CN103940363B - High-precision optical fiber strain low-frequency sensing demodulation method based on wavelet cross-correlation technology - Google Patents

Abstract

The invention discloses a high-precision optical fiber strain low-frequency sensing demodulation method based on wavelet cross-correlation technology, which includes: a data preprocessing step for performing wavelet noise reduction processing on the reference fiber grating reflection spectrum and the sensing fiber grating reflection spectrum , and perform zero-setting processing on the data outside the bandwidth of the reference FBG reflection spectrum and the sensing FBG reflection spectrum after denoising, and obtain the preprocessed reference FBG reflection spectrum and the sensing FBG reflection spectrum; cross-correlation in the wavelet domain step, for calculating the wavelet domain cross-correlation value of the preprocessed reference fiber grating reflection spectrum and the sensing fiber grating reflection spectrum; the peak detection step, for calculating the peak position of the wavelet domain cross-correlation value, and The external strain value corresponding to the reflection spectrum of the sensing fiber grating is obtained according to the peak position.

Description

Demodulation method of high-precision optical fiber strain low-frequency sensing based on wavelet cross-correlation technology

technical field

The invention relates to the technical field of optical fiber sensing, in particular to a high-precision optical fiber strain low-frequency sensing demodulation method based on wavelet cross-correlation technology.

Background technique

Over the past two decades, with the rapid development of optical fiber sensing and optical fiber communication technology, various types of optical fiber sensors (such as Michelson interferometric optical fiber sensors, Fapper interferometric optical fiber sensors, fiber grating sensors, etc.) industry have been widely used. The use of fiber optic sensors for strain measurement is the most common form of application, among which fiber optic grating (FBG) sensors have been a research hotspot in this field due to their advantages of small size, fast response speed, wide range of linear response, and easy reusability. .

At present, the strain measurement accuracy of the FBG strain interrogator widely used in the market is generally 1με. In the fields of bridge deformation monitoring and slope monitoring, the 1με strain accuracy of FBG can meet the actual application requirements. However, in many fields such as terrain deformation observation, acoustic emission monitoring, etc., the strain accuracy of 1με cannot meet the requirements. Therefore, people have proposed many methods to improve the strain measurement accuracy of FBG, such as using phase-shifted fiber Bragg gratings and fiber Bragg grating F-P interferometers to replace ordinary fiber Bragg gratings, and using laser frequency locking technology to improve the measurement accuracy of fiber Bragg gratings. However, most of these techniques are used for the measurement of high-frequency (dynamic) signals, and are rarely suitable for the measurement of low-frequency (quasi-static) signals.

The quasi-static strain measurement resolution of the FBG sensor is mainly determined by the external environmental noise (as a disturbance factor for strain measurement). In order to achieve high-resolution strain measurement, the general practice is to use a strain-free The reference FBG compensates for noise such as temperature and light intensity fluctuations, and then we can obtain strain information by calculating the wavelength change difference between the sensing FBG and the reference FBG. At present, many algorithms have been used to detect the wavelength change of the two FBG sensors, including the centroid detection algorithm (G.Meltz, et al., "Formation of Bragggratings in optical fibers by a transverse holographic method," Opticsletters, 1989), Least squares curve fitting algorithm (A.Ezbiri et., "High resolution instrumentation system for fiber-Bragg grating aerospace sensors," Opticscommunications, 1998) and cross-correlation algorithm (C.Huang, et al., "Demodulation of fiber Bragggrating sensor using cross-correlation algorithm,” Photonics Technology Letters, 2007). Among them, the cross-correlation algorithm can directly distinguish the wavelength difference between the sensing FBG and the reference FBG, has good stability, and practice has proved that it can be used for the demodulation of the FBG sensor. Since 2010, Qinwen Liu of the University of Tokyo in Japan has used the cross-correlation algorithm many times to calculate the position difference of two extremely narrow fiber grating reflection spectra, and obtained good experimental results (Q.Liu, et al., "Realization ofnano static strain sensingwith fiber Bragg gratings interrogated by narrow linewidth tunable lasers,"Optics Express, 2011).

In fact, the calculation of the wavelength position difference of the reflection spectra of the two fiber gratings is essentially to find the time delay of the reflection spectra of the two fiber gratings. Most of the current time delay estimation methods are improved on the basis of generalized correlation time delay estimation, such as adaptive time delay estimation, generalized phase time delay estimation, LMS time delay estimation and so on. These methods can be directly borrowed for high-precision low-frequency demodulation of fiber gratings. But these algorithms require the signal to be stationary, and require the signal and noise to be independent of each other, and the prior knowledge of the known signal and noise, which limits the demodulation accuracy of the method.

