A Peak Detection Algorithm for Fiber Bragg Grating Signals Based on Asymmetric Gaussian Model

Abstract

This invention discloses a peak detection algorithm for fiber Bragg grating signals based on an asymmetric Gaussian model. The algorithm includes: smoothing the acquired fiber Bragg grating spectral signal using a five-point moving average filter to obtain a smoothed spectral signal; performing a first derivative on the smoothed spectral signal and determining the window size based on the locations of the maximum and minimum points of the derivative; resampling the spectral signal within the window at a reduced sampling rate; applying Gaussian fitting to the resampled spectral signal within the window to initially determine the peak position; and introducing an asymmetric Gaussian function model to correct the peak position using the detected peak and achieve precise peak location. Compared with direct peak finding algorithms, polynomial fitting algorithms, Gaussian fitting algorithms, and three-point peak finding algorithms, the improved algorithm presented in this paper has the smallest peak location error.

Description

Technical Field

[0001] This invention belongs to the field of fiber Bragg gratings, and specifically relates to a peak detection algorithm for fiber Bragg grating signals based on an asymmetric Gaussian model. Background Technology

[0002] Fiber Bragg Grating (FBG) sensors are widely used in health and safety monitoring of mines, bridges, dams, and composite structures due to their advantages such as small size, good stability, high accuracy, strong resistance to electromagnetic interference, corrosion resistance, low cost, and passive intrinsic safety. FBG sensors reflect changes in the measured quantity by acquiring the center wavelength drift; the wavelength drift corresponds to a change in the peak position of the reflection spectrum. Therefore, improving the demodulation accuracy of FBG wavelengths is of great significance. FBG sensors are widely used in engineering and industrial fields. Traditional FBG demodulation algorithms suffer from low accuracy, slow operation speed, and poor noise resistance, and can no longer meet the requirements of high-precision, real-time dynamic demodulation systems. Factors such as light source, multiplexing technology, noise, nonlinear temperature drift of measuring devices, and spectral distortion and overlap caused by the external environment are important reasons for the low demodulation accuracy of FBG sensors. Improving these problems has become a research hotspot in recent years.

[0003] Currently, common peak-finding algorithms include direct peak finding (DP), polynomial fitting, Gaussian fitting, three-point peak finding, genetic algorithms, and neural network algorithms. Among these, DP is easy to operate, but requires a high number of spectral sampling points, while portable demodulators typically have fewer sampling points, resulting in lower demodulation accuracy with DP. Polynomial fitting has low computational complexity and is easy to implement, but its peak detection accuracy largely depends on the observed data. Gaussian fitting finds peak points based on the symmetry of the left and right sides of the reflection spectrum signal, requiring strict control over the spectral shape; when the reflection spectrum shape is distorted by noise, the peak detection error of this algorithm increases. Three-point peak finding improves peak-finding accuracy to some extent, but it does not consider the asymmetry of the spectral peaks during the peak-finding process. Existing FBG spectral peak-finding algorithms are mostly analyzed and studied from the perspectives of detection accuracy and noise resistance, with less research on the impact of spectral asymmetry. FBG reflection spectra are non-standard Gaussian spectra with irregular peak shapes. Therefore, the peak finding problem of FBG asymmetric spectrum needs further research, which is of great significance for improving peak finding algorithms and enhancing detection accuracy. Summary of the Invention

[0004] In view of this, the present invention proposes a peak detection algorithm for fiber Bragg grating signals based on an asymmetric Gaussian model, comprising the following steps:

[0005] S1. The acquired fiber Bragg grating spectral signal is smoothed using a five-point moving average filtering method to obtain the smoothed spectral signal.

[0006] S2. Take the derivative of the smoothed spectral signal once, and determine the size of the window based on the location of the maximum and minimum points of the derivative;

[0007] S3. Resample the spectral signal within the window and reduce the sampling rate. Apply Gaussian fitting to the resampled spectral signal within the window to preliminarily determine the position of the peak.

[0008] S4. Introduce an asymmetric Gaussian function model to correct the initially determined peak position.

[0009] Furthermore, the calculation formula for the five-point moving average filtering method described in step S1 is as follows:

[0010]

[0011] In the formula: n is the number of data points, i = 1, 2Λ, n, x i Let y represent the x-coordinate of the i-th point. i This represents the ordinate of the i-th point.

