# Assessing reliability of cm-scale optical fiber strain sensing in high gradient configurations through benchmarking and mechanical modelling

Damiano Gianotti, Sylvain Magne, François Di Paola, Benjamin Sapaly, Yves Van Ingelgem, Iris De Graeve

► To cite this version:

Damiano Gianotti, Sylvain Magne, François Di Paola, Benjamin Sapaly, Yves Van Ingelgem, et al. "Assessing reliability of cm-scale optical fiber strain sensing in high gradient configurations through benchmarking and mechanical modelling." e-Journal of Nondestructive Testing, 2026, LATAM-SHM 2026 - 2nd Latin-American Workshop on Structural Health Monitoring January, 7-9 2026, 31 (2), 10.5828/32456.cea-05513414

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# ASSESSING RELIABILITY OF CM-SCALE OPTICAL FIBER STRAIN SENSING IN HIGH GRADIENT CONFIGURATIONS THROUGH BENCHMARKING AND MECHANICAL MODELLING

DAMIANO GIANOTTI*, **, SYLVAIN MAGNE†, FRANÇOIS DI PAOLA††, BENJAMIN SAPALY†, YVES VAN INGELGEM*, **, IRIS DE GRAEVE**

* Zensor, Witte Patersstraat 4, 1050 Brussel, Belgium
e-mail: damiano.gianotti@zensor.be, web page: https://www.zensor.be

† Université Paris-Saclay, CEA, List, 91120 Palaiseau, France
e-mail: sylvain.magne@cea.fr, web page: https://list.cea.fr

†† Université Paris-Saclay, CEA, Service d'Études Mécaniques et Thermiques (SEMT), 91191 Gif-sur-Yvette, France, e-mail: francois.dipaola@cea.fr, web page : https://www.cea.fr/paris-saclay

** Vrije Universiteit Brussel, Research Group of Sustainable Materials Engineering, Dept of Materials and Chemistry, Pleinlaan 2, 1050 Brussels, Belgium
e-mail: iris.de.graeve@vub.be, web page: https://surf.research.vub.be/

**Key words:** Optical Fiber Sensors (OFS), Fiber Bragg Grating (FBG), Optical Frequency-Domain Reflectometry (OFDR), Frequency-Modulated Continuous Wave (FMCW), Stress concentration, Finite-Element Method (FEM).

**Abstract.** FBG-WDM, FBG-FMCW and OFDR distributed strain monitoring techniques are benchmarked and compared to FEM results, in view of assessing the performance of SHM of complex high-value structures subject to intense stress concentration. The results reveal distinct performance trade-offs: OFDR provides the highest accuracy but fails at high gradients (>100 µε/mm), while FBG-based methods are more robust, but their accuracy is algorithm-dependent due to spectral chirp. The CFG-FMCW technique systematically underestimates peak strains due to spatial filtering, confirming that no single technology is universally optimal for high-gradient monitoring.

## 1 INTRODUCTION

Distributed optical-fiber sensing is widely used in structural-health monitoring (SHM) in industries such as oil & gas, civil infrastructure, rail, aerospace and energy production [1, 2, 3]. Optical fiber sensors (OFS) are passive, immune to electromagnetic interference, embeddable, and provide long-range, multi-parameter measurements of primary measurands (strain, temperature, pressure, external refractive index) and derived quantities (displacement, crack opening, etc.). These attributes make OFS attractive for detecting localised defects and tracking damage progression in high-value metal, concrete and composite structures [4, 5].

However, many structural defects and features (bolted joints, notches, cracks, delaminations) produce centimetre- and sub-centimetre-scale local stress concentrations (LSCs) that generate steep, localized high strain gradients (HSGs). HSGs violate the constant-strain assumption underlying finite-gage sensors and common interrogation algorithms, inducing phenomena such as spectrum chirp, broadening, interference-induced spectral channelling and crosstalk
that can, in turn, result in underestimation, spurious peaks, or a loss of reliable readout. These effects have been documented across both discrete Fiber Bragg Gratings (FBGs) and distributed readout methods such as Optical Frequency-Domain Reflectometry (OFDR).