Wavelet analysis is a powerful tool for dealing with non-stationary signals, and has achieved many successful applications in time delay estimation. Here we introduce the wavelet domain cross-correlation calculation wavelength difference into high-precision low-frequency demodulation of optical fiber strain sensing for the first time. In the future, it is expected to solve the shortcomings of the traditional algorithm for calculating the wavelength difference of the reflection spectrum of optical fiber sensors and improve the measurement accuracy of the entire system. At present, there is no report on using wavelet transform to calculate wavelet domain cross-correlation of reflection spectra of two optical fiber sensors to achieve high-precision strain demodulation.

Contents of the invention

(1) Technical problems to be solved

In view of this, the main purpose of the present invention is to provide a low-frequency demodulation algorithm for high-precision optical fiber strain sensing, which uses wavelet transform technology to calculate the cross-correlation of the reflection spectra of two optical fiber sensors in the wavelet domain, so as to improve the accuracy of optical fiber measurement of low-frequency strain. Demodulation accuracy, and focus on solving the problem that the traditional cross-correlation-based optical fiber sensing demodulation algorithm cannot be used for high-precision demodulation of non-stationary fiber grating sensing signals, requires prior knowledge of known optical fiber sensing signals and noise, and requires optical fiber sensing The problem of the independence of sensing signal and noise.

(2) Technical solution

The invention provides a high-precision optical fiber strain low-frequency sensing demodulation method based on wavelet cross-correlation technology, which is characterized in that it includes:

The data preprocessing step is used to perform wavelet noise reduction processing on the reference fiber Bragg grating reflection spectrum and the sensing fiber Bragg grating reflection spectrum, and set the data outside the bandwidth of the noise-reduced reference fiber Bragg grating reflection spectrum and the sensing fiber Bragg grating reflection spectrum Zero processing to obtain the preprocessed reference fiber grating reflection spectrum and sensing fiber grating reflection spectrum;

The wavelet domain cross-correlation step is used to calculate the wavelet domain cross-correlation value of the preprocessed reference fiber grating reflection spectrum and the sensing fiber Bragg grating reflection spectrum;

The peak detection step is used to obtain the peak position of the cross-correlation value in the wavelet domain, and obtain the external strain value corresponding to the reflection spectrum of the sensing fiber Bragg grating according to the peak position.

(3) Beneficial effects

As can be seen from the foregoing technical solutions, the present invention has the following beneficial effects:

1. A high-precision optical fiber strain low-frequency sensing demodulation algorithm provided by the present invention can effectively improve the accuracy of wavelength demodulation and is superior to traditional cross-correlation algorithms.

2. A high-precision optical fiber strain low-frequency sensing demodulation algorithm provided by the present invention calculates the cross-correlation of two optical fiber sensors in the wavelet domain, which can eliminate the non-stationary noise of the reference optical fiber sensor and the sensing optical fiber sensor.

3. A high-precision optical fiber strain low-frequency sensing demodulation algorithm provided by the present invention calculates the cross-correlation of two optical fiber sensors in the wavelet domain, and does not require prior knowledge of known optical fiber sensing signals and noises, and does not require optical fiber transmission. Signal and noise are independent of each other.

Description of drawings

Fig. 1 is the flow chart of the low-frequency demodulation method of high-precision optical fiber strain sensing provided by the present invention;

Fig. 2 is the actual measurement figure of the reflection spectrum of the two-way fiber grating provided by the present invention;

Fig. 3 (a) is the wavelength demodulation result figure based on the traditional cross-correlation algorithm provided by the present invention;

Fig. 3 (b) is the result figure of the wavelength demodulation based on high-precision optical fiber strain sensing low-frequency demodulation algorithm provided by the present invention;

detailed description

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with specific embodiments and with reference to the accompanying drawings.

The advantages of other aspects of the present invention will be easier to understand and clear by describing the preferred embodiments of the present invention in detail with reference to the accompanying drawings.

