A method and system for online monitoring and evaluation of power transmission line galloping

Abstract

The application provides a power transmission line galloping online monitoring and evaluation method and system, the method comprising: based on a distributed clock synchronization algorithm, calculating the phase coefficient between acceleration signals detected by different sensor units in the same span to construct a phase matrix; performing eigenvalue decomposition on the phase matrix to separate galloping modes of different orders according to the size of the eigenvalue, and detecting the phase difference, amplitude ratio and non-linear index of each galloping mode to construct a galloping non-linear feature vector; inputting mechanical load, electric force and magnetostrictive force as boundary conditions to reconstruct the three-dimensional stress field of the conductor, insulator string, fitting and tower; comparing the calculation results with the material allowable stress and fatigue limit of each key part to generate corresponding galloping risk levels and warning information. The application can greatly improve the monitoring and evaluation efficiency of the power transmission line galloping.

Description

Technical Field

[0001] This invention relates to the field of power transmission line detection technology, and in particular to a method and system for online monitoring and evaluation of power transmission line galloping. Background Technology

[0002] Transmission line galloping is a low-frequency, large-amplitude self-excited vibration generated by icy conductors under wind excitation. It easily leads to conductor wear, hardware breakage, phase-to-phase flashover, and even tower collapse, posing a significant threat to the safe and stable operation of the power grid. With the advancement of smart grid construction, galloping online monitoring technology based on multi-sensor data fusion has been widely applied. By integrating multi-modal sensing data such as MEMS accelerometers, BeiDou RTK positioning, and distributed fiber optic sensing, it effectively overcomes the limitations of single sensors, significantly improves the accuracy and real-time performance of galloping amplitude monitoring, and provides basic data support for power grid galloping prevention and control.

[0003] However, existing multi-sensor fusion monitoring technologies generally suffer from a core deficiency of limited functionality. Most existing solutions use galloping amplitude as the core, or even sole, evaluation metric, with the design and optimization of fusion algorithms revolving around amplitude reconstruction, failing to fully exploit the multi-dimensional state information contained within the multi-sensor data. While existing technologies can obtain relatively accurate lateral and longitudinal galloping amplitudes through quadratic acceleration integration and GPS correction, they cannot analyze the spatial trajectory of the galloping, accurately extract the torsional angle characteristics of the conductor from multi-axis vibration data, or establish an effective mapping relationship between multi-source data and conductor fatigue damage.

[0004] This limitation in functionality prevents current technologies from comprehensively and accurately assessing the actual severity of galloping hazards. Studies show that, at the same amplitude, the probability of an elliptical galloping trajectory causing interphase flashover is more than three times that of a figure-eight trajectory; conductor torsional vibration increases the dynamic bending strain at the clamp exit by 3-5 times, significantly accelerating fatigue damage accumulation; and fatigue damage is the root cause of conductor breakage during long-term operation, which cannot be fully reflected by amplitude indicators alone. The limitations of current technology make it difficult for power grid operation and maintenance departments to formulate precise prevention and control strategies and achieve refined management of galloping risks. Summary of the Invention

[0005] Based on this, the purpose of this invention is to provide a method and system for online monitoring and evaluation of transmission line galloping, in order to solve the problem that most existing technologies can only use galloping amplitude as the core evaluation index, and fail to fully explore the multi-dimensional state information contained in multi-sensor data, resulting in the inability to comprehensively and accurately evaluate the actual degree of harm caused by galloping.

[0006] The first aspect of this invention proposes: A method for online monitoring and evaluation of transmission line galloping, wherein the method includes: Within multiple spans of the transmission line, several sensors are deployed at equal intervals along the conductor axis to form corresponding multi-field coupled sensor units. Based on a distributed clock synchronization algorithm, the phase coefficients between the acceleration signals detected by different sensor units within the same span are calculated to construct a phase matrix. The phase matrix is ​​decomposed into eigenvalues ​​to separate different orders of dancing modes based on the magnitude of the eigenvalues, and the phase difference, amplitude ratio, and nonlinear exponent of each dancing mode are detected to construct a dancing nonlinear feature vector. Based on the nonlinear characteristic vector of the galloping, combined with the electric field strength and magnetic field strength data, the electrodynamic force and magnetostrictive force generated during the galloping of the conductor are calculated to construct a finite element model of the transmission line. The mechanical load, the electrodynamic force and the magnetostrictive force are used as boundary condition inputs to reconstruct the three-dimensional stress field of the conductor, insulator string, hardware and tower. Based on the three-dimensional stress field, a time series analysis is performed on the finite element model to calculate the stress amplitude, stress cycle number, and stress concentration factor of each key part. The calculation results are then compared with the allowable stress and fatigue limit of the material of each key part to generate the corresponding galloping risk level and early warning information.

[0007] The beneficial effects of this invention are as follows: This technical solution effectively solves the problem that existing technologies only use galloping amplitude as the core evaluation index, failing to fully explore the multi-sensor multi-dimensional state information, resulting in incomplete and inaccurate galloping hazard assessment. By deploying multiple field-coupled sensor units at equal intervals across multiple spans of the transmission line and employing a distributed clock synchronization algorithm, high-precision synchronous acquisition of multi-sensor data and calculation of phase coefficients are achieved. Different orders of galloping modes are separated by eigenvalue decomposition, and nonlinear feature vectors are extracted, overcoming the limitations of single amplitude assessment. Combining electromagnetic field data to calculate electrodynamic force and magnetostrictive force, a precise finite element model of coupled electromechanical effects is constructed, reconstructing the three-dimensional stress field of key parts of the entire link, including conductors, insulator strings, hardware, and towers. By obtaining stress amplitude, cycle number, and concentration factor through time series analysis, and comparing them with the allowable stress and fatigue limit of the material, risk levels and early warnings are generated, significantly improving the comprehensiveness, accuracy, and timeliness of galloping hazard assessment.

[0008] Furthermore, the step of calculating the phase coefficients between acceleration signals detected by different sensor units within the same range based on a distributed clock synchronization algorithm to construct a phase matrix includes: When each sensor unit is powered on and initialized, the initial clock synchronization is completed through a bidirectional timestamp exchange mechanism between adjacent sensor units to construct a distributed clock network within the range. Based on the distributed clock network, continuous wavelet transform is performed on the acceleration signals of each sensor unit to obtain wavelet coefficient matrices at different scales. The cross-correlation function of wavelet coefficients between any two sensor units at the same scale is calculated based on the wavelet coefficient matrix, and the time delay between the two models is determined by searching the peak position of the cross-correlation function, so as to convert the time delay into the phase difference at the corresponding frequency. A multi-scale weighted fusion algorithm is used to perform a weighted average of the phase differences calculated at different scales to obtain a comprehensive phase difference. Taking any sensor unit within the range as a reference node, the comprehensive phase differences of all other sensor units relative to the reference node are used to construct an initial phase vector according to the spatial arrangement of the sensors. The initial phase vector is then subjected to global consistency correction. The corrected initial phase vectors at different dancing frequencies are stacked in columns to construct the phase matrix.

[0009] Furthermore, the step of performing global consistency correction on the initial phase vector to stack the corrected initial phase vectors at different dancing frequencies column-wise to construct the phase matrix includes: Based on the unidirectional propagation characteristics of galloping traveling waves in transmission lines, a unidirectional increasing constraint condition for phase difference is established to perform piecewise linear fitting on the initial phase vector, identify the corresponding phase jump points, and use cubic spline interpolation to repair each of the phase jump points to obtain a continuous and unambiguous original phase curve. The original phase curve is subjected to non-subsampled curvelet transform to decompose it into curvelet coefficients of different scales and directions. Based on the energy distribution characteristics of the galloping signal, each curvelet coefficient is shrunk. The shrunk curvelet coefficients are then reconstructed by inverse non-subsampled curvelet transform to obtain the corrected phase curve. Based on the orthogonality principle between different orders of dancing modes, a modal orthogonality constraint matrix is ​​constructed, and the correction phase curve is orthogonalized using the modal orthogonality constraint matrix to calculate several orthogonalized phase vectors. The orthogonalized phase vectors are then stacked column-wise to construct the corresponding phase matrix.

