A high-precision data demodulation method for Brillouin sensors

Abstract

This invention proposes a high-precision data demodulation method for Brillouin sensors, relating to the field of optical fiber communication technology. The key technical points of this invention include: curve fitting of the Brillouin gain spectrum and obtaining the optimal nonlinear least-squares solution of the fitted curve using the Adagrad algorithm; the frequency corresponding to the optimal solution is the Brillouin frequency shift; the Adagrad algorithm updates the parameters using historical gradient information and corrects the parameters of the fitted function during iteration; the frequency shift of the Brillouin gain spectrum is obtained by acquiring the frequency corresponding to the highest point of the fitted function at the end of iteration, thereby obtaining strain information distributed along the optical fiber. This invention has low dependence on initial values, and because there is no historical gradient accumulation at the beginning, the denominator of the learning rate is very small, resulting in a large overall learning rate, thus enabling rapid convergence; this invention improves curve fitting accuracy and offers better real-time performance.

Description

Technical Field

[0001] This invention relates to the field of optical fiber communication technology, and specifically to a high-precision data demodulation method for Brillouin sensors. Background Technology

[0002] The principle of distributed fiber optic strain sensing is as follows: two beams of light are input to both ends of the fiber, and the scattered signals returning from the fiber are calculated into strain and temperature changes. When the pump beam and probe beam meet in the fiber, and the frequency difference is within the Brillouin spectrum, a Brillouin scattering effect occurs, and the intensity of the probe beam is altered by the pump beam. By sweeping the probe beam, the Brillouin gain spectrum characteristics at each location point in the fiber can be measured. The Brillouin frequency shift can be extracted from the Brillouin gain spectrum. Since the Brillouin frequency shift has a linear relationship with the stress and temperature of the fiber within a certain range, the strain and temperature distribution at each location point in the fiber can be calculated by measuring the Brillouin gain spectrum.

[0003] BOTDA sensing systems based on stimulated Brillouin scattering have been widely studied and used. During temperature or stress measurements, BOTDA systems further extract information such as temperature or stress distribution along the optical fiber by extracting the frequency shift of the Brillouin gain spectrum (BGS). Existing technologies have proposed many methods for extracting the Brillouin frequency shift from the Brillouin gain spectrum, such as using the Lorentz curve fitting algorithm. However, this data processing method is slow. Machine learning-based methods for extracting the Brillouin frequency shift have certain advantages; among them, neural networks significantly improve extraction accuracy while slightly increasing processing time.

[0004] However, existing neural network algorithms take too long to process the electrical signal parameters acquired by BOTDA and lack real-time performance. Therefore, it is necessary to select a more efficient machine learning algorithm when extracting the Brillouin frequency shift information of the optical fiber under test. Summary of the Invention

[0005] To address this, the present invention proposes a high-precision data demodulation method for Brillouin sensors, aiming to solve or at least alleviate at least one of the problems mentioned above.

[0006] A high-precision data demodulation method for Brillouin sensors includes the following steps:

[0007] Step 1: Measure the Brillouin gain spectrum of the optical fiber under test using a BOTDA system; the optical fiber under test includes multiple splice points.

[0008] Step 2: Denoise the Brillouin gain spectrum;

[0009] Step 3: Perform curve fitting on the Brillouin gain spectrum after noise reduction;

[0010] Step 4: Use the Adagrad algorithm to obtain the nonlinear least squares optimal solution of the fitted curve. The frequency corresponding to the optimal solution is the Brillouin frequency shift.

[0011] Furthermore, the specific process of step one includes:

[0012] A narrow-linewidth fiber laser is used as the light source and splits into two paths via a fiber coupler. The upper branch beam is intensity-modulated by EOM1 to generate pulsed light, with the EOM1 drive signal coming from an AWG. Subsequently, the pulsed light is amplified by EDFA1 and used as pump light. The lower branch beam is carrier-suppressed by EOM2 and modulated with a first-order double-sideband signal to serve as probe light. The EOM2 drive signal comes from a sinusoidal microwave signal output from a microwave source. The pump pulse light and the dual-frequency probe light are injected into the fiber under test in opposite directions after passing through a fiber circulator and a fiber isolator, respectively. The dual-frequency probe light passes through an optical circulator and a tunable fiber Bragg grating filter, and the -1st-order sideband is selected as the Brillouin signal. A PD is used to detect the Brillouin signal, using AC output mode. An oscilloscope is used to acquire data. The polarization states of the two beams and the optical experimental instruments are all aligned to the slow axis.

