a minimum tensile load step of 20 kN. RTS of the test submarine cable was 1147.65 kN (provided by the manufacturer). The applied tensile load procedure and its variation over time are shown in Figure 4a and b, respectively. References [3,4] indicate that the conventional traction tension for laying three-core submarine cables is approximately 10% RTS, rising to 19% under extreme conditions. The upper load limit of 250 kN (21.8% RTS) established for this experiment fully encompasses the aforementioned range, ensuring the model’s engineering applicability. Two repeated tests were conducted in this study.

4. Results and Analysis

4.1. Length Distribution of Brillouin Frequency Shift

Taking the direction of submarine cable tensile load application as positive, and setting the junction between the external optical unit section and the submarine cable section as 0, the schematic diagram of BOTDR monitoring length is shown in Figure 5a. Here, −16.3–0 m is the external optical unit, and 0–29.1 m is the submarine cable optical unit.

Figure 5b,c show the three-dimensional plots of Brillouin frequency shift vs. length vs. load for the submarine cable fiber in the two repeated tests. The shapes and variation trends of the two 3D plots are consistent, indicating good repeatability of the observed distribution of Brillouin frequency shift with length and load.

From Figure 5b, it can be seen that the initial Brillouin frequency shift distribution curve of the external optical unit is overall higher than that of the submarine cable optical unit. Owing to the absence of structural compression from the outer sheath, armor layer, and filling layer, the external optical unit is exposed to air, resulting in a significantly higher initial Brillouin shift value compared to the submarine cable optical unit. As tensile load increased, the submarine cable optical unit underwent compression from the filling layer’s fan-shaped structure, generating an incremental mechanical component of the Brillouin shift. Consequently, the difference in Brillouin shift between the external optical unit and the submarine cable optical unit progressively diminishes.

As the Brillouin frequency shift is sensitive to both temperature and strain, spatial temperature variations generate a temperature-induced frequency shift component. When superimposed upon the strain-induced signal, this causes the monitored value of strain Brillouin frequency shift ($\Delta v_{\mathrm{B}}$) to deviate from its true value. Sudden changes in the temperature-induced frequency shift may also lead to premature misidentification of F₀ and blur the boundary of the linear segment corresponding to F_m. Using the external optical unit’s mean Brillouin frequency shift for temperature compensation, the strain Brillouin frequency shift ($\Delta v_{\mathrm{B}}$) is obtained by subtracting this compensation value from the cable section’s Brillouin frequency shift. Its distribution is shown in Figure 6.

Note that the external optical unit mean temperature compensation method for BOTDR strain monitoring applies only to laboratory studies with uniform temperature fields. A data-driven real-time prediction framework has been successfully applied to critical linear infrastructure monitoring [37]. The approach of achieving robust field monitoring through collaborative multi-source sensor data analysis can be directly transferred to submarine cable systems. For field applications in submarine cable engineering, ROTDR is recommended to provide distributed temperature data for compensating the BOTDR strain measurements. Specifically, BOTDR and ROTDR share the same fiber optic link embedded within the submarine cable. ROTDR captures high-resolution distributed temperature data across the entire cable length, decoupling the Brillouin frequency shift component generated by temperature. This component is then subtracted from the continuous Brillouin frequency shift distribution obtained from BOTDR, yielding the Brillouin component attributable solely to true strain.

From Figure 6, it can be seen that the spatial distribution of strain Brillouin frequency shift $\Delta v_{\mathrm{B}}$ for the external optical unit section overlaps under various tensile loads and is higher than that of the submarine cable optical unit.

The fiber strain Brillouin frequency shift $\Delta v_{\mathrm{B}}$ of the submarine cable optical unit section varies with tensile load. Under each tensile load, there is a periodic distribution feature along the line with a length of 6.5 m, which is longer than the design pitch (5 m) of this submarine cable. This discrepancy stems not only from factors such as the optical unit being helically wound within the pitch at a specific diameter and its internal fiber redundancy design, but also relates to the mismatched pitches and reverse-twisting across different layers of the submarine cable’s composite structure.

4.2. Tensile Characteristic Quantities from Brillouin Optical Time-Domain Reflectometry Frequency Shift

The cable fiber’s Brillouin frequency shift shows a periodic length distribution with four complete cycles in this study. Considering that the external optical unit section might affect the Brillouin frequency shift of the first length cycle in the submarine cable section, the strain Brillouin frequency shift of the second length cycle was selected for result analysis.