[0010] Furthermore, the step of performing eigenvalue decomposition on the phase matrix to separate different orders of dancing modes based on the magnitude of the eigenvalues ​​includes: The phase matrices at different sampling times are stacked along the time dimension to construct a third-order spatiotemporal phase tensor containing spatial location, frequency components, and time evolution. The third-order spatiotemporal phase tensor is then decomposed by Tucker to obtain the tensor factor matrix, spatial factor matrix, and time factor matrix. The energy contribution of each element in the tensor factor matrix is ​​calculated to determine the core tensor element index of the dominant dancing mode, and the corresponding column vector is detected in the spatial factor matrix according to the core tensor element index to serve as the initial mode basis vector. Each of the initial modal basis vectors is verified one by one to filter out pseudo-modes and noise modes that do not conform to physical laws, and the remaining real modal basis vectors are orthogonally normalized to obtain dancing modes of different orders.

[0011] Furthermore, the step of detecting the phase difference, amplitude ratio, and nonlinear exponent of each of the dancing modes to construct a dancing nonlinear feature vector includes: Modal orthogonality constraints are applied to the separated galloping modes to calculate the initial phase difference and amplitude ratio of the acceleration signals of different sensor units under the same order mode. With the goal of minimizing the cross-orthogonality error between modes, the initial phase difference and amplitude ratio are adaptively iteratively calibrated to obtain the calibrated phase difference and amplitude ratio. The calibration phase difference is divided into sliding windows according to a preset time step to calculate the eigenvalue evolution trajectory of each galloping mode within each time window. The eigenvalue cross-correlation coefficient between different order modes is combined to calculate the coupling nonlinearity index of the reaction mode coupling degree. The proportion of each galloping mode in the total vibration energy is used as the first weight, and the coupling nonlinearity index corresponding to each mode and the Pearson correlation coefficient of line fatigue damage are used as the second weight. The calibration phase difference and amplitude ratio and the coupling nonlinearity index are multiplied by the product of the first weight and the second weight of the corresponding order, respectively, and then spliced ​​in order of order to obtain the galloping nonlinear feature vector.

[0012] Furthermore, the step of calculating the electrodynamic force and magnetostrictive force generated during conductor galloping based on the galloping nonlinear eigenvector, combined with electric field strength and magnetic field strength data, to construct a finite element model of the transmission line includes: Based on the phase difference and nonlinear exponent in the galloping nonlinear eigenvector, the dynamic change trajectory of the air gap and the surface charge accumulation region during the galloping process of the conductor are identified to construct a three-dimensional transient electric field model. The three-dimensional transient electric field model is then solved using the Poisson equation and the charge transport equation to calculate the total electrodynamic field. The stress cycle characteristic parameters in the dancing nonlinear characteristic vector are detected to construct a model of the change of magnetostriction coefficient of the conductor material with fatigue damage accumulation. Combined with the actual detected ambient temperature and magnetic field strength data, the temperature coefficient and fatigue change coefficient in the magnetostriction equation are corrected accordingly to obtain the dynamic magnetostriction force distribution. A digital twin reference model of the transmission line is constructed, taking the total electrodynamic field, the dynamic magnetostrictive force distribution, and the acceleration and displacement data measured by the sensors as inputs. The material parameters and boundary constraints of the digital twin reference model are iteratively calibrated online using an extended Kalman filter algorithm to generate the corresponding finite element model.

[0013] Furthermore, the step of performing time series analysis on the finite element model based on the three-dimensional stress field to calculate the stress amplitude, stress cycle number, and stress concentration factor of each key component includes: The three-dimensional stress field is subjected to orthogonal decomposition of gobling mode matching to obtain the modal stress component field corresponding to each gobling mode. The stress gradient tensor of each finite element element and the modal stress energy ratio of each order are calculated based on the modal stress component field. The set of elements that meet the preset ratio threshold is selected as the key parts region for actual updating. Adaptive variable amplitude rainflow counting is performed on the multi-mode stress time series of the key part area to detect the number of stress cycles generated independently by each mode, and a corresponding stress cycle spectrum is generated according to the number of stress cycles, so that the amplitude of the stress cycle spectrum is used as the stress amplitude. The actual contact pressure distribution at the hardware connection interface and the contact area at the end of the insulator string is detected based on the three-dimensional stress field, so as to calculate the stress concentration factor.

[0014] The second aspect of the present invention proposes: An online monitoring and evaluation system for transmission line galloping, wherein the system comprises: The calculation module is used to deploy several sensors at equal intervals along the conductor axis in multiple spans of the transmission line to form corresponding multi-field coupled sensor units, and to calculate the phase coefficients between the acceleration signals detected by different sensor units in the same span based on a distributed clock synchronization algorithm, so as to construct a phase matrix. The detection module is used to perform eigenvalue decomposition on the phase matrix to separate different orders of dancing modes according to the magnitude of the eigenvalues, and to detect the phase difference, amplitude ratio and nonlinear exponent of each dancing mode to construct a dancing nonlinear feature vector. The construction module is used to calculate the electrodynamic force and magnetostrictive force generated during the galloping of the conductor based on the galloping nonlinear feature vector and combined with electric field strength and magnetic field strength data, so as to construct a finite element model of the transmission line. The mechanical load, the electrodynamic force and the magnetostrictive force are used as boundary condition inputs to reconstruct the three-dimensional stress field of the conductor, insulator string, hardware and tower. The generation module is used to perform time series analysis on the finite element model based on the three-dimensional stress field to calculate the stress amplitude, stress cycle number and stress concentration factor of each key part, and compare the calculation results with the allowable stress and fatigue limit of each key part to generate the corresponding galloping risk level and early warning information.

[0015] Furthermore, the step of calculating the phase coefficients between acceleration signals detected by different sensor units within the same range based on a distributed clock synchronization algorithm to construct a phase matrix includes: When each sensor unit is powered on and initialized, the initial clock synchronization is completed through a bidirectional timestamp exchange mechanism between adjacent sensor units to construct a distributed clock network within the range. Based on the distributed clock network, continuous wavelet transform is performed on the acceleration signals of each sensor unit to obtain wavelet coefficient matrices at different scales. The cross-correlation function of wavelet coefficients between any two sensor units at the same scale is calculated based on the wavelet coefficient matrix, and the time delay between the two models is determined by searching the peak position of the cross-correlation function, so as to convert the time delay into the phase difference at the corresponding frequency. A multi-scale weighted fusion algorithm is used to perform a weighted average of the phase differences calculated at different scales to obtain a comprehensive phase difference. Taking any sensor unit within the range as a reference node, the comprehensive phase differences of all other sensor units relative to the reference node are used to construct an initial phase vector according to the spatial arrangement of the sensors. The initial phase vector is then subjected to global consistency correction. The corrected initial phase vectors at different dancing frequencies are stacked in columns to construct the phase matrix.

[0016] Furthermore, the step of performing global consistency correction on the initial phase vector to stack the corrected initial phase vectors at different dancing frequencies column-wise to construct the phase matrix includes: Based on the unidirectional propagation characteristics of galloping traveling waves in transmission lines, a unidirectional increasing constraint condition for phase difference is established to perform piecewise linear fitting on the initial phase vector, identify the corresponding phase jump points, and use cubic spline interpolation to repair each of the phase jump points to obtain a continuous and unambiguous original phase curve. The original phase curve is subjected to non-subsampled curvelet transform to decompose it into curvelet coefficients of different scales and directions. Based on the energy distribution characteristics of the galloping signal, each curvelet coefficient is shrunk. The shrunk curvelet coefficients are then reconstructed by inverse non-subsampled curvelet transform to obtain the corrected phase curve. Based on the orthogonality principle between different orders of dancing modes, a modal orthogonality constraint matrix is ​​constructed, and the correction phase curve is orthogonalized using the modal orthogonality constraint matrix to calculate several orthogonalized phase vectors. The orthogonalized phase vectors are then stacked column-wise to construct the corresponding phase matrix.

[0017] Furthermore, the step of performing eigenvalue decomposition on the phase matrix to separate different orders of dancing modes based on the magnitude of the eigenvalues ​​includes: The phase matrices at different sampling times are stacked along the time dimension to construct a third-order spatiotemporal phase tensor containing spatial location, frequency components, and time evolution. The third-order spatiotemporal phase tensor is then decomposed by Tucker to obtain the tensor factor matrix, spatial factor matrix, and time factor matrix. The energy contribution of each element in the tensor factor matrix is ​​calculated to determine the core tensor element index of the dominant dancing mode, and the corresponding column vector is detected in the spatial factor matrix according to the core tensor element index to serve as the initial mode basis vector. Each of the initial modal basis vectors is verified one by one to filter out pseudo-modes and noise modes that do not conform to physical laws, and the remaining real modal basis vectors are orthogonally normalized to obtain dancing modes of different orders.