Literature documents numerous measurement errors when these techniques are applied to HSGs, with strain typically quantified in microstrain (με). Peters et al., for example, reported spectrum chirp and channelling, generating multiple Bragg peaks, in a compact-tension epoxy specimen with highly non-uniform stress [6]. Kang et al. illustrated that symmetric peak broadening occurs when controlled linear gradients (up to 100 με/mm) are applied to FBGs of varying lengths and noted that centroid-based estimators remain unbiased for strictly linear gradients [7]. Matveenko et al. compared 5-mm FBGs and ~10-mm OFDR gage lengths on notched glass fiber-reinforced plastics plates and observed OFDR underestimation when gradients (~40 με/mm) caused averaging over the gage length [8]; the larger the gage length, the larger the deviation. OFDR studies on concrete and reinforced elements likewise illustrate both strengths and limits: Bassil et al. successfully retrieved crack opening displacements by OFDR in a four-point bending test (gradients <50 με/mm) using a shear-lag model [4]. Wada et al. used a home-made OFDR readout unit, similar to the one developed by NASA [10], operating at 151 Hz and reported a 30% underestimation of peak strain near bolted joints with ~1.6 mm spatial resolution at gradients ~100 με/mm [5]. Finally, Magne et al. observed artifacts and non-physical OFDR outputs near rebar junctions under seismic loading while FBG data remained more reliable (peak gradients ~30 με/mm) [4].

Taken together, these studies indicate a clear trade-off. On one hand, OFDR offers far superior spatial sampling and peak localization but is sensitive to intra-segment pattern distortion and signal-to-noise limits. FBG and Continuous Fiber Grating (CFG) approaches are robust and highly multiplexable but average over a finite gage length and suffer spectral distortions (chirp) under HSG. Mitigation strategies are also suggested in literature (shorter gratings, centroid/advanced peak algorithms, improved transfer models), yet experimental benchmarks that directly compare quasi-distributed monitoring techniques against consistent finite-element method (FEM) models under controlled HSG remain limited. To the best of our knowledge, this study is the first to provide such a comprehensive, side-by-side comparison, directly addressing this critical gap.

To achieve this, well-controlled HSGs are generated in an aluminium plate with three near-edge holes. Three techniques are benchmarked against FEM predictions: Fiber Bragg Gratings (FBGs) monitored by wavelength-division multiplexing (WDM), Continuous Fiber Gratings (CFGs) monitored by Frequency-Modulated Continuous-Wave (FMCW) and Rayleigh scattering monitored by Optical Frequency-Domain Reflectometry (OFDR). All these techniques enable high-capacity monitoring (up to hundred/thousand FBGs per fiber) and involve a highly coherent tunable laser as light source. Our objectives are to (i) quantify agreement and systematic deviations between sensor outputs and FEM as gradient severity varies, (ii) identify failure modes and their causes (averaging, spectral channelling, correlation breakdown), and (iii) recommend practical readout choices and mitigation strategies for SHM deployments in situations where HSG can be expected.

## 2 DISTRIBUTED OFS READOUT TECHNIQUES USED

This section summarizes the optical-fiber sensing/readout techniques relevant to our HSG experiments: FBGs in their common variants (including Draw-Tower Gratings (DTGs)/CFGs, and Point-by-Point (PbP) type-III gratings) and OFDR using an Optical Backscatter Reflectometer (OBR). Emphasis is placed on inscription methods and interrogation approaches
used in this work, and on the practical effects of finite gage length and steep strain gradients on measurement accuracy.

## 2.1 Fiber Bragg Gratings

An FBG is a periodic refractive-index modulation photowritten in the core of a fiber that reflects light at the Bragg wavelength $\lambda_B$ that depends on both the period $\Lambda$ and the effective index $n_{eff}$ of the guided mode and is given by:

$$ \lambda_B = 2 * n_{eff} * \frac{\Lambda}{N} \qquad (1) $$

where $n_{eff}$ is the effective index, $\Lambda$ is the period and $N$ is the diffraction order, most often equal to unity, except for PbP gratings. All the other wavelengths are transmitted without loss. The reflection coefficient depends on both index modulation and grating length, typically ranging between 2 mm and 10 mm [11, 12, 13]. In standard telecommunication fibers, typical strain/temperature sensitivities are $\approx 1.21 \text{ pm/}\mu\epsilon$ (strain) and $\approx 10-12 \text{ pm/K}$ (temperature) in the C-band (~1.55 $\mu$m), at room temperature, depending on germanium content [12, 13]. FBGs are commonly multiplexed in the spectral domain (WDM), by splitting interrogator bandwidth into sub-bands allocated to individual gratings.

