A method and system for measuring electric field intensity

Abstract

This invention discloses a method and system for measuring electric field strength, applied in the field of electric field strength measurement technology. The method includes: acquiring gas environment parameters of the electrical equipment under test; obtaining optical parameter variation information of each incident laser in the electrical equipment under test during simulation testing using selected incident lasers; determining a first parameter correction amount based on the response curve, refractive index correction factor, and gas density distribution field; determining a second parameter correction amount for each linear optical parameter based on the gas environment parameters; optimizing the electric field strength measurement model of the electrical equipment under test based on the first parameter correction amount and each of the second parameter correction amounts to obtain an optimized electric field strength measurement model; and obtaining the electric field strength result. The electric field strength measurement method and system provided by this invention effectively improve the accuracy and reliability of parameter optimization in the electric field strength measurement process, thereby enabling the acquisition of accurate electric field strength.

Description

Technical Field

[0001] This invention relates to the field of electric field strength measurement technology, and in particular to a method and system for measuring electric field strength. Background Technology

[0002] In high-voltage electrical equipment such as GIS (Gas Insulated Switchgear), SF6 (Sulfur Hexafluoride) gas is the core insulating medium. However, local distortion or abnormal rise in the electric field inside the equipment can easily trigger gas breakdown, leading to serious failures. Therefore, to ensure the safe operation of the equipment, it is essential to monitor the electric field strength in real time.

[0003] Current technology utilizes the electric field-induced second harmonic effect for real-time detection of electric field strength. The principle is that an incident laser, under the induction of an external electric field, interacts with SF6 gas, exciting a second harmonic signal. The electric field strength can be inferred by measuring this second harmonic signal. However, the gas environment inside high-voltage electrical equipment is extremely complex. Besides SF6, other protective gases are present, causing distortion of the second harmonic signal generated by the incident laser. Furthermore, current technology still uses idealized fixed parameters when calculating the electric field strength, leading to a mismatch between the model and the measured signal. This results in the inability to obtain a high-precision true value of the electric field strength, further causing misjudgments of safety and protection failures, ultimately leading to SF6 gas breakdown, equipment explosions, and even large-scale power outages. Summary of the Invention

[0004] This invention provides a method and system for measuring electric field strength, in order to solve the technical problem of inaccurate electric field strength measurement in the prior art, and to achieve the effect of optimizing the relevant parameters of the measured electric field strength to obtain an accurate electric field strength.

[0005] To address the aforementioned technical problems, this invention provides a method and system for measuring electric field strength, the method comprising: Obtain the gas environment parameters of the electrical equipment under test; During the simulation test using selected incident lasers, information on the changes in optical parameters of each incident laser in the electrical device under test is obtained. The gas density distribution field of the electrical equipment under test is obtained by inversion based on the optical parameter change information; Extract the nonlinear optical parameters from the optical parameter change information, and determine the response curve of the nonlinear optical parameters; Based on the differences in gas dispersion of the aforementioned gas environment parameters, a refractive index correction factor is determined; Based on the response curve, the refractive index correction factor, and the gas density distribution field, the first parameter correction amount of the nonlinear optical parameter is determined; Extract each linear optical parameter from the optical parameter change information, and determine the second parameter correction amount for each linear optical parameter based on the gas environment parameters; Based on the first parameter correction amount and each of the second parameter correction amounts, the electric field strength measurement model of the pre-constructed electrical equipment under test is optimized to obtain the optimized electric field strength measurement model. Obtain the electric field strength result output by the electric field strength measurement model.

[0006] Preferably, the step of obtaining the optical parameter variation information of each incident laser in the electrical device under test during the simulation test using selected incident lasers includes: Based on the gas components in the gas environment parameters, the dispersion curve corresponding to each gas component is determined, and the dispersion curve is selected based on a preset threshold to determine the wavelength gradient; Based on the gas density and the preset nonlinear refractive index coefficient in the gas environment parameters, the critical light intensity is obtained, and the light intensity gradient is determined based on the critical light intensity. Based on the topology of the electrical device under test, determine the polarization state combination; Based on the wavelength gradient, the light intensity gradient, and the polarization state combination, each incident laser is selected; Simulation tests were performed based on the various incident lasers to obtain information on the changes in the optical parameters.

[0007] Preferably, the step of obtaining the optical parameter change information based on the tests performed on each incident laser includes: Each incident laser is introduced into the electrical device under test to obtain the relationship between each incident laser and the corresponding detection optical path. Differential calculations are performed on each incident laser and its corresponding detection optical path to obtain the optical parameter variation information of each incident laser in the electrical device under test.