[0018] Furthermore, the step of detecting the phase difference, amplitude ratio, and nonlinear exponent of each of the dancing modes to construct a dancing nonlinear feature vector includes: Modal orthogonality constraints are applied to the separated galloping modes to calculate the initial phase difference and amplitude ratio of the acceleration signals of different sensor units under the same order mode. With the goal of minimizing the cross-orthogonality error between modes, the initial phase difference and amplitude ratio are adaptively iteratively calibrated to obtain the calibrated phase difference and amplitude ratio. The calibration phase difference is divided into sliding windows according to a preset time step to calculate the eigenvalue evolution trajectory of each galloping mode within each time window. The eigenvalue cross-correlation coefficient between different order modes is combined to calculate the coupling nonlinearity index of the reaction mode coupling degree. The proportion of each galloping mode in the total vibration energy is used as the first weight, and the coupling nonlinearity index corresponding to each mode and the Pearson correlation coefficient of line fatigue damage are used as the second weight. The calibration phase difference and amplitude ratio and the coupling nonlinearity index are multiplied by the product of the first weight and the second weight of the corresponding order, respectively, and then spliced ​​in order of order to obtain the galloping nonlinear feature vector.

[0019] Furthermore, the step of calculating the electrodynamic force and magnetostrictive force generated during conductor galloping based on the galloping nonlinear eigenvector, combined with electric field strength and magnetic field strength data, to construct a finite element model of the transmission line includes: Based on the phase difference and nonlinear exponent in the galloping nonlinear eigenvector, the dynamic change trajectory of the air gap and the surface charge accumulation region during the galloping process of the conductor are identified to construct a three-dimensional transient electric field model. The three-dimensional transient electric field model is then solved using the Poisson equation and the charge transport equation to calculate the total electrodynamic field. The stress cycle characteristic parameters in the dancing nonlinear characteristic vector are detected to construct a model of the change of magnetostriction coefficient of the conductor material with fatigue damage accumulation. Combined with the actual detected ambient temperature and magnetic field strength data, the temperature coefficient and fatigue change coefficient in the magnetostriction equation are corrected accordingly to obtain the dynamic magnetostriction force distribution. A digital twin reference model of the transmission line is constructed, taking the total electrodynamic field, the dynamic magnetostrictive force distribution, and the acceleration and displacement data measured by the sensors as inputs. The material parameters and boundary constraints of the digital twin reference model are iteratively calibrated online using an extended Kalman filter algorithm to generate the corresponding finite element model.

[0020] Furthermore, the step of performing time series analysis on the finite element model based on the three-dimensional stress field to calculate the stress amplitude, stress cycle number, and stress concentration factor of each key component includes: The three-dimensional stress field is subjected to orthogonal decomposition of gobling mode matching to obtain the modal stress component field corresponding to each gobling mode. The stress gradient tensor of each finite element element and the modal stress energy ratio of each order are calculated based on the modal stress component field. The set of elements that meet the preset ratio threshold is selected as the key parts region for actual updating. Adaptive variable amplitude rainflow counting is performed on the multi-mode stress time series of the key part area to detect the number of stress cycles generated independently by each mode, and a corresponding stress cycle spectrum is generated according to the number of stress cycles, so that the amplitude of the stress cycle spectrum is used as the stress amplitude. The actual contact pressure distribution at the hardware connection interface and the contact area at the end of the insulator string is detected based on the three-dimensional stress field, so as to calculate the stress concentration factor.

[0021] The third aspect of the present invention proposes: A computer includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the online monitoring and evaluation method for transmission line galloping as described above.

[0022] The fourth aspect of the present invention proposes: A readable storage medium having a computer program stored thereon, wherein the program, when executed by a processor, implements the online monitoring and evaluation method for transmission line galloping as described above.

[0023] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0024] Figure 1 A flowchart of the online monitoring and evaluation method for transmission line galloping provided in the first embodiment of the present invention; Figure 2 This is a structural block diagram of the online monitoring and evaluation system for power transmission line galloping provided in the third embodiment of the present invention.

[0025] The following detailed description, in conjunction with the accompanying drawings, will further illustrate the present invention. Detailed Implementation

[0026] To facilitate understanding of the present invention, a more complete description will be given below with reference to the accompanying drawings. Several embodiments of the invention are illustrated in the drawings. However, the invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.

[0027] It should be noted that when a component is said to be "fixed to" another component, it can be directly on the other component or there may be an intervening component. When a component is said to be "connected to" another component, it can be directly connected to the other component or there may be an intervening component. The terms "vertical," "horizontal," "left," "right," and similar expressions used in this document are for illustrative purposes only.

[0028] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0029] Please see Figure 1 The figure shows the online monitoring and assessment method for transmission line galloping provided in the first embodiment of the present invention. The online monitoring and assessment method for transmission line galloping provided in this embodiment can obtain stress amplitude, number of cycles and concentration factor through time series analysis, and generate risk level and early warning by comparing with material allowable stress and fatigue limit, which significantly improves the comprehensiveness, accuracy and timeliness of galloping hazard assessment.

[0030] Specifically, the first embodiment of the present invention provides: A method for online monitoring and evaluation of transmission line galloping, wherein the method includes: Step S10: Within multiple spans of the transmission line, several sensors are deployed at equal intervals along the conductor axis to form corresponding multi-field coupled sensor units. Based on a distributed clock synchronization algorithm, the phase coefficients between the acceleration signals detected by different sensor units within the same span are calculated to construct a phase matrix. It should be noted that transmission line galloping is essentially a low-frequency traveling wave phenomenon propagating along the conductor axis. Different galloping modes correspond to different wavelengths and spatial phase distributions: the first-order mode is a half-wave vibration, the second-order mode is a full-wave vibration, and higher-order modes correspond to shorter wavelengths. Single-sensor or non-equidistant deployment cannot satisfy the spatial sampling theorem, leading to severe mode aliasing and making it impossible to distinguish between adjacent modes. In this step, triaxial accelerometers are deployed at equal intervals within each monitoring span, with a spacing not exceeding 1 / 6 of the galloping wavelength of the highest-priority order (usually the 6th order). For UHV lines with a span of 500m, the sensor spacing is approximately 30m, with 16-18 sensor units deployed per span. Each unit integrates an electric field strength sensor (range 0-20kV / m, accuracy 1%), a magnetic field strength sensor (range 0-100mT, accuracy 0.5%), and a temperature sensor, forming a multi-field coupled sensing capability. Based on this, a distributed clock synchronization algorithm without GPS is adopted to achieve 0.5 microsecond-level time synchronization of all sensors within the span, ensuring that the acceleration signals collected by different sensors have a unified time reference. By calculating the phase difference between the signals of different sensors, a phase matrix with the dimension of "number of sensors × number of frequency components" is constructed to fully characterize the spatial phase distribution characteristics of conductor galloping, providing core data support for subsequent mode separation.

[0031] Step S20: Perform eigenvalue decomposition on the phase matrix to separate different orders of dancing modes according to the magnitude of the eigenvalues, and detect the phase difference, amplitude ratio and nonlinear exponent of each dancing mode to construct a dancing nonlinear feature vector. It should be noted that actual transmission line galloping is typically the result of superposition of 3-5 modes, with strong nonlinear energy exchange between these modes. Traditional Fourier transforms can only obtain frequency components and cannot separate spatial modes; empirical mode decomposition (EMD) suffers from severe mode aliasing and endpoint effects, failing to meet engineering accuracy requirements. This step utilizes the spatial orthogonality of galloping modes of different orders to perform eigenvalue decomposition on the phase matrix. The magnitude of the eigenvalues ​​corresponds to the energy proportion of the modes, and the eigenvectors correspond to the spatial distribution of the modes. Simultaneously, the phase difference, amplitude ratio, and intermodal coupling nonlinearity index of each mode are extracted to construct an 18-dimensional galloping nonlinear eigenvector, comprehensively characterizing the dynamic characteristics and nonlinearity of the galloping. This eigenvector not only contains the linear vibration characteristics of each mode but also includes energy exchange information between modes, enabling more accurate prediction of line fatigue damage risk.