The basic principles of the high-precision optical fiber strain low-frequency sensing demodulation method based on wavelet cross-correlation technology provided by the present invention are as follows:

Assuming that the reflection spectra of the reference and sensing fiber optic sensors (taking fiber gratings as an example) are x(t) and y(t) respectively, the data within the 3dB bandwidth of the two reflection spectra is s(t), and the other part is z( t), the time delay of the two reflection spectra is taken as t ₀ , then the expressions of x(t) and y(t) are as follows:

x(t)=s(t)+z(t)

(1)

y(t)=s(tt ₀ )+z(t) is called

Therefore, the wavelet transform of x(t) and y(t) can be obtained as follows:

$\begin{array}{c}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span>}^{<span\; class="notranslate">\; +</span><span\; class="notranslate">\; \&infin;</span>}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; b</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span>}^{<span\; class="notranslate">\; +</span><span\; class="notranslate">\; \&infin;</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; b</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span>}^{<span\; class="notranslate">\; +</span><span\; class="notranslate">\; \&infin;</span>}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; b</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span>}^{<span\; class="notranslate">\; +</span><span\; class="notranslate">\; \&infin;</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; b</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Among them, W _{Φ, x} is the wavelet transform, Φ ^* is the mother wavelet, a is the scaling factor, and b is the time translation factor.

Perform cross-correlation calculations on x(t) and y(t) in the wavelet domain to obtain the wavelet domain cross-correlation function of x(t) and y(t)

$\begin{array}{c}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; a</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; b</span>}}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dadb</span>}\\ <span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; a</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>\mathrm{<span\; class="notranslate">\; dadb</span>}\\ <span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; ss</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; zs</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span>\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Among them, W _ss (τ-t ₀ ) is the autocorrelation function of s(t) in the wavelet domain, W _zs (τ) is the cross-correlation function of s(t) and z(t) in the wavelet domain, W _ss (τ -t ₀ ) is much larger than W _zs (τ) and reaches a maximum value at a time delay τ equal to t ₀ . Therefore, to calculate the peak position of the wavelet domain cross-correlation of x(t) and y(t), only the peak position of W _ss (τ-t ₀ ) needs to be calculated, and W _zs (τ) has a great influence on the peak value of the final wavelet cross-correlation The position has no effect, so the influence of the noise z(t) system can be eliminated here. According to the characteristics of cross-correlation, it can be known that τ (equal to t ₀ ) corresponding to the maximum value of W _ss (τ-t ₀ ) is the wavelength difference of the two reflection spectra (for a demodulation system based on a tunable laser, the delay τ has a linear relationship with the wavelength difference), so the wavelength demodulation is realized by finding the peak position of the cross-correlation value of x(t) and y(t) in the wavelet domain, that is, by finding the delay corresponding to the peak position of formula (3) The time τ is converted to obtain the wavelength difference of the two reflection spectra. At the same time, it can be seen from formula (3) that for cross-correlation in the wavelet domain, only when the optical fiber sensing reflection spectrum and the noise signal coincide in time and frequency will the demodulation result be affected. But in fact, the noise is different from the useful reflection spectrum signal, so the cross-correlation calculation in the wavelet domain has the function of noise suppression, which is beneficial to improve the accuracy of wavelength demodulation.

Based on the above principles, Fig. 1 shows the flow chart of the high-precision optical fiber strain sensing low-frequency demodulation method provided by the present invention, Fig. 2 is the actual measurement map of the reflection spectrum of the two-way fiber grating provided by the present invention, and Fig. 3a is provided by the present invention Figure 3b is a graph of the wavelength demodulation results based on the traditional cross-correlation algorithm, and Figure 3b is a graph of the wavelength demodulation results based on the high-precision optical fiber strain sensing low-frequency demodulation algorithm provided by the present invention.

As shown in Figure 1, the low-frequency demodulation method for high-precision optical fiber strain sensing includes:

Data preprocessing step 1 is used to perform wavelet denoising processing on the reference FBG reflection spectrum R1 and the sensing FBG reflection spectrum R2 to obtain the denoised FBG reflection spectra D1 and D2, and eliminate the factors caused by light intensity and external factors in the reflection spectrum. Various noises caused by factors such as the environment; and perform zero-setting processing on data other than the bandwidth of the FBG reflection spectrum D1 and D2 after noise reduction (the bandwidth can be directly seen and determined by the reflection spectrum R1 and R2), reducing the The impact of the used data on the measurement accuracy, get the preprocessed fiber grating reflection spectrum Z1, Z2; finally output the preprocessed results Z1, Z2;

