Submarine cable fault location method and system based on time of arrival and parameter joint estimation

Abstract

This invention discloses a method and system for locating submarine cable faults based on joint estimation of arrival time and parameters, relating to the field of submarine cable monitoring and fault diagnosis technology. Existing technologies suffer from difficulties in synchronizing underwater beacon clocks and mismatch in constant sound velocity models. This invention deploys at least four underwater monitoring beacons along the cable. When each beacon fails, it independently records its local absolute arrival time stamp using its local clock, without hardware time synchronization. The central processing unit aggregates the timestamps and beacon coordinates, and calls a joint parameter estimation mathematical model, a layered sound velocity profile model, and a nonlinear optimization algorithm. The deviation between the three-dimensional location coordinates of the fault point and the local clock of each beacon is used as the parameter to be estimated. The solution is minimized using the sum of squared measurement residuals as the objective function, outputting the optimal estimate of the three-dimensional coordinates of the fault point and the clock deviation. This invention reduces cost and complexity, overcomes model mismatch caused by deep-sea sound velocity stratification, and improves positioning accuracy under asynchronous conditions.

Description

Technical Field

[0001] This invention relates to the field of submarine cable monitoring and fault diagnosis technology, and in particular to a method and system for submarine cable fault location based on joint estimation of arrival time and parameters. Background Technology

[0002] Submarine cables are critical infrastructure supporting global communication and energy interconnection, and their reliable operation is essential. However, the complex marine environment makes them vulnerable to damage from external forces such as anchoring hazards and trawls. In the event of a fault, rapid and accurate location is crucial for minimizing losses and ensuring timely repair. Currently, the mainstream technology for locating external faults in submarine cables is the Time Difference of Arrival (TDOA) method based on underwater acoustic beacons. This method deploys multiple acoustic monitoring nodes (beacons) at known locations along the cable route, calculates the time difference between the arrival of the fault's acoustic signal at different beacons, and combines this with the sound velocity to determine the location of the fault point.

[0003] However, traditional TDOA positioning technology has a core flaw: its implementation is highly dependent on precise clock synchronization between underwater beacons. This is because TDOA calculates the "relative time difference" between different beacons, which must be done under a unified time reference. Achieving high-precision, long-term stable clock synchronization in an underwater environment is extremely difficult: GPS signals cannot penetrate seawater; clock synchronization using underwater acoustic communication is limited in accuracy by the large delay, multipath effects, and noise of the underwater acoustic channel, typically only reaching millisecond levels, and a 1-millisecond time synchronization error can lead to a positioning error of approximately 1.5 meters. Equipping each beacon with a high-precision atomic clock would significantly increase system cost and maintenance burden. Therefore, existing technologies typically employ a two-step method of "synchronization first, then positioning," but this method not only introduces errors in the synchronization process itself, leading to error accumulation, but also increases system complexity and power consumption.

[0004] To reduce reliance on high-precision clock synchronization, asynchronous positioning methods (such as the pseudo-time-of-arrival (PTOA) method) have emerged in existing technologies. These methods supplement unknown time delay deviations (clock deviations) as state variables, jointly estimating the target position. However, such asynchronous positioning methods typically assume that sound speed information is known, or use only a coarse, constant sound speed in the calculation. In actual marine environments, sound speed is significantly affected by temperature, salinity, and hydrostatic pressure, exhibiting distinct stratified variations; sound waves also undergo ray bending during propagation. Forcing a constant sound speed into the model calculation will result in severe model mismatch errors, leading to significant systematic deviations in fault location results and failing to meet the high-precision positioning requirements of deep-sea scenarios.

[0005] Furthermore, the acoustic emission / vibration signals instantaneously generated by submarine cable faults are characterized by wide bandwidth, transient nature, and non-periodicity, and the local clock crystals of each underwater beacon exhibit independent and distinct drift. How to achieve high-precision joint calculation of the three-dimensional coordinates of the fault point based on transient signals in an environment where hardware clock synchronization is not required and sound velocity varies in layers is a pressing technical challenge in the field of submarine cable fault location. Summary of the Invention

[0006] The technical problem to be solved and the technical task proposed by this invention is to improve and refine existing technical solutions, and to provide a submarine cable fault location method based on joint estimation of arrival time and parameters, so as to achieve high-precision three-dimensional location of submarine cable fault points and reduce system complexity and hardware costs. To this end, this invention adopts the following technical solution.

[0007] Firstly, a method for locating submarine cable faults based on joint estimation of arrival time and parameters is provided, the method comprising the following steps: At least four underwater monitoring beacons are deployed along the submarine cable to be monitored. Each beacon monitors the acoustic or vibration signals of the cable and its surrounding environment. When a fault occurs in the submarine cable and transient acoustic or vibration signals are generated, each beacon independently records the local absolute arrival timestamp of the fault signal by its local clock module, and there is no hardware time synchronization between the beacons. Each beacon will upload the recorded local absolute arrival timestamp and corresponding identifier to the central processing unit; The central processing unit receives and aggregates the local absolute arrival timestamps and pre-calibrated geographical coordinates of each beacon. It then invokes the joint parameter estimation mathematical model, the hierarchical sound velocity profile model, and the nonlinear optimization algorithm. Based on the hierarchical sound velocity profile model, it calculates the theoretical propagation time of the signal. The joint parameter estimation mathematical model uses the three-dimensional location coordinates of the fault point and the local clock deviations of each beacon as parameters to be estimated, with the sum of squared measurement residuals as the objective function. The measurement residual for each beacon is its local absolute arrival timestamp minus the theoretical propagation time, and then minus the local clock deviation of that beacon. The nonlinear optimization algorithm is used to minimize the objective function, simultaneously calculating the optimal estimate of the three-dimensional location coordinates of the fault point and the optimal estimate of the local clock deviations of all beacons that minimize the objective function.