[0013] Furthermore, the curve fitting described in step three includes the Lorentz fitting method, and the denoised Brillouin gain spectrum is represented as discrete points (x... i ,y i If so, then the ideal Lorentz curve is established as follows:

[0014]

[0015] Wherein, the function g is a function of the variable x, h is the peak value of the Lorentz curve, c is the center, and w is the bandwidth;

[0016] Use function g on discrete points (x) i ,y i To fit the data, adjust the parameters to continuously approximate (x). i ,y i The mean squared error is used as the objective function to measure the difference between the function g and the denoised measured data.

[0017] Furthermore, the specific process of step four includes:

[0018] Step 4.1, for a given discrete point (x) i ,y i ), calculate its sample gradient l t ;

[0019] Step 4.2: Based on the sample gradient l t Calculate the squared value of the cumulative historical gradient v. t :

[0020] Step 4.3: Based on the square of the cumulative historical gradient v t Calculate the learning rate α t ;

[0021] Step 4: Based on the learning rate α t and sample gradient l t Calculate and obtain parameter θ t ;

[0022] Steps 4 and 5: Iterate through steps 41 to 44 until the termination condition is met. The frequency corresponding to the highest value of function g at that moment is the Brillouin frequency shift value.

[0023] Furthermore, in step four-one, the sample gradient l t The calculation formula is:

[0024]

[0025] In the formula, t represents time, and J(.) represents the objective function.

[0026] Furthermore, in step four-two, the squared historical gradient v is accumulated. t The calculation and update formula is as follows:

[0027] v t =αv t-1 +l t ⊙l t

[0028] In the formula, α is a constant; ⊙ represents the Hadamard product.

[0029] Furthermore, in step four-three, the learning rate α t The calculation formula is:

[0030]

[0031] In the formula, η is a constant; σ is a constant, meaning that the denominator is not zero.

[0032] Furthermore, in step four, the parameter θ t The update formula is:

[0033] θ t =θ t-1 -v⊙l t

[0034] Furthermore, following step four, step five is included: calculating the strain based on the Brillouin frequency shift; the calculation formula for the strain of each fiber segment of the fiber under test is as follows:

[0035]

[0036] In the formula, Δε i Represents the dependent variable; BFS i BFS represents the Brillouin frequency shift value at the i-th sampling point. REF This represents the reference Brillouin frequency shift value for each fiber segment; The strain coefficient represents the Brillouin frequency shift.

[0037] The beneficial technical effects of this invention are:

[0038] This invention involves curve fitting of the Brillouin gain spectrum and using the Adagrad algorithm to obtain the nonlinear least-squares optimal solution of the fitted curve. The frequency corresponding to the optimal solution is the Brillouin frequency shift. The core idea of ​​the Adagrad algorithm is to update the parameters using historical gradient information and correct the parameters of the fitted function during iteration. By obtaining the frequency corresponding to the highest point of the fitted function at the end of the iteration, the frequency shift of the Brillouin gain spectrum is obtained, thereby obtaining the strain information distributed along the optical fiber. This invention has low dependence on the initial value, and because there is no historical gradient accumulation at the beginning, the denominator of the learning rate is very small, resulting in a large overall learning rate. Therefore, it can quickly reach the convergence state, improving the curve fitting accuracy and providing better real-time performance. Attached Figure Description

[0039] The above and other objects, features, and advantages of exemplary embodiments of the present invention will become readily apparent from the following detailed description taken in conjunction with the accompanying drawings. Several embodiments of the invention are illustrated in the drawings by way of example and not limitation, wherein:

[0040] Figure 1 This is a flowchart of a Brillouin sensor high-precision data demodulation method according to an embodiment of the present invention;

[0041] Figure 2 This is a schematic diagram of the Brillouin gain spectrum distribution measured by the BOTDA system in an embodiment of the present invention;

[0042] Figure 3 This is the Brillouin scattering signal fitting result where the initial value deviates from the true value, compared to the method of this invention and the conventional gradient descent optimization algorithm. Detailed Implementation

[0043] The principles and spirit of the invention will now be described with reference to several exemplary embodiments. It should be understood that these embodiments are given merely to enable those skilled in the art to better understand and implement the invention, and are not intended to limit the scope of the invention in any way. Rather, these embodiments are provided to make this disclosure more thorough and complete, and to fully convey the scope of this disclosure to those skilled in the art.