The wavelet domain cross-correlation step 2 is used to calculate the wavelet domain cross-correlation of the two optical fiber grating reflection spectra Z1 and Z2 after data preprocessing, and perform temperature and noise compensation to obtain the wavelet domain cross-correlation result W; Gaussian curve fitting is performed on the domain cross-correlation result W to obtain the result G, so as to improve the measurement accuracy of the peak position. Here, the basic principle of using wavelet domain cross-correlation to realize the wavelength difference detection of two fiber Bragg gratings is as follows: After performing wavelet domain cross-correlation on the reflection spectra of two fiber Bragg gratings, the wavelet domain cross-correlation result W is obtained, and the wavelet domain cross-correlation in the time domain The position corresponding to the peak value of the result W (each sampling data point corresponds to a certain wavelength value) is the wavelength difference between the reflection spectra of the two fiber Bragg gratings, and the result G is obtained by Gaussian fitting of the cross-correlation result W in the wavelet domain. The main purpose is To improve the peak detection accuracy of the next peak detection.

The peak detection step 3 is used to obtain the peak position S of the cross-correlation in the wavelet domain after the Gaussian fitting according to the result G of the Gaussian fitting (that is, the value of the abscissa corresponding to the peak value, that is, the delay τ). Since the peak position S of the wavelet domain cross-correlation result G in the time domain after Gaussian fitting is equal to the center wavelength difference of two fiber gratings (sensing fiber grating and reference fiber grating), we can base on the peak position S, deriving the wavelength variation/strain variation of the sensing fiber grating relative to the reference fiber grating (that is, the external strain value of the sensing fiber grating can be obtained). This is because there is a one-to-one relationship between the change of the central wavelength and the strain value, and the reference fiber grating is not strained, and the sensing fiber grating is strained, so the central wavelength of the sensing fiber grating minus the center of the reference fiber grating The wavelength is the amount of wavelength change caused by the sensing fiber grating due to strain.

Among them, the reference FBG reflection spectrum R1 and the sensing FBG reflection spectrum R2 are obtained by scanning the reference FBG sensor and the sensing FBG sensor with a narrow linewidth tunable laser, and the reference FBG sensor is not subject to external strain , the sensing fiber grating sensor is used to receive the external strain; since the sensing fiber grating and the reference fiber grating have two orthogonal polarization states, we can eliminate the The influence of one of the polarization states of . The tunable laser is required to have a narrow line width and a large tunable range; in order to improve the accuracy of strain measurement, the fiber grating should also have a narrow bandwidth.

In the present invention, the wavelet threshold noise reduction method is used to carry out noise reduction processing on the two fiber grating reflection spectra R1, R2, and eliminate various stationary noises and non-stationary noises caused by factors such as light intensity and external environment in the reflection spectra; Perform zero-setting processing on the data outside the bandwidth of the fiber grating reflection spectrum D1 and D2 after noise reduction, so as to reduce the influence of useless data outside the bandwidth of the fiber grating reflection spectrum D1 and D2 on the measurement accuracy.

In the present invention, wavelet transform is used to calculate the wavelet domain cross-correlation of the two optical fiber grating reflection spectra Z1 and Z2 after data preprocessing, which is used to calculate the reflection peak wavelength difference of the two optical fiber grating reflection spectra Z1 and Z2, and carry out Compensation for temperature and noise; due to the time-frequency analysis capability of wavelet transform, while obtaining the cross-correlation of two fiber grating reflection spectra Z1 and Z2 in the wavelet domain, it can be applied to the cross-correlation calculation of reflection spectra with non-stationary noise. Compared with the traditional cross-correlation calculation, the wavelet cross-correlation calculation has higher wavelength difference calculation accuracy, and has higher flexibility to external interference and noise signals. Finally, Gaussian fitting is performed on the result W of cross-correlation in the wavelet domain to improve the measurement accuracy of the peak position, and finally the wavelength difference of the reflection peaks of the two fiber gratings is obtained through the peak position of the Gaussian fitting result G.

In the present invention, the fiber Bragg grating reflection spectrum R1, R2 can be obtained by a fiber Bragg grating Fabulous interferometer, a phase-shifting fiber grating, and can also be obtained by other interferometric fiber optic sensors; these two fiber Bragg grating reflection spectra, one As a reference, one as a sensor, and their corresponding optical fiber sensors have the same technical indicators (such as reflectivity, bandwidth, free spectrum length, temperature sensitivity coefficient, etc.).