[0008] Preferably, the step of inverting the gas density distribution field of the electrical device under test based on the optical parameter change information includes: Extract the optical response features from the optical parameter change information; Construct a linear integral equation relating the optical response characteristics and the local gas density; The electrical device under test is divided into a three-dimensional voxel mesh, and a system weight matrix of the propagation path trajectory and the three-dimensional voxel mesh is constructed based on the propagation path trajectory of the incident laser. The pre-constructed initial gas density distribution field is processed based on the system weight matrix and the linear integral relationship equation to obtain the predicted optical response characteristics; The initial gas density distribution field is corrected based on the optical response characteristics and the predicted optical response characteristics to obtain the gas density distribution field.

[0009] Preferably, the step of extracting the nonlinear optical parameters from the optical parameter change information and determining the response curve of the nonlinear optical parameters includes: The optical parameter variation information is processed based on the gas density distribution field and the refractive index correction factor to obtain the nonlinear optical response residual; The peak intensity of the incident laser in the optical parameter variation information is extracted as the excitation variable, and the nonlinear optical response residual is correlated and matched to obtain a set of optical response residual pairs. The optical response residual pair is fitted to determine the response curve of the nonlinear optical parameter.

[0010] Preferably, determining the refractive index correction factor based on the gas dispersion differences of the gas environment parameters includes: Based on the gas environment parameters, the theoretical refractive index values ​​of each incident laser are obtained. A reference incident laser is selected, and the refractive index deviation of each of the other incident lasers relative to the reference incident laser is calculated. Based on each of the refractive index deviations, the corresponding spectral dispersion characteristics are obtained. The refractive index correction factor is obtained by normalizing each of the aforementioned spectral dispersion characteristics.

[0011] Preferably, determining the first parameter correction amount of the nonlinear optical parameter based on the response curve, the refractive index correction factor, and the gas density distribution field includes: Based on the refractive index correction factor, the gas density distribution field is mapped to a theoretical linear refractive index distribution and path integral processing is performed to obtain the theoretical linear optical response prediction value. Based on the theoretical linear optical response prediction and the optical parameter variation information, the theoretical nonlinear response curve is obtained; The response curve and the theoretical nonlinear response curve are compared by difference to obtain a nonlinear residual sequence; Based on the optical parameter variation information, the nonlinear sensitivity coefficient is obtained; The nonlinear residual sequence and the nonlinear sensitivity coefficient are compared and inverted to obtain the first parameter correction amount.

[0012] Preferably, the step of comparing and inverting the nonlinear residual sequence with the nonlinear sensitivity coefficient to obtain the first parameter correction includes: An observation vector is constructed based on the nonlinear residual sequence, and a sensitivity matrix is ​​obtained based on the nonlinear sensitivity coefficient. Based on the observation vector and the sensitivity matrix, the mapping equation is obtained; Using the aforementioned mapping equation as a constraint, the pre-constructed regularized objective function is iteratively optimized based on the conjugate gradient technique to obtain the optimal parameter deviation solution; The optimal parameter deviation solution is subjected to mesh mapping processing to obtain the first parameter correction amount of the nonlinear optical parameter.

[0013] Preferably, the step of extracting each linear optical parameter from the optical parameter change information and determining a second parameter correction amount for each linear optical parameter based on the gas environment parameters includes: Extract each linear optical parameter from the optical parameter change information, wherein each linear optical parameter includes at least gas molecule density, phase mismatch coefficient and focusing Rayleigh length; The gas environment parameters are processed to obtain a first correction value for the gas molecule density; Based on the optical parameter change information, a second correction amount and a correction wavelength value for the phase mismatch coefficient are obtained, and based on the correction wavelength value, a third correction amount for the focusing Rayleigh length is obtained; Based on the first correction amount, the second correction amount, and the third correction amount, a second parameter correction amount is determined for each of the linear optical parameters.

