Improving Prediction Accuracy and Extraction Precision of Frequency Shift from Low-SNR Brillouin Gain Spectra in Distributed Structural Health Monitoring

Abstract

In this paper, we studied the possibility of increasing the Brillouin frequency shift (BFS) detection accuracy in distributed fibre-optic sensors by the separate and joint use of different algorithms for finding the spectral maximum: Lorentzian curve fitting (LCF, including the Levenberg–Marquardt (LM) method), the backward correlation technique (BWC) and a machine learning algorithm, the generalized linear model (GLM). The study was carried out on real spectra subjected to the subsequent addition of extreme digital noise. The precision and accuracy of the LM and BWC methods were studied by varying the signal-to-noise ratios (SNRs) and by incorporating the GLM method into the processing steps. It was found that the use of methods in sequence gives a gain in the accuracy of determining the sensor temperature from tenths to several degrees Celsius (or MHz in BFS scale), which is manifested for signal-to-noise ratios within 0 to 20 dB. We have found out that the double processing (BWC + GLM) is more effective for positive SNR values (in dB): it gives a gain in BFS measurement precision near 0.4 °C (428 kHz or 9.3 με); for BWC + GLM, the difference of precisions between single and double processing for SNRs below 2.6 dB is about 1.5 °C (1.6 MHz or 35 με). In this case, double processing is more effective for all SNRs. The described technique’s potential application in structural health monitoring (SHM) of concrete objects and different areas in metrology and sensing were also discussed.

Machine Learning Approaches in Brillouin Distributed Fiber Optic Sensors

“…Nordin et al [151][152][153] proposed the use of GLM to extract temperature. GLM is a generalized form of linear regression that does not assume that the response variables (targets) are normally distributed.…”

“…Specifically, the temperature extraction time was approximately two orders of magnitude faster than the LCF, while the temperature error improvement varied from approximately 0.4 • C to 5 • C, depending on the frequency-tuning step and the temperature conditions. The authors in [151] concluded that GLM in combination with conventional BFS extraction methods, such as LCF, results in a significant increase in temperature accuracy even when the SNR is low. The most important characteristic of the GLM is the easy interpretation, which arises from the algorithm's simplicity and its straightforward implementation.…”

Enhancing the Distributed Acoustic Sensors’ (DAS) Performance by the Simple Noise Reduction Algorithms Sequential Application

“…The correlation peaks were interpreted as events, and only after that, the variational mode decomposition technique was applied to classify different impacts on the sensor. The mentioned study [38] showed that the raw signal of a distributed fiber optic sensor is quite difficult to use for decomposition or for machine learning, so it still requires pre-processing: for example, by Wavelet and Curvelet filtering or/and correlation algorithms [39][40][41][42]. Primary processing of raw data should be implemented on simple mathematical operations, since the volume of processed data is quite high, and the algorithms themselves are implemented with the use of programmable microcontrollers.…”

A Refinement of Backward Correlation Technique for Precise Brillouin Frequency Shift Extraction

“…There are also papers devoted to the use of various methods in conjunction with each other. Thus, in [23], the positive and negative aspects of the joint use of correlation methods and artificial intelligence are evaluated.…”

“…Determining the optimal shift F, at which the convolution maximum was reached, the authors found the position of the maximum of the Brillouin spectrum as fC + F/2, where fC is the center frequency in the scanning range (Figure 1). Theoretically, the dependence of the original and shifted Lorentzian function's convolution value on the value of the shift between them is also a Lorentzian function with twice Fibers 2023, 11, 51 3 of 13 the half-width at half-height (for a derivation, see, for example, [23]). Additionally, since the role of the noise terms decreases when convolution is taken due to statistical averaging, this resulting Lorentzian function (hereinafter referred to as the correlogram) should have a greater SNR than the original BGS.…”