Optical time domain reflection monitoring method and device based on forward and reverse signal joint optimization

Abstract

The invention belongs to the technical field of optical fiber sensing, and relates to an optical time domain reflection monitoring method and device based on forward and reverse signal joint optimization, and the method comprises the steps: obtaining reverse and forward OTDR observation signals of a to-be-measured optical fiber; constructing a reverse OTDR linear signal reconstruction item based on a product of the orthogonal transformation matrix and a to-be-solved first sparse coefficient vector; constructing a forward OTDR linear signal reconstruction item based on the product of the orthogonal transformation matrix and a to-be-solved second sparse coefficient vector; constructing a data fidelity item based on the OTDR observation signal and the linear signal reconstruction item; constructing a joint sparse regular term based on the structural sparsity of the first sparse coefficient vector and the second sparse coefficient vector to be solved; and constructing a spatial constraint regular term based on the continuous smoothness of the reconstructed OTDR linear signal in the space, thereby constructing a joint optimization function and solving the joint optimization function to obtain a first sparse coefficient vector and a second sparse coefficient vector, and further reconstructing the OTDR linear signal to detect the optical fiber to be detected.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of optical fiber sensing technology, in particular to an optical time domain reflectometry method and device based on joint optimization of forward and backward signals and a computer readable storage medium. BACKGROUND

[0002] Optical Time-Domain Reflectometry (OTDR) is a tool for ensuring the safety and stability of optical fiber networks. It diagnoses the status of optical fiber links by transmitting laser pulses to the optical fiber under test and analyzing the backscattered signals returned by the optical fiber under test. It is suitable for long-distance applications such as submarine cables and terrestrial trunk cables.

[0003] The existing backward OTDR monitoring technology receives weak backscattered Rayleigh scattering and Fresnel reflection signals at the transmitting end. By extracting features from the received signals, the continuous signals are converted into quantifiable link characteristic parameters (e.g., optical fiber length and received signal relative power curve), thereby obtaining the Rayleigh scattering characteristics and Fresnel reflection characteristics of the optical fiber under test to assess whether the optical fiber link under test has faults such as compression, bending or breakpoints. However, long-distance transmission results in extremely weak backscattered signals. The small fluctuations in backscattered Rayleigh scattering signals caused by weak events (minor vibrations, fiber stress changes and aging) are almost the same in amplitude as photodetectors, amplifiers and environmental noise, or even overwhelmed by noise signals, resulting in misjudgment of noise as signal fluctuations caused by weak events or misjudgment of signal fluctuations caused by weak event noise as noise, thereby affecting the accuracy of the detection results. Meanwhile, when locating faults, the signal fluctuations caused by weak events are close in amplitude to noise, causing the edges of the optical fiber length and received signal relative power curve to gradually transition and become unclear, making it difficult to define the starting point of the occurrence of weak events on the curve and affecting the fault location accuracy.

[0004] In summary, the existing optical time domain reflectometry monitoring method has the problem of weak backward OTDR signal strength, which is easily overwhelmed by noise signals, thereby affecting the monitoring accuracy and fault point positioning accuracy. SUMMARY

[0005] To this end, the technical problem to be solved by the present application is to overcome the problem of weak backward OTDR signal strength in the existing optical time domain reflectometry monitoring method, which is easily overwhelmed by noise signals, thereby affecting the monitoring accuracy and fault point positioning accuracy.

[0006] To solve the above technical problems, the present application provides an optical time domain reflectometry monitoring method based on joint optimization of forward and backward signals, comprising: obtaining a backward OTDR observation signal and a forward OTDR observation signal of an optical fiber under test; constructing a backward OTDR linear signal reconstruction term based on a product of the orthogonal transformation matrix and the first sparse coefficient vector to be solved; constructing a data fidelity term based on a difference between the backward OTDR observation signal and the backward OTDR linear signal reconstruction term and a difference between the forward OTDR observation signal and the forward OTDR linear signal reconstruction term; constructing a joint sparse regularization term based on the i-th eigenvalue of the first sparse coefficient vector to be solved and the i-th eigenvalue of the second sparse coefficient vector to be solved, and constructing a spatial constraint regularization term based on a spatial continuity and smoothness of the reconstructed backward OTDR linear signal and the forward OTDR linear signal; constructing a joint optimization function with a weighted sum of the data fidelity term, the joint sparse regularization term and the spatial constraint regularization term minimized as an objective, and solving the joint optimization function to obtain the first sparse coefficient vector and the second sparse coefficient vector, thereby reconstructing the backward OTDR linear signal and the forward OTDR linear signal to detect the optical fiber under test.

[0007] Preferably, the data fidelity term is constructed based on a difference between the backward OTDR observation signal and the backward OTDR linear signal reconstruction term and a difference between the forward OTDR observation signal and the forward OTDR linear signal reconstruction term, including: constructing a first data fidelity term based on a square of an L2 norm of the difference between the backward OTDR observation signal and the backward OTDR linear signal reconstruction term; constructing a second data fidelity term based on a square of an L2 norm of the difference between the forward OTDR observation signal and the forward OTDR linear signal reconstruction term; obtaining the data fidelity term based on a weighted sum of the first data fidelity term and the second data fidelity term.

[0008] Preferably, the joint optimization function is expressed as: , , , wherein, represents the joint optimization function; represents the first sparse coefficient vector; represents the second sparse coefficient vector; represents the backward OTDR observation signal; represents the orthogonal transformation matrix; represents a square of an L2 norm; represents the forward OTDR observation signal; represents the data fidelity term; This represents a joint sparse regularization term; This represents the regularization parameter used to control the sparsity of the vector; This represents the i-th eigenvalue in the first sparse coefficient vector; This represents the i-th eigenvalue in the second sparse coefficient vector; Denotes the L2,1 norm; Represents the space constraint regularization term; Indicates the degree of spatial smoothness constraint; Represents the difference operator matrix; This represents the gradient of the reconstructed OTDR linear signal; This indicates the reconstructed inverse OTDR linear signal or the forward OTDR linear signal. This represents the L1 norm.

