Optical time domain reflectometry method and device based on joint optimization of forward and backward signals

Abstract

The application belongs to the technical field of optical fiber sensing, and relates to an optical time domain reflection monitoring method and device based on joint optimization of forward and reverse signals. Reverse and forward OTDR observation signals of a to-be-detected optical fiber are acquired. A reverse OTDR linear signal reconstruction term is constructed based on the product of a orthogonal transformation matrix and a first sparse coefficient vector to be solved. A forward OTDR linear signal reconstruction term is constructed based on the product of the orthogonal transformation matrix and a second sparse coefficient vector to be solved. A data fidelity term is constructed based on the OTDR observation signals and the linear signal reconstruction terms. A joint sparse regularization term is constructed based on the structured sparsity of the first sparse coefficient vector and the second sparse coefficient vector to be solved. A spatial constraint regularization term is constructed based on the continuous smoothness of the reconstructed OTDR linear signal in space. Thus, a joint optimization function is constructed and solved to obtain the first sparse coefficient vector and the second sparse coefficient vector, and the OTDR linear signal is reconstructed to detect the to-be-detected optical fiber.

Description

Technical Field

[0001] This invention relates to the field of fiber optic sensing technology, and in particular to a method, apparatus, and computer-readable storage medium for optical time-domain reflectometry monitoring based on joint optimization of forward and reverse signals. Background Technology

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

[0003] Existing reverse OTDR monitoring technology receives weak backscattered Rayleigh and Fresnel reflection signals at the transmitting end. By extracting features from the received signals, the continuous signal is converted into quantifiable link characteristic parameters (e.g., the relative power curve of fiber length and received signal), thereby obtaining the Rayleigh scattering and Fresnel reflection characteristics of the fiber under test to assess whether there are faults such as compression, bending, or breakage in the fiber link. However, long-distance transmission results in extremely weak backscattered signals. The small fluctuations in the backscattered Rayleigh signals caused by weak events (minor vibrations, fiber stress changes, and aging) are almost the same as the amplitudes of photodetectors, amplifiers, and environmental noise, or even submerged by noise signals. This leads to misjudging noise as signal fluctuations caused by weak events, or vice versa, thus affecting the accuracy of the detection results. At the same time, during fault location, because the signal fluctuations caused by weak events are close to the noise amplitude, the edges of the relative power curve of fiber length and received signal gradually become blurred, making it difficult to define the starting point of the weak event on the curve, thus affecting the accuracy of fault location.

[0004] In summary, existing optical time domain reflectance monitoring methods suffer from weak reverse OTDR signal strength, which is easily overwhelmed by noise signals, thus affecting monitoring accuracy and fault location precision. Summary of the Invention

[0005] Therefore, the technical problem to be solved by the present invention is to overcome the problem that the reverse OTDR signal strength of the existing optical time domain reflectance monitoring method is weak and easily submerged by noise signals, thereby affecting the monitoring accuracy and fault location accuracy.

[0006] To address the aforementioned technical problems, this invention provides an optical temporal reflectance monitoring method based on joint optimization of forward and reverse signals, comprising:

[0007] Acquire the reverse OTDR observation signal and the forward OTDR observation signal of the optical fiber under test;

[0008] 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.

[0009] A data fidelity term is constructed based on the difference between the reverse OTDR observation signal and the reconstructed term of the reverse OTDR linear signal, as well as the difference between the forward OTDR observation signal and the reconstructed term of the forward OTDR linear signal.

[0010] Based on the fact that the i-th eigenvalues ​​of the first sparse coefficient vector to be solved and the second sparse coefficient vector to be solved are both zero or non-zero, a joint sparse regularization term is constructed; based on the spatial continuity and smoothness of the reconstructed reverse OTDR linear signal and the forward OTDR linear signal, a spatial constraint regularization term is constructed.

[0011] A joint optimization function is constructed with the goal of minimizing the weighted sum of the data fidelity term, the joint sparse regularization term, and the spatial constraint regularization term. Solving the joint optimization function yields the first and second sparse coefficient vectors, which are then used to reconstruct the reverse OTDR linear signal and the forward OTDR linear signal for testing the optical fiber under test.

[0012] Preferably, a data fidelity term is constructed based on the difference between the reverse OTDR observation signal and the reconstructed term of the reverse OTDR linear signal, and the difference between the forward OTDR observation signal and the reconstructed term of the forward OTDR linear signal, including:

[0013] The first data fidelity term is constructed based on the square of the L2 norm of the difference between the reverse OTDR observed signal and the reconstructed term of the reverse OTDR linear signal.