In the present invention, when using the fiber Bragg grating method Peru-type interferometer to obtain the two-way fiber grating reflection spectrum R1, R2, the wavelength scanning range of the tunable laser should be greater than a free spectral range of the fiber-optic grating method Peru-type interferometer, so for To improve the dynamic range of the final demodulation algorithm, the strain direction of the sensing fiber grating can be realized by judging the wavelength difference jump value of the two fiber grating reflection spectra R1 and R2, so as to expand the strain measurement dynamics of the entire system algorithm scope.

In the present invention, the two fiber gratings corresponding to the fiber grating reflection spectra R1 and R2 should be in an environment with relatively constant temperature and low noise, such as in a cave or in a stainless steel sealed tube, so as to ensure the correctness of the demodulation result sex.

Please refer to Figure 1. The working principle of the high-precision fiber optic strain low-frequency sensing demodulation algorithm is as follows: firstly, two fiber gratings are scanned by a narrow linewidth tunable laser, and a polarization state in each fiber grating is eliminated by a polarization controller Influenced by the influence of the two channels of FBG reflection spectra R1, R2, and then the two FBG reflection spectra are respectively processed by wavelet threshold noise reduction to eliminate various noises caused by factors such as light intensity and external environment in the reflection spectrum; and then The data outside the bandwidth of the noise-reduced reflection spectrum is set to zero to reduce the impact of useless data on the measurement accuracy; then, through wavelet transform, the wavelet domain of the two fiber grating reflection spectra R1 and R2 after data preprocessing is calculated Cross-correlation to obtain the position difference of the two fiber grating reflection peaks, and compensate for temperature and noise; then Gaussian fitting of the cross-correlation results in the wavelet domain to improve the measurement accuracy of the peak position; finally, obtain the cross-correlation in the wavelet domain Gaussian fitting peak position, and according to the relationship between fiber grating wavelength and strain, derive the external strain value received by sensing fiber grating; here, wavelet transform is a powerful tool for processing non-stationary signals, and the high-precision optical fiber The strain sensing low-frequency demodulation algorithm calculates the cross-correlation of two fiber gratings in the wavelet domain, which can eliminate the non-stationary noise of the reference fiber grating and the sensing fiber grating; It is used for high-precision demodulation of non-stationary FBG sensing signals, requires prior knowledge of FBG sensing signals and noise, and requires FBG sensing signals and noise to be independent of each other.

Please refer to Fig. 2, in order to more clearly explain the working principle of the high-precision optical fiber strain low-frequency sensing demodulation algorithm, the present invention provides a set of measured reflection spectra (the above is the reflection spectrum of the reference fiber grating, and the following is the sensing fiber The reflection spectrum of the grating), the demodulation algorithm is to calculate the wavelet domain cross-correlation of the two fiber Bragg grating reflection spectra in real time at intervals of data (the difference between the two reflection peaks), and then judge the position difference of the two fiber Bragg grating reflection peaks to realize Sensing demodulation.

Please refer to Figure 3(a) and 3(b), in order to further verify the low-frequency demodulation algorithm of high-precision optical fiber strain sensing, the present invention compares and measures the traditional cross-correlation algorithm and high-precision optical fiber strain low-frequency sensing demodulation algorithm Experiments show that the demodulation accuracy of the high-precision optical fiber strain low-frequency sensing demodulation algorithm is better than that of the traditional cross-correlation algorithm (1με causes a wavelength change of about 1.2pm).

The specific embodiments described above have further described the purpose, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above descriptions are only specific embodiments of the present invention, and are not intended to limit the present invention. Within the spirit and principles of the present invention, any modifications, equivalent replacements, improvements, etc., shall be included in the protection scope of the present invention.

Claims (10)