[0044] Those skilled in the art will recognize that embodiments of the present invention can be implemented as a system, apparatus, device, method, or computer program product. Therefore, this disclosure can be specifically implemented in the following forms: entirely hardware, entirely software (including firmware, resident software, microcode, etc.), or a combination of hardware and software. It should be understood herein that any number of elements in the accompanying drawings is for illustrative purposes only and not as a limitation, and any naming is for distinction only and has no limiting meaning.

[0045] This invention provides a high-precision data demodulation method for Brillouin sensors, such as... Figure 1 As shown, the method includes the following steps:

[0046] Step 1: Measure the Brillouin gain spectrum of the optical fiber under test using a BOTDA system; the optical fiber under test includes multiple splice points.

[0047] Step 2: Denoise the Brillouin gain spectrum;

[0048] Step 3: Perform curve fitting on the Brillouin gain spectrum after noise reduction;

[0049] Step 4: Use the Adagrad algorithm to obtain the nonlinear least squares optimal solution of the fitted curve. The frequency corresponding to the optimal solution is the Brillouin frequency shift.

[0050] In this embodiment, preferably, the specific process of step one includes:

[0051] A narrow-linewidth fiber laser is used as the light source and splits into two paths via a fiber coupler. The upper branch beam is intensity-modulated by EOM1 to generate pulsed light, with the EOM1 drive signal coming from an AWG. Subsequently, the pulsed light is amplified by EDFA1 and used as pump light. The lower branch beam is carrier-suppressed by EOM2 and modulated with a first-order double-sideband signal to serve as probe light. The EOM2 drive signal comes from a sinusoidal microwave signal output from a microwave source. The pump pulse light and the dual-frequency probe light are injected into the fiber under test in opposite directions after passing through a fiber circulator and a fiber isolator, respectively. The dual-frequency probe light passes through an optical circulator and a tunable fiber Bragg grating filter, and the -1st-order sideband is selected as the Brillouin signal. A PD is used to detect the Brillouin signal, using AC output mode. An oscilloscope is used to acquire data. The polarization states of the two beams and the optical experimental instruments are all aligned to the slow axis.

[0052] In this embodiment, preferably, the curve fitting in step three includes the Lorentz fitting method, and the denoised Brillouin gain spectrum is represented as discrete points (x... i ,y i If so, then the ideal Lorentz curve is established as follows:

[0053]

[0054] Wherein, the function g is a function of the variable x, h is the peak value of the Lorentz curve, c is the center, and w is the bandwidth;

[0055] Use function g on discrete points (x) i ,y i To fit the data, adjust the parameters to continuously approximate (x). i ,y i The mean squared error is used as the objective function to measure the difference between the function g and the denoised measured data.

[0056] In this embodiment, preferably, step four includes the following specific process:

[0057] Step 4.1, for a given discrete point (x) i ,y i ), calculate the sample gradient l t Sample gradient l t The calculation formula is:

[0058]

[0059] In the formula, t represents time, and J(.) represents the objective function;

[0060] Step 4.2: Based on the sample gradient l t Calculate the squared value of the cumulative historical gradient v. t : The square of the cumulative historical gradient v t The calculation and update formula is as follows:

[0061] v t =αv t-1 +l t ⊙l t

[0062] In the formula, α is a constant; ⊙ represents the Hadamard product;

[0063] Step 4.3: Based on the square of the cumulative historical gradient v t Calculate the learning rate η; learning rate α t The calculation formula is:

[0064]

[0065] In the formula, η is a constant; σ is a constant, meaning to make the denominator non-zero;

[0066] Step 4: Based on the learning rate α t and sample gradient l t Calculate and obtain parameter θ t ; parameter θ t The update formula is:

[0067] θ t =θ t-1 -α t ⊙l t

[0068] Steps 4 and 5: Iterate through steps 41 to 44 until the termination condition is met. The frequency corresponding to the highest value of function g at that moment is the Brillouin frequency shift value.