[0014] The second data fidelity term is constructed based on the square of the L2 norm of the difference between the forward OTDR observation signal and the reconstructed term of the forward OTDR linear signal.

[0015] The data fidelity term is obtained by weighting the first data fidelity term and the second data fidelity term.

[0016] Preferably, the joint optimization function is expressed as:

[0017] ,

[0018] ,

[0019] ,

[0020] in, Represents the joint optimization function; Represents the first sparse coefficient vector; Represents the second sparse coefficient vector; Indicates the reverse OTDR observation signal; Represents an orthogonal transformation matrix; Represents the square of the L2 norm; Indicates a positive OTDR observation signal; Indicates data fidelity; 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.

[0021] Preferably, solving the joint optimization function yields a first sparse coefficient vector and a second sparse coefficient vector, including:

[0022] 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.

[0023] 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.

[0024] 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;

[0025] 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.

[0026] 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;

[0027] 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.

[0028] Step 7: Obtain the original residual norm based on the arithmetic square root of the sum of the squares of the L2 norms of the constraint function values ​​corresponding to each auxiliary variable; obtain the dual residual norm based on the product of the arithmetic square root of the sum of the squares of the L2 norms of the first difference before and after the update of the third auxiliary variable, the second difference before and after the update of the fourth auxiliary variable, and the third difference before and after the update of the fifth auxiliary variable, and the penalty parameter at the k-th iteration.

[0029] Step 8: Determine 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, then update the penalty parameter and dual variable based on the magnitude of the original residual norm and the dual residual norm.

[0030] Step 9: If the original residual norm is greater than the product of the first preset penalty parameter threshold and the dual residual norm, then the product of the penalty parameter value at the k-th iteration and the second preset penalty parameter threshold is used as the updated penalty parameter; calculate the product of the second preset penalty parameter threshold and each updated dual variable respectively, and then update each dual variable again.

[0031] Step 10: If the dual residual norm is greater than the product of the first preset penalty parameter threshold and the original residual norm, then the quotient of the penalty parameter value at the k-th iteration and the second preset penalty parameter threshold is used as the updated penalty parameter; calculate the quotient of each dual variable and the second preset penalty parameter threshold respectively, and update each dual variable again.

[0032] Step 11: Update k=k+1. Take the updated values ​​of each 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 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 obtain the first sparse coefficient vector and the second sparse coefficient vector.

[0033] Preferably, the new joint optimization function is expressed as:

[0034] ,

[0035] in, Represents the new joint optimization function; Indicates the reverse OTDR observation signal; Indicates the first auxiliary variable; Represents the square of the L2 norm; Indicates a positive OTDR observation signal; Indicates the second auxiliary variable; This represents the regularization parameter used to control the sparsity of the vector; Indicates the third auxiliary variable. This represents the i-th eigenvalue in the third auxiliary variable; Indicates the fourth auxiliary variable. This represents the i-th eigenvalue in the fourth auxiliary variable; Indicates the degree of spatial smoothness constraint; Indicates the fifth auxiliary variable; Represents the L1 norm;

[0036] The constraint function corresponding to the first auxiliary variable is expressed as follows:

[0037] ,

[0038] in, Represents an orthogonal transformation matrix; Represents the first sparse coefficient vector;

[0039] The constraint function corresponding to the second auxiliary variable is expressed as follows:

[0040] ,

[0041] in, Represents the second sparse coefficient vector;

[0042] The constraint function corresponding to the third auxiliary variable is expressed as follows:

[0043] ,

[0044] The constraint function corresponding to the fourth auxiliary variable is expressed as:

[0045] ,

[0046] The constraint function corresponding to the fifth auxiliary variable is expressed as follows:

[0047] ,

[0048] in, Represents the difference operator matrix; This represents the gradient of the reconstructed OTDR linear signal; This indicates the reverse OTDR linear signal or the forward OTDR linear signal obtained from the reconstruction.

[0049] Preferably, the update formula for the first sparse coefficient vector is:

[0050] ,

[0051] in, This represents the updated first sparse coefficient vector; Indicates the penalty parameter; Represents an orthogonal transformation matrix; This represents the first auxiliary variable during the k-th iteration; Let represent the first dual variable at the k-th iteration; This represents the third auxiliary variable in the k-th iteration; Let represent the third dual variable at the k-th iteration; Indicates transpose;

[0052] The update formula for the second sparse coefficient vector is:

[0053] ,

[0054] in, This represents the updated second sparse coefficient vector; This represents the second auxiliary variable during the k-th iteration; Denotes the second dual variable at the k-th iteration; This represents the fourth auxiliary variable in the k-th iteration; Let represent the fourth dual variable at the k-th iteration;

[0055] The update formula for the first auxiliary variable is:

[0056] ,

[0057] in, This represents the first auxiliary variable after the update; Represents the identity matrix; Represents the difference operator matrix; Indicates the reverse OTDR observation signal; This represents the fifth auxiliary variable in the k-th iteration; Let represent the fifth dual variable at the k-th iteration;

[0058] The update formula for the second auxiliary variable is:

[0059] ,

[0060] in, This represents the updated second auxiliary variable; Indicates a positive OTDR observation signal;

[0061] The update formulas for the third and fourth auxiliary variables are:

[0062] ,

[0063] ,

[0064] ,

[0065] ,

[0066] in, This represents the i-th feature value in the third auxiliary variable after the update; This represents the i-th feature value in the fourth auxiliary variable after the update; This represents the regularization parameter used to control the sparsity of the vector; express The i-th eigenvalue; express The i-th eigenvalue;

[0067] The update formula for the fifth auxiliary variable is:

[0068] ,

[0069] ,

[0070] in, This represents the updated fifth auxiliary variable; Represents a symbolic function; This indicates the degree of spatial smoothness constraint.

[0071] Preferably, the formula for calculating the predicted values ​​of each dual variable after the update is as follows:

[0072] ,

[0073] in, This represents the predicted value of the nth dual variable after the update; Indicates acceleration parameters; This represents the value of the nth dual variable during the kth iteration; This represents the value of the nth dual variable during the (k-1)th iteration;

[0074] The update formulas for each dual variable are:

[0075] ,

[0076] ,

[0077] ,

[0078] ,

[0079] ,

[0080] ,

[0081] in, This represents the nth dual variable after the update; This represents the constraint function value corresponding to the nth auxiliary variable; This represents the first auxiliary variable after the update; Represents an orthogonal transformation matrix; This represents the updated first sparse coefficient vector; This represents the updated second auxiliary variable; This represents the updated second sparse coefficient vector; This represents the updated third auxiliary variable; This represents the updated fourth auxiliary variable; This represents the updated fifth auxiliary variable; This represents the difference operator matrix.

[0082] Preferably, the reconstructed reverse OTDR linear signal and forward OTDR linear signal are used to detect the optical fiber under test, including:

[0083] The first sparse coefficient vector is orthogonally transformed using an orthogonal transformation matrix to obtain the inverse OTDR linear signal; the second sparse coefficient vector is orthogonally transformed using an orthogonal transformation matrix to obtain the forward OTDR linear signal.

[0084] Based on the loss of the forward and reverse OTDR linear signals, the presence of faults in the optical fiber under test is detected; if a fault is found, the fault location is performed using a bidirectional positioning method based on the forward and reverse OTDR linear signals.

[0085] The present invention also provides an optical temporal reflectance monitoring device based on joint optimization of forward and reverse signals, comprising:

[0086] The signal acquisition module is used to acquire the reverse OTDR observation signal and the forward OTDR observation signal of the optical fiber under test.

[0087] The signal reconstruction module is used to construct a reverse OTDR linear signal reconstruction term based on the product of the orthogonal transformation matrix and the first sparse coefficient vector to be solved; and to construct a forward OTDR linear signal reconstruction term based on the product of the orthogonal transformation matrix and the second sparse coefficient vector to be solved.

[0088] The fidelity term construction module is used to construct data fidelity terms based on the difference between the reverse OTDR observation signal and the reconstructed term of the reverse OTDR linear signal, and the difference between the forward OTDR observation signal and the reconstructed term of the forward OTDR linear signal.

[0089] The regularization term construction module is used to construct a joint sparse regularization term based on the fact that the i-th eigenvalue of the first sparse coefficient vector to be solved and the second sparse coefficient vector to be solved are both zero or non-zero; and to construct a spatial constraint regularization term based on the spatial continuity and smoothness of the reconstructed reverse OTDR linear signal and the forward OTDR linear signal.

[0090] The optimization function construction and solution module is used to construct a joint optimization function with the goal of minimizing the weighted sum of data fidelity terms, joint sparse regularization terms, and spatial constraint regularization terms. Solving the joint optimization function yields the first sparse coefficient vector and the second sparse coefficient vector, thereby reconstructing the reverse OTDR linear signal and the forward OTDR linear signal for testing the optical fiber under test.

[0091] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the above-described optical temporal reflectance monitoring method based on joint optimization of forward and reverse signals.