1. A high-precision optical fiber strain low-frequency sensing demodulation method based on wavelet cross-correlation technology, characterized in that, comprising: The data preprocessing step is used to perform wavelet noise reduction processing on the reference fiber Bragg grating reflection spectrum and the sensing fiber Bragg grating reflection spectrum, and set the data outside the bandwidth of the noise-reduced reference fiber Bragg grating reflection spectrum and the sensing fiber Bragg grating reflection spectrum Zero processing to obtain the preprocessed reference fiber grating reflection spectrum and sensing fiber grating reflection spectrum; The wavelet domain cross-correlation step is used to calculate the wavelet domain cross-correlation value of the preprocessed reference fiber grating reflection spectrum and the sensing fiber Bragg grating reflection spectrum; The peak detection step is used to obtain the peak position of the cross-correlation value in the wavelet domain, and obtain the external strain value corresponding to the reflection spectrum of the sensing fiber Bragg grating according to the peak position. 2. the high precision optical fiber strain low frequency sensing demodulation method according to claim 1, is characterized in that, before described data preprocessing step, comprises: The reference fiber grating reflection spectrum and the sensing fiber Bragg grating reflection spectrum are obtained by scanning the reference fiber Bragg grating sensor and the sensing fiber Bragg grating sensor with a narrow linewidth tunable laser. 3. The high-precision optical fiber strain low-frequency sensing demodulation method according to claim 1, wherein the reference fiber grating sensor is not affected by external strain, and the sensing fiber grating sensor is used to receive the external strain strain. 4. The high-precision optical fiber strain low-frequency sensing demodulation method according to claim 2 is characterized in that, after scanning to obtain the reflection spectrum of the reference fiber grating and the reflection spectrum of the sensing fiber grating, a polarization controller is used to eliminate one of them Influence of polarization state. 5. the high precision optical fiber strain low frequency sensing demodulation method according to claim 1, is characterized in that, described wavelet domain cross-correlation step, specifically comprises: Using wavelet transform to calculate the wavelet domain cross-correlation value of the reference fiber grating reflection spectrum and the sensing fiber grating reflection spectrum after preprocessing; performing temperature and noise compensation on the wavelet domain cross-correlation value; Gaussian fitting is performed on the compensated cross-correlation values in the wavelet domain. 6. The high-precision optical fiber strain low-frequency sensing demodulation method according to claim 5, wherein the peak detection step obtains the peak position according to the wavelet domain cross-correlation value after the Gaussian fitting, and the peak position The corresponding delay value is the wavelength difference between the reference FBG reflection spectrum and the sensing FBG reflection spectrum, and the wavelength difference represents the external strain value. 7. The high-precision optical fiber strain low-frequency sensing demodulation method according to claim 1, characterized in that, the reference fiber grating reflection spectrum and the sensing fiber grating reflection spectrum pass through a tunable laser to scan the fiber grating Fabry type interferometer Or phase-shifted fiber grating, and the fiber Bragg grating F-Per interferometer or phase-shifted fiber grating have the same technical indicators. 8. The high-precision optical fiber strain low-frequency sensing demodulation method according to claim 7, characterized in that, when using a fiber grating method Perkin interferometer to obtain the two-way fiber grating reference fiber grating reflection spectrum and sensing fiber grating When the reflection spectrum is used, the wavelength scanning range of the tunable laser is larger than a free spectrum range of the fiber Bragg grating Fapper interferometer. 9. The high-precision optical fiber strain low-frequency sensing and demodulation method according to claim 7 or 8, wherein the fiber Bragg grating F-Per interferometer or the phase-shifting fiber grating is placed in a relatively constant temperature and low noise environment and scan it. 10. according to claim 7 or 8 described high-precision fiber optic strain low-frequency sensing demodulation method, it is characterized in that, the wavelet domain cross-correlation value of described reference fiber grating reflection spectrum and sensing fiber grating reflection spectrum is calculated as follows: x(t)=s(t)+z(t) y(t)=s(tt ₀ )+z(t) ${\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&infin;</span>}}^{<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&infin;</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; b</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&infin;</span>}}^{<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&infin;</span>}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; b</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>$ ${\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&infin;</span>}}^{<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&infin;</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; b</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&infin;</span>}}^{<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&infin;</span>}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; b</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>$ $\begin{array}{c}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; a</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; b</span>}}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; b</span>}\\ <span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; a</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; b</span>}\\ <span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span>\end{array}$ Wherein, x(t), y(t) are the reference fiber grating reflection spectrum and the sensing fiber grating reflection spectrum respectively, and s(t) is the 3dB bandwidth of the reference fiber grating reflection spectrum and the sensing fiber grating reflection spectrum The data in, z (t) is the data of other parts; t ₀ is the time delay of described reference fiber grating reflection spectrum and sensing fiber grating reflection spectrum; is the wavelet domain cross-correlation function of x(t) and y(t), W _{Φ, x} , W _{Φ, y} , W _{Φ, z} , W _{Φ, s} are x(t), y(t), z( The wavelet transform of t) and s(t), Φ ^* is the mother wavelet, a is the scale factor, b is the time translation factor; W _ss (τ-t ₀ ) is the autocorrelation function of s(t) in the wavelet domain, W _zs (τ) is the cross-correlation function of s(t) and z(t) in the wavelet domain.