A variety of photo-inscription techniques exist. UV interferometry (phase-mask or Lloyd-mirror) historically produced type-I/II gratings using excimer and argon-ion lasers emitting at 248 nm [11]. Draw-Tower Gratings (DTGs) are inscribed using a phase mask on draw tower, as the preform is drawn into fiber [14]. This in-line method produces gratings with mechanical reliability equivalent to pristine fibers [15]. In addition, it allows for significant economies of scale and reduces manufacturing costs since fiber stripping/recoating operations are eliminated. So-called Continuous-Fiber-Gratings (CFGs) are low-reflectivity (<1%) DTGs repeatedly photowritten every 10 mm. As they all exhibit the same nominal Bragg wavelength, is possible to interrogate several hundred gratings onto the same fiber using FMCW or OFDR.

PbP femtosecond inscription with titanium-sapphire (Ti:Sa, 800 nm) or ytterbium (Yb, 1030/515 nm) lasers enables through-coating writing and the formation of type-III void-based gratings; it yields short effective lengths and high thermal stability but may introduce higher insertion loss and reduced multiplexing capability compared with type-I/II FBGs [16].

Common interrogation approaches include Continuous Wave (CW) tunable laser [17], broadband source and spectrometer [18] or filter, and FMCW methods [21, 22]. Mode-hop free CW tunable lasers scan the reflection spectrum and Bragg wavelengths are determined by peak detection algorithms (e.g. mid-height (-3 dB), centroid, Gaussian fit) [19, 20]. FMCW techniques transduce reflector distance into RF beat frequencies using a linearly chirped laser. The laser frequency often follows a symmetric saw-tooth modulation pattern facilitating both Fourier analysis and wavelength measurement. The beat frequencies are proportional to source-sensor distances (thus providing sensor localization) and is given by:

$$ f_b = \frac{2 * n_{eff} * L}{c} * \frac{\Delta f}{T} \qquad (2) $$

where $f_b$ is the beat frequency, $\Delta f$ is the frequency excursion of the laser (typically 120 GHz, i.e. 0.96 nm at 1.55 $\mu$m), $L$ is the distance between sensor and reference reflector (several meters), $T$ is the rise/fall time (e.g. 5 ms) and $c$ is the speed of light in vacuum [21, 22].

In the presence of HSGs, the distributed nature of the FBG induces wavelength chirp and spectral broadening, causing distortion in Bragg spectra and uncertainty degradation. It may
ultimately lead to spectral channelling and spurious peak detection. Reducing the grating length mitigates gradient-induced chirp but increases the full width at half maximum (FWHM) and degrades the Signal-to-Noise Ratio (SNR); these trade-offs govern the choice of grating type and interrogation bandwidth for tests.

## 2.2 Optical Frequency-Domain Reflectometry

As with the FMCW technique, the OFDR technique (as implemented in commercial OBRs) also utilizes a highly coherent laser. However, its frequency is linearly swept over a much wider spectral range (typically several tens of nanometres) and the sweeping time lasts typically several seconds. The laser light is transmitted to the sensing line forming one arm of an interferometer. As the laser is frequency-modulated, the signal backscattered by the sensing line is mixed with the reference signal coming directly from the laser, and the resulting interferogram is recorded. The Rayleigh backscatter profile is then recovered in the spatial domain by Fourier processing of the interferogram (in the frequency domain).

The spatial resolution of both OFDR and FMCW techniques is dictated by the frequency excursion of the laser. An OBR device routinely attains down to ~10 µm spatial resolution [10]-[24, 25, 26]. Strain/temperature profiles are eventually extracted by cross-correlating successive profile segments (gage lengths) against a reference, returning a local frequency shift per segment (sensitivity examples: ≈ 5.55 GHz/µε in O-band, ≈ 6.62 GHz/µε in C-band). The gage length is several millimetres-long (the cross-correlation procedure involves several hundred points) and the number of segments may be up to several thousand over a single fiber.

OBR devices have been applied to long-length gratings [5], discrete gratings [23] and on blank fibers, without gratings [10]. In the following, we will focus on the monitoring of blank fibers. The underlying assumption is that the strain is considered *constant* over the gage length and is expected to experience pure shift with respect to its reference state. In presence of HSGs however, the gage pattern is strongly deformed, potentially rendering the cross-correlation impossible and leading to non-physical results. Here again, reducing gage length mitigates this effect but at the expense of a degraded uncertainty as the cross-correlation is computed over a smaller number of data points.