[0092] The optical temporal reflectance monitoring method based on joint optimization of forward and reverse signals provided in this application has the following advantages:

[0093] Employing a single-end transmission and dual-end reception physical architecture, this invention simultaneously acquires both forward and reverse OTDR observation signals from the optical fiber under test based on laser pulse signal reflection. The clear characteristics of the forward OTDR observation signal are then transferred to the denoising and recovery process of the reverse signal, providing strong guidance for the weak reverse signal. Furthermore, considering the noise influence in the observation signals, this application separates the noise-free OTDR linear signal from the forward and reverse OTDR observation signals through signal reconstruction to improve monitoring accuracy. Specifically, since OTDR signals exhibit sparse characteristics in a specific feature domain—that is, the energy of weak events is concentrated on only a few feature coefficients—this application uses an orthogonal transformation matrix to orthogonally transform the sparse coefficient vector to reconstruct the OTDR linear signal and constructs a data fidelity term to constrain the reconstructed signal to closely match the actual observation signal. Meanwhile, since the scattering or reflection characteristics of the reverse and forward OTDR linear signals caused by weak events at the same location in the optical fiber have spatiotemporal symmetry, meaning that the energy of the weak event will affect both forward and reverse OTDR signals simultaneously, and random noise usually only exists in the single-end signal, this application constructs a joint sparse regularization term by using the i-th eigenvalue of both the first and second sparse coefficient vectors to be solved as zero or non-zero values. Finally, a spatial constraint term is constructed based on the spatial continuity of the normal OTDR signal, and a joint optimization objective function is finally constructed. By performing an orthogonal transformation on the solved sparse coefficient vector, a noise-free OTDR linear signal is reconstructed, realizing the denoising and feature enhancement of the OTDR observation signal. Thus, the denoised signal is used for fault detection and location, effectively improving the accuracy of monitoring results and positioning precision. Attached Figure Description

[0094] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein:

[0095] Figure 1 The flowchart of the optical temporal reflectance monitoring method based on joint optimization of forward and reverse signals provided in this application;

[0096] Figure 2 A schematic diagram of the optical temporal reflectance monitoring device based on joint optimization of forward and reverse signals provided in this application. Detailed Implementation

[0097] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0098] Please see Figure 1 , Figure 1The diagram shows the flowchart of the optical temporal reflectance monitoring method based on joint optimization of forward and reverse signals provided in this application. The method specifically includes:

[0099] S10: Acquire the reverse OTDR observation signal and the forward OTDR observation signal of the optical fiber under test.

[0100] Specifically, if the length of the optical fiber under test is L, the original reverse OTDR observation signal acquired at time t is represented as: The original forward OTDR observation signal is represented as , This represents the number of sampling points. Since the observed signal consists of an ideal noise-free signal and a noisy signal, the two observed signals mentioned above can be modeled as follows:

[0101] ,

[0102] ,

[0103] in, This represents a noise-free inverted OTDR signal, i.e., an inverted OTDR linear signal. This represents the noise signal in the reverse OTDR observation signal; This represents a noise-free positive OTDR signal, i.e., a positive OTDR linear signal; This represents the noise signal in the forward OTDR observation signal; the objective of this application is to reconstruct a noise-free OTDR linear signal from the OTDR observation signal.

[0104] S20: Construct the reverse OTDR linear signal reconstruction term based on the product of the orthogonal transformation matrix and the first sparse coefficient vector to be solved; construct the forward OTDR linear signal reconstruction term based on the product of the orthogonal transformation matrix and the second sparse coefficient vector to be solved.

[0105] This application discovers that although the OTDR linear signal is not sparse in the time domain, it is sparse in some characteristic domains (such as the wavelet domain). Therefore, this application uses an orthogonal transformation matrix to orthogonally transform the sparse coefficient vector to reconstruct the OTDR linear signal. It is worth noting that for the same fiber under test, the positions that cause significant non-zero values ​​in the first and second sparse coefficient vectors are the same or highly correlated, i.e., they have structured sparsity characteristics. This discovery provides a theoretical basis for designing the joint sparse regularization term in this application.

[0106] S30: Construct a data fidelity term based on the difference between the reverse OTDR observation signal and the reconstruction term of the reverse OTDR linear signal, and the difference between the forward OTDR observation signal and the reconstruction term of the forward OTDR linear signal.

[0107] Furthermore, step S30 specifically includes:

[0108] S300: Construct the first data fidelity term based on the square of the L2 norm of the difference between the reverse OTDR observed signal and the reconstructed term of the reverse OTDR linear signal.

[0109] S301: Construct the second data fidelity term 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.

[0110] S302: The data fidelity term is obtained based on the weighted sum of the first data fidelity term and the second data fidelity term.

[0111] Specifically, by constructing data fidelity terms for the reverse OTDR signal and the forward OTDR signal, it can be ensured that the residual between the OTDR signal reconstructed using 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.