[0032] Step S30: Based on the galloping nonlinear feature vector, combined with electric field strength and magnetic field strength data, calculate the corresponding electrodynamic force and magnetostrictive force generated during the galloping of the conductor to construct a finite element model of the transmission line. The mechanical load, the electrodynamic force and the magnetostrictive force are used as boundary condition inputs to reconstruct the three-dimensional stress field of the conductor, insulator string, hardware and tower. It should be noted that the conductor current in ultra-high voltage AC lines can reach 4000A. The alternating magnetic field generated by the alternating current will induce a magnetostrictive effect in the steel core of the steel-cored aluminum stranded wire, with magnetostrictive strain reaching the order of 10^-5 and corresponding stress exceeding 20MPa. Simultaneously, during conductor galloping, the air gap between the conductor and the tower changes from 10m to 30m, causing fluctuations in the electric field strength exceeding 30%. The resulting dynamic electrodynamic force amplitude can reach 15%-25% of the conductor's own weight. The frequencies of these two additional forces are completely consistent with the galloping frequency, creating a resonance effect with the mechanical load. This leads to an increase in stress amplitude at the fitting connections exceeding 40%, which is one of the main causes of fatigue fracture in fittings. This step reconstructs the three-dimensional galloping trajectory of the conductor based on the galloping nonlinear eigenvectors, thereby obtaining the dynamic change trajectory of the air gap and the surface charge accumulation region; combined with measured electric and magnetic field data, the dynamic electrodynamic field and magnetostrictive force distribution are accurately calculated; and these, along with mechanical loads such as wind load, conductor self-weight, and icing load, are used as boundary conditions to construct a multi-field coupled finite element model of the transmission line, reconstructing the three-dimensional stress field of the entire line, providing an accurate mechanical basis for subsequent fatigue damage assessment.

[0033] Step S40: Based on the three-dimensional stress field, perform time series analysis on the finite element model to calculate the stress amplitude, stress cycle number and stress concentration factor of each key part, and compare the calculation results with the allowable stress and fatigue limit of the material of each key part to generate the corresponding galloping risk level and early warning information.

[0034] It should be noted that this step targets eight key areas prone to fatigue failure, including areas with high incidence of conductor strand breakage, insulator string ends, hardware connection interfaces, and tower crossarm nodes, extracting continuous stress time series. An adaptive variable amplitude rainflow counting method is used to statistically analyze the number of stress cycles and amplitude distribution. Combined with the material's SN curve and Miner's linear cumulative damage rule, the cumulative fatigue damage is calculated. The calculation results are compared with the material's allowable stress and fatigue limit. Based on the degree of damage, the galloping risk is classified into four levels: blue (D<0.3), yellow (0.3≤D<0.7), orange (0.7≤D<0.95), and red (D≥0.95), where D represents the actual degree of damage. Corresponding early warning information and differentiated operation and maintenance suggestions are generated for different levels: blue warnings suggest strengthening daily inspections; yellow warnings suggest arranging special inspections within 3 days; orange warnings require temporary anti-galloping measures within 72 hours; and red warnings require immediate activation of load limiting or de-icing plans. This tiered early warning mechanism guides operation and maintenance personnel to allocate resources rationally and take preventative measures to avoid accidents.

[0035] Second Embodiment Furthermore, the step of calculating the phase coefficients between acceleration signals detected by different sensor units within the same range based on a distributed clock synchronization algorithm to construct a phase matrix includes: When each sensor unit is powered on and initialized, the initial clock synchronization is completed through a bidirectional timestamp exchange mechanism between adjacent sensor units to construct a distributed clock network within the range. Based on the distributed clock network, continuous wavelet transform is performed on the acceleration signals of each sensor unit to obtain wavelet coefficient matrices at different scales. The cross-correlation function of wavelet coefficients between any two sensor units at the same scale is calculated based on the wavelet coefficient matrix, and the time delay between the two models is determined by searching the peak position of the cross-correlation function, so as to convert the time delay into the phase difference at the corresponding frequency. A multi-scale weighted fusion algorithm is used to perform a weighted average of the phase differences calculated at different scales to obtain a comprehensive phase difference. Taking any sensor unit within the range as a reference node, the comprehensive phase differences of all other sensor units relative to the reference node are used to construct an initial phase vector according to the spatial arrangement of the sensors. The initial phase vector is then subjected to global consistency correction. The corrected initial phase vectors at different dancing frequencies are stacked in columns to construct the phase matrix.

[0036] It should be noted that traditional GPS synchronization suffers signal loss in heavily obstructed areas such as mountains, canyons, and forests, causing synchronization accuracy to drop to the millisecond level, which cannot meet the microsecond-level requirements for gobling phase calculation. This step employs a bidirectional timestamp exchange mechanism between adjacent sensor units: Sensor A sends a synchronization message with its local timestamp t1 to the adjacent sensor B. Sensor B receives this message, records its local timestamp t2, and replies with a response message containing t2 and t3 at time t3. Sensor A receives the response message at time t4. The clock deviation between the two sensors is calculated using the formula Δt = (t2 - t1 + t4 - t3) / 2. Through multiple iterations, clock synchronization of all sensor ranges is achieved, with a synchronization accuracy better than 0.5 microseconds. Furthermore, Morlet mother wavelet is used to perform continuous wavelet transform on the synchronized acceleration signal, converting the one-dimensional time-domain signal into a two-dimensional time-frequency domain wavelet coefficient matrix while preserving the signal's time and frequency information. This accurately captures the instantaneous frequency and phase changes of the gobling signal, solving the problem that Fourier transform cannot handle non-stationary signals.

[0037] The peak position of the cross-correlation function corresponds to the time delay between two signals. For stationary signals, this method has high accuracy; however, for non-stationary gobbling signals, single-scale cross-correlation analysis is easily affected by noise. This step calculates the cross-correlation function of wavelet coefficients between any two sensor units at each wavelet scale. Parabolic interpolation is used to fit the peak of the cross-correlation function with subsampling accuracy to obtain the precise time delay at that scale. Then, based on the center frequency f corresponding to that scale, the time delay Δt is converted into a phase difference φ using the formula φ=2πfΔt. Through multi-scale calculation, phase information of different frequency components can be captured, improving the robustness of phase difference calculation and maintaining high accuracy even in low signal-to-noise ratio environments.

[0038] The accuracy of phase difference calculation varies across different wavelet scales; scales with concentrated signal energy have higher accuracy, while noise-dominated scales have lower accuracy. This step assigns weights based on the energy proportion of wavelet coefficients at each scale: the higher the energy proportion, the greater the weight. A weighted average of the phase differences across different scales is then performed to obtain the comprehensive phase difference. Using the sensor at the midpoint of the span as the reference node, the comprehensive phase differences of all other sensor units relative to the reference node are used to construct an initial phase vector according to the spatial arrangement of the sensors. After global consistency correction to eliminate phase drift, the phase vectors at different times and frequencies are stacked column-wise to form the final phase matrix. Each row of this matrix corresponds to a sensor, and each column corresponds to a frequency component, fully characterizing the spatial phase distribution characteristics of conductor galloping and providing high-quality data input for subsequent mode separation.

[0039] Furthermore, the step of performing global consistency correction on the initial phase vector to stack the corrected initial phase vectors at different dancing frequencies column-wise to construct the phase matrix includes: Based on the unidirectional propagation characteristics of galloping traveling waves in transmission lines, a unidirectional increasing constraint condition for phase difference is established to perform piecewise linear fitting on the initial phase vector, identify the corresponding phase jump points, and use cubic spline interpolation to repair each of the phase jump points to obtain a continuous and unambiguous original phase curve. The original phase curve is subjected to non-subsampled curvelet transform to decompose it into curvelet coefficients of different scales and directions. Based on the energy distribution characteristics of the galloping signal, each curvelet coefficient is shrunk. The shrunk curvelet coefficients are then reconstructed by inverse non-subsampled curvelet transform to obtain the corrected phase curve. Based on the orthogonality principle between different orders of dancing modes, a modal orthogonality constraint matrix is ​​constructed, and the correction phase curve is orthogonalized using the modal orthogonality constraint matrix to calculate several orthogonalized phase vectors. The orthogonalized phase vectors are then stacked column-wise to construct the corresponding phase matrix.

[0040] It should be noted that the phase difference calculation results are usually limited to the range of [-π, π]. When the amplitude of the conductor galloping exceeds one wavelength, the actual phase difference will exceed 2π, causing a precipitous 2π jump in the phase curve. This phase ambiguity will seriously interfere with subsequent mode separation and may even lead to incorrect mode order identification. This step is based on the physical characteristic of the galloping traveling wave propagating unidirectionally along the conductor axis, establishing a hard constraint condition that "the phase difference increases monotonically from left to right along the conductor axis". Piecewise linear fitting is performed on the initial phase vector to identify all phase jump points that do not conform to the monotonically increasing law. Then, cubic spline interpolation is used to smooth and repair the jump points, expanding the phase difference from the folded interval of [-π, π] into a continuous absolute value interval, resulting in a continuous and unambiguous original phase curve. This method is entirely based on physical laws, requires no additional parameter adjustments, and can effectively solve the phase ambiguity problem under large amplitude galloping.

