KLT-Based Interrogation Technique for FBG Multiplexed Sensor Tracking

Abstract

The Karhunen-Loeve transform (KLT) is used to retrieve the wavelength information of several fiber Bragg gratings (FBGs) that are acting as a multiplexed sensor. The modulated light of a broadband source is launched to the FBG cascade in order to capture the electrical frequency response of the system. Thanks to a dispersive media, the wavelengths of the FBGs are mapped in radiofrequency (RF) delays. Wavelength changes are determined by the amplitude change of the samples in the impulse response, a change which is followed by the eigenvalue calculated by the KLT routine. The use of the KLT routine reduces by three orders of magnitude the amount of points needed to have a sub-degree resolution in temperature sensing, while keeping the accuracy almost intact.

Interrogation of coarsely sampled tilted fiber Bragg grating (TFBG) sensors with KLT

“…2(c) inset, is that the variation of ξ N-4 for a positive refractive index does not follow a linear pattern, but is rather non-monotonic and non-linear, at least for variations of sucrose concentration higher than 6.25%. This behavior was observed also in previous works [26][27][28] due to the core of the KLT, that amplifies the slight variations of the TFBG spectrum into detectable variations of the eigenvalue string, when the cladding modes exhibit a change that is hardly detectable in the strain. This is in general a weakness of the KLT, since it cannot discriminate large changes of refractive index without a complementary algorithm; however.…”

“…The core of the demodulation method is the KLT (Karhunen-Loeve Transform). The KLT has been recently applied in [26,27] to the interrogation of uniform FBG using a coarse spectrometer, and in [28] to the interrogation of FBG arrays in a microwave photonics setup. In these implementations, the KLT was applied as in Maccone's format [29,30], particularly suitable to detect variations of small signals into noise.…”

Review and Analysis of Peak Tracking Techniques for Fiber Bragg Grating Sensors

“…This method, implemented in [ 65 , 66 ] and resembling principal component analysis [ 89 ], is designed for the coarsest wavelength resolution and resolves inter-pixel peak tracking. The KLT is implemented with the following set of calculations [ 65 , 66 , 67 ]: …”

“…When a wavelength shift Δ λ is applied to the FBG, the KLT output exhibits a function that resemble, in waveform, the FBG inner spectrum, and has a periodicity exactly equal to the resolution δλ . This accomplishes the goal of expanding the FBG tracking from a resolution-limited grid to an accurate inter-pixel detection; the curve ξ N (Δ λ ) can be obtained during calibration [ 67 ]. However, the method is limited to a range of Δ λ equal to δλ /2 without ambiguity, and the function is not linear in trend, thus the method has a variable sensitivity.…”

Machine Learning Assisted Fiber Bragg Grating-Based Temperature Sensing

“…This regime is useful to make faster interrogation as the measurement takes less time. Other signal processing methods, e.g., Karhunen-Loeve transform based algorithms [5], have been proposed to improve the detection accuracy in this regime, but these methods are intrinsically limited to a small spectral range, computational intensive and have low tolerance to spectral deformations of the FBG [4].…”