[0069] In this embodiment, preferably, after step four, step five is further included: calculating the strain based on the Brillouin frequency shift; the calculation formula for the strain of each fiber segment of the fiber under test is as follows:

[0070]

[0071] In the formula, Δε i Represents the dependent variable; BFS i BFS represents the Brillouin frequency shift value at the i-th sampling point. REF This represents the reference Brillouin frequency shift value for each fiber segment; The strain coefficient represents the Brillouin frequency shift.

[0072] Another embodiment of the present invention provides a high-precision data demodulation method for Brillouin sensors. First, using, as shown in the example... Figure 2 The BOTDA system shown measures the Brillouin gain spectrum distribution. A narrow-linewidth fiber laser serves as the light source, splitting into two paths via a 90:10 fiber coupler. The upper branch beam undergoes intensity modulation via EOM1 to generate pulsed light, with the EOM1 drive signal originating from CH1 of the AWG. This pulsed light is then amplified by EDFA1 and used as the pump light. The lower branch beam undergoes carrier-suppressed first-order double-sideband modulation via EOM2 and serves as the probe light. The EOM2 drive signal originates from a sinusoidal microwave signal output from a microwave source. The pump pulse and dual-frequency probe light are injected into the fiber under test (BUT) in opposite directions after passing through a fiber circulator and a fiber isolator, respectively. The dual-frequency probe light passes through an optical circulator and a tunable fiber Bragg grating (TFBG) filter, selecting the -1st-order sideband as the Brillouin signal. A PD is used to probe the Brillouin signal; AC output mode is used to improve the signal-to-noise ratio. An oscilloscope is used to acquire data. The BUT fiber is a polarization-maintaining fiber, and the polarization states of both beams and the optical experimental instruments are aligned to the slow axis.

[0073] The acquired Brillouin gain spectrum distribution is demodulated and denoised using digital signal processing. The Brillouin gain spectrum is the frequency-gain curve obtained along the frequency direction at a point in the optical fiber. The Brillouin gain spectrum distribution contains information such as the peak value, frequency shift, and spectral width of the Brillouin gain spectrum obtained at each point along the fiber, as well as the noise acquired during measurement. Before extracting the Brillouin frequency shift information at each point on the fiber, the actual measured data needs to be denoised to initially reduce the impact of noise on the extraction of the Brillouin frequency shift. Then, the Brillouin frequency shift is extracted from the denoised Brillouin gain spectrum distributed along the fiber, and the relationship between the Brillouin frequency shift and temperature and stress is used to convert it into temperature and stress information distributed along the fiber.

[0074] The Brillouin gain spectrum received by the BOTDA system has a profile resembling a Lorentz curve or a Gaussian curve, and in reality, it may lie in a shape between the Lorentz curve and the Gaussian curve. For Brillouin gain spectrum signals with Lorentz curves or Gaussian curves, Brillouin frequency shift information can be extracted using Lorentz curve fitting. Lorentz curve fitting treats the Brillouin gain spectrum received by the BOTDA sensor system as the real signal, iterating to make the ideal Lorentz curve continuously approach the real signal. During the iteration process, the squared error between the real signal and the ideal Lorentz curve is used as the loss function in the Lorentz curve fitting iteration process. In this nonlinear squared problem, solving for the local minimum of the squared error yields the optimal Lorentz fitting curve.

[0075] Therefore, for the gain spectrum of the Brillouin scattering signal, it can be transformed into a method of solving for the optimal solution of nonlinear least squares to fit and obtain the Brillouin frequency shift value. Unlike linear least squares problems, nonlinear least squares problems have no explicit solution, and iterative methods are usually used to gradually approximate the parameters of the fitting function to the required values.

[0076] Existing methods combining the Gauss-Newton method or the LM algorithm can be used to estimate the parameters of the fitting curve for Brillouin scattering signals. However, the Gauss-Newton method has the drawback that when the initial values ​​deviate from the true values, the iteration process may fail to converge, resulting in poor nonlinear curve fitting. The LM algorithm suffers from the difficulty of solving the Jacobian matrix, leading to high overall computational complexity and making it unsuitable for applications with high real-time requirements. Therefore, this invention proposes an Adagrad algorithm—an adaptive learning rate optimization algorithm—to extract the Brillouin frequency shift from the denoised Brillouin gain spectrum distributed along the optical fiber.