[0014] Another aspect of the present invention provides a system for measuring electric field strength, comprising: The acquisition module is used to acquire the gas environment parameters of the electrical equipment under test; The test module is used to obtain information on the changes in optical parameters of each incident laser in the electrical device under test during the simulation test using each selected incident laser. The inversion module is used to invert the gas density distribution field of the electrical equipment under test based on the optical parameter change information; The determination module is used to extract nonlinear optical parameters from the optical parameter change information and determine the response curve of the nonlinear optical parameters; The dispersion module is used to determine the refractive index correction factor based on the gas dispersion differences of the gas environment parameters. The first module is used to determine the first parameter correction amount of the nonlinear optical parameter based on the response curve, the refractive index correction factor and the gas density distribution field; The second module is used to extract each linear optical parameter from the optical parameter change information, and determine the second parameter correction amount for each linear optical parameter based on the gas environment parameters. An optimization module is used to optimize the parameters of the pre-constructed electric field strength measurement model of the electrical equipment under test based on the first parameter correction amount and each of the second parameter correction amounts, so as to obtain the optimized electric field strength measurement model. The results module is used to obtain the electric field strength results output by the electric field strength measurement model.

[0015] Compared with the prior art, the beneficial effects of the present invention are at least one of the following: This invention acquires the gas environment parameters of the electrical equipment under test, obtains optical parameter variation information using selected sets of incident laser tests, and then inverts to obtain a precise gas density distribution field and extracts the response curve of nonlinear optical parameters. Based on this, a refractive index correction factor is determined according to the gas dispersion difference. By fitting the measured response curve with the theoretical response characteristics derived from the refractive index correction factor and gas density distribution field, the first parameter correction amount of the nonlinear optical parameters and the second parameter correction amount of the linear optical parameters are accurately quantified and determined. Finally, these correction amounts are used to optimize the pre-constructed electric field strength measurement model. This effectively overcomes the interference of complex gas non-uniform distribution and nonlinear effects on the measurement signal, significantly improves the accuracy and robustness of parameter optimization during electric field strength measurement, eliminates model mismatch errors, and thus reconstructs a high-fidelity, accurate electric field strength distribution. This avoids the risk of protection failure due to measurement distortion, fundamentally ensuring the safe and stable operation of high-voltage electrical equipment such as GIS. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating a method for measuring electric field strength in one embodiment of the present invention. Figure 2 This is a schematic diagram of the electric field strength measurement system in one embodiment of the present invention; Figure label: The module consists of: 11. Acquisition module; 12. Testing module; 13. Inversion module; 14. Determination module; 15. Dispersion module; 16. First module; 17. Second module; 18. Optimization module; and 19. Result module. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The purpose of providing these embodiments is to make the disclosure of the present invention more thorough and comprehensive. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0018] In the description of this invention, the terms "first," "second," "third," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined with "first," "second," "third," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0019] In the description of this invention, it should be noted that, unless otherwise expressly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to communication within two components. The terms "vertical," "horizontal," "left," "right," "upper," "lower," and similar expressions used herein are for illustrative purposes only and do not indicate or imply that the device or component referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as limiting the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0020] In the description of this invention, it should be noted that, unless otherwise defined, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art. The terminology used in this specification is for the purpose of describing specific embodiments only and is not intended to limit the invention. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0021] In high-voltage equipment such as GIS, existing electric field strength monitoring technology based on electric field-induced second harmonic effect suffers from signal distortion due to neglecting the complex mixed gas environment inside, and model mismatch caused by using idealized fixed parameters. This leads to distorted electric field strength measurement, which in turn causes protection failure and the risk of breakdown and explosion.

[0022] One embodiment of the present invention provides a method for measuring electric field strength. For details, please refer to [link to relevant documentation]. Figure 1 , Figure 1 The diagram shown is a flowchart illustrating a method for measuring electric field strength according to one embodiment of the present invention, including: S1. Obtain the gas environment parameters of the electrical equipment under test; S2. During the simulation test using each selected incident laser, the optical parameter change information of each incident laser in the electrical equipment under test is obtained. S3. The gas density distribution field of the electrical equipment under test is obtained by inversion based on the optical parameter change information; S4. Extract the nonlinear optical parameters from the optical parameter change information and determine the response curve of the nonlinear optical parameters; S5. Determine the refractive index correction factor based on the gas dispersion differences in gas environment parameters; S6. Based on the response curve, refractive index correction factor and gas density distribution field, determine the first parameter correction amount of the nonlinear optical parameters; S7. Extract each linear optical parameter from the optical parameter change information, and determine the second parameter correction amount for each linear optical parameter based on the gas environment parameters. S8. Based on the first parameter correction amount and each of the second parameter correction amounts, optimize the parameters of the pre-constructed electric field strength measurement model of the electrical equipment under test to obtain the optimized electric field strength measurement model. S9. Obtain the electric field strength results output by the electric field strength measurement model.

