Partial discharge quantitative calibration method based on modal decomposition and frequency weighting

Abstract

The invention relates to the field of partial discharge quantitative calibration and electromagnetic simulation analysis, in particular to a partial discharge quantitative calibration method based on modal decomposition and frequency weighting. The method comprises the following steps: acquiring a structure parameter, a defect excitation parameter, an ultrahigh frequency sensor position parameter and a sensitive direction parameter, establishing an electromagnetic model, and performing finite difference time domain simulation to obtain a frequency domain response spectrum; obtaining each modal frequency domain component set through modal expansion and waveguide eigenmode orthogonal projection; performing inverse transformation and wavelet transformation on each modal frequency domain component set to obtain time-frequency energy distribution, and extracting total energy, energy weighted arrival time, dispersion degree and frequency energy spectrum to generate a modal characteristic quantity set; and normalizing the modal characteristic quantity set to obtain a modal quality factor weight and generate a frequency correlation weight function, synthesizing an equivalent calibration transfer function, inverting a discharge current in combination with an actually measured voltage frequency spectrum, and integrating to obtain an apparent discharge quantity. According to the invention, the quantification reliability of apparent discharge capacity can be effectively improved.

Description

Technical Field

[0001] This invention relates to the field of partial discharge quantization calibration and electromagnetic simulation analysis, and in particular to a partial discharge quantization calibration method based on modal decomposition and frequency weighting. Background Technology

[0002] In gas-insulated switchgear (GIS) equipment, partial discharge is one of the most critical electrical characteristics in the early development of insulation defects. The electromagnetic, acoustic, chemical, and optical signals it generates can often be detected before serious equipment failures occur. Therefore, accurate identification and quantitative assessment of partial discharge are crucial for ensuring the safe operation of the power grid. Among existing detection methods, ultra-high frequency (UHF) detection has become the most practical partial discharge monitoring technology in operating GIS due to its strong anti-interference capability, suitability for online monitoring, high temporal resolution, and high positioning accuracy.

[0003] However, achieving quantitative diagnosis in UHF detection presents numerous challenges. GIS (Gas Insulator System) is composed of complex components such as a metal shell, central conductor, basin-type or cylindrical insulators, partitions, expansion joints, flange seams, and branch structures. Its geometry and material parameters vary significantly depending on voltage level, manufacturer, and installation method. These structural characteristics significantly alter the electromagnetic propagation environment within the cavity, causing the electromagnetic waves excited by partial discharge to exhibit pronounced multimodal propagation behavior. Multiple modes, including the TEM fundamental mode, TE11, TM01, and other higher-order modes, propagate simultaneously, and their energy coupling, attenuation characteristics, and dispersion characteristics are all heavily influenced by structural factors. While traditional electromagnetic simulation methods (such as FDTD and FEM) can visualize and analyze electromagnetic wave propagation phenomena in GIS, the simulation models are often based on idealized geometries, homogeneous material assumptions, and limited boundary conditions, making it difficult to fully cover the various loss mechanisms and subtle structural differences in actual GIS equipment. Therefore, although the simulated electric field response approximates the actual situation in terms of trends, it is difficult to directly use for absolute value calibration of the discharge quantity, especially failing to achieve unified quantification across different structural types.

[0004] On the other hand, relying solely on experimental methods for sensor calibration also has significant limitations. First, establishing a full-scale experimental platform applicable to different voltage levels and structural types of GIS is costly and requires a considerable amount of time for device-by-device calibration. Second, many GIS devices are installed in field conditions, and their internal structures cannot be disassembled or modified, making it difficult to conduct controlled standard defect experiments. Third, experimental calibration results are usually only applicable to a specific structure and cannot be transferred to other GIS types, resulting in the long-term inability to establish a unified UHF quantitative calibration system for the industry.

[0005] Current technologies still face significant bottlenecks in the quantification of UHF partial discharge detection: a lack of a unified technical framework that integrates simulation and experiment; difficulty in sharing calibration results across different GIS models; and a lack of physically traceable standardized quantitative indicators for sensor output. Therefore, there is an urgent need for a UHF quantitative calibration method that is universally applicable across different GIS structures and integrates simulation and experimental data. This method should fully leverage the structural transferability advantages of simulation models while compensating for simulation deficiencies through experimental calibration, achieving a standardized mapping relationship between UHF sensor output amplitude and actual discharge quantity. This would provide a solid foundation for the quantitative diagnosis, condition assessment, and intelligent operation and maintenance of GIS equipment.

[0006] Furthermore, in the field of partial discharge quantization calibration and electromagnetic simulation analysis, existing schemes for partial discharge quantization calibration based on GIS structural parameters, defect excitation parameters, UHF sensor position parameters, and sensitive direction parameters typically establish a calibration transfer link based on the sensor electric field time-domain signal or the acquired measured voltage time-domain signal. This involves obtaining the voltage spectrum through transformation and inverting it using the calibration transfer function to obtain the discharge current spectrum, followed by inverse transformation to obtain the discharge current time-domain signal and integration to obtain the apparent discharge quantity. These methods suffer from limitations such as frequency domain response spectrum aliasing, sensitivity of the transfer link to GIS structural parameters and UHF sensor position parameters, and inversion fluctuations caused by changes in the frequency energy spectrum with defect excitation parameters. Existing methods often employ a single propagation channel assumption or rely on empirical frequency band selection and fixed weight processing. When the sensitive direction parameters deviate or the GIS structural parameters differ, phenomena such as electric field time-domain signal distortion and frequency domain response spectrum peak-valley drift easily occur, making it difficult to maintain a consistent calculation scope for the equivalent calibration transfer function, thus causing fluctuations in the correspondence between the voltage spectrum and the discharge current spectrum. Regarding the correlation modeling between the frequency domain response spectrum and the frequency domain component sets of each mode, existing technologies generally lack unified solution constraints for the modal expansion model and the orthogonal projection of waveguide eigenmodes. At the same time, there is a lack of a general processing procedure for the normalization of the modal feature set and the frequency axis consistency of the frequency-related weight function. It is difficult to form a traceable continuous link in the acquisition, transformation, inversion, inverse transformation, integration and other stages, which leads to deviations in the quantitative calibration of apparent discharge under different operating conditions. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention provides a partial discharge quantization calibration method based on mode decomposition and frequency weighting, comprising: S100: Obtain GIS structural parameters, defect excitation parameters, UHF sensor position parameters and sensitive direction parameters, establish an electromagnetic model and perform FDTD time-domain simulation, extract the sensor electric field time-domain signal and transform it to obtain the frequency domain response spectrum; S200: Based on the frequency domain response spectrum, solve the mode coefficient sets of TEM mode, TE11 mode and TM01 mode by orthogonal projection of waveguide eigenmodes, and generate the frequency domain component sets of each mode; S300. Based on the frequency domain component sets of each modality, perform wavelet transform to obtain the time-frequency energy distribution, extract the total energy, energy-weighted arrival time, dispersion and frequency energy spectrum, and generate a modal feature set. S400. Normalize the modal feature set to obtain the modal quality factor weights, and combine them with the frequency energy spectrum to generate a frequency-related weight function; S500: Input the frequency-related weighting function into the transfer function synthesis module, weight and fuse the transfer functions of each mode to generate an equivalent calibration transfer function, collect the measured voltage time-domain signal and transform it to obtain the voltage spectrum, invert the voltage spectrum and the equivalent calibration transfer function to obtain the discharge current spectrum, inversely transform it to obtain the discharge current time-domain signal and integrate it to obtain the apparent discharge quantity.

[0008] Furthermore, the electromagnetic model described in S100 includes an inner conductor, a shell, an insulator, and a phase splitter, and the FDTD time-domain simulation sets a PML absorption boundary.

[0009] Furthermore, the defect excitation parameters mentioned in S100 adopt the parameters of the spike defect model, which consists of the radius of curvature of the conductor surface tip, the tip height, the defect location, and the charge pulse time parameters.

[0010] Furthermore, the defect excitation parameters mentioned in S100 adopt the parameters of the needle plate defect model, which consists of the needle electrode radius, needle plate spacing, defect location and charge pulse time parameters.

[0011] Furthermore, the modal expansion model described in S200 constructs a set of sampling points on the cross section of the GIS waveguide. The set of sampling points covers the neighborhood of the inner conductor, the neighborhood of the inner wall of the outer shell, and the neighborhood of the insulator. Based on the set of sampling points, the orthogonal projection of the intrinsic modes is used to solve the set of modal coefficients.

[0012] Furthermore, the mother wavelet of the wavelet transform described in S300 is the Morlet wavelet, and the time-frequency energy distribution is obtained by the square of the modulus of the wavelet coefficients.

[0013] Furthermore, the energy weighted arrival time mentioned in S300 is obtained by weighted summation of the time-frequency energy distribution on the time axis, and the dispersion is obtained by the second central moment of the time-frequency energy distribution on the time axis.

[0014] Furthermore, the normalization described in S400 adopts maximum and minimum value normalization, and the normalization object includes the total energy, the energy weighted arrival time, and the dispersion.

[0015] Furthermore, the modal quality factor weights mentioned in S400 are obtained by combining the total energy normalized value, the energy-weighted arrival time normalized value, and the dispersion normalized value. The combination relationship includes an energy positive correlation term, an arrival time penalty term, and a dispersion penalty term.

[0016] Furthermore, the frequency-related weighting function in S500 is obtained by multiplying the modal quality factor weights by the frequency energy spectrum, and normalization is performed at each frequency point; the voltage spectrum is shielded in the frequency band where the amplitude of the equivalent calibration transfer function is less than five percent of its maximum amplitude.

[0017] The key innovations of this invention include: (1) Input the frequency domain response spectrum into the mode expansion model, solve the mode coefficient set of TEM mode, TE11 mode and TM01 mode by waveguide eigenmode orthogonal projection, and generate the frequency domain component set of each mode based on the mode coefficient set, so that the frequency domain response spectrum forms a corresponding frequency domain component expression in the dimensions of TEM mode, TE11 mode and TM01 mode.

