PSI - Issue 64

Luca Schenato et al. / Procedia Structural Integrity 64 (2024) 1636–1641 Luca Schenato/ Structural Integrity Procedia 00 (2019) 000 – 000

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The procedure consists of performing the inverse Fourier transform of the reference and subsequent traces for a given position along the FUT and a chosen length of the spatial window of analysis (i.e., gage length) corresponding to N data points of the signal. This moves the domain of analysis from space (i.e., position along the FUT) to frequency (owing to the equivalency above between roundtrip time and position). The so-calculated windowed signal in the frequency domain is called the Rayleigh backscattering spectrum. Very importantly, it is invariant, at the first order, for any joint changes of strain, ∆ , temperature, ∆ , and frequency, ∆ , such that: ∆ = ∆ + ∆ (1) where , are the temperature and strain gage factor, respectively. These factors vary for different types of fiber, but typical values of Ge-doped silica core fiber are ≈ −1.25 GHz/°C , and ≈ −150 MHz/με (Boiron et al. (2020)). Eq. (1) also states that if among the reference and following measurements, the temperature and the strain in the considered portion of FUT changed of ∆ and ∆ , respectively , the two corresponding spectra are frequency shifted, one with respect to the other of ∆ . This shift can be calculated for all the intervals in which the FUT is divided according to the gage length by performing a cross-correlation of the Rayleigh spectra of the reference and following traces. The correlation peak position indicates the frequency shift of a specific interval, i.e., position along the FUT, and via Eq. (1), the corresponding local changes in the sensing parameters among the two measurements. Moreover, the presence of such a marked correlation peak indirectly confirms the existence and persistence of the Rayleigh signature. Finally, the resolution in the frequency shift measurement, and therefore, on the temperature and strain, depends on the raw spatial resolution at which the roundtrip signal is measured and the number of points N of the windows data analysis. The device used in this study is a LUNA OBR 4600 ® , employed here over a wavelength range of 42 nm around 1550 nm, capable of providing a raw spatial resolution of approximately 20 μm . For example, by choosing a gage length of N=4096 points, i.e., Δ ≈ 8 cm , the native resolution in the frequency shift calculation is poorly limited to 1.3 GHz, equivalent to 8.5 με or 1 °C. Despite the coarse native performance, please note that either time or frequency upsampling can be applied, leading to an ameliorated native coarse spatial resolution for a given measurands resolution or, vice versa, a better measurands resolution at a given spatial resolution. Unfortunately, as it is, the procedure described above requires the traces to be spatially aligned to the reference one to perform the correlation analysis in the same section of FUT. For example, whenever the patchcord between the interrogator and the FUT is changed or the FUT is damaged, the alignment is lost, and the measurement cannot be done with this standard approach, which is the one implemented by commercial devices. This same situation occurs when the interrogator is changed; also, in that case, the precise absolute spatial alignment gets lost. The Spectral Correlation Analysis (SCA) method, introduced by Veronese et al. (2020), represents a solution. Basically, for a given window of the reference trace, this method iteratively performs the correlation analysis between this window and delayed windows of the subsequent trace, looking for a marked correlation peak. Due to the uniqueness of a local Rayleigh fingerprint, whenever such a peak is found, the two windows are aligned and correspond to the same physical section of the FUT. The corresponding delay and frequency shift determines the spatial misalignment and the perturbation that specific window underwent with respect to the reference trace. Basically, the SCA method involves calculating a multidimensional correlation dataset. This dataset is a function of the position along the FUT reference trace, the delay between the traces' windows, and the frequency shift. For each position, the method searches for the pair of frequency shift and delay that corresponds to a maximum value of the correlation, i.e., a global peak. In principle, the method could even be used to identify a fiber, or a portion of fiber, connected after an unknown patchcord or sequence of patch cords; this is because SCA can be applied without any guess on the delay with respect to the reference trace. For example, the method has been demonstrated to be so effective to be able to recover and track a single signature among many others even if overlapped, as it may happen for the simultaneous measurement of the many cores of a multicore fiber (Cappelletti et al., (2023)).