[0009] Preferably, solving the joint optimization function yields a first sparse coefficient vector and a second sparse coefficient vector, including: Step 1: Construct the first auxiliary variable of the reverse OTDR linear signal reconstruction term, the second auxiliary variable of the forward OTDR linear signal reconstruction term, the third auxiliary variable of the first sparse coefficient vector, the fourth auxiliary variable of the second sparse coefficient vector, and the fifth auxiliary variable of the gradient of the reconstructed OTDR linear signal; and define the dual variables of each auxiliary variable. Step 2: Replace the reverse OTDR linear signal reconstruction term, forward OTDR linear signal reconstruction term, first sparse coefficient vector, second sparse coefficient vector, and the reconstructed OTDR linear signal gradient in the joint optimization function with each auxiliary variable to obtain a new joint optimization function; construct the constraint function corresponding to each auxiliary variable by making each auxiliary variable equal to the parameter it replaces. Step 3: Let k=0, and set the values ​​of each auxiliary variable, each dual variable, the first sparse coefficient vector, the second sparse coefficient vector, and the penalty parameter for the kth iteration; Step 4: Based on the variable decoupling and collaborative optimization principle of the alternating direction multiplier method, update the first sparse coefficient vector, the second sparse coefficient vector and each auxiliary variable at the k-th iteration to obtain the updated first sparse coefficient vector, the second sparse coefficient vector and each auxiliary variable. Step 5: Based on the updated auxiliary variables, the first sparse coefficient vector, and the second sparse coefficient vector, calculate the constraint function value corresponding to each auxiliary variable; Step 6: Based on the acceleration parameters and the values ​​of each dual variable in the k-th and (k-1)-th iterations, calculate the predicted values ​​of each dual variable after the update; based on the difference between the predicted values ​​of each dual variable after the update and the constraint function values ​​corresponding to each auxiliary variable, obtain the values ​​of the dual variables of each auxiliary variable after the update. Step 7: obtaining the primal residual norm based on the arithmetic square root of the sum of squares of L2 norms of constraint function values corresponding to respective auxiliary variables; obtaining the dual residual norm based on the product of the arithmetic square root of the sum of squares of L2 norms of the first difference value before and after updating the third auxiliary variable, the second difference value before and after updating the fourth auxiliary variable, the third difference value before and after updating the fifth auxiliary variable, and the penalty parameter at the kth iteration; Step 8: judging whether the primal residual norm is less than a preset primal residual tolerance and whether the dual residual tolerance is less than a preset dual residual tolerance; if the primal residual norm is greater than or equal to the preset primal residual tolerance and / or the dual residual tolerance is greater than or equal to the preset dual residual tolerance, updating the penalty parameter and the dual variable based on the sizes of the primal residual norm and the dual residual norm; Step 9: if the primal residual norm is greater than the product of the first preset penalty parameter threshold and the dual residual norm, taking the product of the value of the penalty parameter at the kth iteration and the second preset penalty parameter threshold as the updated penalty parameter; and calculating the product of the second preset penalty parameter threshold and each dual variable respectively, thereby updating each dual variable again; Step 10: if the dual residual norm is greater than the product of the first preset penalty parameter threshold and the primal residual norm, taking the quotient of the value of the penalty parameter at the kth iteration and the second preset penalty parameter threshold as the updated penalty parameter; and calculating the quotient of each dual variable and the second preset penalty parameter threshold, thereby updating each dual variable again; Step 11: updating k=k+1, taking the values of each auxiliary variable, each dual variable, the first sparse coefficient vector, the second sparse coefficient vector and the penalty parameter after the update as the values of each auxiliary variable, each dual variable, the first sparse coefficient vector, the second sparse coefficient vector and the penalty parameter at the kth iteration, returning to execute Step 4 until the primal residual norm is less than the preset primal residual tolerance and the dual residual tolerance is less than the preset dual residual tolerance, thereby obtaining the first sparse coefficient vector and the second sparse coefficient vector.

[0010] Preferably, the new joint optimization function is represented as: , wherein, represents the new joint optimization function; represents the reverse OTDR observation signal; represents the first auxiliary variable; represents the square of L2 norm; represents the forward OTDR observation signal; represents the second auxiliary variable; represents the regularization parameter for controlling the sparsity degree of the vector; represents the third auxiliary variable, denotes the i-th eigenvalue in the third auxiliary variable; denotes the fourth auxiliary variable, denotes the i-th eigenvalue in the fourth auxiliary variable; denotes the spatial smoothness constraint degree; denotes the fifth auxiliary variable; denotes the L1 norm; The constraint function corresponding to the first auxiliary variable is denoted as: , wherein, denotes the orthogonal transformation matrix; denotes the first sparse coefficient vector; The constraint function corresponding to the second auxiliary variable is denoted as: , wherein, denotes the second sparse coefficient vector; The constraint function corresponding to the third auxiliary variable is denoted as: , The constraint function corresponding to the fourth auxiliary variable is denoted as: , The constraint function corresponding to the fifth auxiliary variable is denoted as: , wherein, denotes the difference operator matrix; denotes the gradient of the reconstructed OTDR linear signal; denotes the reconstructed reverse OTDR linear signal or forward OTDR linear signal.

[0011] Preferably, the update formula of the first sparse coefficient vector is: , wherein, denotes the updated first sparse coefficient vector; denotes the penalty parameter; denotes the orthogonal transformation matrix; denotes the first auxiliary variable at the k-th iteration; denotes the first dual variable at the k-th iteration; denotes the third auxiliary variable at the k-th iteration; denotes the third dual variable at the k-th iteration; denotes the transpose; The update formula of the second sparse coefficient vector is: , wherein, denotes the updated second sparse coefficient vector; denotes the second auxiliary variable at the kth iteration; denotes the second dual variable at the kth iteration; denotes the fourth auxiliary variable at the kth iteration; denotes the fourth dual variable at the kth iteration; The update formula of the first auxiliary variable is: , wherein, denotes the updated first auxiliary variable; denotes the identity matrix; denotes the difference operator matrix; denotes the backward OTDR observation signal; denotes the fifth auxiliary variable at the kth iteration; denotes the fifth dual variable at the kth iteration; The update formula of the second auxiliary variable is: , wherein, denotes the updated second auxiliary variable; denotes the forward OTDR observation signal; The update formula of the third auxiliary variable and the fourth auxiliary variable is: , , , , wherein, denotes the ith eigenvalue in the updated third auxiliary variable; denotes the ith eigenvalue in the updated fourth auxiliary variable; denotes the regularization parameter for controlling the sparsity degree of the vector; denotes the ith eigenvalue in denotes the ith eigenvalue in denotes the ith eigenvalue in The update formula of the fifth auxiliary variable is: , , wherein, denotes the updated fifth auxiliary variable; denotes the sign function; denotes the degree of spatial smoothing constraint.

[0012] ​Preferably, the calculation formula of the prediction value of each dual variable after updating is: , wherein, represents the prediction value of the n th dual variable after updating; represents an acceleration parameter; represents the value of the n th dual variable at the k th iteration; represents the value of the n th dual variable at the k-1 th iteration; The update formula of each dual variable is: , , , , , , wherein, represents the n th dual variable after updating; represents the constraint function value corresponding to the n th auxiliary variable; represents the first auxiliary variable after updating; represents an orthogonal transformation matrix; represents the first sparse coefficient vector after updating; represents the second auxiliary variable after updating; represents the second sparse coefficient vector after updating; represents the third auxiliary variable after updating; represents the fourth auxiliary variable after updating; represents the fifth auxiliary variable after updating; represents a difference operator matrix.

[0013] Preferably, the reverse OTDR linear signal and the forward OTDR linear signal are reconstructed to detect the to-be-detected optical fiber, comprising: The first sparse coefficient vector is orthogonally transformed by using the orthogonal transformation matrix to obtain the reverse OTDR linear signal, and the second sparse coefficient vector is orthogonally transformed by using the orthogonal transformation matrix to obtain the forward OTDR linear signal; Based on the loss of the forward OTDR linear signal and the reverse OTDR linear signal, it is detected whether the to-be-detected optical fiber has a fault; if there is a fault, the bidirectional positioning method is used to perform fault positioning based on the forward OTDR linear signal and the reverse OTDR linear signal.