[0018] (2) The frequency domain component set of each mode is inversely transformed to obtain the time domain component of each mode, and wavelet transform is performed to obtain the time-frequency energy distribution. The total energy, energy weighted arrival time, dispersion and frequency energy spectrum are extracted from the time-frequency energy distribution to generate a modal feature set. The modal feature set is further normalized to obtain the modal quality factor weight, and the frequency energy spectrum is combined to generate a frequency-related weight function so that the weight has an adaptive organization form in both the modal dimension and the frequency dimension.

[0019] (3) Input the frequency-related weighting function into the transfer function synthesis module, weight and fuse each mode transfer function to generate an equivalent calibration transfer function, and collect the measured voltage time-domain signal to obtain the voltage spectrum. Invert the voltage spectrum and the equivalent calibration transfer function to obtain the discharge current spectrum, inversely transform the discharge current time-domain signal and integrate it to obtain the apparent discharge quantity, so that the equivalent calibration transfer function and the voltage spectrum are connected in the same inversion link to the apparent discharge quantity.

[0020] The following are its main beneficial effects: (1) Compared with the existing scheme that directly processes the frequency domain response spectrum, the present invention solves the modal coefficient set on the TEM mode, the TE11 mode and the TM01 mode respectively by orthogonally projecting the modal expansion model and the waveguide eigenmodes, and outputs the frequency domain component set of each mode. This makes the subsequent steps of inverse transformation and feature extraction of each mode frequency component set have a clear modal correspondence, so that the transfer function synthesis module has a verifiable modal input basis when performing weighted fusion of each mode transfer function.

[0021] (2) Compared with the existing schemes that use fixed weights or only assign weights to a single dimension for each modal transfer function, the present invention obtains the time-frequency energy distribution and forms the modal feature set by wavelet transform based on the time-domain components of each modality. Then, the modal quality factor weight is obtained by normalizing the modal feature set and combined with the frequency energy spectrum to generate the frequency-related weight function. The frequency-related weight function reflects the differences between the total energy, the energy weighted arrival time, the dispersion and the frequency energy spectrum in each mode. This allows the subsequent weighted fusion of each modal transfer function and the inversion of the discharge current spectrum to have weight support consistent with the modal feature set.

[0022] (3) Compared with the inversion path in the existing scheme that directly corresponds the voltage spectrum with a single calibration transfer function, the present invention drives the transfer function synthesis module to generate the equivalent calibration transfer function through the frequency-related weight function, and completes the inversion of the voltage spectrum and the equivalent calibration transfer function in the same link to obtain the discharge current spectrum, inverse transform to obtain the discharge current time domain signal, and integrates to obtain the apparent discharge quantity. This ensures that the process of obtaining the apparent discharge quantity remains consistent with the weighted fusion of the modal transfer functions under the conditions of changes in the GIS structure parameters, the defect excitation parameters, the UHF sensor position parameters, and the sensitive direction parameters. Attached Figure Description

[0023] Figure 1 A flowchart illustrating a partial discharge quantization calibration method based on modal decomposition and frequency weighting provided in this application embodiment; Figure 2 A geometric structure diagram of a simulation model of a cylindrical GIS provided in this application embodiment; Figure 3 A diagram showing the setting of PML boundaries on the outer layer of a model, provided in an embodiment of this application; Figure 4 This application provides a schematic diagram of the time-domain waveform and frequency-domain spectrum of a sensor electric field under typical defect excitation. Figure 5This is a schematic diagram of the modal decomposition results of a typical field point provided in an embodiment of this application; Figure 6 A schematic diagram of an excitation source provided in an embodiment of this application; Figure 7 A waveform and spectrum diagram of an excitation source provided in an embodiment of this application; Figure 8 A simulation result of the electric field at field point 1 and a schematic diagram of its CWT decomposition are provided for embodiments of this application; Figure 9 A simulation result of the electric field at point 2 and a schematic diagram of its CWT decomposition are provided for embodiments of this application; Figure 10 A simulation result of the electric field at point 3 and a schematic diagram of its CWT decomposition are provided for embodiments of this application; Figure 11 A field point 4 electric field simulation result and its CWT decomposition diagram are provided for embodiments of this application; Figure 12 A simulation result of the electric field at point 5 and a schematic diagram of its CWT decomposition are provided for embodiments of this application; Figure 13 This is a schematic diagram of an equivalent transfer function for field point 1 provided in an embodiment of this application. Detailed Implementation

[0024] Example 1: Refer to Figure 1 This is a flowchart illustrating a partial discharge quantization calibration method based on mode decomposition and frequency weighting provided in an embodiment of the present invention. The flowchart may include at least steps S100-S500: S100: Obtain GIS structural parameters, defect excitation parameters, UHF sensor position parameters and sensitive direction parameters, establish an electromagnetic model and perform FDTD time-domain simulation, extract the sensor electric field time-domain signal and transform it to obtain the frequency domain response spectrum; S200: Based on the frequency domain response spectrum, solve the mode coefficient sets of TEM mode, TE11 mode and TM01 mode by orthogonal projection of waveguide eigenmodes, and generate the frequency domain component sets of each mode; S300. Based on the frequency domain component sets of each modality, perform wavelet transform to obtain the time-frequency energy distribution, extract the total energy, energy-weighted arrival time, dispersion and frequency energy spectrum, and generate a modal feature set. S400. Normalize the modal feature set to obtain the modal quality factor weights, and combine them with the frequency energy spectrum to generate a frequency-related weight function; S500: Input the frequency-related weighting function into the transfer function synthesis module, weight and fuse the transfer functions of each mode to generate an equivalent calibration transfer function, collect the measured voltage time-domain signal and transform it to obtain the voltage spectrum, invert the voltage spectrum and the equivalent calibration transfer function to obtain the discharge current spectrum, inversely transform it to obtain the discharge current time-domain signal and integrate it to obtain the apparent discharge quantity.

[0025] S100: Obtain GIS structural parameters, defect excitation parameters, UHF sensor position parameters and sensitive direction parameters, establish an electromagnetic model and perform FDTD time-domain simulation, extract the sensor electric field time-domain signal and transform it to obtain the frequency domain response spectrum; The S100 process is executed collaboratively by a parameter access unit, a model assembly unit, a simulation calculation unit, an observation extraction unit, and a data solidification unit. Specifically, the parameter access unit reads GIS structural parameters, defect excitation parameters, UHF sensor position parameters, and sensitive direction parameters from equipment structure ledgers, design drawing data, on-site survey records, and sensor installation records. GIS stands for Gas Insulated Switchgear, and UHF stands for Ultra High Frequency. The GIS structural parameters are defined as a set of geometric and dielectric information describing the coaxial cavity and key components, including the outer diameter of the inner conductor, the inner diameter of the outer shell, the axial length, the dimensions of the branch cavity connection, the flange seam and opening boundaries, the shape and installation position of the insulator, the shape and installation position of the phase splitter, the shape and installation position of the conductor support, and the relative permittivity and conductivity parameters of the gas medium. The defect excitation parameters are defined as a set of geometric and temporal information of the equivalent excitation source of partial discharge, including defect type identifier, defect location coordinates, excitation source geometric dimensions, and pulse timing information. The defect type identifier can be either a spike defect model or a needle-plate defect model. The spike defect model consists of the conductor surface tip curvature radius, tip height, defect location, and charge pulse time parameters. The needle-plate defect model consists of the needle electrode radius, needle-plate spacing, defect location, and charge pulse time parameters. The UHF sensor position parameters are defined as a set of spatial constraint information for the sensor's installation within the GIS cavity, including the installation port number, flange reference surface, axial distance, circumferential angle, and installation depth. The sensitive direction parameters are defined as a set of spatial orientation information for the sensor's equivalent receiving direction, including pitch angle, yaw angle, and a reference coordinate system definition. The reference coordinate system is jointly determined by the inner conductor axis direction, the outer shell radial direction, and the circumferential direction. The parameter access unit performs consistency checks on the GIS structural parameters and UHF sensor location parameters. The checks include geometric unit dimensions, coordinate origin definition, component assembly closure, and sensor mounting port validity. It also performs completeness checks on the defect excitation parameters, verifying the match between the defect type identifier and its corresponding geometric parameter set, that the defect location coordinates fall within the reachable region of the electromagnetic model, and that the pulse timing information meets simulation sampling constraints. If the checks fail, the parameter access unit generates a parameter anomaly record and writes it to the simulation task log. Simultaneously, it marks the task status as pending completion and terminates task dispatch from the simulation calculation unit. If the checks pass, the parameter access unit solidifies the GIS structural parameters, defect excitation parameters, UHF sensor location parameters, and sensitive direction parameters into a simulation input configuration structure and submits this structure to the model assembly unit as the basis for subsequent assembly.

[0026] The model assembly unit constructs an electromagnetic model based on the simulation input configuration structure. This electromagnetic model is defined as a three-dimensional discretized computational object containing geometric entities, material properties, boundary conditions, excitation sources, and observation points. Specifically, the model assembly unit assembles the inner conductor, outer shell, insulator, and phase splitter into a coaxial waveguide cavity, and performs geometric refinement on the flange seam and opening boundaries, mapping the defect location coordinates to the inner conductor surface or the insulator neighborhood to form a locally refined defect region. At the material property level, the model assembly unit assigns the relative permittivity and conductivity parameters of the gas medium to the cavity medium volume element, assigns the dielectric parameters of the insulator material to the insulator entity, and sets the inner conductor and outer shell as conductive boundaries. At the excitation source level, the model assembly unit assembles a spike defect model or a needle-plate defect model according to the defect type identifier, and writes the charge pulse time parameters into the excitation waveform generator to form an equivalent excitation source for partial discharge. At the observation point level, the model assembly unit determines the set of observation points based on the UHF sensor's position parameters. This set includes spatial sampling points at the sensor mounting port, the sensor's sensitive direction projection surface, and neighboring buffer sampling points. A direction projection operator is constructed based on the sensitive direction parameters. This operator maps the three-component electric field to scalar electric field observations along the sensitive direction. After assembly, the model assembly unit generates the electromagnetic model structure and transfers it to the simulation calculation unit.