[0112] S40: Based on the fact that the i-th eigenvalue of the first sparse coefficient vector to be solved and the second sparse coefficient vector to be solved are both zero or non-zero, a joint sparse regularization term is constructed; based on the spatial continuity and smoothness of the reconstructed reverse OTDR linear signal and the forward OTDR linear signal, a spatial constraint regularization term is constructed.

[0113] Specifically, based on the structured sparsity characteristics of the first and second sparse coefficient vectors, a joint sparse regularization term is constructed, such that the first and second sparse coefficient vectors are both zero or non-zero at the same position. Meanwhile, the reconstructed OTDR signal is spatially continuous and smooth. Therefore, this application constructs a spatial constraint regularization term to penalize solutions that are spatially discontinuous and drastically changing, thereby obtaining a piecewise smooth optimal solution so that the reconstructed OTDR linear signal conforms to the edge step characteristics of the OTDR linear signal, while suppressing random noise in flat regions.

[0114] S50: A joint optimization function is constructed with the goal of 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, thereby reconstructing the forward OTDR linear signal and the reverse OTDR linear signal for testing the optical fiber under test.

[0115] Specifically, the joint optimization function is expressed as:

[0116] ,

[0117] ,

[0118] ,

[0119] in, Represents the joint optimization function; Represents the first sparse coefficient vector; Represents the second sparse coefficient vector; Indicates the reverse OTDR observation signal; Represents an orthogonal transformation matrix; Represents the square of the L2 norm; Indicates a positive OTDR observation signal; Indicates data fidelity; 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.

[0120] This application, based on a physical structure of "single-end transmission and dual-end synchronous reception," simultaneously acquires the forward and reverse OTDR signals and the reverse OTDR observation signal of the optical fiber under test. It transmits the clear characteristics of the forward OTDR observation signal to the denoising and recovery process of the reverse signal, providing strong guidance for the weak reverse signal. Furthermore, considering the noise influence in the observation signal, this application separates the noise-free OTDR linear signal from the reverse and forward OTDR observation signals through signal reconstruction to improve monitoring accuracy. Specifically, since the OTDR signal has sparse characteristics in a specific feature domain—that is, the energy of weak events is concentrated on only a few feature coefficients—this application uses an orthogonal transformation matrix to orthogonally transform the sparse coefficient vector to reconstruct the OTDR linear signal and constructs a data fidelity term to constrain the reconstructed signal to closely match the actual observation signal. Because the scattering or reflection characteristics of the reverse and forward OTDR linear signals at the same location in the optical fiber caused by weak events have spatiotemporal symmetry, meaning that the energy of the weak event will affect both forward and reverse OTDR signals simultaneously, and random noise usually only exists in the single-end signal, this application constructs a joint sparse regularization term by using the i-th eigenvalue of both the first and second sparse coefficient vectors to be solved as zero or non-zero values; finally, a spatial constraint term is constructed based on the spatial continuity of the normal OTDR signal, and a joint optimization objective function is finally constructed. By performing orthogonal transformation on the solved sparse coefficient vector, a noise-free OTDR linear signal is reconstructed, realizing denoising and feature enhancement of the OTDR observation signal. Thus, the denoised signal is used for fault detection and location, effectively improving the accuracy of monitoring results and positioning precision.

[0121] Furthermore, this application linearizes the spatial constraints using its proximal operator and directly integrates them into the iterative update formula, ensuring that each step has an efficient closed-form solution. Specifically, by solving the joint optimization function, a first sparse coefficient vector and a second sparse coefficient vector are obtained, including:

[0122] 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.

[0123] 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.

[0124] Specifically, the new joint optimization function is expressed as:

[0125] ,

[0126] in, Represents the new joint optimization function; Indicates the reverse OTDR observation signal; Indicates the first auxiliary variable; Represents the square of the L2 norm; Indicates a positive OTDR observation signal; Indicates the second auxiliary variable; This represents the regularization parameter used to control the sparsity of the vector; Indicates the third auxiliary variable. This represents the i-th eigenvalue in the third auxiliary variable; Indicates the fourth auxiliary variable. This represents the i-th eigenvalue in the fourth auxiliary variable; Indicates the degree of spatial smoothness constraint; Indicates the fifth auxiliary variable; This represents the L1 norm.

[0127] The constraint function corresponding to the first auxiliary variable is expressed as follows:

[0128] ,

[0129] in, Represents an orthogonal transformation matrix; Represents the first sparse coefficient vector;

[0130] The constraint function corresponding to the second auxiliary variable is expressed as follows:

[0131] ,

[0132] in, Represents the second sparse coefficient vector;

[0133] The constraint function corresponding to the third auxiliary variable is expressed as follows:

[0134] ,

[0135] The constraint function corresponding to the fourth auxiliary variable is expressed as:

[0136] ,

[0137] The constraint function corresponding to the fifth auxiliary variable is expressed as follows:

[0138] ,

[0139] in, Represents the difference operator matrix; This represents the gradient of the reconstructed OTDR linear signal; This indicates the reverse OTDR linear signal or the forward OTDR linear signal obtained from the reconstruction.