[0012] Furthermore, in step S2, the size of the window is the difference between the x-coordinates of the minimum and maximum points of the derivative.

[0013] Furthermore, step S3 specifically includes:

[0014] S31, the fiber Bragg grating signal is represented as:

[0015]

[0016] Where: λ is the wavelength of the fiber Bragg grating spectrum, λ B Δλ is the center wavelength of the fiber Bragg grating spectrum. B The bandwidth is 3dB, and A is the amplitude of the reflection spectrum;

[0017] Taking the logarithm of both sides of equation (2) gives:

[0018]

[0019] Let: y(λ) = lnI(λ),

[0020] Equation (3) simplifies to:

[0021] y(λ)=aλ 2 +bλ+c (4)

[0022] The values ​​of a, b, and c in equation (4) are determined using the least squares method, and the center wavelength is:

[0023] λ B =-b / 2a (5)

[0024] S32, Let point B be the theoretical peak value λ. B Point D is the maximum value obtained by equation (5). Substituting the maximum value into the fitted second-order Gaussian function when the sampling rate is reduced:

[0025]

[0026] Where a1, a2, b1, b2, c1, and c2 are the parameters of the second-order Gaussian function, determining the coordinates of point D (λ). m ,y2), with λ m Using the standard, a data interval Δλ is selected, and two adjacent data points A and C of D are determined, with coordinates (λ, C, and D) respectively. m -Δλ,y1),(λ m +Δλ, y3), Substituting points A, D, and C into equation (4) respectively, we get:

[0027]

[0028] Calculate the values ​​of a, b, and c, and substitute these three values ​​into equation (5) to obtain...

[0029]

[0030] The center wavelength is calculated using equation (8), and the peak value of the center wavelength is the initially determined peak position.

[0031] Furthermore, step S4 specifically includes:

[0032] The initially determined peak position is verified and compensated using the following formula:

[0033] G(x)=F'+f(t) (9)

[0034] Asymmetric Gaussian model:

[0035]

[0036] Where μ is the time point corresponding to the peak point obtained by the Gaussian fitting function, σ1 is the number of time point samples on the left side of the Gaussian fitting function, and σ2 is the number of time point samples on the right side of the Gaussian fitting function. The criterion for the asymmetric Gaussian function is based on two second-order parameters of the left and right variances. and The specific formula is as follows:

[0037]

[0038] The peak value after compensation is derived from the variance analysis:

[0039]

[0040] Where F' is the peak value initially determined in step S3, and F is the peak value after compensation.

[0041] The beneficial effects of the technical solution provided by this invention are:

[0042] This paper addresses the error problem in peak finding algorithms caused by the asymmetry of the fiber optic reflection spectrum and proposes an improved peak finding algorithm based on an asymmetric Gaussian model. A five-point moving average filtering method is used to process the original spectral signal. An extreme value interval is selected to find the reflection spectrum window. Then, the data within the window is resampled to obtain new data and Gaussian fitted. Based on the fitting results, a relatively suitable wavelength interval is selected to determine three coordinate points for peak detection in the reflection spectrum. The detected peaks are then combined with the asymmetric Gaussian model to correct the peak positions, achieving accurate peak location. Compared with direct peak finding algorithms, polynomial fitting algorithms, Gaussian fitting algorithms, and three-point peak finding algorithms, the improved algorithm in this paper has the smallest peak location error. Attached Figure Description

[0043] Figure 1 This is a flowchart of the fiber Bragg grating signal peak detection algorithm based on the asymmetric Gaussian model of the present invention;

[0044] Figure 2 This is the original fiber Bragg grating spectral waveform of an embodiment of the present invention;

[0045] Figure 3 The image shows the smoothing effect achieved by using the three-point moving average filtering method in an embodiment of the present invention.

[0046] Figure 4 The image shows the smoothing effect achieved by using the five-point moving average filtering method in an embodiment of the present invention.

[0047] Figure 5 The image shows the smoothing effect achieved by using the seven-point moving average filtering method in an embodiment of the present invention.

[0048] Figure 6 This embodiment of the invention determines the local original graphic of the window based on two extreme points;

[0049] Figure 7 This is a curve obtained by taking the derivative after smoothing in an embodiment of the present invention;

[0050] Figure 8 The data resampled within the window in this embodiment of the invention is fitted with a Gaussian curve.