[0027] The simulation unit performs FDTD time-domain simulation on the electromagnetic model structure. FDTD stands for Finite Difference Time Domain, and its operation includes mesh generation, time stepping, boundary absorption, and stability monitoring. Specifically, the simulation unit generates a 3D mesh based on the local refinement region of the defect and the set of observation points. The mesh generation rules include a global mesh size upper limit, a mesh refinement ratio for the defect region, and a mesh refinement ratio for the sensor mounting port neighborhood. Mesh quality indicators include element aspect ratio constraints and a minimum element volume threshold. Subsequently, the simulation unit calculates the time step and writes it into the simulation numerical configuration structure. The simulation numerical configuration structure also includes the number of iteration steps, excitation injection time, observation sampling period, and data buffer window length. Regarding boundary conditions, the simulation unit sets a PML absorbing boundary at the outer boundary of the electromagnetic model. The PML stands for Perfectly Matched Layer, which includes the absorption layer thickness, layered conductivity profile, and updated equation coefficient table. At each time step, the simulation unit statistically analyzes the boundary absorbed energy and records it as a boundary energy monitoring sequence. When the boundary energy monitoring sequence exhibits a rebound characteristic, a boundary parameter rollback mechanism is triggered. This mechanism restores the absorption layer thickness and conductivity profile to the previous stable version and restarts the current simulation task. During time stepping, the simulation unit injects the equivalent excitation source of partial discharge into the discrete grid points corresponding to the defect location, performs alternating updates of the electric and magnetic fields, and simultaneously performs numerical stability monitoring. Numerical stability monitoring includes field overflow detection, energy conservation residual detection, and iteration error growth rate detection. When the monitoring triggers an anomaly threshold, the simulation unit generates a simulation anomaly record and saves it to the simulation task log. Simultaneously, the simulation input configuration structure and simulation numerical configuration structure are written to the version repository to form an immutable snapshot, and the task status is marked as abnormal termination.

[0028] The observation extraction unit extracts the sensor electric field time-domain signal from the time-domain field data stream output by the simulation calculation unit. This sensor electric field time-domain signal is defined as a scalar time-series sequence of the electric field vector at the observation point set after mapping by the direction projection operator. Specifically, the observation extraction unit reads the three-component electric field at the observation point set according to the observation sampling period, performs sensitive direction projection, and performs time-series stitching to form the output product sensor electric field time-domain signal. Simultaneously, it writes the spatial label of the observation point set, the sampling time label, and the simulation task identifier into the observation metadata structure. The observation extraction unit performs DC component removal, endpoint windowing, and bandwidth constraint filtering on the sensor electric field time-domain signal. The bandwidth constraint filtering is determined by the grid spatial resolution and the time step. When preprocessing detects saturation truncation or noise floor drift, the observation extraction unit writes the abnormal interval label into the signal quality label structure and solidifies the signal quality label structure along with the sensor electric field time-domain signal for subsequent link reference. Subsequently, the observation extraction unit performs a frequency domain transformation on the sensor's electric field time-domain signal. The frequency domain transformation uses a discrete Fourier transform to obtain the output product's frequency domain response spectrum. The frequency domain response spectrum is defined as a structured combination of the frequency sampling point sequence and its corresponding amplitude spectrum and phase spectrum, and is indexed and associated with the observation metadata structure. The data solidification unit writes the simulation input configuration structure, electromagnetic model structure, simulation numerical configuration structure, sensor electric field time-domain signal, frequency domain response spectrum, observation metadata structure, and signal quality labeling structure into the calibration database, and generates a task-level traceability record. The traceability record includes a configuration version number, runtime fingerprint, and log summary. The version management strategy adopts an incremental configuration version number and immutable snapshot storage.

[0029] In the engineering implementation scenario, a GIS cavity structure containing insulators and phase splitters is selected as the source of GIS structural parameters. The UHF sensor location parameters at the sensor mounting port and the field-calibrated sensitive direction parameters are selected as the observation configuration. A conductor surface spike defect model is selected as the defect excitation parameter. The simulation task scheduling unit creates task S100 when a structural parameter version change event is triggered. Subsequently, the simulation calculation unit completes mesh generation, boundary absorption configuration, and time-domain step calculation. The observation extraction unit outputs the sensor electric field time-domain signal and frequency-domain response spectrum and stores them in a database. The frequency-domain response spectrum, as the input source of task S200, is written into the frequency-domain response spectrum input position of task S200 for use by the modal expansion model. The sensor electric field time-domain signal, observation metadata structure, and signal quality labeling structure are associated and saved as consistency verification and traceability data, and are indexed with the task for cross-referencing in subsequent main steps.

[0030] In summary, the technical effects of this step are as follows: By unifying and verifying GIS structural parameters, defect excitation parameters, UHF sensor position parameters, and sensitive direction parameters, an auditable simulation input configuration structure is formed to drive the assembly of the electromagnetic model. Through the coordinated operation of FDTD time-domain simulation and PML absorbing boundary, a sensor electric field time-domain signal consistent with the structure propagation conditions is obtained. By performing frequency-domain transformation on the sensor electric field time-domain signal, a structured frequency-domain response spectrum is formed and entered into the S200 mode expansion link.

[0031] S200: Based on the frequency domain response spectrum, solve the mode coefficient sets of TEM mode, TE11 mode and TM01 mode by orthogonal projection of waveguide eigenmodes, and generate the frequency domain component sets of each mode; The S200 is executed collaboratively by a modal expansion model management unit, a cross-sectional sampling construction unit, an intrinsic mode field library unit, an orthogonal projection solution unit, a component reconstruction unit, and a result solidification unit. Its input source is the frequency domain response spectrum output by the S100, which is associated with the same simulation task identifier and observation metadata structure through a task index. Specifically, after receiving the frequency domain response spectrum, the modal expansion model management unit performs a frequency axis consistency check. The frequency axis consistency check includes a monotonicity check of the frequency sampling point sequence, a completeness check of the frequency resolution and the number of sampling points, and a check for missing amplitude and phase spectra. The check results are written to the modal expansion task log. When a frequency sampling point sequence is broken or the amplitude and phase spectra are missing, the modal expansion model management unit marks the frequency domain response spectrum as unprojectable and triggers a backtracking request. The backtracking request is sent back to the corresponding task record of the observation extraction unit of the S100 for recalculation or resampling. When the verification is successful, the modal expansion model management unit solidifies the frequency domain response spectrum into a modal expansion input buffer, and reads the spatial label of the observation point set at the sensor mounting port from the observation metadata structure as the geometric constraint input of the cross-sectional sampling construction unit. At the same time, it reads the electromagnetic model structure summary that is consistent with the simulation task identifier from the calibration database. The electromagnetic model structure summary includes the cross-sectional geometric contours of the inner conductor and the shell, the boundary curves of the insulator crossing region, and the dielectric parameter index, thereby forming the minimum parameter set for subsequent waveguide eigenmode solving and projection calculation.

[0032] The cross-sectional sampling construction unit constructs a GIS waveguide cross-sectional sampling point set under the constraints of the electromagnetic model structure summary. This GIS waveguide cross-sectional sampling point set is defined as a spatial set of sampling points distributed along the cross-sectional region. The sampling point set covers the neighborhood of the inner conductor, the neighborhood of the inner wall of the outer shell, and the neighborhood of the insulator, and maintains a spatially mappable relationship with the observation point set. Specifically, the cross-sectional sampling construction unit first determines the cross-sectional position, which is jointly determined by the axial distance of the mounting port corresponding to the UHF sensor position parameters and the flange reference surface. Then, a basic sampling grid is generated within this cross-section, and boundary fitting processing is performed. This boundary fitting processing projects the sampling points onto a defined distance band between the neighborhood of the outer surface of the inner conductor and the neighborhood of the inner wall of the outer shell. Simultaneously, the sampling point density is increased in the insulator neighborhood according to the dielectric boundary curvature, resulting in a sampling point distribution that satisfies projection stability. The cross-sectional sampling construction unit performs deduplication and minimum spacing constraint checks on the sampling point set and solidifies the point coordinates, point weights, and area labels of the points into a cross-sectional sampling configuration structure. The version number of the cross-sectional sampling configuration structure is bound and saved with the simulation task identifier, forming an auditable and reusable basis for subsequent batch projections.

[0033] The intrinsic mode field library unit generates or reads the waveguide intrinsic mode set based on the cross-sectional sampling configuration structure. The waveguide intrinsic mode set is defined as a set of modal field distributions consistent with the boundary conditions of the coaxial cavity, including the intrinsic field distributions and propagation constant tables for TEM, TE11, and TM01 modes. The TEM mode is a transverse electromagnetic mode, the TE11 mode is a transverse electric mode, and the TM01 mode is a transverse magnetic mode. In one embodiment, the intrinsic mode field library unit operates using a pre-calculated mode field library method. The pre-calculated mode field library is retrieved from the standard cross-sectional parameter index of the same type of GIS, and the modal field distribution is discretized onto the cross-sectional sampling point set to form a modal sampling matrix. In another embodiment, it operates using an online solution method. The online solution method performs intrinsic mode boundary value solving based on the boundary contours of the inner conductor and the outer shell, as well as the insulator dielectric parameter index, and outputs the modal field distribution, which is then mapped onto the cross-sectional sampling point set to form a modal sampling matrix. To adapt to the frequency sampling point sequence of the frequency domain response spectrum, the intrinsic mode field library unit performs interpolation alignment on the propagation constant table and records the interpolation strategy identifier. The interpolation strategy identifier and the cross-sectional sampling configuration structure are jointly entered into the result solidification unit for subsequent review and version traceability.