[0077] The measured Brillouin gain spectrum in the BOTDA system is represented as discrete points (x i ,y iLet (i = 1, 2, ..., n), where n is the number of points on the entire optical fiber, x is the sweep frequency, and y is the Brillouin signal strength. The ideal Lorentz curve is established as follows:

[0078]

[0079] Where g is a function of the variable x, h is the peak value of the Lorentz curve, c is the center, and w is the bandwidth. The function g is applied to the measured discrete points (x... i ,y i To fit the data, adjust the parameters to continuously approximate (x). i ,y i The mean square error (MSE) measures the difference between the function g and the measured data, and is expressed as:

[0080]

[0081] The Adagrad algorithm is used to find the optimal solution for the nonlinear objective function J(h,w,c). When the termination condition is met, the returned function g is found to have the best fit with the measured data. The frequency corresponding to the highest value of function g at that moment is taken as the Brillouin shift value. In the Adagrad algorithm, assuming the objective function is J(θ), the unoptimized gradient descent method updates the parameter θ using a fixed learning rate α. The update formula is as follows:

[0082]

[0083] In the formula, θ i This represents the i-th parameter; This indicates that the objective function J(θ) is in the direction θ. i The gradient is given by the learning rate α, which is a constant.

[0084] The Adagrad algorithm calculates the parameter update amount based on the historical gradient information of each parameter during the parameter update process. The parameter update formula in its objective function is as follows:

[0085]

[0086] In the formula, Represented as the learning rate; η is a constant; σ is a constant, meaning to ensure the denominator is not zero; v t For parameter θ i Historical gradient sum of squares; θ t,i This represents the state of the i-th parameter at time t.

[0087] The Adagrad algorithm updates parameters based on the historical sum of squared gradients of each parameter in the objective function during the process of finding the optimal solution. When the historical sum of squared gradients is small, the update speed is accelerated, allowing the optimization of the objective function to enter the optimal solution search phase more quickly. However, using historical gradients to update parameters can also lead to a decrease in the overall learning rate of the parameters to be updated. As the parameter gradually decreases to zero, the parameter update slows down in the later stages of the iteration. When using the Adagrad algorithm to perform nonlinear minimum fitting on the Brillouin gain spectrum, multiple iterations are not required, so the impact of the slow parameter update in the later stages is not considered.

[0088] The technical effects of the present invention were further verified through experiments.

[0089] The Adagrad algorithm, which utilizes the initial value of the ideal Lorentz curve deviating from the true value, is used to extract the Brillouin frequency shift. To evaluate the performance of the Adagrad algorithm, a conventional gradient descent method is also used to extract the frequency shift from the measured Brillouin gain spectrum. The curve fitting results are as follows: Figure 3 As shown, Figure 3 This section presents the fitting results of Brillouin scattering signals using the Adagrad algorithm and the conventional gradient descent optimization algorithm, with initial values ​​deviating from the true values. It can be seen that when the initial value of the ideal Lorentz curve deviates from the true value, the Adagrad algorithm achieves a better fitting effect in a limited number of iterations compared to the conventional gradient descent algorithm. It is less dependent on the initial value and can reach convergence faster.

[0090] Further feature extraction of the Brillouin gain spectrum was performed using the LM algorithm and the method of this invention. Experimental results show that, under the same number of iterations and initial value assignment conditions, the total feature extraction measurement error of the two algorithms is not much different. However, in terms of signal processing speed, the average time consumed per set of data by the method of this invention is lower than that of the LM algorithm. Therefore, the Adagrad algorithm has better real-time performance.

[0091] Because the Adagrad algorithm starts with no accumulated historical gradients, the denominator of the learning rate is very small, resulting in a large overall learning rate. Therefore, it can reach convergence quickly. The Adagrad algorithm uses an initial incentive to converge and an iterative penalty to adjust the convergence speed, thereby improving curve fitting accuracy and making it more suitable for practical applications.