[0008] This technical solution eliminates the need for underwater hardware clock synchronization, reducing system complexity and cost. It eliminates the need for prior synchronization followed by positioning, fundamentally avoiding the introduction of synchronization errors and reducing the cost, power consumption, and daily maintenance difficulty of beacon hardware. In the deep-sea environment, sound speed exhibits significant stratified variations with temperature, salinity, and depth. This solution uses a stratified sound speed profile model to calculate the theoretical propagation time of the signal, more realistically reflecting the actual propagation path of the sound wave. This effectively overcomes system positioning deviations caused by sound speed model mismatch, improving the accuracy of theoretical propagation time calculation and thus significantly enhancing the positioning accuracy of the fault point. This solution uses the three-dimensional position coordinates of the fault point and the local clock deviations of all beacons simultaneously as parameters to be estimated, performing optimal solutions through the same objective function. This achieves synchronous joint calculation of three-dimensional coordinates and multiple beacon clock deviations, eliminating error propagation and accumulation caused by step-by-step estimation. Mathematical optimization methods ensure that the positioning results are statistically optimal, guaranteeing the stability and robustness of the positioning results even under conditions of large beacon clock drift or measurement noise. By deploying at least four underwater monitoring beacons along the submarine cable to be monitored, and utilizing redundant observation data from multiple points (the local absolute arrival timestamps of each beacon), combined with a joint estimation algorithm, the three-dimensional location coordinates (x, y, z) of the fault point, including its depth, can be directly calculated. This overcomes the limitations of traditional two-dimensional planar positioning, adapts to the actual engineering scenario where the depth of deep-sea cable deployment varies and the spatial location of the fault point is completely unknown, and achieves complete three-dimensional spatial locking of the fault source without hardware synchronization.

[0009] As a preferred technical means, the layered sound velocity profile model is a layered sound velocity function that varies with depth, constructed based on pre-acquired ocean temperature, salinity, and depth data.

[0010] The layered sound velocity profile model is constructed based on real ocean hydrophysical parameters (temperature, salinity, and depth). It can reflect the nonlinear variation of sound velocity with depth in actual sea areas, making the calculation of theoretical propagation time more consistent with the real physical propagation path and further eliminating positioning errors caused by inaccurate environmental parameters.

[0011] As a preferred technical means, the nonlinear optimization solution algorithm is the Levenberg-Marquardt algorithm, and its specific iterative solution process includes: Initialize the parameter vector to be estimated, which is composed of the three-dimensional position coordinates of the fault point and the local clock deviation of each beacon, and set the damping factor and convergence threshold at the same time. In each iteration, the residual vector under the current parameters to be estimated is calculated, and the partial derivatives of the objective function with respect to the three-dimensional position coordinates of the fault point and the clock deviation are calculated to construct the Jacobian matrix; Based on the Jacobian matrix, damping factor, and identity matrix, the incremental normal equation is constructed and solved to calculate the incremental vector of the parameter to be estimated. Update the current parameters to be estimated using the incremental vector; Repeat the above iterative process. Stop iterating when the incremental magnitude of the parameter to be estimated is less than the set convergence threshold or the maximum number of iterations is reached, and output the final three-dimensional location coordinates of the fault point and the optimal estimate of the clock deviation.

[0012] The Levenberg-Marquardt algorithm combines the advantages of the Gauss-Newton method and gradient descent. It adaptively adjusts the iteration step size through a damping factor, exhibiting good global convergence when far from the optimal solution and extremely fast convergence when close to it. The iterative process can stably, quickly, and accurately solve high-dimensional nonlinear least squares problems, ensuring the algorithm's reliability and real-time performance in practical engineering applications. Specifically, by introducing and dynamically adjusting the damping factor, in the early stages of iteration (when the parameters are far from the optimal solution), the algorithm behaves similarly to gradient descent, exhibiting good global convergence and effectively avoiding getting trapped in local minima. In the later stages of iteration (when the parameters are close to the optimal solution), the algorithm behaves similarly to the Gauss-Newton method, utilizing the second-order convergence property provided by the Jacobian matrix to achieve rapid approximation and improve convergence efficiency. When solving the incremental normal equation, by adding a product term of the damping factor and the identity matrix, the coefficient matrix (the transpose of the Jacobian matrix multiplied by the Jacobian matrix plus the damping term) is always positive definite and invertible. Even if there is a strong correlation between the parameters to be estimated (3D coordinates and multiple clock deviations) leading to a singular Jacobian matrix, this algorithm can still stably solve for a reliable incremental vector, avoiding the solution failure caused by the non-invertibility of the matrix in the traditional Gauss-Newton method, and significantly enhancing the numerical stability of this algorithm under different geometric observation conditions. Since it is necessary to simultaneously optimize the 3D position coordinates of the fault point and the local clock deviations of each beacon, the Jacobian matrix structure is relatively complex. By constructing the Jacobian matrix using partial derivatives, the gradient direction of the residuals of each parameter can be characterized, thereby coordinating the optimization step size of multiple variables in the iteration, ensuring the accuracy of the search direction in high-dimensional space, and finally achieving synchronous high-precision convergence of multiple parameters.

[0013] As a preferred technical means, the trigger condition for the sensor in the underwater monitoring beacon to detect the fault signal is: the energy of the detected acoustic or vibration signal in a specific frequency band exceeds a preset threshold, and / or the matching degree between the signal waveform and the pre-stored fault feature waveform library exceeds a set threshold.