[0014] The application also provides an optical time domain reflectometry device based on joint optimization of forward and reverse signals, comprising: The signal acquisition module is configured to acquire a reverse OTDR observation signal and a forward OTDR observation signal of the optical fiber to be detected. The signal reconstruction module is configured to construct a reverse OTDR linear signal reconstruction term based on a product of the orthogonal transformation matrix and the first sparse coefficient vector to be solved, and construct a forward OTDR linear signal reconstruction term based on a product of the orthogonal transformation matrix and the second sparse coefficient vector to be solved. The fidelity term construction module is configured to construct a data fidelity term based on a difference between the reverse OTDR observation signal and the reverse OTDR linear signal reconstruction term and a difference between the forward OTDR observation signal and the forward OTDR linear signal reconstruction term. The regularization term construction module is configured to construct a joint sparse regularization term based on the first sparse coefficient vector to be solved and the second sparse coefficient vector to be solved, and construct a spatial constraint regularization term based on a continuous smoothness of the reconstructed reverse OTDR linear signal and the forward OTDR linear signal in space. The optimization function construction and solving module is configured to construct a joint optimization function with a weighted sum minimization of the data fidelity term, the joint sparse regularization term and the spatial constraint regularization term as a target, and solve the joint optimization function to obtain the first sparse coefficient vector and the second sparse coefficient vector, thereby reconstructing the reverse OTDR linear signal and the forward OTDR linear signal to detect the optical fiber to be detected.

[0015] The application further provides a computer readable storage medium, and the computer readable storage medium stores a computer program.

[0016] The optical time domain reflectometry method based on joint optimization of forward and reverse signals provided by the application has the following beneficial effects: The physical architecture of single-end transmission and double-end reception is adopted, the forward OTDR observation signal and the backward OTDR observation signal based on the laser pulse signal reflection of the optical fiber to be measured are acquired simultaneously, the clear feature of the forward OTDR observation signal is transmitted to the denoising and recovery process of the backward signal, and the weak backward signal is provided with strong guidance; further, considering the noise influence in the observation signal, the noise-free OTDR linear signal is separated from the backward OTDR observation signal and the forward OTDR observation signal through signal reconstruction to improve the monitoring precision; specifically, since the OTDR signal has the sparse characteristic on the specific feature domain, i.e., the energy of the weak event is only concentrated on a few feature coefficients, therefore, the orthogonal transformation matrix is adopted to perform orthogonal transformation on the sparse coefficient vector to reconstruct the OTDR linear signal, and the data fidelity term is constructed to constrain the reconstructed signal to fit the real observation signal; meanwhile, since the scattering or reflection features of the backward OTDR linear signal and the forward OTDR linear signal caused by the weak event at the same position of the optical fiber have the space-time symmetry, i.e., the energy of the weak event will affect the forward and backward OTDR signals simultaneously, and the random noise usually exists in the single-end signal, therefore, the joint sparse regularization term is constructed by taking the i-th feature value of the first sparse coefficient vector to be solved and the second sparse coefficient vector to be solved as zero value or nonzero value; finally, the spatial constraint term is constructed by taking the spatial continuity of the normal OTDR signal, and the joint optimization objective function is finally constructed, the noise-free OTDR linear signal is reconstructed by performing orthogonal transformation on the sparse coefficient vector obtained by solving, the denoising and feature enhancement of the OTDR observation signal are realized, and thus the denoised signal is used for fault detection and positioning, and the monitoring result accuracy and the positioning precision are effectively improved. BRIEF DESCRIPTION OF DRAWINGS

[0017] In order to make the content of the present application more easily understood, the present application will be further described in detail below according to the specific embodiments of the present application and in combination with the drawings, in which: Figure 1 The flow chart of the optical time domain reflection monitoring method based on the joint optimization of the forward and backward signals provided by the present application is shown in the figure; Figure 2 The structure schematic diagram of the optical time domain reflection monitoring device based on the joint optimization of the forward and backward signals provided by the present application is shown in the figure. DETAILED DESCRIPTION

[0018] The present application will be further described below in combination with the drawings and specific embodiments, so that the person skilled in the art can better understand the present application and implement it, but the embodiments are not as the limitation of the present application.

[0019] Please refer to Figure 1 , Figure 1A flow chart of the OTDR method based on joint optimization of forward and backward signals is shown, and the method specifically comprises: S10: Obtain the backward OTDR observation signal and the forward OTDR observation signal of the optical fiber to be measured.

[0020] Specifically, if the length of the optical fiber to be measured is L, the original backward OTDR observation signal collected at time t is represented as , and the original forward OTDR observation signal is represented as , The number of sampling points is represented as since the observation signal is composed of an ideal noise-free signal and a noise signal, and the above two observation signals can be modeled as: , , Among them, represents the noise-free backward OTDR signal, i.e., the backward OTDR linear signal; represents the noise signal in the backward OTDR observation signal; represents the noise-free forward OTDR signal, i.e., the forward OTDR linear signal; represents the noise signal in the forward OTDR observation signal; the target of the present application is to reconstruct the noise-free OTDR linear signal from the OTDR observation signal.

[0021] S20: Based on the product of the orthogonal transformation matrix and the first sparse coefficient vector to be solved, construct the backward OTDR linear signal reconstruction term; based on the product of the orthogonal transformation matrix and the second sparse coefficient vector to be solved, construct the forward OTDR linear signal reconstruction term.

[0022] The present application finds that the OTDR linear signal is not sparse in the time domain, but is sparse in some feature domains (such as wavelet domain), therefore, the present application adopts the orthogonal transformation matrix to orthogonally transform the sparse coefficient vector to reconstruct the OTDR linear signal. It is worth noting that for the same optical fiber to be measured, the positions causing significant non-zero values in the first sparse coefficient vector and the second sparse coefficient vector are the same or highly correlated, i.e., both have the characteristics of structured sparsity, which provides a theoretical basis for the design of the joint sparse regularization term of the present application.

[0023] S30: Based on the difference between the backward OTDR observation signal and the backward OTDR linear signal reconstruction term and the difference between the forward OTDR observation signal and the forward OTDR linear signal reconstruction term, construct the data fidelity term.

[0024] Further, step S30 specifically comprises: S300: constructing a first data fidelity term based on a square of an L2 norm of a difference between the reverse OTDR observation signal and a reverse OTDR linear signal reconstruction term.

[0025] S301: constructing a second data fidelity term based on a square of an L2 norm of a difference between the forward OTDR observation signal and a forward OTDR linear signal reconstruction term.

[0026] S302: obtaining a data fidelity term based on a weighted sum of the first data fidelity term and the second data fidelity term.

[0027] Specifically, through the data fidelity terms constructed for the reverse OTDR signal and the forward OTDR signal, it can be ensured that the residual error between the OTDR signal reconstructed by the first sparse coefficient vector and the second sparse coefficient vector and the original observation signal is minimized, thereby ensuring the accuracy of the reconstructed signal.

[0028] S40: constructing a joint sparse regularization term based on the i-th eigenvalue of the first sparse coefficient vector to be solved and the second sparse coefficient vector to be solved being zero or non-zero, and constructing a spatial constraint regularization term based on the continuous smoothness of the reconstructed reverse OTDR linear signal and the forward OTDR linear signal in space.

