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.

Keywords: BFS extraction; BOTDA; Brillouin scattering; concrete; data processing; distributed fibre-optic sensors; machine learning; structural health monitoring.

Figure 1

The classical approach of the BFS extraction process (a) in comparison with the proposed study (b).

Figure 2

A schematic diagram combined using real data, describing the method operation principle (blue graph—forward spectrum; orange graph—backward spectrum with its shifted copy; dotted line—backward correlation function).

Figure 3

Illustration of taking the integral procedure.

Figure 4

The use of GLM for BFS extraction.

Figure 5

Experimental BOTDA setup.

Figure 6

Data processing principle.

Figure 7

The absolute error results obtained after data processing: (a) −2 dB single processing; (b) −2 dB double processing (c) 3 dB single processing; (d) 3 dB double processing; (e) 6 dB single processing (f); 6 dB double processing; (g) 20 dB single processing; (h) 20 dB double processing.

Figure 8

Measurement precision demonstrated by studied methods: (a) LM; (b) BWC.

Figure 9

Prediction accuracy demonstrated by studied methods: (a) LM; (b) BWC.