[0092] Although the operations of the method of the invention are described in a specific order in the accompanying drawings, this does not require or imply that the operations must be performed in that specific order, or that all the operations shown must be performed to achieve the desired result. Additionally or alternatively, certain steps may be omitted, multiple steps may be combined into one step, and / or one step may be broken down into multiple steps.

[0093] While the spirit and principles of the invention have been described with reference to several specific embodiments, it should be understood that the invention is not limited to the disclosed specific embodiments, and the division of aspects does not imply that features in these aspects cannot be combined for benefit; such division is merely for ease of description. The invention is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

Claims

1. A high-precision data demodulation method for Brillouin sensors, characterized in that, Includes the following steps: Step 1: Measure the Brillouin gain spectrum of the optical fiber under test using a BOTDA system; the optical fiber under test includes multiple splice points. Step 2: Denoise the Brillouin gain spectrum; Step 3: Perform curve fitting on the denoised Brillouin gain spectrum. The curve fitting includes the Lorentz fitting method. The denoised Brillouin gain spectrum is represented as discrete points. The ideal Lorentz curve is then established as follows: ； Where g represents a function of the variable x, h is the peak value of the Lorentz curve, c is the center, and w is the bandwidth; the function g is applied to discrete points Perform a fitting process and adjust the parameters to continuously approximate the desired result. Mean squared error is used as the objective function to measure the degree of difference between the function g and the denoised measured data. Step 4: Use the Adagrad algorithm to obtain the nonlinear least-squares optimal solution of the fitted curve. The frequency corresponding to the optimal solution is the Brillouin shift; including: Step 4.1, for a given discrete point Calculate its sample gradient ; Step 4.2: Based on the sample gradient Calculate the square of the updated cumulative historical gradient : Step 43: Based on the square of the cumulative historical gradient Calculate the learning rate ; Step 4: Based on the learning rate and sample gradient Calculate and obtain parameters ; Steps 4 and 5: Iterate through steps 41 to 44 until the termination condition is met. The frequency corresponding to the highest value of function g at that moment is the Brillouin frequency shift value.

2. The Brillouin sensor high-precision data demodulation method according to claim 1, characterized in that, The specific process of step one includes: A narrow-linewidth fiber laser is used as the light source and splits into two paths via a fiber coupler. The upper branch beam is intensity-modulated by EOM1 to generate pulsed light, with the EOM1 drive signal coming from an AWG. Subsequently, the pulsed light is amplified by EDFA1 and used as pump light. The lower branch beam is carrier-suppressed by EOM2 and modulated with a first-order double-sideband signal to serve as probe light. The EOM2 drive signal comes from a sinusoidal microwave signal output from a microwave source. The pump pulse light and the dual-frequency probe light are injected into the fiber under test in opposite directions after passing through a fiber circulator and a fiber isolator, respectively. The dual-frequency probe light passes through an optical circulator and a tunable fiber Bragg grating filter, and the -1st-order sideband is selected as the Brillouin signal. A PD is used to detect the Brillouin signal, using AC output mode. An oscilloscope is used to acquire data. The polarization states of the two beams and the optical experimental instruments are all aligned to the slow axis.

3. The Brillouin sensor high-precision data demodulation method according to claim 1, characterized in that, Sample gradient in step four. The calculation formula is: ； In the formula, t represents time. This represents the objective function.

4. The Brillouin sensor high-precision data demodulation method according to claim 3, characterized in that, In step four two, the square of the accumulated historical gradient is calculated. The calculation and update formula is as follows: + ； In the formula, It is a constant; This represents the Hadamard product.

5. The Brillouin sensor high-precision data demodulation method according to claim 4, characterized in that, Learning rate in step four three The calculation formula is: ； In the formula, It is a constant; It is a constant, meaning that the denominator is not zero.

6. The Brillouin sensor high-precision data demodulation method according to claim 5, characterized in that, Step 44 parameters The update formula is: 。 7. A high-precision data demodulation method for Brillouin sensing according to any one of claims 1-6, characterized in that, Step five follows step four: calculating the strain based on the Brillouin frequency shift; the formula for calculating the strain of each fiber segment under test is as follows: ； In the formula, Indicates the dependent variable; Indicates the first Brillouin frequency shift values ​​at each sampling point; This represents the reference Brillouin frequency shift value for each fiber segment; The strain coefficient represents the Brillouin frequency shift.

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