[0029] Specifically, based on the structured sparsity characteristics of the first sparse coefficient vector and the second sparse coefficient vector, the joint sparse regularization term is constructed, so that the first sparse coefficient vector and the second sparse vector are simultaneously zero or non-zero at the same position; at the same time, the reconstructed OTDR signal is continuous and smooth in space, therefore, the present application punishes the solution which is discontinuous and changes dramatically in space by constructing the spatial constraint regularization term, thereby obtaining a piecewise smooth optimal solution to make the reconstructed OTDR linear signal conform to the edge step characteristics of the OTDR linear signal, while suppressing the random noise in the flat area.

[0030] S50: constructing a joint optimization function with the weighted sum of the data fidelity term, the joint sparse regularization term and the spatial constraint regularization term as the minimum target; solving the joint optimization function to obtain the first sparse coefficient vector and the second sparse coefficient vector, thereby reconstructing the forward OTDR linear signal and the reverse OTDR linear signal to detect the optical fiber to be measured.

[0031] Specifically, the joint optimization function is represented as: , , , wherein, represents the joint optimization function; represents the first sparse coefficient vector; denotes a second sparse coefficient vector; denotes a backward OTDR observation signal; denotes an orthogonal transformation matrix; denotes a square of L2 norm; denotes a forward OTDR observation signal; denotes a data fidelity term; denotes a joint sparse regularization term; denotes a regularization parameter for controlling the sparsity of a vector; denotes an i-th eigenvalue in the first sparse coefficient vector; denotes an i-th eigenvalue in the second sparse coefficient vector; denotes an L2,1 norm; denotes a spatial constraint regularization term; denotes a spatial smoothness constraint degree; denotes a difference operator matrix; denotes a gradient of the reconstructed OTDR linear signal; denotes a reconstructed backward OTDR linear signal or a reconstructed forward OTDR linear signal; denotes an L1 norm.

[0032] The present application obtains the forward and reverse OTDR signals and the reverse OTDR observation signal of the optical fiber to be tested based on the physical structure of "single-end transmission and double-end synchronous reception", transmits the clear features of the forward OTDR observation signal to the denoising and recovery process of the reverse signal, provides strong guidance for the weak reverse signal, further considers the noise influence in the observation signal, separates the noise-free OTDR linear signal from the reverse and forward OTDR observation signals through signal reconstruction to improve the monitoring accuracy, specifically, the OTDR signal has the sparse characteristics on the specific feature domain, that is, the energy of the weak event is only concentrated on a few characteristic coefficients, therefore, the present application adopts the orthogonal transformation matrix to orthogonally transform the sparse coefficient vector to reconstruct the OTDR linear signal, and constructs the data fidelity term to constrain the reconstructed signal to fit the real observation signal, at the same time, the scattering or reflection features of the reverse and forward OTDR linear signals at the same position of the optical fiber caused by the weak event have the space-time symmetry, that is, the energy of the weak event will affect the forward and reverse OTDR signals at the same time, and the random noise usually only exists in the single-end signal, therefore, the present application constructs the joint sparse regularization term by taking the i-th eigenvalue of the first sparse coefficient vector to be solved and the i-th eigenvalue of the second sparse coefficient vector to be solved as zero value or non-zero value, finally, the spatial constraint term is constructed by taking the spatial continuity of the normal OTDR signal, and the joint optimization objective function is finally constructed, the noise-free OTDR linear signal is reconstructed by orthogonally transforming the sparse coefficient vector obtained by solving, the denoising and feature enhancement of the OTDR observation signal are realized, so that the denoised signal is used for fault detection and positioning, and the monitoring result accuracy and positioning precision are effectively improved.

[0033] Further, the spatial constraint is linearized by its proximal operator and directly integrated into the iterative update formula, so that each step has an efficient closed-form solution, specifically, the first sparse coefficient vector and the second sparse coefficient vector are obtained by solving the joint optimization function, including: Step 1: constructing the first auxiliary variable of the reverse OTDR linear signal reconstruction term, the second auxiliary variable of the forward OTDR linear signal reconstruction term, the third auxiliary variable of the first sparse coefficient vector, the fourth auxiliary variable of the second sparse coefficient vector, and the fifth auxiliary variable of the reconstructed OTDR linear signal gradient, and defining the dual variables of each auxiliary variable.

[0034] Step 2: replacing the reverse OTDR linear signal reconstruction term, the forward OTDR linear signal reconstruction term, the first sparse coefficient vector, the second sparse coefficient vector and the reconstructed OTDR linear signal gradient in the joint optimization function with the auxiliary variables to obtain a new joint optimization function; constructing the constraint functions corresponding to each auxiliary variable by equating each auxiliary variable with the parameter replaced by it.

[0035] Specifically, the new joint optimization function is represented as: , wherein, represents the new joint optimization function; represents the backward OTDR observation signal; represents the first auxiliary variable; represents the square of L2 norm; represents the forward OTDR observation signal; represents the second auxiliary variable; represents the regularization parameter for controlling the sparsity degree of the vector; represents the third auxiliary variable, represents the ith eigenvalue in the third auxiliary variable; represents the fourth auxiliary variable, represents the ith eigenvalue in the fourth auxiliary variable; represents the degree of spatial smoothing constraint; represents the fifth auxiliary variable; represents the L1 norm.

[0036] The constraint function corresponding to the first auxiliary variable is represented as: , wherein, represents the orthogonal transformation matrix; represents the first sparse coefficient vector; The constraint function corresponding to the second auxiliary variable is represented as: , wherein, represents the second sparse coefficient vector; The constraint function corresponding to the third auxiliary variable is represented as: , The constraint function corresponding to the fourth auxiliary variable is represented as: , The constraint function corresponding to the fifth auxiliary variable is represented as: , wherein, represents the difference operator matrix; represents the gradient of the reconstructed OTDR linear signal; represents the reconstructed backward OTDR linear signal or forward OTDR linear signal.

[0037] Step 3: Let k = 0, and set the values of each auxiliary variable, each dual variable, the first sparse coefficient vector, the second sparse coefficient vector and the penalty parameter in the kth iteration.

[0038] In an embodiment of the present application, each auxiliary variable, each dual variable, and the first sparse coefficient vector and the second sparse coefficient vector in the k = 0 iteration are set as zero vectors.

[0039] Step 4: Based on the variable decoupling and collaborative optimization principle of the alternating direction multiplier method, the first sparse coefficient vector, the second sparse coefficient vector and each auxiliary variable in the kth iteration are updated, so as to obtain the updated first sparse coefficient vector, the second sparse coefficient vector and each auxiliary variable.

[0040] Specifically, the update formula of the first sparse coefficient vector is: , wherein, denotes the updated first sparse coefficient vector; denotes the penalty parameter; denotes the orthogonal transformation matrix; denotes the first auxiliary variable in the kth iteration; denotes the first dual variable in the kth iteration; denotes the third auxiliary variable in the kth iteration; denotes the third dual variable in the kth iteration; denotes the transpose.

[0041] The update formula of the second sparse coefficient vector is: , wherein, denotes the updated second sparse coefficient vector; denotes the second auxiliary variable in the kth iteration; denotes the second dual variable in the kth iteration; denotes the fourth auxiliary variable in the kth iteration; denotes the fourth dual variable in the kth iteration.