[0034] After receiving the frequency domain response spectrum, the cross-sectional sampling configuration structure, and the modal sampling matrix, the orthogonal projection solving unit solves for the modal coefficient set by orthogonal projection according to the waveguide eigenmodes. Specifically, the orthogonal projection solving unit first maps the frequency domain response spectrum to a sampling point response vector at each frequency sampling point. The sampling point response vector is formed by the amplitude spectrum and phase spectrum under the influence of sampling point weights to form a complex domain observation. Then, based on modal orthogonality, a projection inner product operation is constructed. The projection inner product operation is jointly determined by the sampling point weights, boundary condition consistency weights, and insulator neighborhood medium weights, thereby obtaining the projection results corresponding to the TEM mode, TE11 mode, and TM01 mode at the same frequency sampling point. The orthogonal projection solving unit performs linear solving on the projection results to obtain the modal coefficient set, which is defined as the set of coefficient sequences corresponding to the TEM mode, TE11 mode, and TM01 mode respectively on the frequency sampling point sequence. To suppress the impact of noise-labeled intervals on coefficient solving, the orthogonal projection solving unit reads the signal quality label structure fixed in S100 and applies weight reduction processing to the corresponding frequency intervals. Simultaneously, it performs continuity constraint checks on the coefficient sequence. When a sharp peak occurs, the continuity constraint check triggers a local smoothing and recalculation strategy, and the trigger position is written into the modal coefficient quality record. This modal coefficient quality record, along with the modal coefficient set, is fixed together, forming the basis for linkage with abnormal frequency bands in subsequent time-frequency analysis stages.

[0035] The component reconstruction unit generates frequency domain component sets for each mode based on the modal coefficient set and the modal sampling matrix. Each frequency domain component set is defined as a set of frequency domain component sequences corresponding to the TEM mode, TE11 mode, and TM01 mode respectively on the frequency sampling point sequence. It consists of a component amplitude sequence, a component phase sequence, and a component complex spectrum sequence for each mode, and retains the alignment marker with the same frequency axis as the frequency domain response spectrum. Specifically, at each frequency sampling point, the component reconstruction unit multiplies the modal coefficient set with the field response template of the corresponding mode and projects it onto the direction projection operator corresponding to the sensitive direction parameter to form a modal component spectrum consistent with the sensor observation definition. Then, the component spectrum of each mode is checked for consistency with the original frequency domain response spectrum at the amplitude and phase layer. The check includes the amplitude and phase deviation threshold after component superposition and the consistency of phase expansion. If the check fails, it is recorded as a reconstruction anomaly and sent back to the orthogonal projection solution unit to trigger parameter back-off recalculation. The result solidification unit writes the output product modal coefficient set and each modal frequency domain component set into the calibration database, and writes each modal frequency domain component set into the input position of each modal frequency domain component set of S300 for inverse transform and wavelet transform to call. At the same time, it saves the modal coefficient quality record, the cross-sectional sampling configuration structure version number and the interpolation strategy identifier of the intrinsic mode field library unit as accompanying metadata, forming a traceable link across the main steps.

[0036] In summary, the technical effects of this step are as follows: By mapping the frequency domain response spectrum to the sampling point set of the GIS waveguide cross section and performing orthogonal projection of the waveguide eigenmodes, a set of modal coefficients consistent with the propagation mechanism is formed. Under the constraint of the modal field distribution, the modal coefficient set is reconstructed into components, forming a structured set of frequency domain components for each mode, aligned with the frequency axis. By inputting each set of frequency domain components into the input position of S300, the link from the overall frequency domain response to the decomposable modal characterization is completed.

[0037] S300. Based on the frequency domain component sets of each modality, perform wavelet transform to obtain the time-frequency energy distribution, extract the total energy, energy-weighted arrival time, dispersion and frequency energy spectrum, and generate a modal feature set. The S300 is executed collaboratively by an inverse transform processing unit, a time-frequency analysis configuration unit, a wavelet transform calculation unit, a feature extraction unit, and a result solidification unit. Its input source is the frequency domain component sets of each mode output by the S200, and an associated index is established through the same simulation task identifier and observation metadata structure. Specifically, after receiving the frequency domain component sets of each mode, the inverse transform processing unit first performs a frequency axis consistency check. The check objects include the monotonicity of the frequency sampling point sequence, the length consistency of the component amplitude sequence and the component phase sequence, and the expansion continuity of the component phase sequence. The check conclusion is written to the feature calculation task log. When a break in the frequency sampling point sequence or an abnormal jump in the phase sequence is detected, the inverse transform processing unit writes an abnormal interval label and triggers a backtracking recalculation request. The backtracking recalculation request points to the corresponding task record of the component reconstruction unit of the S200. Upon successful verification, the inverse transform processing unit performs an inverse discrete Fourier transform on each modal frequency domain component set to obtain the modal time domain components. Each modal time domain component is defined as a set of time domain waveform sequences corresponding to the TEM mode, TE11 mode, and TM01 mode, respectively, under a unified sampling period and unified start and end times. A modal identifier, sampling period, and start and end time labels are written into each time domain waveform. The inverse transform processing unit performs endpoint extension and baseline correction on each modal time domain component. Endpoint extension uses either mirror extension or zero-value extension, while baseline correction uses a sliding window mean elimination method. Simultaneously, it reads the signal quality labeling structure fixed in S100 and applies a weighting mask to the labeled interval. This weighting mask participates in the weight accumulation during subsequent time-frequency energy calculations to prevent noise-labeled intervals from dominating the output of characteristic quantities.

[0038] The time-frequency analysis configuration unit assembles a time-frequency analysis configuration structure after the inverse transform processing unit outputs the time-domain components of each modality. This configuration structure is defined as a structured combination of the mother wavelet, scale sequence, time sampling parameters, and boundary processing parameters required for wavelet transform calculation. The mother wavelet is a Morlet wavelet, the scale sequence is generated by jointly mapping the frequency sampling point sequence and the sampling period, and the boundary processing parameters are determined by the endpoint extension method, window length, and overlap length. The minimum set of the scale sequence includes a lower scale bound, an upper scale bound, and a scale stepping rule. The lower and upper scale bounds are obtained by constraining the effective bandwidth and sampling period of each modal time-domain component. The scale stepping rule consists of logarithmic equal-segmentation or linear equidistant segmentation. The time sampling parameters include the number of sampling points and time labels, and the boundary processing parameters include the extension length and boundary suppression coefficient. The time-frequency analysis configuration unit writes the time-frequency analysis configuration structure into the version repository and generates a configuration version number. The configuration version number is bound and saved with the simulation task identifier, forming the basis for subsequent batch recalculation and audit playback. When a change in sampling period or frequency sampling point sequence is detected, the time-frequency analysis configuration unit triggers the increment of the configuration version number and freezes the old version structure. The new version structure enters the wavelet transform calculation unit as the only input configuration.

[0039] The wavelet transform computation unit performs continuous wavelet transform on each modal time-domain component based on the time-frequency analysis configuration structure, and outputs a wavelet coefficient matrix. Specifically, the wavelet transform computation unit generates Morlet wavelet kernels scale-by-scale according to the scale sequence and performs convolution operations with each modal time-domain component. The convolution operation uses boundary processing parameters to suppress and update the kernels in the endpoint extension region, thereby obtaining the wavelet coefficient matrix on the time axis and scale axis. The wavelet transform computation unit performs modulus-square operation on the wavelet coefficient matrix to generate a time-frequency energy distribution. The time-frequency energy distribution is defined as a two-dimensional distribution structure representing energy density on the time axis and frequency axis, where the frequency axis is mapped from the scale sequence and aligned with the frequency sampling point sequence. To ensure cross-modal comparability, the wavelet transform computation unit performs energy normalization preprocessing on the time-frequency energy distribution. The normalization preprocessing adopts the method of normalizing the total energy within the same mode or the maximum value of the same frequency axis, and the normalization method identifier is written into the time-frequency energy metadata structure. When the normalization preprocessing produces a zero-energy interval or an abnormal peak interval, the wavelet transform computation unit triggers an abnormal smoothing strategy. The abnormal smoothing strategy adopts a combination of median filtering and neighborhood interpolation, and the triggered interval is written into the time-frequency anomaly record.

[0040] After the wavelet transform calculation unit outputs the time-frequency energy distribution, the feature extraction unit extracts the total energy, energy-weighted arrival time, dispersion, and frequency energy spectrum, and generates a set of modal features. The total energy is defined as the weighted sum of the time-frequency energy distribution along the time and frequency axes. The feature extraction unit performs a discrete integral approximation based on the time sampling parameters and frequency axis mapping parameters in the time-frequency energy metadata structure and outputs the total energy field. The energy-weighted arrival time is defined as the first-order moment feature of the time-frequency energy distribution along the time axis. The feature extraction unit first performs marginal accumulation of the time-frequency energy distribution along the frequency axis to obtain the time energy sequence, then performs a weighted summation of the time energy sequence according to the time label and divides it by the total energy to obtain the energy-weighted arrival time field. Simultaneously, it reads the signal quality label structure, performs weighted accumulation on the labeled intervals, and writes the arrival time confidence flag. The dispersion is defined as the second-order central moment feature of the time energy sequence around the energy-weighted arrival time. The feature extraction unit calculates the second-order central moment of the time energy sequence and outputs the dispersion field, adding a normalization flag and a window length flag to the dispersion field for subsequent cross-task alignment. The frequency energy spectrum is defined as the marginalized accumulation result of the time-frequency energy distribution along the time axis. The feature extraction unit accumulates the time-frequency energy distribution along the time axis to obtain the frequency energy spectrum field, and performs bandwidth clipping and smoothing on the frequency energy spectrum field. The bandwidth clipping boundary is determined by the lower and upper scale bounds in the time-frequency analysis configuration structure, and the smoothing is completed by the sliding window mean method. The feature extraction unit writes the total energy field, energy-weighted arrival time field, dispersion field, and frequency energy spectrum field corresponding to the TEM mode, TE11 mode, and TM01 mode into the modal feature set. The modal feature set also includes the simulation task identifier, modal identifier, time-frequency analysis configuration structure version number, and time-frequency anomaly record index, forming the minimum input set for subsequent weight calculation. In the extended implementation, the modal feature set also includes time-frequency anomaly records and arrival time confidence indicators as quality screening fields for subsequent link linkage calls. As a result, the solidification unit writes the modal feature set into the calibration database and into the modal feature set input position of S400. At the same time, it establishes an index mapping of the frequency energy spectrum field at the frequency energy spectrum input position of S400 to ensure that S400 can directly call the normalized and frequency-related weight function.

