Issue 78

C. Vendittozzi et alii, Fracture and Structural Integrity, 78 (2026) 519-540; DOI: 10.3221/IGF-ESIS.78.30

Wavelength-to-strain conversion and drift handling FBGs were selected because they provide compact, lightweight, and electromagnetically immune strain sensing with straightforward multiplexing on a single fiber, which is advantageous for integration on complex aerostructures and in proximity to electrical systems [3, 4]. An FBG consists of a periodic modulation of the fiber core refractive index that reflects a narrow band of wavelengths centered at the Bragg wavelength B  , governed by the Bragg condition:

B  

2 Λ eff n

(2)

where eff n is the effective refractive index of the guided mode and Λ is the grating period. Under axial strain, Λ changes and eff n varies through the photoelastic effect, producing a measurable shift Δλ that is approximately proportional to strain for the operating range considered here [3, 4]. In the present analysis, the measured wavelength shift is converted to axial strain using Eq. (3), with low-frequency trends mitigated as described below. Following integrity screening, wavelength streams were converted to normalized strain. For each channel, the normalized strain signal was computed as:

   t p      ,0 1 j j j e





  t

,0

j 





p

(3)

,

0.22



e

  j t  is the axial strain measured by sensor (j),

  j t  is the instantaneous Bragg wavelength returned by the

where

interrogator, ,0 j  is the reference Bragg wavelength computed as the median value over an initial quiet interval, and e p is the effective photoelastic coefficient of the fiber. In the absence of a dedicated calibration for the installed sensors, e p was assumed equal to 0.22, a commonly adopted nominal value for standard silica fibers. Strain values were then expressed in microstrain as:     6 , 10 j j t t     (4) Because temperature was not measured during the campaign, the low-frequency component of the wavelength-derived strain may include thermal contributions, slow strain-transfer effects, and quasi-static mechanical response. This component was not interpreted quantitatively in the present study. Instead, after strain conversion, the signals were detrended and high pass filtered at 0.5 Hz using a fourth-order IIR filter so that the subsequent analysis focused on transient and mid-frequency response components. This filtering step should not be interpreted as temperature compensation. It reduces slow drift in the analyzed records, but it cannot separate thermal wavelength shifts from mechanically meaningful quasi-static strain. It may also attenuate low-frequency mechanical information associated with sustained load transfer. Therefore, the present workflow supports event-centered spectral characterization but does not provide quantitative interpretation of long duration or quasi-static strain trends. Time–frequency estimation: STFT and multitaper configurations The event-centered strain responses considered in this study are transient and nonstationary. Therefore, the analysis was performed in the time–frequency domain using windowed spectral estimators configured to balance time localization, frequency resolution, and estimator stability. Three complementary configurations were evaluated to examine the trade-offs between time localization, frequency resolution, and estimator stability. The main Hann and multitaper estimates were compared using the same frame length and hop. Let   xj n be the detrended and high-pass filtered microstrain signal from sensor (j), sampled at s f = 1.0 kHz. For each analysis frame centered at time index m, a length-L segment is windowed and transformed to obtain a time–frequency power map. Hann STFT [17]. Using a Hann window w[n], the short-time Fourier transform is:



L

1

    n X mk x n mHwne     H,j 0 , j  



2 / 

i

kn L

(5)

524