[0042] Specifically, in the update of the first sparse coefficient vector, the deviation between the first dual variable penalizes and Since the third auxiliary variable is the auxiliary variable of , the third dual variable penalizes and deviation between and, and the penalty intensity of constraint violation is controlled by a penalty parameter; similarly, in the first sparse coefficient vector update, a second dual variable penalty deviation between and, and the penalty intensity of constraint violation is controlled by a penalty parameter; similarly, in the first sparse coefficient vector update, a second dual variable deviation between and, and the penalty intensity of constraint violation is controlled by a penalty parameter; similarly, in the first sparse coefficient vector update, a second dual variable auxiliary variable auxiliary variable, thus a fourth dual variable penalty deviation between and, and the penalty intensity of constraint violation is controlled by a penalty parameter; similarly, in the first sparse coefficient vector update, a second dual variable deviation between and, and the penalty intensity of constraint violation is controlled by a penalty parameter; similarly, in the first sparse coefficient vector update, a second dual variable

[0043] The update formula of the first auxiliary variable is: , wherein, denotes the updated first auxiliary variable; denotes a unit matrix; denotes a difference operator matrix; denotes a reverse OTDR observation signal; denotes the fifth auxiliary variable at the kth iteration; denotes the fifth dual variable at the kth iteration.

[0044] The update formula of the second auxiliary variable is: , wherein, denotes the updated second auxiliary variable; denotes a forward OTDR observation signal; The present application simultaneously scales or sets to zero and , which can ensure the joint sparse characteristics, and specifically, the update formulae of the third auxiliary variable and the fourth auxiliary variable are: , , , , wherein, denotes the i-th eigenvalue of the updated third auxiliary variable; denotes the i-th eigenvalue of the updated fourth auxiliary variable; denotes a regularization parameter for controlling the sparsity degree of the vector; denotes the i-th eigenvalue in denotes the i-th eigenvalue in denotes the i-th eigenvalue in denotes the i-th eigenvalue in

[0045] The update formula of the fifth auxiliary variable is: , , wherein, denotes the updated fifth auxiliary variable; denotes a sign function; denotes a spatial smoothness constraint degree; denotes element-wise multiplication.

[0046] Step 5: Based on the updated respective auxiliary variables, the first sparse coefficient vector and the second sparse coefficient vector, the constraint function values corresponding to the respective auxiliary variables are calculated.

[0047] Specifically, the calculation formula of the constraint function values corresponding to the respective auxiliary variables is as follows: , , , , , wherein, denotes the constraint function value corresponding to the first auxiliary variable; denotes the constraint function value corresponding to the second auxiliary variable; denotes the constraint function value corresponding to the third auxiliary variable; denotes the constraint function value corresponding to the fourth auxiliary variable; denotes the constraint function value corresponding to the fifth auxiliary variable.

[0048] Step 6: Based on the acceleration parameter and the values of the respective dual variables at the kth iteration and the (k-1)th iteration, the predicted values of the updated respective dual variables are calculated; based on the difference between the predicted values of the updated respective dual variables and the constraint function values corresponding to the respective auxiliary variables, the values of the dual variables of the updated respective auxiliary variables are obtained.

[0049] Specifically, the calculation formula of the predicted values of the updated respective dual variables is as follows: , wherein, denotes the predicted value of the updated nth dual variable; denotes the acceleration parameter; denotes the value of the nth dual variable at the kth iteration; denotes the value of the nth dual variable at the (k-1)th iteration; The update formula of the respective dual variables is: , wherein, denotes the updated n-th dual variable; denotes the constraint function value corresponding to the n-th auxiliary variable.

[0050] Step 7: obtain the primal residual norm based on the arithmetic square root of the sum of squares of L2 norms of the constraint function values corresponding to the respective auxiliary variables; obtain the dual residual norm based on the product of the arithmetic square root of the sum of squares of L2 norms of the first difference value before and after the update of the third auxiliary variable, the second difference value before and after the update of the fourth auxiliary variable, the third difference value before and after the update of the fifth auxiliary variable, and the penalty parameter at the k-th iteration.

[0051] Specifically, the calculation formula of the primal residual norm is as follows: , the calculation formula of the dual residual norm is as follows: , Step 8: judge whether the primal residual norm is less than the preset primal residual tolerance and whether the dual residual tolerance is less than the preset dual residual tolerance; if the primal residual norm is greater than or equal to the preset primal residual tolerance and / or the dual residual tolerance is greater than or equal to the preset dual residual tolerance, update the penalty parameter and the dual variable based on the size of the primal residual norm and the dual residual norm.

[0052] Step 9: if the primal residual norm is greater than the product of the first preset penalty parameter threshold and the dual residual norm, take the product of the value of the penalty parameter at the k-th iteration and the second preset penalty parameter threshold as the updated penalty parameter; calculate the product of the second preset penalty parameter threshold and each updated dual variable respectively, thereby updating each dual variable again.

[0053] Step 10: if the dual residual norm is greater than the product of the first preset penalty parameter threshold and the primal residual norm, take the quotient of the value of the penalty parameter at the k-th iteration and the second preset penalty parameter threshold as the updated penalty parameter; calculate the quotient of each dual variable and the second preset penalty parameter threshold, thereby updating each dual variable again.

[0054] Step 11: update k=k+1, take the values of each updated auxiliary variable, each dual variable, the first sparse coefficient vector, the second sparse coefficient vector and the penalty parameter as the values of each auxiliary variable, each dual variable, the first sparse coefficient vector, the second sparse coefficient vector and the penalty parameter at the k-th iteration, return to execute Step 4 until the primal residual norm is less than the preset primal residual tolerance and the dual residual tolerance is less than the preset dual residual tolerance, thereby obtaining the first sparse coefficient vector and the second sparse coefficient vector.

[0055] Specifically, the first preset penalty parameter threshold and the second preset penalty parameter threshold are both greater than 1, the first preset penalty parameter threshold is used to judge whether the original residual and the dual residual are significantly unbalanced, and a commonly used value thereof is 10, and the second preset penalty parameter threshold is used to increase or decrease the proportion of the penalty parameter and the dual variable, and a commonly used value thereof is 2.

[0056] In steps 9-11, the application designs an optimization solving strategy of residual fitting and adaptive penalty parameter adjustment, and adjusts the penalty parameter dynamically by monitoring the original residual and the dual residual, so as to balance the convergence speed and stability.

[0057] Further, the reverse OTDR linear signal and the forward OTDR linear signal are reconstructed to detect the to-be-tested optical fiber, including: The first sparse coefficient vector is orthogonally transformed by using the orthogonal transformation matrix to obtain the reverse OTDR linear signal, and the second sparse coefficient vector is orthogonally transformed by using the orthogonal transformation matrix to obtain the forward OTDR linear signal.

[0058] Based on the loss of the forward OTDR linear signal and the reverse OTDR linear signal, it is detected whether the to-be-tested optical fiber has a fault, and if there is a fault, a bidirectional positioning method is used to position the fault based on the forward OTDR linear signal and the reverse OTDR linear signal.

[0059] Based on the above-mentioned embodiment, the application provides an optical time domain reflectometry method based on joint optimization of forward and reverse signals, as shown in the following Figure 2 The device specifically includes: A signal acquisition module 10 is configured to acquire a reverse OTDR observation signal and a forward OTDR observation signal of a to-be-tested optical fiber.