[0041] In the engineering implementation scenario, the modal frequency domain component sets output by S200 are derived from the orthogonal projection solution of the sampling point set of the cross section corresponding to the sensor mounting port. The inverse transform processing unit performs discrete Fourier inverse transform on each modal frequency domain component set to obtain the modal time domain components. The time-frequency analysis configuration unit freezes the time-frequency analysis configuration structure composed of Morlet wavelet and scale sequence and then delivers it to the wavelet transform calculation unit for operation. The wavelet transform calculation unit outputs the time-frequency energy distribution and delivers it to the feature extraction unit to calculate the total energy field, energy weighted arrival time field, dispersion field and frequency energy spectrum field. Finally, the result solidification unit forms the modal feature set and writes it into the input position of S400, realizing the cross-main step connection from the modal frequency domain component sets of S200 to the modal feature set of S400.

[0042] In summary, this step transforms the frequency domain component sets of each mode into time domain components under unified sampling conditions, and constructs the time-frequency energy distribution through continuous wavelet transform driven by Morlet wavelets. Based on the time-frequency energy distribution, the total energy, energy-weighted arrival time, dispersion, and frequency energy spectrum are extracted to form a structured modal feature set. This modal feature set serves as the direct source of the input positions for the S400 modal feature set and the frequency energy spectrum, supporting the continuous operation of subsequent normalization and weight function generation processes.

[0043] S400. Normalize the modal feature set to obtain the modal quality factor weights, and combine them with the frequency energy spectrum to generate a frequency-related weight function; The S400 is executed collaboratively by a feature access and verification unit, a normalization processing unit, a modal quality factor weight generation unit, a frequency correlation weight function generation unit, an anomaly handling and recording unit, and a version management and result solidification unit. Its input source is the modal feature set output by the S300. The modal feature set includes the total energy field, energy weighted arrival time field, dispersion field, and frequency energy spectrum field corresponding to the TEM mode, TE11 mode, and TM01 mode, and carries the simulation task identifier, modal identifier, time-frequency analysis configuration structure version number, and time-frequency anomaly record index. Specifically, after receiving the modal feature set, the feature access and verification unit first performs field integrity verification. The field integrity verification includes non-empty verification of the total energy field, consistency verification of the time label of the energy weighted arrival time field, consistency verification of the window length identifier of the dispersion field, and frequency axis alignment identifier verification of the frequency energy spectrum field. The verification results are written to the weight generation task log. When there is a missing field, inconsistent frequency axis alignment identifier, or the time-frequency abnormal record index indicates that the abnormal interval coverage is too large, the abnormal processing and recording unit generates an abnormal alarm entry and triggers a backtracking request. The backtracking request points to the task record corresponding to the result solidification unit of S300. The backtracking request carries the abnormal interval label and the modality identifier that needs to be recalculated, thereby forming an automated recalculation trigger condition that links across main steps. When the verification passes, the feature access and verification unit solidifies the modal feature set into a weight generation input cache and reads the minimum input set from the modal feature set. The minimum input set consists of the total energy field, the energy-weighted arrival time field, the dispersion field, and the frequency energy spectrum field. The minimum input set is used as a required field in the subsequent calculation link to participate in the generation of modal quality factor weights and frequency-related weight functions. Other accompanying fields, such as the time-frequency anomaly record index and the arrival time confidence flag, are used as optional extended fields to participate in anomaly screening and stability control.

[0044] The normalization processing unit performs maximum and minimum value normalization on the modal feature set. Maximum and minimum value normalization is defined as a method of mapping the same feature field to a range of zero to one within the same simulation task identifier range according to its minimum and maximum values. The normalization object includes the total energy field, the energy-weighted arrival time field, and the dispersion field. Specifically, the normalization processing unit aggregates the total energy fields of the TEM mode, TE11 mode, and TM01 mode according to the simulation task identifier to form a total energy aggregation set, calculates the minimum and maximum values ​​on the total energy aggregation set, and then maps the total energy fields of each mode to obtain the total energy normalized value field and writes it into the normalization result record. The normalization processing unit uses the same method to normalize the energy-weighted arrival time field and the dispersion field, obtaining the energy-weighted arrival time normalized value field and the dispersion normalized value field. The normalization processing unit introduces an anomaly screening threshold when calculating the minimum and maximum values. This threshold is constrained by the time-frequency anomaly record index and the arrival time confidence flag. When the anomaly screening threshold is hit, the corresponding modality's feature field is marked as an anomaly sample and written to the anomaly sample registration table. This table is managed by the anomaly processing and recording unit and archived by the version management and result solidification unit. The normalization processing unit also writes a normalization range identifier and a field scale identifier to the normalization result record. The normalization range identifier describes the source range of the minimum and maximum values, while the field scale identifier describes the inheritance relationship between the time label and the window length identifier, thus maintaining the traceability and auditability of subsequent weight calculations.

[0045] The modal quality factor weight generation unit generates modal quality factor weights after the normalization processing unit outputs the total energy normalized value field, the energy-weighted arrival time normalized value field, and the dispersion normalized value field. These modal quality factor weights are defined as scalar weights characterizing the reliability of modal contributions and correspond one-to-one with modal identifiers. Specifically, the modal quality factor weight generation unit is equipped with a quality factor configuration structure, which includes an energy positive correlation term configuration, an arrival time penalty term configuration, and a dispersion penalty term configuration. The energy positive correlation term configuration is directly driven by the total energy normalized value field. The arrival time penalty term configuration is driven by the energy-weighted arrival time normalized value field and converted into penalty components according to a penalty mapping table. The dispersion penalty term configuration is driven by the dispersion normalized value field and converted into penalty components according to a penalty mapping table. The modal quality factor weight generation unit performs a combination operation on the energy positive correlation term, the arrival time penalty term, and the dispersion penalty term to obtain the initial quality factor value. It then applies non-negative truncation and upper bound constraints to the initial quality factor value. The upper bound constraints are limited by the weight range identifier in the quality factor configuration structure, thereby avoiding weight distortion caused by anomalous samples. The modal quality factor weight generation unit normalizes and merges the initial quality factor values ​​corresponding to the TEM mode, TE11 mode, and TM01 mode. Normalization and merging are defined as summing and normalizing the initial quality factor values ​​of each mode under the same simulation task identifier and outputting the modal quality factor weight field, ensuring that the modal quality factor weight field is comparable within the same simulation task identifier. When outputting the modal quality factor weight field, the modal quality factor weight generation unit simultaneously outputs the quality factor configuration structure version number and the anomalous sample registration table index, and writes the modal quality factor weight field into the modal quality factor weight result set. This result set serves as the input source for the frequency correlation weight function generation unit, and is bound to the simulation task identifier by the version management and result solidification unit.

[0046] After obtaining the modal quality factor weight result set and the frequency energy spectrum field, the frequency-related weight function generation unit generates a frequency-related weight function. This frequency-related weight function is defined as a sequence of weight functions that allocate contributions to different modes along the frequency axis and corresponds one-to-one with the mode identifier. Specifically, the frequency-related weight function generation unit first performs a frequency axis consistency check on the frequency energy spectrum field. The frequency axis consistency check verifies the frequency axis alignment identifier against the frequency axis mapping parameters output by S300. After successful verification, the frequency energy spectrum fields of the TEM mode, TE11 mode, and TM01 mode are written into the spectrum cache structure. The frequency-related weight function generation unit generates modal weight allocation values ​​point-by-point according to the frequency sampling point sequence. The modal weight allocation values ​​are obtained by performing a dot product mapping between the modal quality factor weight field and the corresponding mode's frequency energy spectrum field. At each frequency sampling point, the modal weight allocation values ​​for the three modes are normalized. This normalization process is defined as summing and normalizing the modal weight allocation values ​​for the three modes at the same frequency sampling point and outputting the frequency-related weight function field, ensuring a consistent allocation relationship at each frequency sampling point. The frequency-related weight function generation unit introduces a frequency band validity screening rule into the normalization process. This rule is constrained by the smoothed version of the frequency energy spectrum field and the abnormal sample registration table. When a mode experiences consecutive low-energy or spike noise label hits in a certain frequency band, the anomaly handling and recording unit generates a frequency band label record and applies a weight reduction coefficient to the modal weight allocation value of that mode in that frequency band. The weight reduction coefficient is derived from the penalty mapping table of the quality factor configuration structure and is archived in the frequency band label record archive. The frequency-related weight function generation unit writes the output frequency-related weight function field into the frequency-related weight function result set, and simultaneously writes the frequency band annotation record index, quality factor configuration structure version number, and normalized result record index into the result metadata structure, thereby forming a recalculated and auditable weight function generation chain.

[0047] At the end of this step, the version management and result consolidation unit consolidates the modal quality factor weight result set and the frequency-related weight function result set. The consolidated content includes the simulation task identifier, time-frequency analysis configuration structure version number, quality factor configuration structure version number, and normalized result record index. The results are then written to the calibration database to form weight version entries. Specifically, when the version management and result consolidation unit detects a change in the time-frequency analysis configuration structure version number, a change in the quality factor configuration structure version number, or a change in the abnormal sample registration table index, it triggers the increment of weight version entries and freezes the old entries. After freezing the old entries, the new entries are set as effective entries and written to the effectiveness identifier field. The effectiveness identifier field is read by S500 and used for weight consistency selection in the transfer function synthesis module. The version management and result consolidation unit writes the frequency-related weight function result set into the frequency-related weight function input position of S500, and simultaneously writes the modal quality factor weight result set into the frequency-related weight function generation source record of S500, forming a cross-main step connection relationship from the modal feature set of S300 to the frequency-related weight function of S500. The unit also writes a mapping description of the output field name and subsequent input position of this step into the task log. The output field name includes the modal quality factor weight and the frequency-related weight function, and the subsequent input position includes the frequency-related weight function input position of S500.