# 3 DESCRIPTION OF THE EXPERIMENT

## 3.1 Plate design

A 2 mm-thick aluminium plate (80×765 mm²; Young modulus E ~ 70 GPa, Poisson ratio v ~ 0.33) was used to generate localized stress concentration and strong strain gradients for sensor validation. Three circular holes of different diameters were intentionally waterjet-cut close to the edge (4 mm edge-to-hole gap). Then seven holes were machined at both extremities to screw 12-mm large mechanical stops on the front side. The plate design is shown on Fig. 1.

Four optical fibers were epoxy-bonded at room-temperature (Araldite 2011, Hunstman) along the entire length of the plate edge, on both front and reverse sides, close to each hole:

**Fiber #1 (front):** on which three type-I FBGs (8-mm long) were photowritten at CEA List on a Talbot setup using a Krypton fluoride (KrF) laser (@248 nm) at 1551.16 nm, 1560.68 nm, and 1569.44 nm, and polyimide (PI)-recoated.

**Fiber #2 (reverse):** comprised twelve type-III PbP gratings (3-mm long) photowritten at CEA List using a doubled Yb femtosecond laser (@515 nm) spanning 1520.17 nm – 1579.58 nm, and PI-recoated.
<figure><img src="image_3.png" /><figcaption>**Figure 1:** Schematic of the front side of a 2 mm-thick aluminium test plate (80×765 mm²) used to generate HSGs. The design features three circular holes of increasing diameter (30 mm, 40 mm and 50 mm) machined off-centre and close to the edge (4 mm gap) to create localized stress concentrations under axial load. Hole centres in mm (x, y) are located at: #1 (200, 19), #2 (356, 24), #3 (548, 29).</figcaption></figure>

**Fiber #3 (front):** bought from FBGS for FMCW use, on which CFGs (9-mm long, 10 mm spacing) were photowritten at 1546 nm on draw tower, and armocer-recoated.

**Fiber #4 (reverse):** blank SMF28 fiber used both as OFDR sensing line and as lead for fiber #2 (looped onto the plate). Grating positions along each fiber and their relative distances to hole centres are shown in Figure 2. To ensure a common spatial reference for all measurements, data from the reverse-mounted fibers (CFGs and FBGs Type-III) were inverted to align with the coordinate system of the front-mounted OFDR fiber.

<figure><img src="image_4.png" /><figcaption>**Figure 2:** (Left) Fiber layout on both front and reverse sides of the plate (not to scale). (Right) Photo of the epoxy-bonding of fiber #2, mounted on reverse side, with PbP gratings glowing red light.</figcaption></figure>

## 3.2 Readout instrumentations

OFDR measurements were performed with a Luna OBR4613 operating in the O-band [24]. This choice was motivated by the fact that the sensing line interrogated by the OBR was the same as that used for the type-III FBGs (in the C-band) and we wanted to avoid any Bragg resonance on the OBR signal. The OBR device was tuned over 62.38 nm (centred at $\lambda$ = 1309.55 nm), leading to a practical spatial resolution of 9 µm.
Discrete type-I and -III FBGs were interrogated with a Luna Hyperion Si-255 module [27], operating in the “Enhanced visibility” (EV) mode, with a scan rate of 10 Hz and a scan range of 160 nm. We chose the factory-preset peak detection algorithm #132 (0.5 nm Peak (EV)).

Finally, the CFGs were monitored with a Sensuron RTS125+ FMCW device [28] providing up to 2048 measurement points per fiber over a sensing length of 13 meters and a spatial sampling of 6.35 mm. A spatial smoothing filter is activated by default in order to improve the SNR (it extends over ±2 measurement points). Furthermore, the acquisition rate is strain range dependent. The maximum acquisition rate is 100 Hz for strain ranges within ±800 με. It decreases with larger strain ranges (e.g. 73 Hz for the range [1545.5 nm–1549.0 nm]).

### 3.3 Test protocol

The plate was installed in a Lloyd LR30K loading machine using claws to impose clamped boundary conditions at both extremities. Both claws were put in contact with the mechanical stops before gripping the plate. A 2500 N load cell was used to measure the tensile force. The lower claw was fixed onto the table, and the upper one was fixed onto the crosshead that may be moved up to 870 mm. The complete experimental setup is depicted in Figure 3.

<figure><img src="image_5.png" /><figcaption>**Figure 3:** The experimental setup showing the aluminium plate installed in the Lloyd LR30K Plus loading machine and readout instrumentation setup. The left panel displays the front side of the plate, the centre panel shows the reverse side, and the figure on the right gives an overview of the global setup.</figcaption></figure>

Loading was performed quasi-statically up to representative loads (e.g., 2360 N) for direct comparisons with FEM predictions. To ensure the reliability of the results, the loading protocol was repeated several times. These repetitions revealed the presence of mechanical creep, which introduced a notable experimental limitation. At high applied forces, the load tended to decline over time, whereas at low forces, it exhibited a slight increase. The system demonstrated the greatest stability in the medium-force range, and consequently, this range was prioritized for acquiring stable and repeatable measurements for analysis.