[0060] A signal reconstruction module 20 is configured to construct a reverse OTDR linear signal reconstruction item based on a product of an orthogonal transformation matrix and a first sparse coefficient vector to be solved, and construct a forward OTDR linear signal reconstruction item based on a product of the orthogonal transformation matrix and a second sparse coefficient vector to be solved.

[0061] A fidelity item construction module 30 is configured to construct a data fidelity item based on a difference between the reverse OTDR observation signal and the reverse OTDR linear signal reconstruction item and a difference between the forward OTDR observation signal and the forward OTDR linear signal reconstruction item.

[0062] The regular term construction module 40 is configured to construct a joint sparse regular term based on the i-th eigenvalue of the first sparse coefficient vector to be solved and the i-th eigenvalue of the second sparse coefficient vector to be solved being zero or non-zero, and construct a spatial constraint regular term based on the continuous smoothness of the reconstructed reverse OTDR linear signal and the forward OTDR linear signal in space.

[0063] The optimization function construction and solving module 50 is configured to construct a joint optimization function with the data fidelity term, the joint sparse regular term and the spatial constraint regular term as a weighted sum and minimum, and solve the joint optimization function to obtain the first sparse coefficient vector and the second sparse coefficient vector, so as to reconstruct the reverse OTDR linear signal and the forward OTDR linear signal for detecting the optical fiber to be measured.

[0064] The embodiment of the present application also provides a computer readable storage medium, and the computer readable storage medium stores a computer program, and the computer program is processed to implement the steps of the optical time domain reflectometry method based on joint optimization of forward and reverse signals.

[0065] The optical time domain reflectometry method based on joint optimization of forward and reverse signals is further explained and described below through specific embodiments: 1. A high-stability distributed feedback laser with a center wavelength of 1550 nm is used to generate optical pulses with a pulse width adjustable in the range of 10 ns to 20 μs through an acousto-optic modulator. The pulse peak power can be adjusted according to the length of the optical fiber to be measured, and a typical value is usually 10 dBm to 23 dBm.

[0066] 2. A 99:1 asymmetric optical coupler is connected in series between the laser and the optical circulator. The laser emits laser pulses, the laser pulses enter through port 1 of the optical circulator and are output from port 2 to the optical fiber to be measured, and the asymmetric optical coupler couples out 1% of the transmitted optical power into the forward signal receiving channel. The backscattered light returned from the optical fiber to be measured enters from port 2 of the optical circulator and is output from port 3 to the reverse signal receiving channel.

[0067] 3. A high-sensitivity avalanche photodiode is used to detect the weak backscattered light in the reverse signal receiving channel with a signal intensity of-50 dBm to-70 dBm. A common PIN photodiode is used to receive the relatively strong signal in the forward signal receiving channel.

[0068] 4. A dual-channel, high-sampling-rate analog-to-digital converter is used to synchronously digitize and collect the signals collected by the two photodiodes, and the two signals are processed to ensure that the processed forward OTDR observation signal and reverse OTDR observation signal are accurately aligned on the time axis.

[0069] 5. The architecture of field programmable gate array + digital processor or high-performance embedded industrial computer receives forward OTDR observation signal and backward OTDR observation signal, and executes the steps of the optical time domain reflectometry method based on joint optimization of forward and backward signals provided by the above embodiments, so as to obtain reconstructed noise-free forward OTDR linear signal and backward OTDR linear signal.

[0070] 6. The forward OTDR linear signal and the backward OTDR linear signal are subjected to event detection, positioning and loss analysis, and the OTDR curve, the event list and the alarm information are displayed in a graphical manner on the user interface, so as to realize detection of the optical fiber to be detected.

[0071] Compared with the prior art, the application has the following remarkable beneficial effects through the innovative "single-end transmission and double-end synchronous reception" physical architecture and the advanced "forward and backward signal joint optimization" algorithm model: I. The signal-to-noise ratio and the dynamic range are greatly improved: The application creatively uses the forward signal with energy far stronger than the backscattering Rayleigh scattering as the "anchor point" information with high signal-to-noise ratio. Through the joint optimization model, the clear features of the forward signal are effectively transmitted to the denoising and recovery process of the backward signal, which is equivalent to providing strong guidance for the weak backward signal. Experiments show that under the same test conditions, the method can improve the dynamic range of the system by at least 10 dB, so that the weak events (such as initial cable aging and small stress changes) that were previously submerged in noise can be clearly presented, significantly enhancing the detection sensitivity of the system.

[0072] II. The false alarm rate and the missed alarm rate are significantly reduced, and the monitoring reliability is improved: The traditional OTDR technology cannot distinguish between real weak events and random noise peaks. The application utilizes the common physical nature of events in forward and backward signals, which is "structured sparse", and constrains it through joint sparse regularization terms. This means that only the characteristics of significant energy response appearing at the same position in the forward and backward signals will be identified as real events, while random noise appearing in a single signal will be effectively suppressed. This "double verification" mechanism fundamentally improves the anti-interference ability of the system, significantly reduces false alarms caused by noise, and also avoids missing real weak events due to low signal-to-noise ratio.

[0073] Third, higher positioning and identification accuracy is achieved: The "spatial constraint regularization term" introduced in the joint optimization model integrates the prior knowledge of "spatial local continuity" of the optical cable event in the physical world into the algorithm. This constraint encourages the algorithm to find a piecewise smooth optimal solution, thereby accurately reconstructing the edge of the event (such as the step feature of the breakpoint and the fusion point), while strongly smoothing the noise in the non-event area. This makes the edge of the event feature curve steeper and clearer, solves the problem of blurred event starting point caused by noise in traditional methods, significantly improves the positioning accuracy, and helps to more accurately identify the event type (such as breakage or bending).

[0074] Fourth, real-time monitoring is guaranteed, and dynamic monitoring requirements are met: Unlike traditional methods that rely on multiple measurements to improve signal-to-noise ratio, the present application can obtain high-quality monitoring results through a single measurement. Efficient optimization solving algorithms (such as improved algorithms based on ADMM) guarantee the rapidity of signal processing, enabling the system to respond and warn nearly in real time to dynamically changing events (such as submarine geological activities, third-party intrusion, ship anchor damage, etc.), which is crucial for ensuring the safety of long-distance key optical cable links.

[0075] Those skilled in the art will understand that embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can take the form of entirely hardware embodiments, entirely software embodiments, or embodiments combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage, etc.) containing computer-usable program code.

[0076] The present application is described with reference to flowcharts and / or block diagrams according to the methods, devices (systems), and computer program products of the embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, as well as the combination of flows and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing apparatus to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing apparatus produce a device that implements the functions specified in the flow Figure 1 The device that implements the functions specified in one or more flows and / or blocks. Figure 1 The device that implements the functions specified in one or more flows and / or blocks.

[0077] These computer program instructions can also be stored in a computer-readable storage medium that can direct the computer or other programmable data processing apparatus to work in a specific manner, so that the instructions stored in the computer-readable storage medium produce a manufactured product including instruction devices that implement the functions specified in the flowFigure 1 one or more processes and / or functions described in one or more blocks. Figure 1 one or more blocks.