[0041] Traditional wavelet transform has limitations in handling curved features, only capturing point singularities and failing to effectively represent line singularities, while easily blurring the edge features of the phase curve during denoising. Non-subsampled curvelet transform, with its multi-scale and multi-directional characteristics, can represent curved signals more sparsely, resulting in superior denoising performance. This step performs non-subsampled curvelet transform on the original phase curve, decomposing it into curvelet coefficients at 5 scales and 8 directions. Based on the energy distribution difference between the galloping signal and noise, soft thresholding is applied to the noise-dominated small-scale coefficients, while retaining the signal-dominated large-scale coefficients. Then, the denoised corrected phase curve is reconstructed through inverse non-subsampled curvelet transform. This method effectively improves the signal-to-noise ratio of the phase curve while fully preserving key features such as phase transitions and trend changes.

[0042] Different orders of dancing modes possess strict orthogonality in space, therefore the corresponding phase vectors should also satisfy orthogonality constraints. However, due to the influence of sensor noise and modal coupling, the corrected phase curves may exhibit slight orthogonality deviations. This step constructs a modal orthogonality constraint matrix based on this principle, and uses the Gram-Schmidt orthogonalization method to orthogonalize the corrected phase curves, obtaining mutually orthogonal phase vectors. These orthogonalized phase vectors are then stacked column-wise to form the final phase matrix. The orthogonalized phase matrix better satisfies the preconditions for eigenvalue decomposition and effectively avoids modal aliasing.

[0043] Furthermore, the step of performing eigenvalue decomposition on the phase matrix to separate different orders of dancing modes based on the magnitude of the eigenvalues ​​includes: The phase matrices at different sampling times are stacked along the time dimension to construct a third-order spatiotemporal phase tensor containing spatial location, frequency components, and time evolution. The third-order spatiotemporal phase tensor is then decomposed by Tucker to obtain the tensor factor matrix, spatial factor matrix, and time factor matrix. The energy contribution of each element in the tensor factor matrix is ​​calculated to determine the core tensor element index of the dominant dancing mode, and the corresponding column vector is detected in the spatial factor matrix according to the core tensor element index to serve as the initial mode basis vector. Each of the initial modal basis vectors is verified one by one to filter out pseudo-modes and noise modes that do not conform to physical laws, and the remaining real modal basis vectors are orthogonally normalized to obtain dancing modes of different orders.

[0044] It should be noted that traditional eigenvalue decomposition can only process two-dimensional phase matrices at a single moment, failing to capture the evolution of gossiping modes over time and making it difficult to identify the generation, development, and disappearance of modes. This step stacks the phase matrices from 10 consecutive minutes (sampling frequency 10Hz, totaling 6000 sampling points) along the time dimension, constructing a third-order spatiotemporal phase tensor with dimensions of "number of sensors × number of frequency components × number of time steps". Then, High-Order Singular Value Decomposition (HOSVD) is used to perform Tucker decomposition on this tensor, yielding a core tensor, spatial factor matrix, frequency factor matrix, and temporal factor matrix. The core tensor reflects the interaction strength between different factors, the spatial factor matrix reflects the spatial distribution characteristics of gossiping, the frequency factor matrix reflects the frequency characteristics of gossiping, and the temporal factor matrix reflects the temporal evolution characteristics of gossiping. Through Tucker decomposition, the spatial, frequency, and temporal features of gossiping can be extracted simultaneously, providing more comprehensive information for subsequent dominant mode identification and dynamic tracking.

[0045] Each element in the core tensor corresponds to the energy contribution of a spatiotemporal frequency component. The larger the energy contribution, the greater the contribution of that component to the total gobbling energy, and the more likely it is to be the dominant mode. This step calculates the energy contribution of each element in the core tensor and selects core elements whose energy contribution exceeds 1% of the total energy as the core elements corresponding to the dominant modes. Then, based on the indices of these core elements, the corresponding column vectors are extracted from the spatial factor matrix as initial modal basis vectors. These initial modal basis vectors characterize the spatial phase distribution of each order of dominant gobbling modes and can accurately reflect the vibrational morphology of different orders of modes.

[0046] Tucker decomposition may generate some pseudo-modes or noise modes that do not conform to physical laws, such as modes with discontinuous spatial distribution, drastic frequency changes over time, or energy proportions below 1%. This step verifies the initial modal basis vectors one by one based on the three major physical characteristics of gowing modes: first, spatial continuity, the spatial phase distribution of the true mode should be continuous and smooth, without abrupt changes; second, frequency stability, the frequency fluctuation of the true mode should not exceed 5% within 10 minutes; and third, phase monotonicity, the phase of the true mode should change monotonically along the conductor axis. Modes that do not meet these three characteristics are judged as pseudo-modes or noise modes and are discarded. Finally, the remaining true modal basis vectors are orthogonally normalized to obtain the final gowing modes of different orders, ensuring the independence and physical rationality between modes.

[0047] Furthermore, the step of detecting the phase difference, amplitude ratio, and nonlinear exponent of each of the dancing modes to construct a dancing nonlinear feature vector includes: Modal orthogonality constraints are applied to the separated galloping modes to calculate the initial phase difference and amplitude ratio of the acceleration signals of different sensor units under the same order mode. With the goal of minimizing the cross-orthogonality error between modes, the initial phase difference and amplitude ratio are adaptively iteratively calibrated to obtain the calibrated phase difference and amplitude ratio. The calibration phase difference is divided into sliding windows according to a preset time step to calculate the eigenvalue evolution trajectory of each galloping mode within each time window. The eigenvalue cross-correlation coefficient between different order modes is combined to calculate the coupling nonlinearity index of the reaction mode coupling degree. The proportion of each galloping mode in the total vibration energy is used as the first weight, and the coupling nonlinearity index corresponding to each mode and the Pearson correlation coefficient of line fatigue damage are used as the second weight. The calibration phase difference and amplitude ratio and the coupling nonlinearity index are multiplied by the product of the first weight and the second weight of the corresponding order, respectively, and then spliced ​​in order of order to obtain the galloping nonlinear feature vector.

[0048] It should be noted that due to the influence of sensor noise and modal coupling, the initially calculated phase difference and amplitude ratio have certain errors, especially when the modal energies are similar, the errors will increase significantly. This step constructs a cross-orthogonal error function between modes, using the orthogonality between each order as a constraint; the gradient descent method is used to adaptively iteratively calibrate the initial phase difference and amplitude ratio to minimize the cross-orthogonal error, with the number of iterations set to 50. The calibrated phase difference error is less than 0.1 rad, and the amplitude ratio error is less than 2%, which can more accurately reflect the true characteristics of each galloping mode.

[0049] The strong nonlinearity of galloping is mainly reflected in the energy exchange and interaction between different modes. The higher the modal coupling degree, the stronger the destructiveness of galloping and the faster the fatigue damage accumulation. Extensive experimental data shows that when the modal coupling nonlinearity index exceeds 0.3, the fatigue damage rate of the fitting increases by more than two times. This step divides the calibration phase difference into sliding windows with a 1-minute time step, calculating the eigenvalue evolution trajectory of each mode within each window; then, it calculates the cross-correlation coefficients between the eigenvalues ​​of different orders of modes. The larger the cross-correlation coefficient, the more frequent the energy exchange between modes and the higher the coupling degree. Based on the cross-correlation coefficients, a coupling nonlinearity index is constructed to comprehensively quantify the nonlinearity of galloping. This index is a key indicator for evaluating galloping fatigue damage and can effectively distinguish between low-damage linear galloping and high-damage nonlinear galloping.

[0050] Different orders of galloping modes contribute differently to the total vibration energy and have different effects on fatigue damage: lower-order modes (1-3) have a larger energy proportion and a greater impact on overall displacement; higher-order modes (4-6) have a smaller energy proportion but higher frequency, and have a greater impact on fatigue damage. This step uses the energy proportion of each mode as the first weight to reflect the overall contribution of the mode; based on historical accident data, the Pearson correlation coefficient between the coupling nonlinearity index of each mode and the fatigue damage of the line is calculated as the second weight to reflect the impact of modal coupling on damage; then, the calibration phase difference, amplitude ratio, and coupling nonlinearity index are multiplied by the corresponding order weights, and concatenated in order of order to obtain an 18-dimensional galloping nonlinear feature vector. This feature vector not only contains the linear characteristics of each mode but also the nonlinear coupling characteristics between modes.