[0140] 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.

[0141] In one embodiment of this application, when k=0, each auxiliary variable, each dual variable, and the first sparse coefficient vector and the second sparse coefficient vector are all set to zero vectors.

[0142] 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, so as to obtain the updated first sparse coefficient vector, the second sparse coefficient vector and each auxiliary variable.

[0143] Specifically, the update formula for the first sparse coefficient vector is:

[0144] ,

[0145] in, This represents the updated first sparse coefficient vector; Indicates the penalty parameter; Represents an orthogonal transformation matrix; This represents the first auxiliary variable during the k-th iteration; Let represent the first dual variable at the k-th iteration; This represents the third auxiliary variable in the k-th iteration; Let represent the third dual variable at the k-th iteration; This indicates transpose.

[0146] The update formula for the second sparse coefficient vector is:

[0147] ,

[0148] in, This represents the updated second sparse coefficient vector; This represents the second auxiliary variable during the k-th iteration; Denotes the second dual variable at the k-th iteration; This represents the fourth auxiliary variable in the k-th iteration; Let represent the fourth dual variable at the k-th iteration.

[0149] Specifically, when updating the first sparse coefficient vector, the first dual variable is used. punish and The deviation between them is due to the third auxiliary variable. for The auxiliary variable, therefore, utilizes the third dual variable. punish and The deviation between them is considered, and the penalty parameter is used to control the intensity of the penalty for constraint violation; similarly, when updating the first sparse coefficient vector, the second dual variable is used. punish and The deviation between them, due to the fourth auxiliary variable for The auxiliary variable, therefore, utilizes the fourth dual variable. punish and The deviation between the constraints is considered, while the penalty parameter is used to control the intensity of the penalty for constraint violation.

[0150] The update formula for the first auxiliary variable is:

[0151] ,

[0152] in, This represents the first auxiliary variable after the update; Represents the identity matrix; Represents the difference operator matrix; Indicates the reverse OTDR observation signal; This represents the fifth auxiliary variable in the k-th iteration; Let represent the fifth dual variable in the k-th iteration.

[0153] The update formula for the second auxiliary variable is:

[0154] ,

[0155] in, This represents the updated second auxiliary variable; Indicates a positive OTDR observation signal;

[0156] This application will be approved and Simultaneous scaling or zeroing ensures joint sparsity; specifically, the update formulas for the third and fourth auxiliary variables are as follows:

[0157] ,

[0158] ,

[0159] ,

[0160] ,

[0161] in, This represents the i-th feature value in the third auxiliary variable after the update; This represents the i-th feature value in the fourth auxiliary variable after the update; This represents the regularization parameter used to control the sparsity of the vector; express The i-th eigenvalue; express The i-th eigenvalue.

[0162] The update formula for the fifth auxiliary variable is:

[0163] ,

[0164] ,

[0165] in, This represents the updated fifth auxiliary variable; Represents a symbolic function; Indicates the degree of spatial smoothness constraint; This indicates element-wise multiplication.

[0166] 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.

[0167] Specifically, the formulas for calculating the constraint function values ​​corresponding to each auxiliary variable are as follows:

[0168] ,

[0169] ,

[0170] ,

[0171] ,

[0172] ,

[0173] in, This represents the value of the constraint function corresponding to the first auxiliary variable; This represents the constraint function value corresponding to the second auxiliary variable; This represents the constraint function value corresponding to the third auxiliary variable; This represents the constraint function value corresponding to the fourth auxiliary variable; This represents the constraint function value corresponding to the fifth auxiliary variable.

[0174] 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.

[0175] Specifically, the formulas for calculating the predicted values ​​of each dual variable after the update are as follows:

[0176] ,

[0177] in, This represents the predicted value of the nth dual variable after the update; Indicates acceleration parameters; This represents the value of the nth dual variable during the kth iteration; This represents the value of the nth dual variable during the (k-1)th iteration;

[0178] The update formulas for each dual variable are:

[0179] ,

[0180] in, This represents the nth dual variable after the update; This represents the constraint function value corresponding to the nth auxiliary variable.