[0014] By setting dual triggering conditions of frequency band energy threshold and waveform feature matching, marine environmental noise and other non-fault interference signals can be effectively filtered out, preventing beacons from being falsely triggered by environmental noise and recording false timestamps, thereby improving the signal-to-noise ratio of signal detection and the accuracy of fault location.

[0015] As a preferred technical means, the deployment of the underwater monitoring beacons must meet the geometric constraint that at least four beacons are not coplanar in three-dimensional space, so as to ensure the observability of the three-dimensional position coordinates of the fault point and the clock deviation parameters.

[0016] Since the joint estimation model contains multiple parameters to be estimated, such as three-dimensional spatial coordinates and multiple clock deviations, the non-coplanar deployment of four or more beacons can mathematically guarantee that the system of equations has a unique solution (i.e., observability), effectively avoiding the degradation of positioning results or the occurrence of multiple solutions due to the rank deficiency of the geometric matrix, and ensuring the feasibility of three-dimensional positioning from the perspective of physical architecture.

[0017] As a preferred technical means: the initial guess value of the three-dimensional location coordinates of the fault point is the arithmetic mean or geometric center of the geographical location coordinates of all underwater monitoring beacons, and the initial guess value of the local clock deviation of each underwater monitoring beacon is zero.

[0018] Using the geometric center of the beacon deployment area as the initial coordinates of the fault point and setting the initial value of the clock deviation to zero is close to reality. This can effectively avoid the nonlinear optimization algorithm from falling into the local minimum trap, shorten the algorithm's iteration convergence time, and improve the overall computational efficiency and robustness of the algorithm.

[0019] Secondly, a submarine cable fault location system based on joint estimation of arrival time and parameters is provided. The system employs the aforementioned submarine cable fault location method based on joint estimation of arrival time and parameters, and includes: An underwater monitoring network includes at least four underwater monitoring beacons deployed along the submarine cable to be monitored. Each underwater monitoring beacon is equipped with a sensor, a local clock module, and a data communication module. The sensor is used to detect broadband transient acoustic or vibration signals excited by a fault in the submarine cable. The local clock module is used to independently record the local absolute arrival timestamp of the signal when the fault signal is detected, and the underwater monitoring beacons do not perform hardware time synchronization. A data transmission network is used to transmit the local absolute arrival timestamp and its corresponding unique identifier recorded by each of the underwater monitoring beacons to the central processing unit. The central processing unit receives and aggregates the local absolute arrival timestamps from all underwater monitoring beacons and the pre-calibrated geographical coordinates of each beacon. It then calculates the theoretical propagation time of the signal based on a hierarchical sound velocity profile model. Using a joint parameter estimation mathematical model, it takes the three-dimensional location coordinates of the fault point and the local clock deviations of each beacon as parameters to be estimated, with the sum of squared measurement residuals as the objective function. A nonlinear optimization algorithm is then used to minimize the objective function, simultaneously calculating the optimal estimate of the three-dimensional location coordinates of the fault point and the optimal estimate of the local clock deviations of all beacons that minimize the objective function.

[0020] Since the underwater monitoring beacons do not synchronize their time using hardware, the system does not require high-precision atomic clocks, wireless timing modules, or complex synchronization communication protocols. The beacons only need basic signal detection, local clock recording, and data transmission functions, significantly simplifying the hardware structure and reducing power consumption. Each beacon independently integrates a sensor, a local clock module, and a data communication module, enabling it to independently complete the sensing, recording, and transmission chain. A single point of failure will not affect the normal operation of other beacons. This allows the system to expand its monitoring range by simply adding corresponding beacon nodes when facing submarine cables of varying lengths or in more complex environments, demonstrating excellent spatial scalability. Complex data aggregation, hierarchical sound velocity model calculations, and high-dimensional nonlinear joint estimation are centralized in the central processing unit. This centralized architecture allows the system to be deployed on powerful shore-based control stations or cloud servers, eliminating the need to deploy high-performance computing equipment in harsh underwater environments and ensuring the stability and accuracy of calculations during multi-parameter joint solutions. The system cuts off the chain of synchronous error propagation in traditional systems at its source. At the same time, the central processing unit, with its hierarchical sound velocity profile model and joint parameter estimation mathematical model, can directly calculate the three-dimensional spatial location of the fault point in a real marine environment where the clock is asynchronous and the sound velocity varies, thereby improving the reliability and anti-interference capability of the entire positioning system in harsh and complex deep-sea environments.

[0021] As a preferred technical means: the nonlinear optimization solution algorithm pre-stored in the central processing unit is the Levenberg-Marquardt algorithm, and its solution process includes: Initialize the parameter vector to be estimated, which is composed of the three-dimensional position coordinates of the fault point and the local clock deviation of each beacon, and set the damping factor and convergence threshold at the same time. In each iteration, the residual vector under the current parameters to be estimated is calculated, and the partial derivatives of the objective function with respect to the three-dimensional position coordinates of the fault point and the clock deviation are calculated to construct the Jacobian matrix; Based on the Jacobian matrix, damping factor, and identity matrix, the incremental normal equation is constructed and solved to calculate the incremental vector of the parameter to be estimated. Update the current parameters to be estimated using the incremental vector; Repeat the above iterative process. Stop iterating when the incremental magnitude of the parameter to be estimated is less than the set convergence threshold or the maximum number of iterations is reached, and output the final three-dimensional location coordinates of the fault point and the optimal estimate of the clock deviation.