[0023] First, the gas environment parameters of the electrical equipment under test (EDT) are acquired. Acquiring these parameters is a fundamental step for subsequent laser simulation and optical parameter analysis. This step involves collecting basic state information such as the type of gas inside the equipment, temperature, pressure, humidity, and flow rate. The gas environment parameters are acquired using multiple sensors deployed both inside and outside the equipment. Temperature sensors use a PT100 platinum resistance thermometer for real-time acquisition; pressure sensors use a piezoresistive pressure transmitter to acquire absolute and relative pressure data; gas composition sensors use a non-dispersive infrared sensor and a photoacoustic spectroscopy sensor to identify SF6 and its decomposition products; humidity sensors use a polymer thin-film capacitive sensor to obtain gas moisture content; and flow rate sensors use a thermal mass flow sensor to monitor gas flow. These sensors communicate through a data acquisition unit, which synchronously acquires signals at a fixed sampling frequency and performs analog-to-digital conversion, converting analog signals into digital signals before uploading them to the processing terminal. The processing terminal filters, reduces noise, and calibrates the acquired raw data, eliminating abnormal data caused by environmental interference and equipment vibration, resulting in a stable and reliable gas environment parameter dataset. This dataset provides realistic boundary conditions for subsequent incident laser simulation tests, offers a basic reference for optical parameter variation analysis, and provides direct input data for judging gas dispersion differences and calculating refractive index correction factors, ensuring the accuracy and reliability of subsequent inversion of the gas density distribution field and optimization of the electric field strength measurement model.

[0024] Furthermore, during simulation testing using selected incident lasers, the optical parameter changes of each incident laser in the electrical device under test (DUT) are obtained. Based on the gas composition in the gas environment parameters, the dispersion curve corresponding to each gas component is determined, and the dispersion curve is selected based on a preset threshold to determine the wavelength gradient. Based on the gas density and a preset nonlinear refractive index coefficient in the gas environment parameters, the critical light intensity is obtained, and the light intensity gradient is determined based on the critical light intensity. Based on the topology of the DUT, the polarization state combination is determined. Based on the wavelength gradient, light intensity gradient, and polarization state combination, each incident laser is selected. Simulation testing is performed using each incident laser to obtain the optical parameter change information. Each incident laser is then introduced into the DUT to obtain the relationship between each incident laser and its corresponding detection optical path. Differential decomposition processing is performed on each incident laser and its corresponding detection optical path to obtain the optical parameter change information of each incident laser in the DUT.

[0025] Step S2 provides core data support for subsequent inversion of the gas density distribution field and optimization of the electric field strength measurement model, ensuring the accuracy and reliability of subsequent steps. Specifically, the optical parameter variation information refers to the changes in parameters such as refractive index, absorption coefficient, scattering coefficient, and nonlinear polarizability of the incident laser as it propagates inside the electrical equipment under test, influenced by the gas environment and propagation path. The incident laser refers to the laser beam with a specific wavelength, intensity, and polarization state selected according to the test requirements. The dispersion curve refers to the relationship between the refractive index of different gas components and wavelength at different laser wavelengths. The wavelength gradient refers to the fixed interval between the selected incident laser wavelengths. The critical intensity refers to the minimum intensity at which the laser induces a nonlinear optical effect in the gas. The intensity gradient refers to the fixed interval between the selected incident laser intensities. The polarization state combination refers to the combination of incident laser polarization directions determined according to the equipment topology. The topology refers to the overall structure of the internal cavity shape, electrode arrangement, and gas flow path of the electrical equipment under test. The probe optical path refers to the optical path system that works in conjunction with the incident laser to receive the laser signal after it has been acted upon by the gas inside the equipment. The differential calculation processing refers to the processing method that calculates the difference between the incident laser signal and the corresponding probe optical path signal, eliminates interference signals, and extracts the effective optical parameter variation data.