Furthermore, the mechanical stop introduced a second order bending stress component, superimposed onto the expected pure tensile stress. This unwanted bending contribution may be easily corrected for since the bending strain profiles are identical, but of opposite sign on both sides of the plate; one side is under compression while the other is under tension. Therefore, one may write:
$$ \epsilon_{\text{tensile}} = \frac{\epsilon_{\text{front}} + \epsilon_{\text{reverse}}}{2}, \quad \epsilon_{\text{bending}} = \frac{\epsilon_{\text{front}} - \epsilon_{\text{reverse}}}{2} \qquad (3) $$

For each force, the bending profile was extracted over low-gradient zones (away from the holes) and adjusted by a polynomial fit. The differing sample periods (OFDR: 5-10 mm; FMCW: 6.35 mm) are reconciled by linearly interpolating FMCW strains onto the OFDR grid. The resulting fitted bending profiles were then subtracted from both OFDR and type-III FBG strain profiles and added to both FMCW and type-I FBG strain profiles to yield pure tensile strain profiles.

## 3.4 Finite-Element simulation

A 2D plane-stress FEM model was built in Cast3M [29]. A structured mesh with local refinement near the holes was used to capture steep strain gradients. The boundary conditions used are as follows: on one edge, zero axial displacement is imposed; on the other edge, uniformly distributed pressure is imposed, accompanied by a uniform axial displacement relationship. The mechanical problem is solved under the assumption of small strains and linear elastic behaviour. Post-processing extracted the strain profile along the plate edge, from which strain gradients were determined (Figure. 4).

Intense strain peaks occur at each edge-to-hole gap, and their amplitude increases with increasing hole diameter due to the associated higher stress concentration. The maximum strain value measured is ~2500 με under an axial load of 2360 N while the minimum value is 175 με. The stress concentration factor is thus 14.2, observed on hole #3. Under the same load, the corresponding strain gradients also reach large values at inflection points located ≈ ±2.5 mm away from the stress peaks (e.g., ≈ 214 με/mm at hole #2 and ≈ 164 με/mm at hole #1), with a maximum strain gradient ≈ 223 με/mm on hole #3.

The maximum stress at 2360 N was ≈ 175 MPa, comparable to typical Rp 0.2 values for common aluminium alloys (200 MPa). The elastic assumption is thus valid anywhere on the plate and we also assume a negligible residual strain near peaks. To further validate this approach, a non-linear simulation incorporating large deformations (i.e., a quadratic strain-displacement relationship) was also performed. This analysis revealed no notable discrepancies with the results obtained under the linear assumption.

<figure><img src="image_6.png" /><figcaption>Figure 4: Computed strain profile along the plate edge for a representative axial load of 2360 N (blue line). Also shown is the strain gradient profile (green line, graduated axis on the right).</figcaption></figure>
# 4 EXPERIMENTAL RESULTS

<figure><img src="image_7.png" /><figcaption>**Figure 5:** (a) Comparison of strain profiles from all optical sensing techniques at a constant load of 1187 N (bending-corrected), showing the close agreement of OFDR with the FEM prediction. (b) Strain profiles from FEM, FBG, and FMCW sensors under several increasing load, demonstrating the linear scaling of strain.</figcaption></figure>

As an example, Figure 5(a) shows the strain profiles along the specimen under an applied load of 1187 N, obtained from all OFS techniques and compared with the associated FEM simulation. The OFDR profile exhibits the highest peak values, closely matching the FEM prediction. The CFG-FMCW data reproduced the spatial distribution but with much lower peak magnitudes. Both type-I and type-III FBG measurements follow the FEM trend at peak positions. Away from peaks, the different sensing methods show close agreement within the uncertainty limit (except near claws, as a consequence of St-Venant's principle).

Fig. 5(b) shows a subset of strain profiles obtained with CFGs interrogated by FMCW at different pulling forces, compared to FEM and FBG data. The FMCW technique consistently underestimates peak magnitudes compared with FBG and FEM. In both cases the CFG-FMWC response is lower than expected. This can be explained by the presence of the smoothing filter, which induces an averaging effect.