To find the characteristic quantities of the Brillouin frequency shift of the submarine cable optical unit under tensile load, this paper studied strain Brillouin frequency shift quantities such as amplitude $\Delta v_{\mathrm{y}}$, value $\Delta v_{\mathrm{p}}$, and stable peak value $v_{\mathrm{m}}$. The definitions of $\Delta v_{\mathrm{y}}$ and $v_{\mathrm{m}}$ are shown in Figure 7.

4.2.1. Strain Brillouin Frequency Shift Amplitude $\Delta v_{\mathrm{y}}$

The variation in strain Brillouin frequency shift amplitude $\Delta v_{\mathrm{y}}$ of the submarine cable optical unit with tensile load F_i under different tensile loads is shown in Figure 8.

$\Delta v_{\mathrm{y}}$ reflects the maximum range of strain fluctuation within a single-cycle length, characterizing the degree of local stress concentration. From Figure 8, it can be seen that $\Delta v_{\mathrm{y}}$ has a nonlinear exponential function relationship with F_i, which is not convenient for tensile mechanical monitoring.

4.2.2. Strain Brillouin Frequency Shift Peak Mean Value $\Delta v_{\mathrm{p}}$

The ratio of the peak value to the mean value of the strain Brillouin frequency shift of the submarine cable optical unit is defined as the Brillouin frequency shift peak mean value $\Delta v_{\mathrm{p}}$. The peak mean value $\Delta v_{\mathrm{p}}$ describes the degree of non-uniformity in the spatial distribution of strain. The variation in the Brillouin frequency shift peak mean value $\Delta v_{\mathrm{p}}$ with tensile load F_i is shown in Figure 9.

From Figure 9, it can be seen that during the tensile loading process, the peak mean value $\Delta v_{\mathrm{p}}$ gradually decreases, indicating that as the tensile load increases and the multi-layer structure of the submarine cable compresses, the strain distribution along the optical unit tends to become more uniform.

The correlation coefficient between $\Delta v_{\mathrm{p}}$ and tensile load is only 0.85, making it unable to precisely quantify the tensile load on the submarine cable. However, it can be used to judge whether the optical unit–submarine cable system has entered a state of complete coupling.

4.2.3. Brillouin Frequency Shift Stable Peak Value $v_{\mathrm{m}}$

During the loading process of the next tensile load level, the response of the fiber Brillouin frequency shift exhibits fluctuating changes and gradually tends to stabilize. This paper proposes concepts such as the stable segment of Brillouin frequency shift and stable peak value.

Within the 5 min duration of each tensile load application, the 120 s segment with minimal fluctuation is selected as the stable segment of the strain Brillouin frequency shift $\Delta v_{\mathrm{B}}$. The time series of peak values $v_{\mathrm{m}}$ for this stable segment is extracted.

As shown in Figure 10, the orange bars represent the extracted stable segments of strain Brillouin frequency shift. The overall trend of the Brillouin frequency shift stable peak value $v_{\mathrm{m}}$ has a certain correlation with the tensile load F_i, but it is affected by noise disturbance.

4.2.4. Brillouin Frequency Shift Stable Average Peak Value $v_{\mathrm{F}}$

The average value of the 120 s time series of stable Brillouin frequency shift peaks $v_{\mathrm{m}}$ was calculated as the stable average Brillouin frequency shift peak $v_{\mathrm{F}}$. The Brillouin frequency shift stable average peak values $v_{\mathrm{F}}$ under different loads are presented in Figure 10. Its correlation study and sensing model with the submarine cable tensile load F_i are described below.

4.3. Brillouin Frequency Shift Tensile Sensing Model

As shown in Figure 11, the three-core submarine cable tensile sensing model exhibited a critical sensing tensile load F₀ and a minimum sensing tensile load F_m, thereby validating the tensile load sensing theories outlined in Section 2.2.2 and Section 2.2.3.

Below the critical sensing tensile load F₀ (90 kN, 7.84% RTS in this study), the stable average Brillouin frequency shift peak $v_{\mathrm{F}}$ is extremely small. In this state, the existence of fiber excess length within the optical unit prevents the submarine cable from sensing strain.