[0026] The process of obtaining optical parameter variation information during simulation testing using selected incident lasers involves first deeply analyzing the gas components in the gas environment parameters and using a high-precision molecular spectral database to retrieve absorption cross-section data of each component under different pressure and temperature conditions, as well as discrete data points showing the real part of the refractive index as a function of wavelength. A fine dispersion curve covering the ultraviolet to infrared band is then plotted using a numerical interpolation algorithm. Next, a lower threshold for transmittance greater than 90% and a sensitivity optimization criterion for maximizing the difference in dispersion slope are set. Three to five characteristic wavelength points located within the gas transparency window and exhibiting significantly different dispersion characteristics are intelligently selected from the continuous spectrum to construct a wavelength gradient that can decouple the effects of temperature and density. Subsequently, based on the gas environment... The real-time gas density distribution mean and pre-stored nonlinear refractive index coefficient in the parameters are used to calculate the critical light intensity required to detect the nonlinear phase shift. A safe upper limit for the light intensity is determined by strictly comparing it with the ionization breakdown threshold of the gas. Within this dynamic safe range, six to ten power levels are divided from the weak light linear response region to the strong light nonlinear saturation region using linear or logarithmic intervals to form a light intensity gradient that can fully characterize the evolution of the nonlinear effect. Simultaneously, based on the complex topology of the electrical equipment under test, the direction of the internal main electric field vector is pre-estimated using the finite element method. Three linear polarization states—parallel to the main electric field direction, perpendicular to the main electric field direction, and at a 45-degree angle to the main electric field—are set as the polarization state combination that maximizes the detection of the induced birefringence effect. Finally, the wavelength gradient is... A full-factor orthogonal matching process is performed using the combination of light intensity gradient and polarization state to select dozens of sets of incident laser parameters with specific physical meaning and detection targeting. Subsequently, a Mach-Zehnder interferometer digital model or a femtosecond-level time-resolved pump-probe timing measurement model is constructed in a high-fidelity multiphysics simulation platform, including a frequency-stabilized laser source module, a high extinction beam-to-beam ratio module, a nonlinear interaction region, and a high-sensitivity detection module. The selected incident laser beams are then introduced as detection beams into a three-dimensional digital twin model of the device, integrating the real gas density distribution field and the initial electric field intensity distribution field. During light wave propagation, the step-by-step Fourier method is used to solve the nonlinear Schrödinger equation or the rigorous coupled-wave analysis equation, which includes Kerr effect and Raman scattering terms, to simulate... The complex nonlinear interaction process between the pseudo-optical wave and the non-uniform medium and strong electric field was investigated. The complex amplitude signals of the reference optical path (before it passed through the interaction region) and the probe optical path (after it passed through the equipment) were recorded simultaneously. A fast Fourier transform algorithm was used to perform high-resolution spectral analysis on the time-domain waveforms of both signals and accurately extract the fundamental frequency component. Then, high-precision differential calculations were performed on the phase and amplitude spectra of the two signals using complex division to completely eliminate the laser's own frequency drift and intensity noise, as well as systematic errors introduced by optical components. This allowed for the precise separation and extraction of multidimensional optical parameter changes, such as phase delay, light intensity attenuation rate, spectral broadening, and polarization rotation angle, caused solely by the non-uniform gas density distribution and electric field-induced nonlinear effects.This method, based on physical mechanisms to adaptively select laser parameters and combining dual-path differential detection with numerical wave equation solving, ensures comprehensive coverage of the gas's linear response, nonlinear growth, and saturation regions during testing. It effectively decouples the cross-coupling effects of density field changes and electric field effects on the optical signal, providing high-signal-to-noise ratio and physically well-understood raw data support for subsequent inversion of high spatial resolution gas density distribution fields and accurate correction of nonlinear optical parameters.

[0027] Furthermore, the gas density distribution field of the electrical equipment under test is obtained by inverting the optical parameter variation information. Optical response features are extracted from the optical parameter variation information; a linear integral relationship equation between the optical response features and the local gas density is constructed; the electrical equipment under test is divided into a three-dimensional voxel mesh, and a system weight matrix between the propagation path trajectory and the three-dimensional voxel mesh is constructed based on the propagation path trajectory of the incident laser; the pre-constructed initial gas density distribution field is processed based on the system weight matrix and the linear integral relationship equation to obtain the predicted optical response features; the initial gas density distribution field is corrected based on the optical response features and the predicted optical response features to obtain the final gas density distribution field.