[0048] In the engineering implementation scenario, the offline calibration server receives the modal feature set solidified by S300 and triggers a weight generation job. The triggering is driven by a state change event of the simulation task identifier and written into the job queue. Each entry in the job queue includes the simulation task identifier, the time-frequency analysis configuration structure version number, and the modal identifier set. The normalization processing unit normalizes the maximum and minimum values ​​of the total energy field, the energy weighted arrival time field, and the dispersion field and forms a normalization result record. The modal quality factor weight generation unit generates a modal quality factor weight result set based on this. The frequency-related weight function generation unit merges the modal quality factor weight result set with the frequency energy spectrum field to generate a frequency-related weight function result set. Finally, the version management and result solidification unit solidifies it into a weight version entry and writes it into the frequency-related weight function input position of S500 for the transfer function synthesis module to call.

[0049] Summary of the technical effects of this step: This step normalizes the total energy field, energy-weighted arrival time field, and dispersion field of the modal feature set by applying maximum and minimum value normalization, forming a normalized feature representation that can directly participate in weight calculation. Modal quality factor weights are generated based on the combined operation of energy positive correlation terms, arrival time penalty terms, and dispersion penalty terms. These modal quality factor weights are then fused with the frequency energy spectrum field to generate a frequency-related weight function, forming a modal allocation representation on the frequency axis. The frequency-related weight function serves as the direct source of the input position for the S500's frequency-related weight function, maintaining version consistency and traceability of the modal weighting link during cross-step calls.

[0050] S500: Input the frequency-related weighting function into the transfer function synthesis module, weight and fuse the transfer functions of each mode to generate an equivalent calibration transfer function, collect the measured voltage time-domain signal and transform it to obtain the voltage spectrum, invert the voltage spectrum and the equivalent calibration transfer function to obtain the discharge current spectrum, inversely transform it to obtain the discharge current time-domain signal and integrate it to obtain the apparent discharge quantity.

[0051] The S500 consists of a transfer function synthesis module, a measured acquisition and synchronization unit, a frequency domain transformation unit, a frequency domain inversion unit, a time domain reconstruction and integration unit, a frequency band shielding and anomaly recording unit, and a version management and result solidification unit. Its input sources include the frequency-related weighting function output from the S400, and the mode transfer functions corresponding to the TEM mode, the TE11 mode, and the TM01 mode. The mode transfer function represents the frequency domain mapping relationship between the discharge current and the sensor output. This mapping relationship is constrained by the mode propagation boundary conditions, sensor position parameters, and sensitive direction parameters, and is solidified into the transfer function library during the offline modeling stage. The transfer function library establishes index entries according to the simulation task identifier and includes mode identifiers, frequency axis alignment identifiers, and version number fields. Specifically, after receiving the frequency-related weight function, the version management and result solidification unit first performs a weight version consistency check. The weight version consistency check reads the version number of the quality factor configuration structure and the normalized result record index written by S400, and compares them with the version number field of the transfer function library entry. If the version number field is inconsistent, a version conflict record is generated and a backtracking request is triggered. The backtracking request carries the simulation task identifier and is sent back to the result solidification position of S400 to complete the weight version entry switching. If the version number field is consistent, the frequency-related weight function is written to the weight input cache, and the frequency axis alignment identifier is used as the unified frequency axis constraint for subsequent frequency domain operations.

[0052] The transfer function synthesis module generates an equivalent calibration transfer function after reading the frequency-related weight function and the modal transfer function. This equivalent calibration transfer function is a synthesized transfer relationship obtained by fusing the TEM modal transfer function, the TE11 modal transfer function, and the TM01 modal transfer function on the same frequency axis according to their respective weights, frequency-by-frequency. Specifically, the transfer function synthesis module first performs a frequency axis alignment check on the modal transfer functions. This check examines the consistency of the frequency sampling point sequences of the three modal transfer functions based on the frequency axis alignment identifier. If there is inconsistency, the frequency resampling subunit is invoked to perform interpolation resampling. The interpolation resampling subunit generates resampling results using a frequency sampling point sequence consistent with the S300 frequency energy spectrum and writes them into the resampling record. After frequency axis alignment is completed, the transfer function synthesis module reads the weight values ​​of the frequency-related weight function at the corresponding frequency sampling points point by point according to the frequency sampling point sequence. It then multiplies these weight values ​​with the complex response of the corresponding modal transfer function at that frequency sampling point. Finally, it adds the product results of the three modes point by point to obtain the frequency domain response sequence of the equivalent calibration transfer function. Furthermore, the transfer function synthesis module extracts the amplitude trajectory of the equivalent calibration transfer function and calculates the maximum amplitude value. The maximum amplitude value is written into the amplitude reference field, and a shielding threshold field is generated based on the amplitude reference field. The shielding threshold field corresponds to five percent of the maximum amplitude value. The frequency band shielding and anomaly recording unit determines the frequency sampling point sequence of the equivalent calibration transfer function point by point. When the amplitude of the equivalent calibration transfer function at a certain frequency sampling point is lower than the shielding threshold field, the frequency sampling point is marked as a shielded frequency point and written into the frequency band shielding label field. The frequency band shielding label field is fixed along with the equivalent calibration transfer function for direct reading by the subsequent frequency domain inversion unit.

[0053] The measured acquisition and synchronization unit acquires the measured voltage time-domain signal and performs acquisition link consistency processing. The measured voltage time-domain signal is a time-domain voltage sequence output from the UHF sensor via preamplification and data acquisition link. The time-domain voltage sequence carries a sampling time stamp and channel identifier and is written into the acquisition buffer according to the sampling frequency set by the acquisition configuration structure. Specifically, the measured acquisition and synchronization unit starts the acquisition operation when the trigger conditions are met. The trigger conditions include the partial discharge event trigger identifier and the acquisition window opening identifier of the online monitoring system. The partial discharge event trigger identifier is obtained by the threshold detection subunit performing threshold determination on the amplitude envelope of the original voltage sequence. The acquisition window opening identifier is generated by the acquisition task scheduler based on the event trigger time stamp and window length parameters. The measurement acquisition and synchronization unit performs DC bias cancellation processing on the acquired measured voltage time-domain signal and writes it into the preprocessed voltage time-domain signal field. The DC bias cancellation processing calculates the mean based on the silent interval at the leading edge of the acquisition window and performs subtraction correction on the entire window sequence. The measurement acquisition and synchronization unit also performs anti-aliasing filtering processing on the preprocessed voltage time-domain signal field and writes it into the filtered voltage time-domain signal field. The anti-aliasing filtering processing generates finite impulse response filter coefficients based on the cutoff frequency parameter in the acquisition configuration structure and performs convolution operation. The filter coefficients and convolution operation log are written into the processing record field. After preprocessing, the measurement acquisition and synchronization unit outputs the filtered voltage time-domain signal field to the frequency domain transformation unit as the input source for subsequent voltage spectrum generation.

[0054] The frequency domain transformation unit performs a Discrete Fourier Transform (DFT) on the filtered voltage time-domain signal field. The DFT is a numerical transformation process from a time-domain sequence to a frequency-domain sequence and is bound to the frequency axis alignment identifier. Specifically, the frequency domain transformation unit reads the frequency axis alignment identifier to determine the frequency sampling point sequence and performs windowing processing on the filtered voltage time-domain signal field. The windowing processing uses window type parameters compatible with the S300 time-frequency analysis configuration structure to generate a window sequence and performs point-by-point multiplication. The window type parameters and window sequence are written into the window configuration field. Subsequently, a Discrete Fourier Transform operation is performed to obtain the voltage spectrum field. The voltage spectrum field corresponds one-to-one with the frequency sampling point sequence and contains amplitude and phase components. The frequency domain transformation unit outputs the voltage spectrum field to the frequency domain inversion unit as inversion input, and simultaneously writes the window configuration field and processing record field into the spectrum metadata structure. The spectrum metadata structure is fixed along with the voltage spectrum field.

[0055] The frequency domain inversion unit combines the voltage spectrum field with the equivalent calibration transfer function to generate the discharge current spectrum. The inversion is a frequency domain deconvolution operation with the introduction of regularization constraints to suppress ill-conditioned frequency point amplification. Specifically, the frequency domain inversion unit reads the frequency band shielding label field and performs shielding frequency point zeroing processing on the voltage spectrum field. The shielding frequency point zeroing processing writes the voltage spectrum amplitude component and phase component of the labeled frequency point into the shielding replacement record field and sets it to zero. Subsequently, an inversion operation with a regularization term is performed on the unlabeled frequency points. The regularization adopts Tikhonov regularization, which is a numerical stabilization strategy that superimposes a smoothing term in the inversion denominator. The frequency domain inversion unit generates a regularized intensity field based on the noise amplitude reference field output by the noise estimation subunit. The noise estimation subunit calculates the variance of the filtered voltage time domain signal field in the silent interval of the acquisition window and maps it to the frequency domain noise reference. The frequency domain inversion unit reads the voltage spectrum field and the complex response of the equivalent calibration transfer function at each unlabeled frequency point, performs complex division, and superimposes the regularization intensity field to form the discharge current spectrum field. The discharge current spectrum field is bound to the frequency sampling point sequence and carries the regularization intensity field, the masking replacement record field, and the inversion operation log. Further, the frequency domain inversion unit writes an anomaly code field to the inversion operation log. The anomaly code field is generated by the overflow detection subunit when the complex division result exceeds the numerical range, triggering the frequency band masking and anomaly recording unit to add the corresponding frequency point to the incremental update entry of the frequency band masking label field. The incremental update entry is then archived by the version management and result solidification unit.

[0056] The time-domain reconstruction and integration unit performs an inverse transform on the discharge current spectrum field to obtain the discharge current time-domain signal, and integrates the discharge current time-domain signal to obtain the apparent discharge quantity. Specifically, the time-domain reconstruction and integration unit performs an inverse discrete Fourier transform operation on the discharge current spectrum field to obtain the discharge current time-domain signal field, and performs time-domain zero-drift correction processing on the discharge current time-domain signal field. The time-domain zero-drift correction processing performs subtraction correction based on the mean of the silent interval and writes it into the zero-drift correction record field. Furthermore, the time-domain reconstruction and integration unit performs integration window determination processing on the discharge current time-domain signal field. This process reads the energy-weighted arrival time field output by S300 and combines it with the energy envelope of the discharge current time-domain signal field to locate the main pulse interval. The energy envelope is obtained by the sliding energy calculation subunit accumulating point-by-point in the time domain. The start and end timestamps of the main pulse interval are written into the integration window field. After the integration window field is determined, the time-domain reconstruction and integration unit performs numerical integration on the discharge current time-domain signal field within the interval defined by the integration window field to obtain the apparent discharge quantity field. The numerical integration operation uses a trapezoidal integration subunit to accumulate point-by-point and writes the results into the integration operation log. The apparent discharge quantity field is bound to the simulation task identifier, channel identifier, and acquisition timestamp. When the results are solidified, it is written into the calibration result data structure along with the equivalent calibration transfer function version number, frequency-related weight function version number, and regularization intensity field, thereby maintaining a traceable record of the calibration link.