Figure 6 presents selected OFDR strain profiles obtained with two gage lengths (5 mm and 10 mm), comparing the results from two different reconstruction methods. Initially, using a *fixed reference* pattern (zero strain), the OFDR results are in good agreement with FEM, as shown in Fig. 6(a) and 6(b). However, above ~1500 N the instrument's internal cross-correlation procedure (see section 2.2.) may fail due to HSGs distortion of the Rayleigh scattered pattern. This failure produces non-physical strain values, which are visible for load 1984 N (6a) around hole #3 and (6.b) around holes #1, #2 and #3. Reducing the gage length alleviates this issue to some extent but does not solve it. This result highlights an intrinsic limitation of the fixed-reference approach under steep gradient conditions.

To mitigate this effect, a *moving reference* procedure was implemented, where each new Rayleigh pattern was correlated with the previous one. The resulting profiles, shown in Fig. 6(c) and 6(d), are successfully reconstructed across the entire load range without the previously observed outliers. While this technique alleviates correlation breakdown, it does so at the expense of introducing cumulative error that limits its applicability for long-term SHM. Moreover, this approach is limited to laboratory use, whenever the load is under control and
<figure><img src="image_8.png" /><figcaption>**Figure 6:** Selected OFDR strain profiles reconstructed using a *fixed reference* (a, b) and a *moving reference* (c, d) pattern, compared with FEM predictions for 5-mm and 10-mm gage lengths, respectively. The fixed reference, while accurate at lower loads, fails above ~1500 N as HSGs distort the Rayleigh backscatter signature. The moving-reference procedure successfully reconstructs the profiles across the full load range</figcaption></figure>

progressively increased, which is rarely the case in practical outdoor situations.

To provide a more rigorous quantitative comparison between OFDR and CGF-FMCW, a linear regression analysis was performed on peak strain data vs. applied load. The resulting regression plots (Figure 7) confirm a strong linear relationship for all sensing technologies. The analysis shows that the regression line for OFDR (5-mm gage length) is close to FEM predictions, albeit overestimated for hole #3. In contrast, the regression line for the CFGs data obtained by FMCW exhibits a consistently lower slope. This visually illustrates the systematic underestimation of peak strain magnitude.

Beyond the quantitative analysis of peak strain, the spectral response of the FBG sensors provides direct insight into the physical effects of HSGs, as illustrated in Figure 8. Fig. 8(a) shows the evolution of the reflection spectrum for the type-I FBG (8-mm long, $\lambda_0 = 1569.44$ nm) near Hole #3, the region of maximum HSG. As the load increases, the spectrum shifts to longer wavelengths due to tensile strain but reveals significant spectral broadening and distortion. This phenomenon, known as spectrum chirp, is a direct consequence of the non-uniform strain field across the grating's finite length [6, 7, 8]. This effect complicates the precise determination of a single Bragg wavelength and is the primary source of measurement error for FBGs in high-gradient conditions. For weakly-reflecting grating (non-saturated) grating, the spectral shape is linked to the Fourier Transform of the spatial distribution of the coupling coefficient $\kappa(z)$ [17]. However, retrieving the intra-grating strain profile from the spectral shape alone is an ill-posed problem, because its reconstruction via Fourier Transform also requires a phase spectrum.
<figure><img src="image_9.png" /><figcaption>**Figure 7:** Linear regression analysis of peak strain as a function of applied load for OFDR and CFG-FMCW technologies, compared with FEM predictions. The plots show the linear fits for data collected near (a) Hole #3 (50 mm), (b) Hole #2 (40 mm), and (c) Hole #1 (30 mm).</figcaption></figure>

The FBG spectra are sampled every 8 pm by the Si-255 unit. The on-board Enlight software determines peak locations by first digitally filtering the raw spectrum and then applying a zero-crossing procedure to its derivative [27]. Among all peak detection algorithms [19, 20], correlation- and Gaussian/p polynomial-based methods are probably the most accurate in absence of chirp, but can be hindered significantly when chirp is induced. Conversely, we identify the -3 dB and centroid methods as the simplest and most chirp tolerant. Figure 8(b) compares the strain measurements derived from the same spectra using the on-board zero-crossing (Enlight), -3 dB and centroid methods. Although the algorithms were applied to the same input data, we note a maximum load-dependent discrepancy of up to ±12% between the algorithms, attributed to variations in spectrum shape vs. load.