[0028] The purpose of inverting the gas density distribution field of the electrical equipment under test based on the optical parameter change information is to transform the optical changes obtained by global optical path measurement into the gas density distribution at each point in the internal space of the equipment, so as to provide a spatial distribution basis for subsequent electric field calculation. The gas density distribution field describes the distribution data of gas density at various locations within the three-dimensional space of the electrical equipment under test. The optical response characteristics are characteristic quantities that directly reflect the gas effect, such as light intensity attenuation, phase change, and polarization change, extracted from the information on changes in optical parameters. The linear integral relationship equation is a mathematical equation describing the integral relationship between the optical response characteristics and the local gas density at each point along the laser propagation path. The three-dimensional voxel grid is a set of regular three-dimensional small units formed by dividing the internal space of the electrical equipment under test at a certain resolution. Each unit represents an independent spatial location. The propagation path trajectory is the actual spatial optical path formed by the incident laser after refraction, reflection, and transmission inside the equipment. The system weight matrix is ​​a mapping matrix that characterizes which voxels each laser path passes through and the length of the path within each voxel. The initial gas density distribution field is a priori uniform or approximately uniform three-dimensional density initial value given based on gas environment parameters. The predicted optical response characteristics are simulated optical signals obtained by forward calculation from the current gas density distribution. Through continuous correction, the predicted value is made to approach the measured value and eventually converge to obtain the true distribution.

[0029] The gas density distribution field obtained by inverting optical parameter variation information involves first accurately extracting optical response features, including phase retardation, intensity attenuation rate, and polarization rotation angle, from multi-dimensional optical parameter variation information containing multiple wavelengths, intensities, and polarization states. Based on Gladstone-Dale's law and Beer-Lambert's law, a set of integral equations describing the cumulative effect of the optical response features along the laser propagation path and its linear relationship with local gas density and temperature is constructed. Then, using a high-precision computer-aided design model, the internal three-dimensional space of the electrical equipment under test is discretized into hundreds of thousands of cubic voxel meshes with independent density, temperature, and composition properties. Monte Carlo ray tracing algorithms or deterministic ray casting algorithms are then used to accurately calculate the density distribution field for each selected beam. The propagation path of the emitted laser passes through the geometric length, incident angle, and direction cosine of each voxel, and a large sparse system weight matrix is ​​constructed based on this to characterize the intersection weights of the optical path and the spatial voxels. Then, a uniformly constructed initial gas density distribution field based on macroscopic average pressure and temperature estimation is set as the starting point for iteration. The system weight matrix is ​​used to perform a forward projection operation on this initial field and solve the radiative transfer equation to simulate the predicted optical response characteristics that should occur when light passes through this assumed density field. The measured optical response characteristics are then compared with the predicted optical response characteristics in a refined manner, wavelength-wise, path-wise, and polarization-wise comparison, to calculate the residual vector containing measurement noise, system errors, and model mismatch errors. A total variational regularization constraint term and a Tikhonov regularization constraint term are introduced. Regularization constraints are used to suppress reconstruction artifacts, eliminate ill-conditioned solution oscillations, and ensure the spatial continuity and physical smoothness of the density field. Algebraic reconstruction techniques combined with the conjugate gradient method and the Levenberg-Marquardt algorithm are employed to back-project the residuals along the original optical path and update the density values ​​of the corresponding voxels using an adaptive relaxation factor. In each iteration, the regularization coefficient is dynamically adjusted to balance data fidelity and solution smoothness. Simultaneously, non-negativity constraints and a maximum density threshold constraint are applied to ensure the physical feasibility of the solution. Through hundreds or even thousands of iterations, the initial gas density distribution field is continuously corrected until the root mean square error between the measured and predicted values ​​converges to a preset threshold and the density field distribution no longer changes significantly in three consecutive iterations. The final output accurately reflects the internal structure of the equipment. This high-resolution three-dimensional gas density distribution field, characterized by complex non-uniform states such as thermal convection due to conductor heating, aggregation of decomposition products due to partial discharge, or gas stratification due to gravity, can be reconstructed from one-dimensional path integral measurement data into a three-dimensional spatial density distribution using an iterative inversion method based on the principle of multi-source optical tomography. This effectively solves the problem that traditional single-point sensors cannot detect internal density gradients and local anomaly regions, eliminates the systematic deviation in refractive index calculation caused by the assumption of uniform gas distribution, and provides a physically accurate medium environment benchmark for subsequent accurate separation of linear effects caused by density non-uniformity and nonlinear effects caused by electric field. It also ensures the spatial accuracy and temporal dynamics of the input parameters of the electric field intensity measurement model.

[0030] Then, nonlinear optical parameters are extracted from the optical parameter variation information to determine the response curves of the nonlinear optical parameters. Based on the gas density distribution field and refractive index correction factor, the optical parameter variation information is processed to obtain the nonlinear optical response residuals. The incident laser peak intensity is extracted from the optical parameter variation information as the excitation variable, and correlation matching is performed on the nonlinear optical response residuals to obtain a set of optical response residual pairs. The set of optical response residual pairs is then fitted to determine the response curves of the nonlinear optical parameters.