[0022] By pre-installing the Levenberg-Marquardt algorithm, which is highly stable and has a fast convergence speed, in the central processing unit, the system can efficiently and stably complete data processing when facing complex sea conditions and multi-parameter joint solutions, which greatly improves the accuracy and reliability of the system's positioning results.

[0023] As a preferred technical means, the trigger condition for the sensor in the underwater monitoring beacon to detect the fault signal is: the energy of the detected acoustic or vibration signal in a specific frequency band exceeds a preset threshold, and / or the matching degree between the signal waveform and the pre-stored fault feature waveform library exceeds a set threshold.

[0024] The triggering mechanism of this technical solution enables the system to have a strong ability to resist environmental noise interference, avoids the transmission and processing of invalid data, reduces the bandwidth occupation of the data transmission network and the computing power consumption of the central processing unit, and ensures the reliability and low power consumption of fault monitoring at the system level.

[0025] As a preferred technical means, the central processing unit is further configured to convert the optimal estimated value of the three-dimensional location coordinates of the fault point obtained by solving into geographic coordinates and output them to the display device for visualization; at the same time, it uses the optimal estimated value of the local clock deviation of each beacon obtained by solving to evaluate the operational health status of the local clock of each underwater monitoring beacon.

[0026] While locating faults, the system also features human-computer interaction and self-checking functions. Converting coordinates to geographic coordinates and displaying them directly assists maintenance personnel in quickly dispatching repair vessels; and using clock deviation estimates to assess the health status of beacon clocks can provide early warnings of excessive beacon clock drift or failure risks, enabling proactive preventative maintenance of the underwater monitoring network and improving the system's intelligent operation and maintenance level.

[0027] Beneficial effects: 1. Completely eliminates the need for underwater clock synchronization: This invention uses a joint estimation algorithm to synchronously estimate and compensate for the clock deviations of each beacon during the positioning process, thereby completely eliminating the dependence on high-precision, high-cost underwater clock synchronization equipment or complex synchronization processes, and avoiding the introduction of synchronization errors at the source.

[0028] 2. Significantly improved positioning accuracy: Since the transmission and accumulation of synchronization error in the traditional two-step method of "synchronization first, positioning later" is avoided, the positioning accuracy of this invention is mainly limited by signal measurement noise and beacon geometry, and theoretically can reach a higher upper limit of positioning accuracy.

[0029] 3. Significantly reduced system complexity and cost: The beacon does not need to be equipped with a high-precision clock or participate in synchronous communication, which simplifies the hardware design, reduces the cost per point and the overall cost of the system, and also reduces the power consumption and maintenance complexity of the system.

[0030] 4. Strong algorithm versatility: The core algorithm is a mature nonlinear least squares optimization problem, exhibiting good stability and ease of implementation and deployment on various computing platforms, thus facilitating engineering applications. Attached Figure Description

[0031] Figure 1 This is a flowchart illustrating the overall workflow of the method of the present invention.

[0032] Figure 2 This is a comparison chart of the results of implementation examples of the present invention. Detailed Implementation

[0033] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings.

[0034] Example 1 This embodiment provides a method for locating submarine cable faults based on joint estimation of arrival time and parameters, such as... Figure 1 As shown, it includes the following steps: Step S1: System Deployment and Initialization At least four underwater monitoring beacons (preferably eight in this embodiment) are deployed along the submarine cable to be monitored at preset intervals (preferably 1 to 20 kilometers). Each underwater monitoring beacon is equipped with a sensor, a local clock module, and a data communication module.

[0035] Complete the deployment and location determination of the underwater beacon, and record the beacon information (including unique identifier and geographic coordinates). , The data is entered into the central processing unit database. All beacons enter a low-power listening state, continuously monitoring the acoustic or vibration signals of the cable body and its surrounding environment.

[0036] The deployment of underwater monitoring beacons must meet the geometric constraint that at least four beacons are not coplanar in three-dimensional space to ensure the observability of the three-dimensional position coordinates of the fault point and the clock deviation parameters.

[0037] Step S2: Fault Occurrence and Signal Detection When a submarine cable fails due to insulation breakdown, conductor breakage, or external mechanical damage (such as anchor damage or trawl), a large amount of energy is released instantaneously at the fault point, which excites broadband acoustic emission signals and / or vibration waves propagating along the cable.

[0038] Each beacon is continuously monitored by built-in sensors (such as hydrophones or accelerometers). A fault is determined to have occurred when the energy of the detected acoustic or vibration signal in a specific frequency band exceeds a preset threshold, and / or the match between the signal waveform and the pre-stored fault characteristic waveform library exceeds a set threshold.

[0039] Step S3: Timestamp Recording Beacons at different distances from the fault point sequentially detected the fault signal. Upon detecting a signal characteristic that met the triggering conditions, each beacon immediately recorded its local absolute arrival timestamp via its local clock module. (i=1,2,…,N, where N is the total number of beacons).

[0040] The beacons are not synchronized in hardware; that is, the time bases of each beacon are independent of each other, allowing for unknown clock deviations of milliseconds or even larger. .

[0041] Step S4: Data Transmission and Aggregation Each underwater monitoring beacon, via an underwater acoustic communication link or a fiber optic communication link via a submarine cable, will contain at least its unique identifier and the recorded timestamp. The data packets are uploaded to the central processing unit on the water surface or shore.