<figure><img src="image_10.png" /><figcaption>**Figure 8:** (a) Spectral response of the 8-mm type-I FBG located near Hole #, illustrating the effect of spectrum chirp and broadening under increasing applied load. (b) Evolution of strain vs. load, derived from the same spectra, as determined by several peak detection algorithms (-3 dB, centroid, zero-crossing of derivative).</figcaption></figure>

# 5 DISCUSSION AND CONCLUSIONS

For the first time (to our knowledge), we provide a benchmark of several cm-scale optical fiber distributed strain monitoring techniques: FBG-WDM, CFG-FMCW and OFDR, compared to FEM predictions, in view of assessing the performance of SHM of complex high-value structures subject to intense stress concentration. These comparative results highlight distinct strengths and limitations of those technologies when exposed to HSGs.
The OFDR technique delivers the closest agreement with FEM under moderate loads, capturing peak strain values with high accuracy. However, correlation breakdown occurs once Rayleigh patterns suffer strong distortion producing non-physical outputs. The moving reference strategy may restore agreement in laboratory conditions, but it accumulates error over time and cannot reliably handle sudden strain changes, which limits its practical use for SHM.

FBGs interrogated in WDM appear less sensitive to HSGs than OFDR or CFG-FMCW, as already witnessed in an earlier study [4], owing to chirp-tolerant algorithms commonly used for Bragg detection. However, Bragg wavelengths are algorithm dependent as well, particularly in presence of chirp. Moreover, under severe gradients (> 100 με/mm for 10-mm long FBGs), interference effects may even generate spurious peaks, leading to false detection [6,7].

The CFG-FMCW technique reproduces the spatial strain distribution accurately. However, peak strains are strongly damped in HSG zones due to spatial filtering, as shown in section 4. The FWHM of the transfer function is of the same order as the FWHM of the strain peaks.

Taken together, these findings confirm that no single technique provides a universally reliable solution under high-gradient conditions to obtain high-fidelity strain profiles. Short-length FBGs associated to chirp-tolerant peak detection algorithms offer robustness against distorted measurement for field deployments. The OFDR technique enables high-resolution strain monitoring provided that strain is gradually controlled (moving reference), which may be of limited relevance in practical situations. Finally, the CFG-FMCW technique is effective for low-gradient zones. Further experiments are underway without the spatial filter. These distinctions provide practical guidance for SHM practitioners when selecting sensing strategies for structures expected to undergo localized stress concentrations.

## Acknowledgements

This work was done within the Marie Skłodowska-Curie Action (MSCA) USES2 (Uses of novel UltraSonic and Seismic Embedded Sensors for the NDE and SHM of infrastructures and human-built objects), funded by the European Research Executive Agency (REA), grant No 101072599. The CFG-FMCW data were partly treated by Q. Baudis and R. Carpine (CEA List/DIN) within the DTHOR Project.

## REFERENCES

[1] Lopez-Higuera, J.M., Rodriguez Cobo, L., Quintela Incera, A. and Cobo, A. Fiber optic sensors in structural health monitoring, *J. Lightwave Technol.* (2011), 29:587-608.

[2] Abbas, S., Li, F. and Qiu, J. A Review on SHM techniques and current challenges for characteristic investigation of damage in composite material components of aviation industry, *Mater. Perform. Charact.* (2018), 7:224-258.

[3] Bado M.F. and Casas, J.R. A Review of Recent Distributed Optical Fiber Sensors Applications for Civil Engineering SHM, *Sensors MDPI* (2021), 21:1818-1900.

[4] Magne S., Rougeault S., Desmarchelier R., Chaudat T., Vasic S., Wang F., Hervé-Secourgeon E., Voldoire F. In situ distributed strain monitoring of a small-scale reinforced concrete structure using combined FBG/OFDR fiber optics sensing for assessment of its seismic degradation mechanisms, 12th IWSHM, Stanford (CA), USA, 10-12 September 2019.

[5] Wada, D., Igawa, H., Tamayama, M., Kasai T., Arizono, H., Murayama, H. Real-time stress concentration monitoring of aircraft structure during flights using optical fiber distributed sensor with high spatial resolution, in: Niepokolczycki, A., Komorowski, J. (eds) ICAF 2019 -Springer, Lecture Notes in Mechanical Engineering (2020), 1082-1090.
[6] Peters, K., Studer, M., Botsis, J., Iocco, A., Limberger, H. and Salathé, R. Embedded optical FBG sensor in a nonuniform strain field: measurements and simulations, *Exp. Mech.* (2001), **41**:19-28.