[0051] Figure 9 The data resampled within the window in this embodiment of the invention is fitted with a second-order Gaussian curve.

[0052] Figure 10 The peak error of Δλ in the embodiments of the present invention is given for different values ​​from 0.01 to 0.7 nm.

[0053] Figure 11 This is an asymmetric Gaussian model used in an embodiment of the present invention;

[0054] Figure 12 This is a graph showing the three-point peak finding and asymmetric Gaussian model curves of an embodiment of the present invention;

[0055] Figure 13 This is an image after asymmetric Gaussian correction according to an embodiment of the present invention. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0057] refer to Figure 1 , Figure 1 This is a flowchart of the fiber Bragg grating signal peak detection algorithm based on the asymmetric Gaussian model of the present invention.

[0058] The fiber Bragg grating signal peak detection algorithm based on an asymmetric Gaussian model described in this invention uses a broadband light source (BBS) with stable high output power and a wide spectral density. Key performance indicators include: wavelength range of 1480nm–1640nm, power of 10mW, and the fiber Bragg grating (FBG) provided by Shandong Shenghai Fiber Optic Technology Co., Ltd., with a center wavelength of (1552±0.1nm), reflectivity greater than or equal to 90%, 3dB bandwidth less than or equal to 0.25nm, side-mode suppression ratio greater than or equal to 15dB, grating length of 10mm, and fiber type YOFC HT. The system consists of a 9 / 125-14 / 155(300), a temperature control chamber, and a spectrometer (Yokogawa AQ6370D). Features include a wavelength range of 600–1700 nm, high wavelength accuracy of ±0.01 nm, high wavelength resolution of 0.02 nm, a large dynamic range of 78 dB (typical value), a wide power range of +20 to -90 dBm, and rapid measurement in 0.2 seconds (100 nm span). Figure 3 As shown, the light emitted from the BBS reaches the FBG via a coupler. The FBG has wavelength-selective transmittance, and light matching the center wavelength of the FBG is reflected. The temperature of the constant temperature test chamber is set to 20℃ to ensure the stability of noise and other parameters, and its reflection spectrum is observed using a spectrometer. The theoretical wavelength of the fiber optic grating obtained by the spectral demodulator is 1552.815 nm.

[0059] The method in this embodiment includes the following steps:

[0060] S1. The acquired fiber Bragg grating spectral signal is smoothed using a five-point moving average filtering method to obtain the smoothed spectral signal.

[0061] FBG (Fiber Bragg Grating) sensing systems are susceptible to interference from electrical components and the external environment during engineering applications, resulting in noise in the reflectance spectrum and affecting peak-finding accuracy. Therefore, smoothing the FBG reflectance spectrum signal is necessary before peak-finding to eliminate "glitch" and "false peaks" caused by signal noise. Common smoothing methods for FBG spectrum signals include three-point moving average filtering, five-point moving average filtering, and seven-point moving average filtering. The calculation formulas are as follows:

[0062] Three-point moving average filtering method:

[0063]

[0064] Five-point moving average filtering method:

[0065]

[0066] Seven-point moving average filtering method:

[0067]

[0068] Where: n is the number of data points, i = 1, 2Λ, n, x i Let y represent the x-coordinate of the i-th point. i This represents the ordinate of the i-th point.

[0069] refer to Figure 2 , Figure 3 , Figure 4 and Figure 5 , Figure 2 This is the original fiber Bragg grating spectral waveform of an embodiment of the present invention. Figure 3 This is a diagram showing the smoothing effect achieved by using the three-point moving mean filtering method in an embodiment of the present invention. Figure 4 This is a diagram showing the smoothing effect achieved by using the five-point moving mean filtering method in an embodiment of the present invention. Figure 5 The image shows the smoothing effect achieved by using the seven-point moving average filtering method in an embodiment of the present invention.

[0070] Analysis shows that, Figure 2 The original image. Figure 3 The three-point moving average filtering method cannot completely eliminate noise in the spectral signal, and its smoothing effect is poor. Figure 5 The seven-point moving average filtering method has a significant smoothing effect, but it loses some signal characteristics. Meanwhile... Figure 4 Five-point moving average filtering avoids the shortcomings of the above methods and effectively removes false peaks contained in the spectral signal.

[0071] S2. Take the derivative of the smoothed spectral signal once, and determine the window size based on the location of the maximum and minimum points of the derivative.