[0042] The central processing unit receives and aggregates timestamp data from all N underwater monitoring beacons. Simultaneously, it obtains the pre-calibrated and stored geographic coordinates of each beacon. At this point, the central processing unit has obtained the complete input dataset for subsequent fault location calculations: the local absolute arrival timestamps of each beacon. and their corresponding coordinates Furthermore, there is no need for clock synchronization between beacons.

[0043] Step S5: Construction of the joint parameter estimation model The central processing unit is based on the received dataset It calls a pre-stored joint parameter estimation mathematical model. The principle of the joint parameter estimation mathematical model is to establish and solve the optimal solution of the following nonlinear equation system: For each beacon i, its recorded local absolute arrival timestamp satisfy:

[0044] in: Let be the three-dimensional coordinates of the fault point to be determined; For the signal to propagate from the fault point P to the beacon The theoretical propagation time; c is the speed of sound in the medium (from the layered sound speed profile model). Sure); Denotes the Euclidean norm; The unknown local clock offset of the i-th beacon; To measure noise, it is usually assumed to be zero-mean Gaussian white noise.

[0045] Simultaneously, the central processing unit invokes a pre-stored layered sound velocity profile model. This model is a layered sound velocity function c(z) that varies with depth, constructed based on pre-acquired ocean temperature, salinity, and depth data. Specifically, the seawater is layered into a mixing layer, a prime mover layer, and a deep-sea isothermal layer, with each layer assigned a corresponding sound velocity calculation function, forming a mapping relationship from depth z to sound velocity c.

[0046] When calculating the theoretical propagation time, a layered sound velocity profile model is used for sound ray tracking calculation. Snell's law is combined with numerical integration to calculate the actual path and propagation time of the sound wave from the fault point to each beacon, thereby effectively overcoming the model mismatch error caused by sound ray bending.

[0047] Step S6: Formation of the nonlinear optimization problem The fault location problem is transformed into solving the following nonlinear least squares optimization problem:

[0048] in, This is a vector consisting of all beacon clock offsets.

[0049] The variables to be optimized are:

[0050] The physical meaning of the objective function is: to simultaneously search for the optimal combination of fault location and clock deviation while minimizing the sum of the squared residuals of the sum of the local absolute arrival timestamps of all beacons and the theoretical propagation time and clock deviation.

[0051] Step S7: Iterative optimization solution The Levenberg-Marquardt (LM) algorithm is used to minimize the objective function, and the output is the solution that minimizes the objective function. Minimize the optimal estimate of the fault location And the optimal estimate of the clock deviation of each beacon. This allows for direct fault location without requiring all beacons to be pre-synchronized.

[0052] The specific iterative solution process of the LM algorithm is as follows: (1) Parameter initialization Set the initial estimated value of the fault location. Initial estimates of clock offsets for each beacon , forming the parameter vector The initial guess for the fault location is preferably the arithmetic mean or geometric center of the geographical coordinates of all underwater monitoring beacons. The initial guess for the local clock deviation of each underwater monitoring beacon is preferably the zero vector. Simultaneously, a damping factor is set. (Preferred) and convergence threshold (Preferred) ).

[0053] (2) Calculate the residual vector In the k-th iteration, calculate the current parameters. The residual vector below Its i-th component is:

[0054] (3) Calculate the Jacobian matrix Calculate the Jacobian matrix of the objective function with the current parameters. The elements in the i-th row are the partial derivatives with respect to each parameter to be estimated.

[0055] For the position coordinate parameters, the partial derivatives are calculated as follows:

[0056]

[0057]

[0058] in, Let be the Euclidean distance between the estimated location of the fault point in the k-th iteration and the i-th beacon.

[0059] For the clock skew parameter, the partial derivative is calculated as follows:

[0060] in, It is the Kronecker delta symbol, which is 1 when i=j and 0 otherwise.

[0061] (4) Construct and solve the incremental normal equations Construct and solve the incremental normal equations:

[0062] Obtain parameter increment Where I is the identity matrix, Let be the damping factor for the k-th iteration.

[0063] (5) Update the parameter vector Update parameter vector:

[0064] (6) Determine convergence Determine convergence. If... If the maximum number of iterations is reached, the iteration is terminated and the optimal solution is output. , Otherwise, adjust the damping factor according to the change in the objective function value. Then return to step (2) to continue the iteration.

[0065] The specific adjustment strategy is as follows: if the objective function value decreases, then reduce the damping factor. To accelerate convergence; if the objective function value increases, increase the damping factor. This enhances stability.

[0066] Step S8: Result Output and Application The coordinates of the fault point obtained by the solution The data is converted to geographic coordinates and output to a display device (such as an electronic chart terminal) for visualization, enabling precise location of the fault. Simultaneously, the optimal estimates of the local clock offsets of each beacon are obtained through the solution process. Assess the operational health status of the local clocks of each underwater monitoring beacon.

[0067] If the estimated clock deviation exceeds a preset threshold or shows an accelerating drift trend, a beacon maintenance warning will be issued. The system automatically issues an alarm and generates a report. Based on the location results, maintenance personnel can quickly dispatch a repair vessel to the designated sea area.

[0068] Numerical verification of method embodiments To illustrate the effects of the present invention more specifically, a simplified but complete numerical embodiment is described below.

[0069] Suppose that in a 100-kilometer-long submarine cable system, N=8 underwater monitoring beacons are deployed, and their location coordinates (in meters) in a certain local coordinate system are: B1=(3996.6,-3991.5,-1044.9); B2=(2854.8,-2543.8,-1038.8); B3=(1705.6,-1715.1,-1041.9); B4=(557.1,-578.1,-1060.3 ); B5=(581.4,584.1,-1052.1); B6=(1715.4,1713.2,-1035.9); B7=(3144.4,2863.4,-1059.0); B8=(3993.0,4010.0,-1033.6).