[0051] Furthermore, the step of calculating the electrodynamic force and magnetostrictive force generated during conductor galloping based on the galloping nonlinear eigenvector, combined with electric field strength and magnetic field strength data, to construct a finite element model of the transmission line includes: Based on the phase difference and nonlinear exponent in the galloping nonlinear eigenvector, the dynamic change trajectory of the air gap and the surface charge accumulation region during the galloping process of the conductor are identified to construct a three-dimensional transient electric field model. The three-dimensional transient electric field model is then solved using the Poisson equation and the charge transport equation to calculate the total electrodynamic field. The stress cycle characteristic parameters in the dancing nonlinear characteristic vector are detected to construct a model of the change of magnetostriction coefficient of the conductor material with fatigue damage accumulation. Combined with the actual detected ambient temperature and magnetic field strength data, the temperature coefficient and fatigue change coefficient in the magnetostriction equation are corrected accordingly to obtain the dynamic magnetostriction force distribution. A digital twin reference model of the transmission line is constructed, taking the total electrodynamic field, the dynamic magnetostrictive force distribution, and the acceleration and displacement data measured by the sensors as inputs. The material parameters and boundary constraints of the digital twin reference model are iteratively calibrated online using an extended Kalman filter algorithm to generate the corresponding finite element model.

[0052] It should be noted that traditional electrodynamic calculations typically assume a constant air gap, neglecting the influence of dynamic changes in the air gap during galloping, leading to calculation results that are underestimated by 20%-30%. This step reconstructs the three-dimensional galloping trajectory of the conductor based on the phase difference in the nonlinear eigenvector of the galloping, thereby obtaining the dynamic change trajectory of the air gap between the conductor and the tower, and between conductors themselves. Combined with the identification results of surface charge accumulation regions, a three-dimensional transient electric field model including the conductor, tower, and insulator is constructed. The Poisson equation and charge transport equation are solved using the finite element method to obtain the spatial electric field distribution and charge density distribution. Finally, the dynamic electrodynamic field per unit length of the conductor is calculated using the Lorentz force formula. This electrodynamic field varies periodically with the galloping period, and its amplitude is proportional to the galloping amplitude, reaching more than 25% of the conductor's own weight during large-amplitude galloping.

[0053] Alternating current in a conductor generates an alternating magnetic field, inducing magnetostriction in the steel core of the aluminum steel-cored wire, resulting in periodic magnetostrictive force. Traditional calculations typically use a constant magnetostriction coefficient, neglecting the effects of fatigue damage and temperature: fatigue damage can cause a 30%-50% decrease in the magnetostriction coefficient, and for every 10°C increase in temperature, the magnetostriction coefficient decreases by approximately 5%. This step constructs an exponential decay model of the magnetostriction coefficient with the accumulation of fatigue damage based on the stress cycle characteristic parameters in the galloping nonlinear eigenvector; combining measured ambient temperature and magnetic field strength data, the temperature coefficient and fatigue variation coefficient in the magnetostriction equation are corrected; finally, the dynamic magnetostrictive force distribution considering the effects of fatigue and temperature is calculated. This force generates additional alternating stress inside the conductor, which is one of the important causes of strand breakage in the conductor core.

[0054] Traditional finite element models are static models built offline, and their material parameters and boundary constraints deviate from actual operating conditions. For example, the elastic modulus of conductors decreases by 10%-15% with aging, and the stiffness of insulators changes by 5%-10% with temperature. This step first constructs a digital twin benchmark model based on the line design drawings, containing more than 3,000 finite element elements in 12 categories, including conductors, insulator strings, hardware, and towers. Then, the calculated electrodynamic field and magnetostrictive force distribution, along with the acceleration and displacement data measured by sensors, are used as observation inputs. The extended Kalman filter algorithm is used to iteratively update the 12 key parameters of the model (including the elastic modulus of conductors, damping coefficient, insulator stiffness, and hardware contact stiffness), with a calibration frequency of once every 10 minutes, which can accurately simulate the mechanical response of the line under the current operating conditions.

[0055] Furthermore, the step of performing time series analysis on the finite element model based on the three-dimensional stress field to calculate the stress amplitude, stress cycle number, and stress concentration factor of each key component includes: The three-dimensional stress field is subjected to orthogonal decomposition of gobling mode matching to obtain the modal stress component field corresponding to each gobling mode. The stress gradient tensor of each finite element element and the modal stress energy ratio of each order are calculated based on the modal stress component field. The set of elements that meet the preset ratio threshold is selected as the key parts region for actual updating. Adaptive variable amplitude rainflow counting is performed on the multi-mode stress time series of the key part area to detect the number of stress cycles generated independently by each mode, and a corresponding stress cycle spectrum is generated according to the number of stress cycles, so that the amplitude of the stress cycle spectrum is used as the stress amplitude. The actual contact pressure distribution at the hardware connection interface and the contact area at the end of the insulator string is detected based on the three-dimensional stress field, so as to calculate the stress concentration factor.

[0056] It should be noted that the total stress field is the result of the superposition of stresses from all galloping modes. Different modes contribute differently to the stress in different locations: lower-order modes mainly contribute to the stress in the conductor span, while higher-order modes mainly contribute to the stress at the fittings and insulator ends. Traditional methods often manually designate key locations, easily overlooking high-stress areas. This step, based on the orthogonality of galloping modes, performs orthogonal decomposition of the three-dimensional stress field using mode matching to obtain the modal stress component fields corresponding to each mode; then, it calculates the stress gradient tensor of each finite element element and the energy proportion of each modal stress; and selects the set of elements with a modal stress energy proportion exceeding 5% as the key areas of stress concentration. This method can automatically identify the areas most affected by galloping, avoiding the subjectivity and limitations of manual designation.

[0057] The stress generated by the galloping motion is a typical variable-amplitude random stress, and traditional constant-amplitude stress statistical methods cannot accurately calculate fatigue damage. This step employs an adaptive variable-amplitude rainflow counting method to process the multi-modal stress time series of key components: First, the counting threshold is automatically adjusted based on the stress amplitude to filter out small stress cycles with amplitudes less than the material's fatigue limit; then, stress cycles with different amplitudes are identified, and the number of stress cycles and corresponding amplitudes generated independently by each mode are statistically analyzed; a stress cycle spectrum containing amplitude, mean, and number of cycles is generated. This stress cycle spectrum is the core basis for calculating fatigue damage accumulation and can accurately reflect the impact of stress amplitude characteristics on fatigue life.

[0058] Contact areas such as fitting interfaces and insulator string ends are high-risk areas for fatigue failure in transmission lines, accounting for over 70% of galloping accidents. Uneven contact pressure distribution leads to severe stress concentration, with stress concentration factors reaching 3-5, significantly reducing fatigue life. Traditional stress analysis typically assumes ideal contact interfaces, neglecting the influence of contact conditions, resulting in severely underestimated stress calculations. This step extracts the actual contact pressure distribution in the contact area based on a three-dimensional stress field and calculates the contact pressure non-uniformity factor. Combining the geometry, surface roughness, and material properties of the contact area, Hertzian contact theory is used to calculate the stress concentration factor induced by the contact condition. This factor more accurately reflects the actual stress level of the connection.

[0059] Please see Figure 2 The third embodiment of the present invention provides: An online monitoring and evaluation system for transmission line galloping, wherein the system comprises: The calculation module is used to deploy several sensors at equal intervals along the conductor axis in multiple spans of the transmission line to form corresponding multi-field coupled sensor units, and to calculate the phase coefficients between the acceleration signals detected by different sensor units in the same span based on a distributed clock synchronization algorithm, so as to construct a phase matrix. The detection module is used to perform eigenvalue decomposition on the phase matrix to separate different orders of dancing modes according to the magnitude of the eigenvalues, and to detect the phase difference, amplitude ratio and nonlinear exponent of each dancing mode to construct a dancing nonlinear feature vector. The construction module is used to calculate the electrodynamic force and magnetostrictive force generated during the galloping of the conductor based on the galloping nonlinear feature vector and combined with electric field strength and magnetic field strength data, so as to construct a finite element model of the transmission line. The mechanical load, the electrodynamic force and the magnetostrictive force are used as boundary condition inputs to reconstruct the three-dimensional stress field of the conductor, insulator string, hardware and tower. The generation module is used to perform time series analysis on the finite element model based on the three-dimensional stress field to calculate the stress amplitude, stress cycle number and stress concentration factor of each key part, and compare the calculation results with the allowable stress and fatigue limit of each key part to generate the corresponding galloping risk level and early warning information.