When the tensile load reaches the critical sensing tensile load F₀, the stable average peak value $v_{\mathrm{F}}$ increases abruptly. In this state, the fiber excess length within the optical unit has been exhausted by the increased strain of the submarine cable under the action of F₀, and the sensitivity of $v_{\mathrm{F}}$ to the submarine cable tensile load F_i is enhanced.

It should be noted that, due to the minimum tensile load step of 20 kN of the tension machine used in this test, the sensing model between the stable average peak value $v_{\mathrm{F}}$ and the tensile load F_i within the range from the critical sensing tensile load F₀ (90 kN) to the minimum sensing tensile load F_m (110 kN) could not be obtained. This limitation is significantly mitigated in practical submarine cable deployment scenarios. Driven by the stringent requirements of offshore operations, high-resolution load regulation is commonly adopted during submarine cable laying to avoid over-tensioning, and commercial submarine cable laying equipment can thus continuously capture load responses across the entire F₀–F_m interval, enabling seamless monitoring of the transition phase from fiber excess length exhaustion to complete coupling between the optical unit and the cable body. Furthermore, in engineering applications, the model only needs to identify F₀ (where fiber excess length is exhausted) through the abrupt change in $v_{\mathrm{F}}$ and achieve continuous monitoring of the tensile load via the linear relationship.

When the tensile load exceeds the minimum sensing tensile load F_m (110 kN, approximately 9.58% RTS in this study), a significant linear relationship exists between the stable average peak value $v_{\mathrm{F}}$ and the submarine cable tensile load F_i, with a correlation coefficient of 0.98 and a tensile sensitivity coefficient $C_{\mathrm{vF}}$ of 0.03788 MHz/kN.

Based on the above research, the sensing model between the stable average Brillouin frequency shift peak $v_{\mathrm{F}}$ and the tensile load F_i for the three-core submarine cable is given by Equation (12):

$$\begin{gathered} \begin{array}{c}\Delta v_{\mathrm{F}}=\left\{\begin{array}{c}0\hspace{1em}(0<F_{\mathrm{i}}<F_0)\\ f(F_{\mathrm{i}})\hspace{1em}(F_0<F_{\mathrm{i}}<F_{\mathrm{m}})\\ C_{\mathrm{vF}}\Delta F_{\mathrm{i}}\hspace{1em}(F_{\mathrm{m}}<F_{\mathrm{i}})\end{array}\right.\end{array} \\ {C}_{\mathrm{vF}}=0.03788 \mathrm{MHz}/\mathrm{kN} \left(\text{HYJQF41-F-38/66}\right) \end{gathered}$$

(12)

Table 2. Comparison of Strain-Induced Brillouin Frequency Shift Characteristics for Tensile Load Monitoring.

Characteristic Quantity	Functional Relationship	R2	Applicable Scenario
$\Delta v_{\mathrm{y}}$	$\Delta v_{\mathrm{y}}=\exp (1.45+9.9\times {10}^{-4}{F}_{\mathrm{i}}+6.3\times {10}^{-6}{F}_{\mathrm{i}}^2)$	1	Used for diagnosing local mechanical state or stress concentration phenomena inside the submarine cable.
$\Delta v_{\mathrm{p}}$	$\Delta v_{\mathrm{p}}=0.91998-0.00121F_{\mathrm{i}}$	0.8488	Used for determining the coupling state between the optical unit and the cable body.
$v_{\mathrm{m}}$	-	-	Unable to quantify the corresponding tensile load, used to intuitively grasp the overall trend of load application.
$v_{\mathrm{F}}$	$\left\{\begin{array}{c}{v}_{\mathrm{F}}+1.73149=0\hspace{1em}(0<F_{\mathrm{i}}<90 \mathrm{kN})\hfill \\ \Delta v_{\mathrm{F}}=f(F_{\mathrm{i}})\hspace{1em}(90 \mathrm{kN}<F_{\mathrm{i}}<110 \mathrm{kN})\hfill \\ v_{\mathrm{F}}+3.13802=0.03788F_{\mathrm{i}}\hspace{1em}(110 \mathrm{kN}<F_{\mathrm{i}})\hfill \end{array}\right.$	0.9800	Used for identifying small-load states of the submarine cable, accurately quantifying larger loads, and providing failure warnings under ultimate loads.

compares the functional relationships, correlation coefficients, and applicable scenarios of the strain Brillouin frequency shift characteristic quantities: amplitude $\Delta v_{\mathrm{y}}$, peak mean value $\Delta v_{\mathrm{p}}$, stable peak value $v_{\mathrm{m}}$, and stable average peak value $v_{\mathrm{F}}$. The results indicate that $v_{\mathrm{F}}$ reflects the overall tensile load level of submarine cables, covering the full range of engineering monitoring requirements including minor load identification, major load quantification, and ultimate load warning.