[0070] In position A cable breakage fault occurred. Assume a layered sound velocity profile model is used in the water. The average speed of sound is approximately 1500 m / s.

[0071] Each beacon has an unknown local clock offset. (Unit: seconds), respectively: ; ; ; ; ; ; ; .

[0072] Noise measurement The noise is zero-mean Gaussian white noise with a standard deviation of 1 ms. The actual local absolute arrival timestamps recorded by each beacon are:

[0073] in, For the signal from the fault point propagation to beacon The actual theoretical propagation time is calculated based on the layered sound velocity profile model.

[0074] Will and Input the joint estimation algorithm of this invention. After Levenberg-Marquardt iteration, the algorithm converges. Output the fault location estimate: .

[0075] In contrast, if the traditional two-step method is used, i.e., clock synchronization is performed using beacon 1 as a time reference, and then TDOA positioning is performed, the positioning error is approximately 1096.6 meters. However, using the method of this invention, the positioning error is approximately 365.4 meters. Figure 2 As shown.

[0076] Accuracy improvement = (1096.6 - 365.4) / 1096.6 × 100% ≈ 66.7% Example 2: Submarine Cable Fault Location System Based on Joint Estimation of Time of Arrival and Parameters This embodiment provides a submarine cable fault location system based on joint estimation of arrival time and parameters. The system employs the method described in Embodiment 1. The system includes: an underwater monitoring network, a data transmission network, a central processing unit, and a result output unit.

[0077] (a) Underwater monitoring network The underwater monitoring network consists of at least four (preferably eight in this embodiment) underwater monitoring beacons deployed along the submarine cable to be monitored. Each underwater monitoring beacon has a built-in sensor, a local clock module, and a data communication module.

[0078] 1. Sensor The sensors employ high-sensitivity hydrophones (acoustic sensors) or accelerometers (vibration sensors) to monitor acoustic or vibration signals of the cable itself and its surrounding environment in real time. Since submarine cable faults can instantly generate broadband transient acoustic / vibration signals, the sensors, with their broadband response characteristics, can effectively capture such sudden signals.

[0079] The sensor is triggered when the energy of the detected acoustic or vibration signal in a specific frequency band (e.g., 1kHz to 10kHz) exceeds a preset threshold, and / or the signal waveform matches a pre-stored fault characteristic waveform library to a set threshold. This triggering mechanism effectively filters marine environmental noise and other non-fault interference signals, preventing beacons from being falsely triggered by environmental noise and recording false timestamps.

[0080] 2. Local clock module The local clock module uses a clock counter driven by a common crystal oscillator. When the sensor detects a fault signal and the trigger condition is met, the local clock module immediately latches the current clock count and generates a local absolute arrival timestamp. (i=1,2,…,N, where N is the total number of beacons). No hardware time synchronization is performed between the beacons; that is, the time bases of each beacon are independent, allowing for unknown clock deviations on the order of milliseconds or even larger. .

[0081] 3. Data communication module The data communication module is used to package the recorded local absolute arrival timestamp and the beacon's unique identifier, and upload them to the data transmission network via an underwater acoustic communication link or an optical fiber communication link built into the submarine cable.

[0082] (ii) Data transmission network The data transmission network includes an underwater acoustic communication gateway, an optical fiber channel in a submarine fiber optic composite cable, and shore-based receiving equipment. Its function is to reliably and stably transmit the timestamp data collected by the underwater monitoring network to the central processing unit. Each beacon transmits data via a communication module. Data packet reporting (where, For the first A unique identifier for an underwater monitoring beacon. The data (with its recorded local absolute arrival timestamp) is transmitted via network or fiber optic cable and eventually converges to the central processing unit.

[0083] (iii) Central Processing Unit The central processing unit (CPU) is deployed at a shore-based control station or cloud server and possesses high-performance computing capabilities. The CPU pre-stores: Layered sound velocity profile model: A layered sound velocity function varying with depth, constructed based on pre-acquired ocean temperature, salinity, and depth data. Specifically, seawater is stratified into a mixing layer, a prime mover layer, and a deep-sea isotherm layer, with each layer assigned a corresponding sound velocity calculation function, forming a mapping relationship from depth z to sound velocity c. For example, this can be constructed using Munk model expressions or cubic spline interpolation.

[0084] Joint parameter estimation mathematical model: Defines the three-dimensional location coordinates of the fault point and the local clock deviation of each beacon as parameters to be estimated, and the formula for calculating the theoretical propagation time.

[0085] Nonlinear optimization solution algorithm program: This embodiment is the Levenberg-Marquardt (LM) algorithm program, which is used to perform the minimization solution of the objective function.

[0086] Beacon Intrinsic Parameter Database: Stores the pre-calibrated geographic coordinates of all underwater beacons. .

[0087] The central processing unit is configured to perform the following operations: Receive and aggregate local absolute arrival timestamps from all underwater monitoring beacons and the pre-marked geographical coordinates of each beacon; The theoretical propagation time of the signal is calculated based on a layered sound velocity profile model; The mathematical model based on joint parameter estimation uses the three-dimensional location coordinates of the fault point and the local clock deviation of each beacon as the parameters to be estimated, and the sum of squared residuals as the objective function. The objective function is minimized using a nonlinear optimization algorithm (LM algorithm). The optimal estimates of the three-dimensional location coordinates of the fault point that minimize the objective function and the optimal estimates of the local clock deviations of all beacons are calculated simultaneously.