[0072] The first derivative reflects the change in the slope of the original spectral curve. Since the slope of a Gaussian function changes significantly near its peak, the two extreme points of the derivative can be found by taking the first derivative of the smoothed spectrum, thus determining the window size. The window size is selected as follows: the center wavelength of the FBG reflectance spectrum is 1552.815 nm. Figure 6 To determine the local original image of the window based on two extreme points, spectral "side lobes" were eliminated after smoothing; based on this, the derivative was obtained as follows: Figure 7 The curve was plotted, and the spectral ranges corresponding to the maximum and minimum values ​​were determined from the graph. Then, the range of the center wavelength was determined based on the slope change. Through calculation, the derivative reached its maximum value at 1552.6 nm and its minimum value at 1553.0 nm, with a spectrum ranging from 1552.6 to 1553.0 nm, and the difference between the two values ​​was 0.4 nm.

[0073] To verify the impact of window size on peak finding accuracy, window sizes of 0.2, 0.4, and 0.6 nm were used. Figure 5 It can be seen that when the window size is 0.4nm, the peak error is below 5pm.

[0074] S3. Resample the spectral signal within the window, reducing the sampling rate. Apply Gaussian fitting to the resampled spectral signal within the window to preliminarily determine the peak positions. (Reference) Figure 8 and Figure 9 , Figure 8 The data resampled within the window in this embodiment of the invention is fitted with a Gaussian curve. Figure 9 The data resampled within the window in this embodiment of the invention is fitted with a second-order Gaussian curve.

[0075] The resampling interval determines the number of data points. Different numbers of data points will lead to different fitting results, different maximum values, and the final center wavelength will change with the number of data points.

[0076] S31, the fiber Bragg grating signal is represented as:

[0077]

[0078] Where: λ is the wavelength of the fiber Bragg grating spectrum, λ B Δλ is the center wavelength of the fiber Bragg grating spectrum.B The bandwidth is 3dB, and A is the amplitude of the reflection spectrum;

[0079] Taking the logarithm of both sides of the above equation, we get:

[0080]

[0081] Let: y(λ) = lnI(λ),

[0082] Mode Simplified to:

[0083] y(λ)=aλ 2 +bλ+c

[0084] The least squares method is used to determine the equation y(λ)=aλ 2 The values ​​of a, b, and c in +bλ+c, and the center wavelength are:

[0085] λ B = -b / 2a

[0086] S32, Let point B be the theoretical peak value λ. B Point D is the point through equation λ. B The maximum value obtained by calculating -b / 2a is substituted into the function fitted when the sampling rate is reduced.

[0087]

[0088] Where a1, a2, b1, b2, c1, and c2 are the parameters of the second-order Gaussian function, determining the coordinates of point D (λ). m ,y2), with λ m Using the standard, a data interval Δλ is selected, and two adjacent data points A and C of D are determined, with coordinates (λ, C, and D) respectively. m -Δλ,y1),(λ m +Δλ, y3), Substitute points A, D, and C into the equation y(λ)=aλ 2 +bλ+c yields:

[0089]

[0090] Calculate the values ​​of a, b, and c, and substitute these three values ​​into the equation λ. B = -b / 2a

[0091]

[0092] Figure 10 This represents the peak error of Δλ for different values ​​ranging from 0.01 to 0.7 nm. (From...) Figure 7It can be seen that as Δλ increases, the peak error first decreases and then increases, and the peak error reaches its minimum at 0.31nm, where the peak error is 0.2pm.

[0093] The center wavelength is calculated, and the peak value of the center wavelength is the initially determined peak position.

[0094]

[0095] a1=1837(-1.296e+09,1.296e+09)

[0096] b1=1553(-2.062e+04,2.373e+04)

[0097] c1=1.258(-1.182e+05,1.182e+05)

[0098] a2=-1856(-1.292e+09,1.292e+09)

[0099] b2=1553(-9.908e+04,1.022e+05)

[0100] c2=1.839(-3.668e+05,3.668e+05)

[0101] Based on the above formula and the range of parameters obtained when performing a second-order Gaussian fitting on the current data, the coordinates of the maximum value point are obtained. The x-coordinate corresponding to the maximum value is λ. m .

[0102] S4. Introduce an asymmetric Gaussian function model to correct the initially determined peak position.