[0057] At the end of this step, the version management and result consolidation unit consolidates the equivalent calibration transfer function, voltage spectrum field, discharge current spectrum field, discharge current time-domain signal field, and apparent discharge quantity field. It then writes the apparent discharge quantity field into the apparent discharge quantity output interface, which is connected to the calibration report generation unit and outputs structured results according to channel identifiers. Specifically, the version management and result consolidation unit writes the frequency band masking annotation field, resampling record, masking replacement record field, inversion calculation log, and integration calculation log into the audit log library. The audit log library is indexed with the simulation task identifier and supports playback by channel identifier. When the frequency band masking annotation field shows consecutive incremental update entries on the same device, the version management and result consolidation unit triggers a weight version review task and writes the review task entry into the task queue. The review task entry is sent back to the S400 to read the modal feature set and complete the recalculation of the frequency-related weight function. The triggering condition and the returned record together constitute an automated closed loop between this step and the previous steps.

[0058] In the engineering implementation scenario, a UHF sensor is installed on the casing of the on-site GIS equipment and connected to the preamplifier unit and data acquisition card via a coaxial cable. The data acquisition card writes the measured voltage time-domain signal into the acquisition buffer and triggers the start-up processing of the measured acquisition and synchronization unit. The offline calibration server preloads the modal transfer function entries corresponding to the same device and the frequency-related weight function entries output by S400. The transfer function synthesis module generates an equivalent calibration transfer function and solidifies the shielding threshold field and the frequency band shielding label field. After the frequency domain transformation unit generates the voltage spectrum field, it is handed over to the frequency domain inversion unit to perform inversion according to the frequency band shielding label field to obtain the discharge current spectrum field. The time domain reconstruction and integration unit outputs the discharge current time-domain signal field and completes integration to generate the apparent discharge quantity field. The apparent discharge quantity field is written to the apparent discharge quantity output interface and synchronously stored in the database along with the calibration result data structure. The calibration report generation unit reads the apparent discharge quantity field and audit log entries from the calibration result data structure to generate a verifiable record.

[0059] In summary, this step integrates the frequency-related weighting function with the three modal transfer functions to generate an equivalent calibration transfer function. It then constrains the frequency range of the inversion operation using a frequency band masking annotation field, forming a calibration transfer relationship consistent with the weight version. Based on the equivalent calibration transfer function, a frequency domain inversion with Tikhonov regularization is performed on the voltage spectrum, outputting the discharge current spectrum and reconstructing the discharge current time-domain signal. The apparent discharge quantity field is then obtained by limiting the integration interval using an integration window field. Through the linkage between the version number field, the audit log library, and the task queue, the correspondence between the calibration output and the weight and transfer function entries is solidified.

[0060] In a preferred embodiment, this embodiment uses a typical cylindrical gas-insulated switchgear (GIS) as the object, and details the implementation process of the method of the present invention: including electromagnetic modeling and FDTD simulation, electromagnetic mode decomposition, modal feature extraction, construction of modal quality factors and frequency-related weights, synthesis of equivalent calibration transfer functions, and experimental data calibration. This embodiment verifies the accuracy and engineering applicability of the method through simulation and measured data.

[0061] Step (1): Electromagnetic modeling and FDTD simulation; This step aims to establish an electromagnetic model of the GIS and obtain the sensor's electric field response through time-domain simulation. The specific details are as follows: Model Construction: A simplified coaxial waveguide model was constructed based on the structural dimensions of the cylindrical GIS (such as the outer diameter of the inner conductor, the inner diameter of the outer shell, and the axial length) and the dielectric properties (such as the relative permittivity of the gas and the insulator material parameters). The model includes key components such as the inner conductor, the outer shell, the insulator, and the phase splitter. Partial discharge defects were simulated as charge pulse excitation sources generated by the spike or needle-plate models. The spike defect model consists of the conductor surface tip curvature radius, tip height, defect location, and charge pulse time parameters; the needle-plate defect model consists of the needle electrode radius, needle-plate spacing, defect location, and charge pulse time parameters.

[0062] Figure 2 A geometric structure diagram of a simulation model of a cylindrical GIS provided in this application embodiment, such as... Figure 2 As shown, the model includes the positions of the inner conductor, outer shell, and insulator. The model uses a three-dimensional coordinate system, with the defect point located on the surface of the inner conductor and the sensor mounted at a designated position on the outer shell.

[0063] FDTD Simulation Setup: The GIS model is simulated in the temporal domain using the three-dimensional finite-domain difference (FDTD) method. The simulation mesh uses cubic elements (10mm × 10mm × 10mm), with a total mesh size of approximately 10^6. The time step is automatically determined by the Courant-Friedrichs-Lewy (CFL) condition and is on the order of picoseconds (ps). A perfectly matched layer (PML) is set as the absorbing boundary to eliminate the influence of boundary reflections and ensure that the simulation focuses on the propagation of UHF band electromagnetic waves within the GIS cavity.

[0064] Figure 3 This application provides a PML boundary setting diagram on the outer layer of the model, with a thickness of 5-10 mesh elements, for absorbing outward waves.

[0065] Electric field response acquisition: The time-domain electric field response was acquired in the sensitive direction of the built-in UHF sensor through FDTD simulation, denoted as... Its frequency domain form is obtained through Fourier transform:

[0066] in, The time-domain signal of the electric field at the sensor location; The frequency domain representation of the electric field at the sensor location is obtained by Fourier transform. Angular frequency is an angular quantity that represents frequency. Imaginary unit, satisfying ; Time variable, integral variable; The integral symbol indicates the summation operation for continuous signals. The base of the natural logarithm (approximately 2.71828), used for complex exponential functions; : Time differential element.

[0067] Figure 4 This application provides a schematic diagram of the time-domain waveform and frequency-domain spectrum of a sensor electric field under typical defect excitation, as shown in the embodiments. Figure 4 As shown in the simulation results, there are obvious resonance peaks in the GIS cavity, reflecting the standing wave characteristics.

[0068] This step obtained reliable electric field response data through FDTD simulation, laying the foundation for subsequent mode decomposition. The simulation convergence condition was that the field decayed to -30dB or the maximum step size (100,000 steps) was reached to ensure the stability of the results.

[0069] Step (2): Electromagnetic mode decomposition: This step, based on waveguide eigenmode theory, decomposes the frequency-domain electric field response into independent modal components to analyze multimodal propagation effects. The specific details are as follows: Modal expansion theory: The electromagnetic field in a GIS waveguide can be considered as a superposition of a set of eigenmodes (such as TEM, TE11, TM01, etc.). Based on the dyadic Green's function and waveguide theory, the frequency domain electric field can be expanded modally as follows:

[0070] in, Spatial location Frequency domain electric field at that location; Spatial location vector, representing a point within the GIS cavity; : Modal order index, used to identify waveguide eigenmodes (such as TEM, TE11, TM01). : No. The excitation coefficients of a mode represent the frequency at which the mode is excited. The amplitude below; : No. The eigenfield distribution of each propagation mode is determined by the waveguide boundary conditions.

[0071] Orthogonal projection solution: Utilizing the orthogonality of eigenmodes in the GIS cross section A sampling point set is set up (covering the neighborhood of the inner conductor, the neighborhood of the inner wall of the outer shell, and the neighborhood of the insulator), and the excitation coefficient is calculated by projection:

[0072] in, : The complex conjugate; The cross-section of the GIS waveguide, used for the integration region; : The symbol for surface integral, representing the area in a cross-section Integrals on; : Area differential element.

[0073] Modal component definition: at the sensor location In the sensitive directions, the modal field is projected as a scalar electric field, and the first... Frequency domain components of the mode:

[0074] in, : No. The frequency domain components of the mode, at the sensor position Projection at the location; Sensor position vector; This represents the field value at the sensor for this mode. The total frequency domain electric field is the sum of the modal components:

[0075] in, Total frequency domain electric field; The modal time-domain components are obtained through inverse Fourier transform:

[0076] in, : No. The time-domain components of the modality are obtained by the inverse Fourier transform; : Constant factor, derived from the normalization of the Fourier transform.

[0077] The total time-domain signal is:

[0078] in, The total time-domain electric field signal is the sum of the time-domain components of each mode.

[0079] This step uses mode decomposition to separate the mixed electric field response into mode components such as TEM, TE11, and TM01, providing a foundation for subsequent feature extraction.

[0080] Figure 5 The modal decomposition result of a typical field point provided in the embodiment of this application is shown in the figure. Figure 5 The continuous wavelet transform (CWT) decomposition of the electric field signal is shown to visualize the time-frequency characteristics, but this step focuses on mode decomposition, and the CWT details are expanded in step (3).

[0081] Step (3): Modal feature extraction; This step quantifies the propagation characteristics of each mode through wavelet transform and feature extraction, generating a set of modal feature quantities. The specific details are as follows: Continuous wavelet transform (CWT): for modal time-domain components Performing CWT yields the time-frequency distribution:

[0082] in: : No. The wavelet coefficients of the mode represent the scale. Peaceful relocation The following time-frequency analysis results; The scaling parameter is inversely proportional to the frequency in the wavelet transform. ); : Time shift, representing the center time of the wavelet window; Mother wavelet function; in this embodiment, Morlet wavelet is used. Complex conjugate of the mother wavelet;

[0083] in, : No. The time-frequency energy distribution of a mode is proportional to the square of the modulus of the wavelet coefficients; The proportional sign indicates a proportional relationship; Feature extraction: from Extracting three types of modal features: Total Modal Energy : Represents the total energy of the mode across the entire time-frequency plane:

[0084] in, : No. The total energy of the modes is obtained by integrating the time-frequency energy distribution; : Double integral symbol, indicating simultaneous integration with respect to frequency and time; Angular frequency differential element.