[0088] In addition, the central processing unit is also configured as follows: The optimal estimated value of the three-dimensional location coordinates of the fault point obtained by solving is converted into geographic coordinates and output to a display device for visualization. The optimal estimate of the local clock deviation of each beacon is obtained by solving the problem to assess the operational health status of the local clock of each underwater monitoring beacon. If the estimated clock deviation exceeds the preset threshold (e.g., 10ms) or shows an accelerating drift trend, a beacon maintenance warning is issued.

[0089] (iv) Result Output Unit The output unit includes a graphic display terminal, an audible and visual alarm, and a report generation system. It maps the fault location coordinates P onto an electronic nautical chart or cable route diagram, visually displaying the fault location and generating a maintenance report. Simultaneously, it uses the estimated clock deviation δ to assess the time reference health status of each underwater beacon.

[0090] System Implementation Workflow Based on the above system, this embodiment describes in detail the workflow of the positioning system.

[0091] Step A1: System Deployment and Initialization The deployment and location of underwater beacons are completed, and the beacon information (including unique identifiers and geographic coordinates) is entered into the central processing unit database. All beacons enter a low-power listening state to continuously monitor acoustic or vibration signals of the cable body and the surrounding environment.

[0092] Step A2: Fault Occurrence and Signal Detection When a submarine cable fails due to insulation breakdown, conductor breakage, or external mechanical damage, a large amount of energy is released instantaneously at the fault point, generating a broadband acoustic emission signal and / or vibration waves propagating along the cable. Each beacon continuously monitors the cable through built-in sensors. When the energy of the detected acoustic or vibration signal in a specific frequency band (e.g., 1kHz to 10kHz) exceeds a preset threshold, and / or the match between the signal waveform and the pre-stored fault characteristic waveform library exceeds a set threshold, a fault is determined to have occurred.

[0093] Step A3: Timestamp Recording Beacons at different distances from the fault point sequentially detected the fault signal. Upon detecting a signal characteristic that met the triggering conditions, each beacon immediately recorded its local absolute arrival timestamp via its local clock module. (i=1,2,…,N, where N is the total number of beacons). Hardware time synchronization is not performed between the beacons.

[0094] Step A4: Data Transmission and Aggregation Each underwater monitoring beacon, via an underwater acoustic communication link or a fiber optic communication link via a submarine cable, will contain at least its unique identifier and the recorded timestamp. The data packets are uploaded to a central processing unit located on the water surface or shore. The central processing unit receives and aggregates the timestamp data from all N underwater monitoring beacons. Simultaneously, it obtains the pre-calibrated and stored geographic coordinates of each beacon. .

[0095] Step A5: Joint parameter estimation and solution The central processing unit invokes the pre-stored joint parameter estimation mathematical model, layered sound velocity profile model, and nonlinear optimization solution algorithm to perform the following operations: The theoretical propagation time of the signal is calculated based on a layered sound velocity profile model; The joint parameter estimation mathematical model takes the three-dimensional location coordinates of the fault point and the local clock deviation of each beacon as the parameters to be estimated, and takes the sum of squared residuals as the objective function. The objective function is minimized using a nonlinear optimization algorithm, and the optimal estimates of the three-dimensional location coordinates of the fault point and the local clock deviations of all beacons are calculated simultaneously to minimize the objective function.

[0096] Step A6: Output and Application of Results The central processing unit will solve for the coordinates of the fault point. The data is converted to geographic coordinates and output to a display device (such as an electronic chart terminal) for visualization, enabling precise location of the fault. Simultaneously, the optimal estimates of the local clock offsets of each beacon are obtained through the solution process. The system assesses the operational health of the local clocks of each underwater monitoring beacon. It automatically issues alarms and generates reports. Based on the location results, maintenance personnel can quickly dispatch repair vessels to the designated sea area.

[0097] The above are specific embodiments of the present invention, which demonstrate the substantial features and progress of the present invention. Based on the actual needs of use, equivalent modifications in shape, structure, etc., can be made to it according to the teachings of the present invention, and all such modifications are within the scope of protection of this solution.

Claims

1. A method for locating submarine cable faults based on joint estimation of arrival time and parameters, characterized in that, Includes the following steps: At least four underwater monitoring beacons are deployed along the submarine cable to be monitored, and each beacon monitors the acoustic or vibration signals of the cable and the surrounding environment. When a fault occurs in the submarine cable and transient acoustic or vibration signals are generated, each beacon independently records the local absolute arrival timestamp of the fault signal by its local clock module, and there is no hardware time synchronization between the beacons. Each beacon will upload the recorded local absolute arrival timestamp and corresponding identifier to the central processing unit; After receiving and aggregating the local absolute arrival timestamps of each beacon and the pre-marked geographical coordinates of each beacon, the central processing unit calls the joint parameter estimation mathematical model, the layered sound velocity profile model, and the nonlinear optimization solution algorithm. The theoretical propagation time of the signal is calculated based on a layered sound velocity profile model; The joint parameter estimation mathematical model uses the three-dimensional location coordinates of the fault point and the local clock deviations of each beacon as parameters to be estimated, and the sum of squared measurement residuals as the objective function. The measurement residual of each beacon is its local absolute arrival timestamp minus the theoretical propagation time minus the local clock deviation of that beacon. The nonlinear optimization algorithm is used to minimize the objective function, and the optimal estimated values ​​of the three-dimensional location coordinates of the fault point and the optimal estimated values ​​of the local clock deviations of all beacons are calculated simultaneously to minimize the objective function.