The core value of distributed fiber optic sensing lies in simultaneously capturing strain distribution along the entire cable length, enabling precise localization of overloaded sections, stress concentration zones, and abnormal deformation segments. This study employs BOTDR distributed sensing technology for tensile load monitoring, establishing a dual-threshold segmented sensing model for submarine cable tensile mechanical states. This achieves synergistic monitoring through quantitative assessment of macro-level tensile loads and precise localization of micro-level stresses.

4.4. Strain Transfer Efficiency Analysis and Sensor Model Validation

4.4.1. Strain Transfer Efficiency

The physical essence of the minimum sensing tensile load F_m is the starting point where the optical unit and the submarine cable achieve sufficient coupling, i.e., the strain transfer efficiency η stabilizes at its highest level. The strain transfer efficiency η can be derived from Equation (7):

$$\eta ={\displaystyle \frac{{\epsilon }_{\mathrm{f}}}{{\epsilon }_{\mathrm{c}}}}$$

(13)

Based on the sensing model proposed above and the fiber Brillouin sensing theory Equation (14), the fiber strain ${\epsilon }_{\mathrm{f}}$ based on the sensor monitoring values can be derived from the typical strain coefficient $C_{\mathsf{\epsilon }0}=0.0483 \mathrm{MHz}/\mathsf{\mu }\mathsf{\epsilon }$ and stable average peak value $v_{\mathrm{F}}$:

$${\epsilon }_{\mathrm{f}}={\displaystyle \frac{v_{\mathrm{F}}-v_{\mathrm{F}0}}{C_{\mathsf{\epsilon }0}}}$$

(14)

Meanwhile, according to Hooke’s law in Equation (15), the strain in submarine cables ${\epsilon }_{\mathrm{c}}$, derived from theoretical calculations based on tensile load F_i and structural parameters $A_{\mathrm{c}}{E}_{\mathrm{c}}$, is as follows:

$${\epsilon }_{\mathrm{c}}={\displaystyle \frac{F_{\mathrm{i}}}{A_{\mathrm{c}}{E}_{\mathrm{c}}}}$$

(15)

Here, the structural parameter $A_{\mathrm{c}}{E}_{\mathrm{c}}$ can be obtained from Table 1 as 1.39 × 10⁹ N. Figure 12 presents a comparison of fiber strain ${\epsilon }_{\mathrm{f}}$ versus submarine cable strain ${\epsilon }_{\mathrm{c}}$.

When F_m = 110 kN, the strain transfer efficiency $\eta ={\epsilon }_{\mathrm{f}}/{\epsilon }_{\mathrm{c}}=66.25717/79.10533\approx 0.837$. When η approaches 1 and remains relatively stable, it signifies that the submarine cable has completed its overall structural compaction and settlement. The optical unit has achieved full rigid coupling with the main cable structure, with no further significant relative movement or stress redistribution occurring internally. Therefore, η first reaching and stabilizing above 0.8 can be judged as entering a stable and reliable sensing interval for monitoring.

From Figure 12, it can be seen that above the minimum sensing tensile load, the measured and theoretical values are close. Due to neglected helix angle effects, the equivalent stiffness E_c in theoretical calculations is overestimated, such that the strain curve is in reality steeper than shown. However, the spiral structure within the submarine cable exhibits a very small laying angle, with a correction coefficient approaching unity. Consequently, the corrected values obtained after spiral correction remain within the experimental error range of the measured values. The strong linear correlation established in this experiment between the stable average peak value $v_{\mathrm{F}}$ of the submarine cable optical unit’s Brillouin frequency shift and the tensile load F_i has been verified theoretically.

4.4.2. Discussion of Error Sources and Uncertainty Quantification

To verify the reliability of the core parameters of the dual-threshold segmented sensing model,

Table 3. Comparison of Critical Thresholds and Tensile Sensitivity Coefficients (Experimental vs. Theoretical Values).