[7] Kang, D.H., Park, S.O., Hong, C.S and Kim, C.G. The signal characteristics of reflected spectra of FBG sensors with strain gradients and grating lengths, *NDT E Int.* (2005), **38**:712–718.

[8] Matveenko, V., Kosheleva, N., Serovaev, G. and Fedorov, A. Measurement of gradient strain fields with fiber-optic sensors, *Sensors MDPI* (2023), **23**:410-421.

[9] Bassil, A., Niederleithinger, E., Wang, X., Kadoke, D., Chapeleau, X., Leduc, D., Abraham, O., Breithaupt, M. and Potschke, S. Distributed fiber optic sensors for multiple crack monitoring in reinforced concrete structures, 12th IWSHM, Stanford (CA), USA, 10-12 September 2019.

[10] Froggatt, M. and Moore, J. High-spatial-resolution distributed strain measurement in optical fiber with Rayleigh scatter, *Appl. Opt.* (1998), **37**:1735-1740.

[11] Kashyap, R. *Fiber Bragg Gratings*. Academic Press (1999).

[12] Othonos, A. Fiber Bragg gratings, *Rev. Sci. Instrum.* (1997), **68**:4309–4341.

[13] Rao, Y.J. In-fibre Bragg grating sensors, *Meas. Sci. Technol.* (1997), **8**:355-375.

[14] Chojetzki, C., Rothhardt, M.W., Ommer, J., Unger, S., Schuster, K. and Mueller, H.R. High-reflectivity draw-tower FBG—arrays and single gratings of type II, *Opt. Eng.* (2005)

[15] Butov, O.V., Przhiaikovskii, D.V., Lopunov, A.I. and Pnev, A.B. Strength properties of femtosecond-induced defects and weak Bragg gratings for distributed optical fiber sensors, *Opt. Laser Technol.* (2023), **162**:109271-109276.

[16] He, J., Xu, B., Xu, X., Liao, C. and Wang, Y. Review of femtosecond-laser-inscribed FBG: fabrication technologies and sensing applications, *Photonic Sens.* (2012), **11**:203–226.

[17] Measures, R.M., Ohn, M.M., Huang, S.Y., Bigue, J., and Fan, N.Y. Tunable laser demodulation of various FBG sensing modalities, *Smart Mater. Struct.* (1998), **7**:237-247.

[18] Ecke, W., Latka, I., Willsch, R., Reutlinger, A., and Graue, R. Fibre optic sensor network for spacecraft health monitoring, *Meas. Sci. Technol.* (2001), **12**:974-980.

[19] Tosi, D., Review and analysis of peak tracking techniques for FBG Sensors, *Sensors MDPI* (2017), **17**:2368-2402.

[20] Tosi, D., Olivero, M. and Perrone, G. Performance analysis of peak tracking techniques for FBG interrogation systems, *J. Microw. Optoelectron. Electromagn. Appl.* (2012), **11**:252-262.

[21] Uttam, D. and Culshaw, B. Precision time domain reflectometry in optical fiber systems using a frequency modulated continuous wave ranging technique, *J. Lightwave Technol.* (1985), **3**:971–977.

[22] Zheng, J. Analysis of optical frequency-modulated continuous-wave interference, *Appl. Opt.* (2004), **43**:4189–4198.

[23] Childers, B.A., Froggatt, M.E., Allison, S.G., Moore T.C., Hare D.A., Batten C.F., Jegley, D.C. Use of 3000 Bragg grating strain sensors distributed on four 8-m optical fibers during static load tests of a composite structure, Proc. SPIE (2001), **4332**:133–142.

[24] Luna OBR 4600 : https://www.lunainc.com/product/obr-4600.

[25] Eickhoff W. and Ulrich, R. Optical frequency domain reflectometry in single-mode fiber, *Appl. Phys. Lett.* (1981), **39**:693–695.

[26] Soller, B.J., Gifford, D.K., Wolfe, M.S. and Froggatt, M.E. High resolution optical frequency domain reflectometry for characterization of components and assemblies, *Opt. Express* (2005), **13**:666-674.

[27] Luna HYPERION si255 : https://www.lunainc.com/product/hyperion-si255.

[28] RTS125+: https://www.sensuron.com/products-2-2_trashed/rts125-dfos-system/.

[29] Gounand, S., Verpeaux, P., Pascal, S., Di Paola, F. and Berthinier, C. Cast3M, a problem-solving software for structural and fluid analysis, *ECCOMAS 2024*, Lisbon (Portugal)