[0078] These computer program instructions can also be loaded into computer or other programmable data processing devices, so that a series of operation steps are performed on the computer or other programmable data processing devices to generate computer-implemented processes, so that the instructions executed on the computer or other programmable data processing devices provide steps for implementing the function described in one or more processes and / or functions described in one or more blocks. Figure 1 one or more processes and / or functions described in one or more blocks. Figure 1 one or more blocks.

[0079] Obviously, the above embodiments are only examples for the purpose of clarity, and are not limiting to the embodiments. Based on the above description, other different forms of changes or variations can also be made by those skilled in the art. Here, it is not necessary and impossible to enumerate all the embodiments. The obvious changes or variations derived therefrom are still within the protection scope of the present application.

Claims

1. A method for optical time domain reflectometry based on joint optimization of forward and backward signals, characterized in that, The method comprises the following steps: Obtaining a reverse OTDR observation signal and a forward OTDR observation signal of a fiber to be detected; Based on the product of the orthogonal transformation matrix and the first sparse coefficient vector to be solved, a reverse OTDR linear signal reconstruction term is constructed; based on the product of the orthogonal transformation matrix and the second sparse coefficient vector to be solved, a forward OTDR linear signal reconstruction term is constructed; Based on the difference between the reverse OTDR observation signal and the reverse OTDR linear signal reconstruction term and the difference between the forward OTDR observation signal and the forward OTDR linear signal reconstruction term, a data fidelity term is constructed; Based on the i-th eigenvalue of the first sparse coefficient vector to be solved and the second sparse coefficient vector to be solved being zero or non-zero, a joint sparse regularization term is constructed; based on the continuity and smoothness of the reconstructed reverse OTDR linear signal and the forward OTDR linear signal in space, a spatial constraint regularization term is constructed; A joint optimization function is constructed by minimizing the weighted sum of the data fidelity term, the joint sparse regularization term and the spatial constraint regularization term; the joint optimization function is solved to obtain the first sparse coefficient vector and the second sparse coefficient vector, so as to reconstruct the reverse OTDR linear signal and the forward OTDR linear signal, thereby detecting the fiber to be detected. 2.The optical time domain reflectometry method based on joint optimization of forward and backward signals according to claim 1, wherein, Based on the difference between the reverse OTDR observation signal and the reverse OTDR linear signal reconstruction term and the difference between the forward OTDR observation signal and the forward OTDR linear signal reconstruction term, a data fidelity term is constructed, comprising: Based on the square of the L2 norm of the difference between the reverse OTDR observation signal and the reverse OTDR linear signal reconstruction term, a first data fidelity term is constructed; Based on the square of the L2 norm of the difference between the forward OTDR observation signal and the forward OTDR linear signal reconstruction term, a second data fidelity term is constructed; The data fidelity term is obtained based on the weighted sum of the first data fidelity term and the second data fidelity term. 3.The optical time domain reflectometry method based on joint optimization of forward and backward signals according to claim 1, characterized in that, The joint optimization function is represented as: ， ， ， wherein, denotes a joint optimization function; denotes a first sparse coefficient vector; denotes a second sparse coefficient vector; denotes a backward OTDR observation signal; denotes an orthogonal transformation matrix; denotes a square of L2 norm; denotes a forward OTDR observation signal; denotes a data fidelity term; denotes a joint sparse regularization term; denotes a regularization parameter for controlling the sparsity degree of a vector; denotes an i-th eigenvalue in the first sparse coefficient vector; denotes an i-th eigenvalue in the second sparse coefficient vector; denotes an L2,1 norm; denotes a spatial constraint regularization term; denotes a spatial smoothness constraint degree; denotes a difference operator matrix; denotes a gradient of the reconstructed OTDR linear signal; denotes a reconstructed backward OTDR linear signal or a forward OTDR linear signal; denotes an L1 norm.

4. The optical time domain reflectometry method based on joint optimization of forward and backward signals according to claim 1, characterized in that, The joint optimization function is solved to obtain the first sparse coefficient vector and the second sparse coefficient vector, comprising: Step 1: constructing a first auxiliary variable of the reverse OTDR linear signal reconstruction term, a second auxiliary variable of the forward OTDR linear signal reconstruction term, a third auxiliary variable of the first sparse coefficient vector, a fourth auxiliary variable of the second sparse coefficient vector, and a fifth auxiliary variable of the reconstructed OTDR linear signal gradient; and defining the dual variables of each auxiliary variable; Step 2: replacing the reverse OTDR linear signal reconstruction term, the forward OTDR linear signal reconstruction term, the first sparse coefficient vector, the second sparse coefficient vector and the reconstructed OTDR linear signal gradient in the joint optimization function with the auxiliary variables to obtain a new joint optimization function; constructing the constraint functions corresponding to each auxiliary variable by equating each auxiliary variable to the parameter replaced by it; Step 3: setting k=0 and setting the values of each auxiliary variable, each dual variable, the first sparse coefficient vector, the second sparse coefficient vector and the penalty parameter at the k-th iteration. Step 4: based on the variable decoupling and collaborative optimization principle of the alternating direction method of multipliers, the first sparse coefficient vector, the second sparse coefficient vector and each auxiliary variable at the kth iteration are updated, so as to obtain the updated first sparse coefficient vector, the second sparse coefficient vector and each auxiliary variable; Step 5: based on the updated each auxiliary variable, the first sparse coefficient vector and the second sparse coefficient vector, the constraint function value corresponding to each auxiliary variable is calculated; Step 6: based on the acceleration parameter and the values of each dual variable at the kth iteration and the (k-1)th iteration, the predicted value of each dual variable after updating is calculated; based on the difference between the predicted value of each dual variable after updating and the constraint function value corresponding to each auxiliary variable, the value of the dual variable of each auxiliary variable after updating is obtained; Step 7: based on the arithmetic square root of the sum of squares of the L2 norms of the constraint function values corresponding to each auxiliary variable, the original residual norm is obtained; based on the arithmetic square root of the sum of squares of the L2 norms of the first difference before and after the third auxiliary variable is updated, the second difference before and after the fourth auxiliary variable is updated, and the third difference before and after the fifth auxiliary variable is updated, and the product of the penalty parameter at the kth iteration, the dual residual norm is obtained; Step 8: it is judged whether the original residual norm is less than the preset original residual tolerance and whether the dual residual tolerance is less than the preset dual residual tolerance, if the original residual norm is greater than or equal to the preset original residual tolerance and / or the dual residual tolerance is greater than or equal to the preset dual residual tolerance, the penalty parameter and the dual variable are updated based on the size of the original residual norm and the dual residual norm; Step 9: if the original residual norm is greater than the product of the first preset penalty parameter threshold and the dual residual norm, the product of the value of the penalty parameter at the kth iteration and the second preset penalty parameter threshold is taken as the updated penalty parameter; the product of the second preset penalty parameter threshold and each dual variable after updating is calculated respectively, so as to update each dual variable again; Step 10: if the dual residual norm is greater than the product of the first preset penalty parameter threshold and the original residual norm, the quotient of the value of the penalty parameter at the kth iteration and the second preset penalty parameter threshold is taken as the updated penalty parameter; the quotient of each dual variable and the second preset penalty parameter threshold is calculated respectively, so as to update each dual variable again; Step 11: update k=k+1, take the values of each auxiliary variable, each dual variable, the first sparse coefficient vector, the second sparse coefficient vector and the penalty parameter after updating as the values of each auxiliary variable, each dual variable, the first sparse coefficient vector, the second sparse coefficient vector and the penalty parameter at the kth iteration, return to execute step 4 until the original residual norm is less than the preset original residual tolerance and the dual residual tolerance is less than the preset dual residual tolerance, and the first sparse coefficient vector and the second sparse coefficient vector are obtained.