[0181] Step 7: Obtain the original residual norm by taking the arithmetic square root of the sum of the squares of the L2 norms of the constraint function values ​​corresponding to each auxiliary variable; obtain the dual residual norm by taking the arithmetic square root of the sum of the squares of the L2 norms of the first difference before and after the update of the third auxiliary variable, the second difference before and after the update of the fourth auxiliary variable, and the third difference before and after the update of the fifth auxiliary variable, and the penalty parameter at the k-th iteration.

[0182] Specifically, the original residual norm The calculation formula is:

[0183] ,

[0184] Dual residual norm The calculation formula is:

[0185] ,

[0186] Step 8: Determine 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, then update the penalty parameter and dual variable based on the magnitude of the original residual norm and the dual residual norm.

[0187] Step 9: If the original residual norm is greater than the product of the first preset penalty parameter threshold and the dual residual norm, then the product of the penalty parameter value at the k-th iteration and the second preset penalty parameter threshold is used as the updated penalty parameter; calculate the product of the second preset penalty parameter threshold and each updated dual variable respectively, and then update each dual variable again.

[0188] Step 10: If the dual residual norm is greater than the product of the first preset penalty parameter threshold and the original residual norm, then the quotient of the penalty parameter value at the k-th iteration and the second preset penalty parameter threshold is used as the updated penalty parameter; calculate the quotient of each dual variable and the second preset penalty parameter threshold respectively, and update each dual variable again.

[0189] Step 11: Update k=k+1. Take the updated values ​​of each 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 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 obtain the first sparse coefficient vector and the second sparse coefficient vector.

[0190] Specifically, both the first preset penalty parameter threshold and the second preset penalty parameter threshold are greater than 1. The first preset penalty parameter threshold is used to determine whether the original residual and the dual residual are significantly unbalanced, and its commonly used value is 10. The second preset penalty parameter threshold is used to increase or decrease the ratio of the penalty parameter and the dual variable, and its commonly used value is 2.

[0191] In steps 9 to 11, this application designs an optimization solution strategy for residual fitting and adaptive penalty parameter adjustment. By monitoring the original residual and the dual residual and dynamically adjusting the penalty parameter, the convergence speed and stability are balanced.

[0192] Furthermore, the reverse OTDR linear signal and the forward OTDR linear signal are reconstructed for testing the fiber under test, including:

[0193] The first sparse coefficient vector is orthogonally transformed using an orthogonal transformation matrix to obtain the inverse OTDR linear signal; the second sparse coefficient vector is orthogonally transformed using an orthogonal transformation matrix to obtain the forward OTDR linear signal.

[0194] Based on the loss of the forward and reverse OTDR linear signals, the presence of faults in the optical fiber under test is detected; if a fault is found, the fault location is performed using a bidirectional positioning method based on the forward and reverse OTDR linear signals.

[0195] Based on the optical temporal reflectance monitoring method based on joint optimization of forward and reverse signals provided in the above embodiments, this application also provides an optical temporal reflectance monitoring device based on joint optimization of forward and reverse signals, such as... Figure 2 As shown, the device specifically includes:

[0196] The signal acquisition module 10 is used to acquire the reverse OTDR observation signal and the forward OTDR observation signal of the optical fiber under test.

[0197] The signal reconstruction module 20 is used to construct a reverse OTDR linear signal reconstruction term based on the product of the orthogonal transformation matrix and the first sparse coefficient vector to be solved; and to construct a forward OTDR linear signal reconstruction term based on the product of the orthogonal transformation matrix and the second sparse coefficient vector to be solved.

[0198] The fidelity term construction module 30 is used to construct data fidelity terms based on the difference between the reverse OTDR observation signal and the reconstructed term of the reverse OTDR linear signal, and the difference between the forward OTDR observation signal and the reconstructed term of the forward OTDR linear signal.

[0199] The regularization term construction module 40 is used to construct a joint sparse regularization term based on the fact that the i-th eigenvalue of the first sparse coefficient vector to be solved and the second sparse coefficient vector to be solved are both zero or non-zero; and to construct a spatial constraint regularization term based on the spatial continuity and smoothness of the reconstructed reverse OTDR linear signal and the forward OTDR linear signal.

[0200] The optimization function construction and solution module 50 is used to construct a joint optimization function with the goal of minimizing the weighted sum of data fidelity terms, joint sparse regularization terms, and spatial constraint regularization terms; the joint optimization function is solved 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 for testing the optical fiber under test.

[0201] This application also provides a computer-readable storage medium storing a computer program that, when processed, implements the steps of the optical temporal reflectance monitoring method based on joint optimization of forward and reverse signals described above.