[0085] Energy-weighted arrival time The group delay characterizing the mode is the energy-weighted average arrival time.

[0086] in, : No. The energy-weighted arrival time of a mode represents the average time of the pulse centroid.

[0087] Modal dispersion Quantization waveform broadening, expressed as the standard deviation on the time axis:

[0088] in, .

[0089] Simultaneously, the modal frequency energy spectrum is defined. :

[0090] in, : No. The frequency energy spectrum of a mode is obtained by integrating the time-frequency energy distribution over time.

[0091] This step obtains the time-frequency energy distribution of each mode through wavelet transform and extracts key features. Figures 6 to 12 The simulation results of electric fields at different points and their CWT decompositions are presented, verifying the effectiveness of the characteristic quantities.

[0092] Figures 6 to 10 The CWT results for multiple field points are displayed, where modal characteristics such as energy concentration regions and time broadening are clearly visible. This embodiment uses field point 1 as an example; the quantitative results are as follows: TEM mode... , , TE11 mode , , ;TM01 mode , , These data indicate that the TEM mode has the highest energy, arrives earliest, and exhibits the smallest dispersion, which is consistent with theoretical expectations.

[0093] Step (4): Construct modal quality factors and frequency-related weights; This step, based on feature normalization, generates modal quality factors and frequency-related weighting functions for adaptive weighting. The specific details are as follows: Feature normalization: Normalize modal features to eliminate the influence of dimensions. Energy normalization: Calculate the normalized energy weights :

[0094] The denominator is the sum of the total energy of all modes, ensuring... .

[0095] Arrival time normalization: Calculating relative arrival time :

[0096] in, and These are the minimum and maximum arrival times for all modes, respectively; Small positive numbers (e.g.) Prevent division by zero.

[0097] Dispersion normalization: Calculating the degree of dispersion :

[0098] in, and These are the minimum and maximum dispersions for all modes, respectively.

[0099] Modal quality factor construction: Constructing a comprehensive quality factor based on normalized feature quantities. :

[0100] in, For arrival time sensitivity coefficient (controlling the weight of early arrival mode); This is the dispersion sensitivity coefficient (for suppressing severely dispersion modes). (Coefficient) and Based on experience (e.g.) , This can be optimized and adjusted.

[0101] Frequency-related weight function generation: The quality factor is combined with the frequency energy spectrum to generate frequency-related weights. :

[0102] in, This represents the modal frequency energy spectrum. For any... The weights satisfy normalization: .

[0103] Formula rationality assessment: Normalization formula (e.g.) ) is a standard min-max normalization variant used to scale features to the [0,1] interval, which is reasonable and numerically stable.

[0104] Quality factor formula Using an exponential penalty term ( The method weights delay and dispersion based on the principle that weights are negatively correlated with reliability in information theory, which is reasonable and adaptive.

[0105] Weighting function formula

[0106] in, : No. The normalized energy weight of a mode represents the proportion of that mode's energy to the total energy; : Summation index, used to iterate through all modalities, and similar; : No. The relative arrival times of the modes are normalized to the [0,1] interval; The minimum weighted arrival time of energy for all modes; The maximum value of the weighted arrival time of energy for all modes; Small positive numbers (e.g.) ), to prevent the denominator from being zero; : No. The normalized dispersion of the mode is normalized to the [0,1] interval; The minimum value of the dispersion of all modes; The maximum value of the dispersion across all modes; : No. The quality factor of a mode is a combination of energy, time of arrival, and dispersion. Arrival time sensitivity coefficient, which controls the weight of the early arrival mode; Dispersion sensitivity coefficient, a weight for suppressing severely dispersed modes; : No. Mode at frequency Frequency-related weights at each location; The base of the natural logarithm, used in exponential functions.

[0107] This step generates adaptive weights through normalization and weighting. Taking field point 1 as an example, the modal quality factor is: TEM TE11 TM01 In the 300-600MHz band, the frequency-related weights are dominated by TEM (weights 0.85-0.93), while in the 700-1100MHz band, the weight of TE11 increases (0.35-0.42), indicating that the weights can dynamically reflect the modal contributions.

[0108] Step (5): Construct an equivalent calibration transfer function and calibrate the discharge quantity based on the experimentally measured data; This step synthesizes the equivalent transfer function and verifies the accuracy of the method by calculating the apparent discharge quantity through inversion. The specific details are as follows: Equivalent calibration transfer function synthesis: Modal transfer function Determined by the Green's function, it reflects the transfer relationship from the partial discharge current to the sensor's electric field. The overall transfer function is the sum of the modes:

[0109] Using frequency-related weights Construct the equivalent calibration transfer function:

[0110] This function incorporates modal weights and adapts to actual propagation conditions.

[0111] Figure 13 The equivalent transfer function of field point 1 is shown. As can be seen, under weight adjustment, the function curve is smooth and focuses on the main frequency band.

[0112] Experimental data calibration: Acquiring the measured time-domain signal of the UHF sensor output voltage. The frequency domain spectrum is obtained through Fourier transform. :

[0113] use Inversion of partial discharge current spectrum estimate :

[0114] The inversion process incorporates regularization (such as Tikhonov regularization) to suppress ill-conditioned frequency bands. The time-domain current is obtained through inverse Fourier transform. :

[0115] Apparent discharge quantity Perform time integration:

[0116] The integration window is determined by the energy envelope and focuses on the main pulse region.

[0117] in, The overall transfer function represents the frequency domain mapping of the partial discharge current to the sensor's electric field; : No. The modal transfer function is obtained from Green's function and modal analysis; The equivalent calibration transfer function is obtained by weighted fusion based on frequency-related weights. The frequency domain spectrum of the measured voltage signal is obtained by Fourier transform. The measured voltage time-domain signal was acquired from a UHF sensor. The estimated value of the partial discharge current spectrum is obtained by inversion calculation; The estimated value of the time-domain signal of the partial discharge current is obtained by inverse Fourier transform; The estimated value of the apparent discharge quantity is obtained by integrating the current over time. : Abbreviation for Partial Discharge, used as a subscript.

[0118] Verification results: Taking a single measurement as an example, the sensor output signal... After processing , compared with the field calibrator reference value The comparison showed an error of only 6.6%, verifying the accuracy of the method.

Claims

1. A partial discharge quantization calibration method based on mode decomposition and frequency weighting, characterized in that, include: S100: Obtain GIS structural parameters, defect excitation parameters, UHF sensor position parameters and sensitive direction parameters, establish an electromagnetic model and perform FDTD time-domain simulation, extract the sensor electric field time-domain signal and transform it to obtain the frequency domain response spectrum; S200: Based on the frequency domain response spectrum, solve the mode coefficient sets of TEM mode, TE11 mode and TM01 mode by orthogonal projection of waveguide eigenmodes, and generate the frequency domain component sets of each mode; S300. Based on the frequency domain component sets of each modality, perform wavelet transform to obtain the time-frequency energy distribution, extract the total energy, energy-weighted arrival time, dispersion and frequency energy spectrum, and generate a modal feature set. S400. Normalize the modal feature set to obtain the modal quality factor weights, and combine them with the frequency energy spectrum to generate a frequency-related weight function; S500: Input the frequency-related weighting function into the transfer function synthesis module, weight and fuse the transfer functions of each mode to generate an equivalent calibration transfer function, collect the measured voltage time-domain signal and transform it to obtain the voltage spectrum, invert the voltage spectrum and the equivalent calibration transfer function to obtain the discharge current spectrum, inversely transform it to obtain the discharge current time-domain signal and integrate it to obtain the apparent discharge quantity.

2. The method according to claim 1, characterized in that, The electromagnetic model described in S100 includes an inner conductor, a shell, an insulator, and a phase splitter. The FDTD time-domain simulation sets a PML absorption boundary.

3. The method according to claim 1, characterized in that, The defect excitation parameters mentioned in S100 adopt the parameters of the spike defect model. The spike defect model consists of the radius of curvature of the conductor surface tip, the tip height, the defect location, and the charge pulse time parameters.

4. The method according to claim 1, characterized in that, The defect excitation parameters mentioned in S100 are adopted from the needle plate defect model parameters. The needle plate defect model consists of the needle electrode radius, needle plate spacing, defect location and charge pulse time parameters.

5. The method according to claim 1, characterized in that, The mode expansion model described in S200 constructs a set of sampling points on the cross section of the GIS waveguide. The set of sampling points covers the neighborhood of the inner conductor, the neighborhood of the inner wall of the outer shell, and the neighborhood of the insulator. Based on the set of sampling points, the orthogonal projection of the intrinsic modes is used to solve the set of mode coefficients.

6. The method according to claim 1, characterized in that, The mother wavelet of the wavelet transform described in S300 is the Morlet wavelet, and the time-frequency energy distribution is obtained by the square of the modulus of the wavelet coefficients.

7. The method according to claim 1, characterized in that, The energy weighted arrival time mentioned in S300 is obtained by weighted summation of the time-frequency energy distribution on the time axis, and the dispersion is obtained by the second central moment of the time-frequency energy distribution on the time axis.

8. The method according to claim 1, characterized in that, The normalization described in S400 uses maximum and minimum value normalization, and the normalization object includes the total energy, the energy weighted arrival time, and the dispersion.

9. The method according to claim 1, characterized in that, The modal quality factor weights described in S400 are obtained by combining the normalized total energy value, the normalized energy-weighted arrival time value, and the normalized dispersion value. The combination relationship includes an energy positive correlation term, an arrival time penalty term, and a dispersion penalty term.

10. The method according to claim 1, characterized in that, The frequency-related weighting function of S500 is obtained by multiplying the modal quality factor weights by the frequency energy spectrum, and normalization is performed at each frequency point; the voltage spectrum is shielded in the frequency band where the amplitude of the equivalent calibration transfer function is less than five percent of its maximum amplitude.

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