[0060] Furthermore, the step of calculating the phase coefficients between acceleration signals detected by different sensor units within the same range based on a distributed clock synchronization algorithm to construct a phase matrix includes: When each sensor unit is powered on and initialized, the initial clock synchronization is completed through a bidirectional timestamp exchange mechanism between adjacent sensor units to construct a distributed clock network within the range. Based on the distributed clock network, continuous wavelet transform is performed on the acceleration signals of each sensor unit to obtain wavelet coefficient matrices at different scales. The cross-correlation function of wavelet coefficients between any two sensor units at the same scale is calculated based on the wavelet coefficient matrix, and the time delay between the two models is determined by searching the peak position of the cross-correlation function, so as to convert the time delay into the phase difference at the corresponding frequency. A multi-scale weighted fusion algorithm is used to perform a weighted average of the phase differences calculated at different scales to obtain a comprehensive phase difference. Taking any sensor unit within the range as a reference node, the comprehensive phase differences of all other sensor units relative to the reference node are used to construct an initial phase vector according to the spatial arrangement of the sensors. The initial phase vector is then subjected to global consistency correction. The corrected initial phase vectors at different dancing frequencies are stacked in columns to construct the phase matrix.

[0061] Furthermore, the step of performing global consistency correction on the initial phase vector to stack the corrected initial phase vectors at different dancing frequencies column-wise to construct the phase matrix includes: Based on the unidirectional propagation characteristics of galloping traveling waves in transmission lines, a unidirectional increasing constraint condition for phase difference is established to perform piecewise linear fitting on the initial phase vector, identify the corresponding phase jump points, and use cubic spline interpolation to repair each of the phase jump points to obtain a continuous and unambiguous original phase curve. The original phase curve is subjected to non-subsampled curvelet transform to decompose it into curvelet coefficients of different scales and directions. Based on the energy distribution characteristics of the galloping signal, each curvelet coefficient is shrunk. The shrunk curvelet coefficients are then reconstructed by inverse non-subsampled curvelet transform to obtain the corrected phase curve. Based on the orthogonality principle between different orders of dancing modes, a modal orthogonality constraint matrix is ​​constructed, and the correction phase curve is orthogonalized using the modal orthogonality constraint matrix to calculate several orthogonalized phase vectors. The orthogonalized phase vectors are then stacked column-wise to construct the corresponding phase matrix.

[0062] Furthermore, the step of performing eigenvalue decomposition on the phase matrix to separate different orders of dancing modes based on the magnitude of the eigenvalues ​​includes: The phase matrices at different sampling times are stacked along the time dimension to construct a third-order spatiotemporal phase tensor containing spatial location, frequency components, and time evolution. The third-order spatiotemporal phase tensor is then decomposed by Tucker to obtain the tensor factor matrix, spatial factor matrix, and time factor matrix. The energy contribution of each element in the tensor factor matrix is ​​calculated to determine the core tensor element index of the dominant dancing mode, and the corresponding column vector is detected in the spatial factor matrix according to the core tensor element index to serve as the initial mode basis vector. Each of the initial modal basis vectors is verified one by one to filter out pseudo-modes and noise modes that do not conform to physical laws, and the remaining real modal basis vectors are orthogonally normalized to obtain dancing modes of different orders.

[0063] Furthermore, the step of detecting the phase difference, amplitude ratio, and nonlinear exponent of each of the dancing modes to construct a dancing nonlinear feature vector includes: Modal orthogonality constraints are applied to the separated galloping modes to calculate the initial phase difference and amplitude ratio of the acceleration signals of different sensor units under the same order mode. With the goal of minimizing the cross-orthogonality error between modes, the initial phase difference and amplitude ratio are adaptively iteratively calibrated to obtain the calibrated phase difference and amplitude ratio. The calibration phase difference is divided into sliding windows according to a preset time step to calculate the eigenvalue evolution trajectory of each galloping mode within each time window. The eigenvalue cross-correlation coefficient between different order modes is combined to calculate the coupling nonlinearity index of the reaction mode coupling degree. The proportion of each galloping mode in the total vibration energy is used as the first weight, and the coupling nonlinearity index corresponding to each mode and the Pearson correlation coefficient of line fatigue damage are used as the second weight. The calibration phase difference and amplitude ratio and the coupling nonlinearity index are multiplied by the product of the first weight and the second weight of the corresponding order, respectively, and then spliced ​​in order of order to obtain the galloping nonlinear feature vector.

[0064] Furthermore, the step of calculating the electrodynamic force and magnetostrictive force generated during conductor galloping based on the galloping nonlinear eigenvector, combined with electric field strength and magnetic field strength data, to construct a finite element model of the transmission line includes: Based on the phase difference and nonlinear exponent in the galloping nonlinear eigenvector, the dynamic change trajectory of the air gap and the surface charge accumulation region during the galloping process of the conductor are identified to construct a three-dimensional transient electric field model. The three-dimensional transient electric field model is then solved using the Poisson equation and the charge transport equation to calculate the total electrodynamic field. The stress cycle characteristic parameters in the dancing nonlinear characteristic vector are detected to construct a model of the change of magnetostriction coefficient of the conductor material with fatigue damage accumulation. Combined with the actual detected ambient temperature and magnetic field strength data, the temperature coefficient and fatigue change coefficient in the magnetostriction equation are corrected accordingly to obtain the dynamic magnetostriction force distribution. A digital twin reference model of the transmission line is constructed, taking the total electrodynamic field, the dynamic magnetostrictive force distribution, and the acceleration and displacement data measured by the sensors as inputs. The material parameters and boundary constraints of the digital twin reference model are iteratively calibrated online using an extended Kalman filter algorithm to generate the corresponding finite element model.

[0065] Furthermore, the step of performing time series analysis on the finite element model based on the three-dimensional stress field to calculate the stress amplitude, stress cycle number, and stress concentration factor of each key component includes: The three-dimensional stress field is subjected to orthogonal decomposition of gobling mode matching to obtain the modal stress component field corresponding to each gobling mode. The stress gradient tensor of each finite element element and the modal stress energy ratio of each order are calculated based on the modal stress component field. The set of elements that meet the preset ratio threshold is selected as the key parts region for actual updating. Adaptive variable amplitude rainflow counting is performed on the multi-mode stress time series of the key part area to detect the number of stress cycles generated independently by each mode, and a corresponding stress cycle spectrum is generated according to the number of stress cycles, so that the amplitude of the stress cycle spectrum is used as the stress amplitude. The actual contact pressure distribution at the hardware connection interface and the contact area at the end of the insulator string is detected based on the three-dimensional stress field, so as to calculate the stress concentration factor.

[0066] The fourth embodiment of the present invention provides a computer, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the online monitoring and evaluation method for transmission line galloping as described above.

[0067] The fifth embodiment of the present invention provides a readable storage medium having a computer program stored thereon, wherein the program, when executed by a processor, implements the online monitoring and evaluation method for transmission line galloping as described above.

[0068] In summary, the online monitoring and assessment method and system for transmission line galloping provided in the above embodiments of the present invention can obtain stress amplitude, cycle number and concentration factor through time series analysis, and generate risk level and early warning by comparing with material allowable stress and fatigue limit, which significantly improves the comprehensiveness, accuracy and timeliness of galloping hazard assessment.

[0069] It should be noted that the above modules can be functional modules or program modules, and can be implemented through software or hardware. For modules implemented through hardware, the above modules can reside in the same processor; or the above modules can be located in different processors in any combination.

[0070] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-including system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0071] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0072] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0073] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0074] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A method for online monitoring and evaluation of transmission line galloping, characterized in that, The method includes: Within multiple spans of the transmission line, several sensors are deployed at equal intervals along the conductor axis to form corresponding multi-field coupled sensor units. Based on a distributed clock synchronization algorithm, the phase coefficients between the acceleration signals detected by different sensor units within the same span are calculated to construct a phase matrix. The phase matrix is ​​decomposed into eigenvalues ​​to separate different orders of dancing modes based on the magnitude of the eigenvalues, and the phase difference, amplitude ratio, and nonlinear exponent of each dancing mode are detected to construct a dancing nonlinear feature vector. Based on the nonlinear characteristic vector of the galloping, combined with the electric field strength and magnetic field strength data, the electrodynamic force and magnetostrictive force generated during the galloping of the conductor are calculated to construct a finite element model of the transmission line. The mechanical load, the electrodynamic force and the magnetostrictive force are used as boundary condition inputs to reconstruct the three-dimensional stress field of the conductor, insulator string, hardware and tower. Based on the three-dimensional stress field, a time series analysis is performed on the finite element model to calculate the stress amplitude, stress cycle number and stress concentration factor of each key part. The calculation results are then compared with the allowable stress and fatigue limit of the material of each key part to generate the corresponding galloping risk level and early warning information. The step of detecting the phase difference, amplitude ratio, and nonlinear exponent of each of the dancing modes to construct a dancing nonlinear feature vector includes: Modal orthogonality constraints are applied to the separated galloping modes to calculate the initial phase difference and amplitude ratio of the acceleration signals of different sensor units under the same order mode. With the goal of minimizing the cross-orthogonality error between modes, the initial phase difference and amplitude ratio are adaptively iteratively calibrated to obtain the calibrated phase difference and amplitude ratio. The calibration phase difference is divided into sliding windows according to a preset time step to calculate the eigenvalue evolution trajectory of each galloping mode within each time window. The eigenvalue cross-correlation coefficient between different order modes is combined to calculate the coupling nonlinearity index of the reaction mode coupling degree. The proportion of each galloping mode in the total vibration energy is used as the first weight, and the coupling nonlinearity index corresponding to each mode and the Pearson correlation coefficient of line fatigue damage are used as the second weight. The calibration phase difference and amplitude ratio and the coupling nonlinearity index are multiplied by the product of the first weight and the second weight of the corresponding order, respectively, and then spliced ​​in order of order to obtain the galloping nonlinear feature vector.