5. The OTDR method based on joint optimization of forward and backward signals according to claim 4, characterized in that, The new joint optimization function is represented as: ， wherein, denotes a new joint optimization function; denotes a backward OTDR observation signal; denotes a first auxiliary variable; denotes a square of L2 norm; denotes a forward OTDR observation signal; denotes a second auxiliary variable; denotes a regularization parameter for controlling the sparsity degree of the vector; denotes a third auxiliary variable, denotes the i-th eigenvalue in the third auxiliary variable; denotes a fourth auxiliary variable, denotes the i-th eigenvalue in the fourth auxiliary variable; denotes a spatial smoothing constraint degree; denotes a fifth auxiliary variable; denotes a L1 norm; The constraint function corresponding to the first auxiliary variable is represented as: ， wherein denotes an orthogonal transformation matrix; denotes a first sparse coefficient vector; The constraint function corresponding to the second auxiliary variable is represented as: ， wherein denotes a second sparse coefficient vector; The constraint function corresponding to the third auxiliary variable is represented as: ， The constraint function corresponding to the fourth auxiliary variable is represented as: ， The constraint function corresponding to the fifth auxiliary variable is represented as: ， wherein, denotes a difference operator matrix; denotes a gradient of the reconstructed OTDR linear signal; denotes a reconstructed backward OTDR linear signal or a reconstructed forward OTDR linear signal.

6. The OTDR method based on joint optimization of forward and backward signals according to claim 4, characterized in that, The update formula of the first sparse coefficient vector is: ， wherein, denotes the updated first sparse coefficient vector; denotes a penalty parameter; denotes an orthogonal transformation matrix; denotes a first auxiliary variable at the kth iteration; denotes a first dual variable at the kth iteration; denotes a third auxiliary variable at the kth iteration; denotes a third dual variable at the kth iteration; denotes a transpose; The update formula of the second sparse coefficient vector is: ， wherein, denotes the updated second sparse coefficient vector; denotes a second auxiliary variable at the kth iteration; denotes a second dual variable at the kth iteration; denotes a fourth auxiliary variable at the kth iteration; denotes a fourth dual variable at the kth iteration; The update formula of the first auxiliary variable is: ， wherein denotes the updated first auxiliary variable; denotes the identity matrix; denotes the difference operator matrix; denotes the back OTDR observation signal; denotes the fifth auxiliary variable at the kth iteration; denotes the fifth dual variable at the kth iteration; The update formula of the second auxiliary variable is: ， wherein, represents the updated second auxiliary variable; represents a forward OTDR observation signal; The update formula of the third auxiliary variable and the fourth auxiliary variable is: ， ， ， ， wherein, denotes the i-th eigenvalue in the updated third auxiliary variable; denotes the i-th eigenvalue in the updated fourth auxiliary variable; denotes a regularization parameter for controlling the sparsity of the control vector; denotes the i-th eigenvalue in the updated third auxiliary variable; denotes the i-th eigenvalue in the updated third auxiliary variable; The update formula of the fifth auxiliary variable is: ， ， wherein, represents the updated fifth auxiliary variable; represents a sign function; represents a degree of spatial smoothness constraint.

7. The OTDR method based on joint optimization of forward and backward signals according to claim 4, characterized in that, The calculation formula of the prediction value of each dual variable after updating is: ， wherein, denotes the prediction of the n-th dual variable after update; denotes the acceleration parameter; denotes the value of the n-th dual variable at the k-th iteration; denotes the value of the n-th dual variable at the k-1-th iteration; The update formula of each dual variable is: ， ， ， ， ， ， wherein, denotes the updated nthdual variable; denotes the value of the constraint function corresponding to the nthauxiliary variable; denotes the updated first auxiliary variable; denotes the orthogonal transformation matrix; denotes the updated first sparse coefficient vector; denotes the updated second auxiliary variable; denotes the updated second sparse coefficient vector; denotes the updated third auxiliary variable; denotes the updated fourth auxiliary variable; denotes the updated fifth auxiliary variable; denotes the difference operator matrix. 8.The optical time domain reflectometry method based on joint optimization of forward and backward signals according to claim 1, characterized in that, The reverse OTDR linear signal and the forward OTDR linear signal are reconstructed to detect the to-be-tested optical fiber, including: The first sparse coefficient vector is orthogonally transformed by using the orthogonal transformation matrix to obtain the reverse OTDR linear signal; the second sparse coefficient vector is orthogonally transformed by using the orthogonal transformation matrix to obtain the forward OTDR linear signal; Based on the loss of the forward OTDR linear signal and the reverse OTDR linear signal, it is detected whether the to-be-tested optical fiber has a fault; if there is a fault, the bidirectional positioning method is used to position the fault based on the forward OTDR linear signal and the reverse OTDR linear signal.

9. An optical time domain reflectometry device based on joint optimization of forward and backward signals, characterized in that, Including: The signal acquisition module is configured to acquire a reverse OTDR observation signal and a forward OTDR observation signal of the to-be-tested optical fiber; The signal reconstruction module is configured to construct a reverse OTDR linear signal reconstruction term based on a product of the orthogonal transformation matrix and the first sparse coefficient vector to be solved, and construct a forward OTDR linear signal reconstruction term based on a product of the orthogonal transformation matrix and the second sparse coefficient vector to be solved; The fidelity term construction module is configured to construct a data fidelity term based on a difference between the reverse OTDR observation signal and the reverse OTDR linear signal reconstruction term and a difference between the forward OTDR observation signal and the forward OTDR linear signal reconstruction term; The regularization term construction module is configured to construct a joint sparse regularization term based on the first sparse coefficient vector to be solved and the second sparse coefficient vector to be solved, the i-th eigenvalue of which is zero or non-zero, and construct a spatial constraint regularization term based on a continuous smoothness of the reverse OTDR linear signal and the forward OTDR linear signal in space; The optimization function construction and solving module is configured to construct a joint optimization function with a weighted sum of the data fidelity term, the joint sparse regularization term and the spatial constraint regularization term as a minimum, and solve the joint optimization function to obtain the first sparse coefficient vector and the second sparse coefficient vector, so as to reconstruct the reverse OTDR linear signal and the forward OTDR linear signal to detect the to-be-tested optical fiber.

10. A computer-readable storage medium, characterized in that, The computer program is stored on the computer readable storage medium and is executed by the processor to implement the steps of the optical time domain reflectometry method based on joint optimization of forward and reverse signals according to any one of claims 1 to 8. The computer program is stored on the computer readable storage medium and is executed by the processor to implement the steps of the optical time domain reflectometry method based on joint optimization of forward and reverse signals according to any one of claims 1 to 8.

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