[0031] Extracting nonlinear optical parameters from the optical parameter variation information and determining the response curve is to isolate the nonlinear contribution of the laser-gas interaction, providing a basis for subsequent parameter correction. Nonlinear optical parameters are physical quantities describing the nonlinear change of the refractive index of a gas with light intensity under a strong light field. The response curve is a functional relationship characterizing the nonlinear optical parameters as a function of the excitation variable. The nonlinear optical response residual is the change in optical parameters caused solely by nonlinear effects after deducting the effects of linear dispersion and absorption. The excitation variable is the peak intensity of the incident laser. The optical response residual pair consists of a data pair composed of the peak intensity and the corresponding nonlinear optical response residual. Fitting is performed by approximating the data pair set with a mathematical function to obtain a continuous variation relationship.

[0032] Extracting nonlinear optical parameters from optical parameter variation information and determining their response curves involves first using the high-resolution three-dimensional gas density distribution field obtained from previous steps and the refractive index correction factor calculated based on gas dispersion differences to perform refined linear background subtraction processing on the original optical parameter variation information. Specifically, this involves subtracting the theoretical linear optical response prediction value calculated by integrating the gas density distribution field along the laser propagation path from the measured total phase delay and total light intensity attenuation rate. This separates the nonlinear optical response residuals purely induced by strong light fields or high electric fields. The core of this step is to eliminate the dominant linear density effect interference, retaining only those reflecting nonlinear physical processes such as the Kerr effect or stimulated scattering. The weak signal of the process is then extracted from the raw data of each test condition, and the peak intensity of the incident laser or the square of the local electric field intensity in the corresponding optical path space is extracted as the excitation variable. This excitation variable represents the intensity of the energy source driving the nonlinear effect. Subsequently, each nonlinear optical response residual is strictly time-stamp aligned and spatially matched with its corresponding excitation variable to construct a set of optical response residual pairs containing multiple data points. This set intuitively shows the discrete distribution law of the nonlinear signal intensity changing with the excitation energy. Then, least squares regression analysis or robust fitting algorithm is used to perform curve fitting on the set of optical response residual pairs. In the fitting process, the fitting is set according to the nonlinear optical theoretical model, such as the cubic polarizability model. The mathematical form of the composite function is usually a quadratic function or a cubic polynomial. Through iterative optimization algorithms, the slope coefficient, intercept term, and higher-order nonlinear coefficients of the fitted curve are continuously adjusted to minimize the sum of squared residuals between the fitted curve and discrete data points. This results in a nonlinear optical parameter response curve that continuously characterizes the evolution of nonlinear optical parameters with respect to the excitation variable. From this curve, the initial slope characterizing the nonlinear refractive index coefficient, the threshold light intensity characterizing the saturation effect, and the inflection point characteristics characterizing higher-order nonlinear effects are extracted. This curve construction method based on linear background stripping and excitation variable correlation matching effectively solves the technical problem of strong linear backgrounds submerging weak nonlinear signals. This is demonstrated by using test data from multiple sets of different light intensities. The complete nonlinear response trajectory is reconstructed from the points, avoiding the shortcomings of single-point measurement in distinguishing between linear noise and nonlinear true value. This ensures that the extracted nonlinear optical parameters have clear physical meaning and high confidence, providing accurate characteristic benchmarks and data support for subsequent quantification of the deviation between theoretical models and actual working conditions, as well as for calculating the correction of the first parameter. At the same time, the response curve can also serve as a characteristic fingerprint for diagnosing whether there is abnormal discharge or impurity contamination inside the gas, because different gas components or fault states will significantly change the shape and saturation threshold of the response curve. This achieves a leap from single numerical measurement to full characteristic curve analysis, greatly improving the electric field strength measurement model's ability to characterize complex nonlinear effects and its correction accuracy.

[0033] Secondly, based on the differences in gas dispersion due to gas environment parameters, the refractive index correction factor is determined. Based on the gas environment parameters, the theoretical refractive index values ​​of each incident laser are obtained. A reference incident laser is selected, and the refractive index deviation of each of the other incident lasers relative to the reference incident laser is calculated. The corresponding spectral dispersion characteristics are then obtained based on each refractive index deviation. The refractive index correction factor is obtained by normalizing each spectral dispersion characteristic.