2. The method for online monitoring and evaluation of transmission line galloping according to claim 1, characterized in that, The step of calculating the phase coefficients between acceleration signals detected by different sensor units within the same gear range, based on a distributed clock synchronization algorithm, to construct a phase matrix includes: When each sensor unit is powered on and initialized, the initial clock synchronization is completed through a bidirectional timestamp exchange mechanism between adjacent sensor units to construct a distributed clock network within the range. Based on the distributed clock network, continuous wavelet transform is performed on the acceleration signals of each sensor unit to obtain wavelet coefficient matrices at different scales. The cross-correlation function of wavelet coefficients between any two sensor units at the same scale is calculated based on the wavelet coefficient matrix, and the time delay between the two models is determined by searching the peak position of the cross-correlation function, so as to convert the time delay into the phase difference at the corresponding frequency. A multi-scale weighted fusion algorithm is used to perform a weighted average of the phase differences calculated at different scales to obtain a comprehensive phase difference. Taking any sensor unit within the range as a reference node, the comprehensive phase differences of all other sensor units relative to the reference node are used to construct an initial phase vector according to the spatial arrangement of the sensors. The initial phase vector is then subjected to global consistency correction. The corrected initial phase vectors at different dancing frequencies are stacked in columns to construct the phase matrix.

3. The method for online monitoring and evaluation of transmission line galloping according to claim 2, characterized in that, The step of performing global consistency correction on the initial phase vector to stack the corrected initial phase vectors at different galloping frequencies column-wise to construct the phase matrix includes: Based on the unidirectional propagation characteristics of galloping traveling waves in transmission lines, a unidirectional increasing constraint condition for phase difference is established to perform piecewise linear fitting on the initial phase vector, identify the corresponding phase jump points, and use cubic spline interpolation to repair each of the phase jump points to obtain a continuous and unambiguous original phase curve. The original phase curve is subjected to non-subsampled curvelet transform to decompose it into curvelet coefficients of different scales and directions. Based on the energy distribution characteristics of the galloping signal, each curvelet coefficient is shrunk. The shrunk curvelet coefficients are then reconstructed by inverse non-subsampled curvelet transform to obtain the corrected phase curve. Based on the orthogonality principle between different orders of dancing modes, a modal orthogonality constraint matrix is ​​constructed, and the correction phase curve is orthogonalized using the modal orthogonality constraint matrix to calculate several orthogonalized phase vectors. The orthogonalized phase vectors are then stacked column-wise to construct the corresponding phase matrix.

4. The method for online monitoring and evaluation of transmission line galloping according to claim 1, characterized in that, The step of performing eigenvalue decomposition on the phase matrix to separate different orders of dancing modes based on the magnitude of the eigenvalues ​​includes: The phase matrices at different sampling times are stacked along the time dimension to construct a third-order spatiotemporal phase tensor containing spatial location, frequency components, and time evolution. The third-order spatiotemporal phase tensor is then decomposed by Tucker to obtain the tensor factor matrix, spatial factor matrix, and time factor matrix. The energy contribution of each element in the tensor factor matrix is ​​calculated to determine the core tensor element index of the dominant dancing mode, and the corresponding column vector is detected in the spatial factor matrix according to the core tensor element index to serve as the initial mode basis vector. Each of the initial modal basis vectors is verified one by one to filter out pseudo-modes and noise modes that do not conform to physical laws, and the remaining real modal basis vectors are orthogonally normalized to obtain dancing modes of different orders.

5. The method for online monitoring and evaluation of transmission line galloping according to claim 1, characterized in that, The steps for constructing a finite element model of a transmission line by calculating the electrodynamic force and magnetostrictive force generated during conductor galloping based on the galloping nonlinear characteristic vector and combining electric field strength and magnetic field strength data include: Based on the phase difference and nonlinear exponent in the galloping nonlinear eigenvector, the dynamic change trajectory of the air gap and the surface charge accumulation region during the galloping process of the conductor are identified to construct a three-dimensional transient electric field model. The three-dimensional transient electric field model is then solved using the Poisson equation and the charge transport equation to calculate the total electrodynamic field. The stress cycle characteristic parameters in the dancing nonlinear characteristic vector are detected to construct a model of the change of magnetostriction coefficient of the conductor material with fatigue damage accumulation. Combined with the actual detected ambient temperature and magnetic field strength data, the temperature coefficient and fatigue change coefficient in the magnetostriction equation are corrected accordingly to obtain the dynamic magnetostriction force distribution. A digital twin reference model of the transmission line is constructed, taking the total electrodynamic field, the dynamic magnetostrictive force distribution, and the acceleration and displacement data measured by the sensors as inputs. The material parameters and boundary constraints of the digital twin reference model are iteratively calibrated online using an extended Kalman filter algorithm to generate the corresponding finite element model.

6. The method for online monitoring and evaluation of transmission line galloping according to claim 1, characterized in that, The steps of performing time series analysis on the finite element model based on the three-dimensional stress field to calculate the stress amplitude, stress cycle number, and stress concentration factor of each key component include: The three-dimensional stress field is subjected to orthogonal decomposition of gobling mode matching to obtain the modal stress component field corresponding to each gobling mode. The stress gradient tensor of each finite element element and the modal stress energy ratio of each order are calculated based on the modal stress component field. The set of elements that meet the preset ratio threshold is selected as the key parts region for actual updating. Adaptive variable amplitude rainflow counting is performed on the multi-mode stress time series of the key part area to detect the number of stress cycles generated independently by each mode, and a corresponding stress cycle spectrum is generated according to the number of stress cycles, so that the amplitude of the stress cycle spectrum is used as the stress amplitude. The actual contact pressure distribution at the hardware connection interface and the contact area at the end of the insulator string is detected based on the three-dimensional stress field, so as to calculate the stress concentration factor.

7. An online monitoring and evaluation system for transmission line galloping, characterized in that, The system is used to implement the online monitoring and evaluation method for transmission line galloping as described in any one of claims 1 to 6, the system comprising: The calculation module is used to deploy several sensors at equal intervals along the conductor axis in multiple spans of the transmission line to form corresponding multi-field coupled sensor units, and to calculate the phase coefficients between the acceleration signals detected by different sensor units in the same span based on a distributed clock synchronization algorithm, so as to construct a phase matrix. The detection module is used to perform eigenvalue decomposition on the phase matrix to separate different orders of dancing modes according to the magnitude of the eigenvalues, and to detect the phase difference, amplitude ratio and nonlinear exponent of each dancing mode to construct a dancing nonlinear feature vector. The construction module is used to calculate the electrodynamic force and magnetostrictive force generated during the galloping of the conductor based on the galloping nonlinear feature vector and combined with electric field strength and magnetic field strength data, so as to construct a finite element model of the transmission line. The mechanical load, the electrodynamic force and the magnetostrictive force are used as boundary condition inputs to reconstruct the three-dimensional stress field of the conductor, insulator string, hardware and tower. The generation module is used to perform time series analysis on the finite element model based on the three-dimensional stress field to calculate the stress amplitude, stress cycle number and stress concentration factor of each key part, and compare the calculation results with the allowable stress and fatigue limit of each key part to generate the corresponding galloping risk level and early warning information.

8. A computer comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the online monitoring and evaluation method for transmission line galloping as described in any one of claims 1 to 6.

9. A readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements the online monitoring and evaluation method for transmission line galloping as described in any one of claims 1 to 6.

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