[0103] The initially determined peak position is verified and compensated using the following formula:

[0104] G(x) = F' + f(t)

[0105] Asymmetric Gaussian model, reference Figure 11 , Figure 11 The asymmetric Gaussian model for an embodiment of the present invention is as follows:

[0106]

[0107] μ represents the time point corresponding to the peak point obtained by the Gaussian fitting function, σ1 represents the number of time point samples on the left side of the Gaussian fitting function, and σ2 represents the number of time point samples on the right side of the Gaussian fitting function. (Asymmetric Gaussian)

[0108] The function's judgment is based on two second-order parameters of the left and right variances. and The specific formula is as follows:

[0109]

[0110] refer to Figure 12 , Figure 12 The comparison between the three-point peak finding and the asymmetric Gaussian model curve in the embodiment of the present invention shows that the ordinate of the asymmetric Gaussian model curve is 10. -3 The change is on the order of magnitude smaller than the curve obtained after three-point peak finding, and it is near the zero-point curve. By superimposing the two curves, a new curve is obtained as follows: Figure 13 As shown, Figure 13 This is an image after asymmetric Gaussian correction according to an embodiment of the present invention. Figure 13 It contains two curves: one is the curve after finding the peak at three points, and the other is the curve corrected by the above method. It can be seen that the peak point has shifted.

[0111] The peak value after compensation is derived from the variance analysis:

[0112]

[0113] Where F' is the initially determined peak value, and F is the compensated peak value.

[0114] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A peak detection algorithm for fiber Bragg grating signals based on an asymmetric Gaussian model, characterized in that, Includes the following steps: S1. The acquired fiber Bragg grating spectral signal is smoothed using a five-point moving average filtering method to obtain the smoothed spectral signal. S2. Take the derivative of the smoothed spectral signal once, and determine the size of the window based on the location of the maximum and minimum points of the derivative; S3. Resample the spectral signal within the window, reducing the sampling rate. Apply Gaussian fitting to the resampled spectral signal within the window to preliminarily determine the peak positions; specifically: S31, the fiber Bragg grating signal is represented as: （2） in: The wavelength of the fiber Bragg grating spectrum. The center wavelength of the fiber Bragg grating spectrum. The bandwidth is 3dB, and A is the amplitude of the reflection spectrum; Taking the logarithm of both sides of equation (2) gives: （3） make: , , , Equation (3) simplifies to: （4） The values ​​of a, b, and c in equation (4) are determined using the least squares method, and the center wavelength is: （5） S32, Let point B be the theoretical peak value. Point D is the maximum value obtained by equation (5). Substituting the maximum value into the function of the second-order Gaussian fitting when the sampling rate is reduced: （6） Where a1, a2, b1, b2, c1, and c2 are the parameters of a second-order Gaussian function, determining the coordinates of point D. , ),by Select data intervals as the standard. Determine two adjacent data points A and C of D, with coordinates as follows: , (), , Substituting points A, D, and C into equation (4) yields: （7） Calculate the values ​​of a, b, and c, and substitute these three values ​​into equation (5) to obtain... （8） The center wavelength is calculated using equation (8), and the peak value of the center wavelength is the initially determined peak position. S4. Introduce an asymmetric Gaussian function model to correct the initially determined peak position; specifically: The initially determined peak position is verified and compensated using the following formula: （9） Asymmetric Gaussian model: （10） in, The time point corresponding to the peak point obtained by the Gaussian fitting function. This represents the number of time-point samples on the left side of the Gaussian fitting function. The time point sampling number represents the right-hand side of the Gaussian fitting function. The criterion for the asymmetric Gaussian function is based on two second-order parameters of the left and right variances. and The specific formula is as follows: （11） The peak value after compensation is derived from the variance analysis: （12） Where F' is the peak value initially determined in step S3, and F is the peak value after compensation.

2. The fiber Bragg grating signal peak detection algorithm based on an asymmetric Gaussian model according to claim 1, characterized in that, The calculation formula for the five-point moving average filtering method mentioned in step S1 is as follows: （1） in: n The number of data points , xi Indicates the first i The x-coordinates of the points yi Indicates the first i The ordinates of the points.

3. The fiber Bragg grating signal peak detection algorithm based on an asymmetric Gaussian model according to claim 1, characterized in that, In step S2, the size of the window is the difference between the x-coordinates of the minimum and maximum points of the derivative.

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