[0202] The optical temporal reflectance monitoring method based on joint optimization of forward and reverse signals will be further explained and illustrated below through specific embodiments:

[0203] 1. A highly stable distributed feedback laser with a center wavelength of 1550nm is used to generate optical pulses with pulse widths adjustable in the range of 10ns to 20μs through an acousto-optic modulator; wherein, the peak power of the pulse can be adjusted according to the length of the optical fiber under test, and the typical value is usually 10dBm to 23dBm.

[0204] 2. Connect a 99:1 asymmetric optical coupler in series between the laser and the optical circulator. The laser emits a laser pulse, which enters through port 1 of the optical circulator and is output from port 2 to the optical fiber under test. The asymmetric optical coupler couples out 1% of the emitted light power to the forward signal receiving channel. The backscattered light returning from the optical fiber under test enters through port 2 of the optical circulator and is output from port 3 to the reverse signal receiving channel.

[0205] 3. Utilize a high-sensitivity avalanche photodiode to detect weak backscattered light with signal strength in the range of -50dBm to -70dBm in the reverse signal receiving channel; utilize a common PIN photodiode to receive the stronger signal in the forward signal receiving channel.

[0206] 4. Use a dual-channel, high-sampling-rate analog-to-digital converter to synchronously digitize the signals acquired by the two photodiodes, and process the two signals to ensure that the processed forward OTDR observation signal and reverse OTDR observation signal are precisely aligned on the time axis.

[0207] 5. Using a field-programmable gate array (FPGA) + digital processor architecture or a high-performance embedded industrial computer, the forward OTDR observation signal and the reverse OTDR observation signal are received, and the steps of the optical time-domain reflectometry monitoring method based on joint optimization of forward and reverse signals provided in the above embodiments are executed, thereby obtaining the reconstructed noise-free forward OTDR linear signal and reverse OTDR linear signal.

[0208] 6. Perform event detection, location, and loss analysis on the forward and reverse OTDR linear signals, and display the OTDR curves, event lists, and alarm information graphically on the user interface to achieve the detection of the fiber under test.

[0209] Compared with existing technologies, this application achieves the following significant advantages through its innovative "single-end transmission, dual-end synchronous reception" physical architecture and advanced "forward and reverse signal joint optimization" algorithm model:

[0210] I. Significantly Improved Signal-to-Noise Ratio and Dynamic Range: This application creatively utilizes the forward signal, whose energy is far stronger than that of the backscattered Rayleigh signal, as an "anchor" for high signal-to-noise ratio. Through a joint optimization model, the clear characteristics of the forward signal are effectively transmitted to the denoising and recovery process of the reverse signal, essentially providing strong guidance for the weak reverse signal. Experiments show that, under the same test conditions, this method can improve the dynamic range of the system by at least 10 dB, allowing weak events that were previously submerged by noise (such as initial fiber optic cable aging and minor stress changes) to be clearly presented, significantly enhancing the system's detection sensitivity.

[0211] II. Significantly reduced false alarm and false negative rates, improving monitoring reliability: Traditional OTDR technology struggles to distinguish between genuine weak events and random noise spikes. This application leverages the shared physical nature of "structured sparsity" in both forward and reverse signals, constrained by a joint sparse regularization term. This means that only events exhibiting significant energy responses simultaneously at specific locations in both forward and reverse signals are identified as genuine events, while random noise appearing only in a single signal is efficiently suppressed. This "dual verification" mechanism fundamentally enhances the system's anti-interference capability, significantly reduces false alarms caused by noise, and avoids missing genuine weak events due to excessively low signal-to-noise ratios.

[0212] Third, higher positioning and identification accuracy is achieved: The "spatial constraint regularization term" introduced in the joint optimization model incorporates the prior knowledge of the "spatial local continuity" of optical cable events in the physical world into the algorithm. This constraint encourages the algorithm to find the optimal solution with piecewise smoothness, thereby accurately reconstructing the edges of events (such as the step features of breakpoints and weld points), while strongly smoothing noise in non-event areas. This makes the edges of the event characteristic curves steeper and clearer, solving the problem of blurred event starting points due to noise in traditional methods, significantly improving positioning accuracy, and helping to more accurately identify event types (such as whether it is a break or a bend).

[0213] Fourth, it ensures real-time monitoring and meets dynamic monitoring needs: Unlike traditional methods that rely on averaging multiple measurements to improve the signal-to-noise ratio, this application can obtain high-quality monitoring results with a single measurement. Efficient optimization algorithms (such as the improved algorithm based on ADMM) ensure rapid signal processing, enabling the system to respond to and issue early warnings in near real-time to dynamically changing events (such as seabed geological activity, third-party intrusions, and ship anchor damage), which is crucial for ensuring the safety of long-distance critical optical cable links.

[0214] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0215] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0216] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0217] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0218] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

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 the 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 the 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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