Group	F0	Fm	${\mathit{C}}_{\mathbf{vF}}$
Test 1	90 kN	110 kN	0.03788 MHz/kN
Test 2	90 kN	110 kN	0.03637 MHz/kN
Theoretical Value	-	-	0.03475 MHz/kN

summarizes the critical sensing tensile load F₀, minimum sensing tensile load F_m, and tensile sensitivity coefficient $C_{\mathrm{vF}}$ obtained from two repeated tensile tests and theoretical calculations. F₀ is 90 kN and F_m is 110 kN measured in both tests; the absolute error between the experimental $C_{\mathrm{vF}}$ value and the theoretical value is $\Delta =\left|\overline{k}-k_e\right|=0.002375 \mathrm{MHz}/\mathrm{kN}$, and the relative error is $\delta ={\displaystyle \frac{\Delta }{k_e}}\times 100\%=6.83\%$, which is within the engineering acceptable error margin (10%), verifying the accuracy of the dual-threshold sensing model.

There is an error between the experimentally measured tensile sensitivity coefficient $C_{\mathrm{vF}}$ and the theoretical value, mainly from three aspects: first, the uncertainty of submarine cable material parameters, whose calculation depends on parameters of each structural layer, and actual material properties may deviate from nominal values due to manufacturing tolerances, cable production variations, or environmental aging, leading to deviations in axial stiffness calculation; second, the variability in fiber strain coefficient $C_{\epsilon 0}$, where the theoretical typical value differs from the inherent parameters of actual optical fibers, and temperature interference from friction during stretching affects temperature–strain decoupling; third, the estimation error of structural parameters, where uneven helical stranding causes non-uniform strain distribution along the cable, reducing the calculation accuracy and fitting effect of $C_{\mathrm{vF}}$.

It is noteworthy that traditional deterministic analysis provides only single-parameter values, failing to comprehensively support engineering decisions in complex marine environments. Integrating a probabilistic framework to quantify parameter uncertainty is increasingly vital for ensuring the reliability of monitoring systems for complex engineering structures [38]. The core parameters of the dual-threshold sensing model (F₀, F_m, $C_{\mathrm{vF}}$) are influenced by multi-source uncertainties stemming from materials, structures, and the environment. Future research may employ Monte Carlo simulations or Bayesian inference to incorporate these uncertainties into the output monitoring results, thereby quantifying the confidence intervals for F₀, F_m and $C_{\mathrm{vF}}$.

5. Conclusions

This paper established a BOTDR monitoring platform for tensile testing of a 66 kV three-core fiber-optic composite submarine cable, studying the length distribution characteristics of the fiber’s Brillouin frequency shift under tensile load in the submarine cable optical unit, the characteristic quantities for characterization, and the sensing model. The following conclusions were obtained:

(1)

The strain relationship between the optical fibers, optical units, and submarine cables was clarified based on a three-layer mechanical structure (cable, optical unit, fiber) during the process of increasing tensile load.

(2)

A laboratory-applicable monitoring method was developed, which uses the mean Brillouin frequency shift of an external optical unit for temperature compensation, addressing the cross-sensitivity issue using BOTDR itself. For field applications, ROTDR-based temperature compensation is recommended.

(3)

The Brillouin frequency shift of the cable’s optical unit exhibits a periodic distribution along the pitch under tensile load, with a period slightly longer than the helical pitch. This periodicity becomes more distinct with increasing load.

(4)

The stable average peak value of the Brillouin shift $v_{\mathrm{F}}$ was identified as the optimal characteristic quantity for tensile load characterization, showing the highest linear correlation with load F_i (R² = 0.98) among several candidates.

(5)

A dual-threshold three-segment sensing model was established. Below the critical load F₀ (90 kN, 7.84% RTS), sensing is hindered by fiber excess length; above the minimum sensing load F_m = 110 kN (9.58% RTS), $v_{\mathrm{F}}$ correlates strongly with F_i, yielding a tensile sensitivity $C_{\mathrm{vF}}$ of 0.03788 MHz/kN. The model was verified both theoretically and experimentally.

The proposed framework provides a methodological foundation for transitioning from qualitative strain observation to quantitative mechanical state assessment of submarine cables, enhancing the safety and reliability of offshore wind farm power transmission.