2. The submarine cable fault location method based on joint estimation of arrival time and parameters according to claim 1, characterized in that, The layered sound velocity profile model is a layered sound velocity function that varies with depth, constructed based on pre-acquired ocean temperature, salinity, and depth data.

3. The submarine cable fault location method based on joint estimation of arrival time and parameters according to claim 1, characterized in that, The nonlinear optimization solution algorithm is the Levenberg-Marquardt algorithm, and its specific iterative solution process includes: Initialize the parameter vector to be estimated, which is composed of the three-dimensional position coordinates of the fault point and the local clock deviation of each beacon, and set the damping factor and convergence threshold at the same time. In each iteration, the residual vector under the current parameters to be estimated is calculated, and the partial derivatives of the objective function with respect to the three-dimensional position coordinates of the fault point and the clock deviation are calculated to construct the Jacobian matrix; Based on the Jacobian matrix, damping factor, and identity matrix, the incremental normal equation is constructed and solved to calculate the incremental vector of the parameter to be estimated. Update the current parameters to be estimated using the incremental vector; Repeat the above iterative process. Stop iterating when the incremental magnitude of the parameter to be estimated is less than the set convergence threshold or the maximum number of iterations is reached, and output the final three-dimensional location coordinates of the fault point and the optimal estimate of the clock deviation.

4. The submarine cable fault location method based on joint estimation of arrival time and parameters according to claim 1, characterized in that, The triggering conditions for the sensor in the underwater monitoring beacon to detect the fault signal are: the energy of the detected acoustic or vibration signal in a specific frequency band exceeds a preset threshold, and / or the matching degree between the signal waveform and the pre-stored fault feature waveform library exceeds a set threshold.

5. The submarine cable fault location method based on joint estimation of arrival time and parameters according to claim 1, characterized in that, The deployment of the underwater monitoring beacons must meet the geometric constraint that at least four beacons are not coplanar in three-dimensional space to ensure the observability of the three-dimensional position coordinates of the fault point and the clock deviation parameters.

6. The submarine cable fault location method based on joint estimation of arrival time and parameters according to claim 1, characterized in that, The initial guess value for the three-dimensional location coordinates of the fault point is the arithmetic mean or geometric center of the geographical coordinates of all underwater monitoring beacons, and the initial guess value for the local clock deviation of each underwater monitoring beacon is zero.

7. A submarine cable fault location system based on joint estimation of arrival time and parameters, characterized in that, The system employs a submarine cable fault location method based on joint estimation of arrival time and parameters as described in any one of claims 1 to 6, and the system comprises: An underwater monitoring network includes at least four underwater monitoring beacons deployed along the submarine cable to be monitored. Each underwater monitoring beacon is equipped with a sensor, a local clock module, and a data communication module. The sensor is used to detect broadband transient acoustic or vibration signals excited by a fault in the submarine cable. The local clock module is used to independently record the local absolute arrival timestamp of the signal when the fault signal is detected, and the underwater monitoring beacons do not perform hardware time synchronization. A data transmission network is used to transmit the local absolute arrival timestamp and its corresponding unique identifier recorded by each of the underwater monitoring beacons to the central processing unit. The central processing unit receives and aggregates the local absolute arrival timestamps from all underwater monitoring beacons and the pre-calibrated geographical coordinates of each beacon. It then calculates the theoretical propagation time of the signal based on a hierarchical sound velocity profile model. Using a joint parameter estimation mathematical model, it takes the three-dimensional location coordinates of the fault point and the local clock deviations of each beacon as parameters to be estimated, with the sum of squared measurement residuals as the objective function. A nonlinear optimization algorithm is then used to minimize the objective function, simultaneously calculating the optimal estimate of the three-dimensional location coordinates of the fault point and the optimal estimate of the local clock deviations of all beacons that minimize the objective function.

8. A submarine cable fault location system based on joint estimation of arrival time and parameters according to claim 7, characterized in that, The nonlinear optimization algorithm pre-stored in the central processing unit is the Levenberg-Marquardt algorithm, and its solution process includes: Initialize the parameter vector to be estimated, which is composed of the three-dimensional position coordinates of the fault point and the local clock deviation of each beacon, and set the damping factor and convergence threshold at the same time. In each iteration, the residual vector under the current parameters to be estimated is calculated, and the partial derivatives of the objective function with respect to the three-dimensional position coordinates of the fault point and the clock deviation are calculated to construct the Jacobian matrix; Based on the Jacobian matrix, damping factor, and identity matrix, the incremental normal equation is constructed and solved to calculate the incremental vector of the parameter to be estimated. Update the current parameters to be estimated using the incremental vector; Repeat the above iterative process. Stop iterating when the incremental magnitude of the parameter to be estimated is less than the set convergence threshold or the maximum number of iterations is reached, and output the final three-dimensional location coordinates of the fault point and the optimal estimate of the clock deviation.

9. A submarine cable fault location system based on joint estimation of arrival time and parameters according to claim 7, characterized in that, The triggering conditions for the sensor in the underwater monitoring beacon to detect the fault signal are: the energy of the detected acoustic or vibration signal in a specific frequency band exceeds a preset threshold, and / or the matching degree between the signal waveform and the pre-stored fault feature waveform library exceeds a set threshold.

10. A submarine cable fault location system based on joint estimation of arrival time and parameters according to claim 7, characterized in that, The central processing unit is also configured to: convert the optimal estimated value of the three-dimensional location coordinates of the fault point obtained by solving into geographic coordinates and output them to the display device for visualization; at the same time, use the optimal estimated value of the local clock deviation of each beacon obtained by solving to evaluate the operational health status of the local clock of each underwater monitoring beacon.

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