[0034] The core of determining the refractive index correction factor based on gas dispersion differences in gas environment parameters is to correct the refractive index deviation when lasers of different wavelengths propagate in a gas, ensuring the accuracy of subsequent optical parameter calculations and model optimization. Gas dispersion differences refer to the differences in the rate and trend of refractive index change with wavelength for different gas components at different incident laser wavelengths. The refractive index correction factor is a coefficient used to correct the refractive index calculation deviation caused by dispersion effects during laser propagation. The theoretical refractive index value is the ideal refractive index value calculated based on gas environment parameters and dispersion laws, excluding external interference. The reference incident laser is a laser selected from various incident lasers as a comparison benchmark. The refractive index deviation is the difference between the theoretical refractive index values ​​of the other incident lasers and the theoretical refractive index value of the reference incident laser. Spectral dispersion characteristics characterize the law of refractive index deviation with wavelength for different wavelength lasers. Normalization is a method of converting spectral dispersion characteristics of different orders of magnitude to the same numerical range, eliminating the influence of dimensions.

[0035] Determining the refractive index correction factor based on the gas dispersion differences in gas environment parameters involves first thoroughly analyzing the mole fraction, absolute pressure, and thermodynamic temperature of the gas components within the gas environment parameters. Then, using a high-precision molecular spectroscopy database, the static polarizability and resonance frequency parameters of each gas component under standard conditions are retrieved. Next, the Siddle equations are substituted to calculate the theoretical refractive index values ​​for each selected incident laser wavelength under the current actual operating conditions. This theoretical refractive index value represents the rate at which light waves propagate through a specific wavelength in a gas at an ideal homogeneous medium, relative to the speed of light in a vacuum. It is a fundamental physical quantity describing the optical density of the gas. Finally, from a selection of multiple working wavelengths, a wavelength located at the center of the gas transparency window and exhibiting the most stable linear response is chosen. As a reference incident laser, this reference wavelength typically has the smallest absorption cross-section and the gentlest dispersion slope. Using this as a reference zero point, the theoretical refractive index difference (i.e., refractive index deviation) relative to this reference incident laser is calculated for each of the other working wavelengths. This deviation quantifies the degree of difference in the propagation speed of different colors of light in the same medium, directly reflecting the spectral dispersion characteristics of the gas. Then, all calculated refractive index deviations are normalized by dividing the refractive index of the reference wavelength by one, resulting in a dimensionless refractive index correction factor. This correction factor is essentially a weighted coefficient characterizing the proportion of sensitivity to changes in the gas refractive index at different wavelengths. It describes the additional phase difference produced by non-reference wavelengths relative to the reference wavelength when the gas density changes by a unit. The factor relating the optical delay or path length variation eliminates the problem of capturing minute changes in absolute refractive index, which is often on a massive scale. This normalization process transforms complex dispersion relationships into simple proportionality coefficients, allowing subsequent calculations to directly map measurements at the reference wavelength linearly to other wavelengths without requiring repeated solutions to complex equations of state. This method, based on first-principles calculations and relative deviation analysis, accurately captures the subtle dispersion evolution of mixed gases under high pressure and high temperature conditions, avoiding systematic errors introduced by standard atmospheric empirical constants. It ensures that the correction factor adapts in real-time to the actual gas state inside the equipment. Its core advantage lies in constructing a factor independent of absolute density values ​​using dispersion differences between multiple wavelengths. The relative measurement scale provides crucial mathematical constraints for the subsequent separation of the temperature and density fields. This is because the effect of temperature changes on the refractive index has a specific proportional relationship at different wavelengths, while the effect of density changes follows the Gladstone-Dale law. By introducing this precise refractive index correction factor, the cross-coupling effect of temperature and density on the optical signal can be effectively decoupled in the subsequent inversion algorithm, significantly improving the spatial resolution and accuracy of the gas density distribution field inversion. Simultaneously, this factor also serves as a benchmark for the theoretical linear response, used to compare with the measured nonlinear response curve to quantify model deviations. This ensures that the electric field strength measurement model can accurately distinguish between linear distortions caused by non-uniform gas distribution and nonlinear distortions caused by strong electric fields.Ultimately, accurate modeling and correction of the optical propagation characteristics under multi-physics environment inside high-voltage electrical equipment were achieved.

[0036] Next, based on the response curve, refractive index correction factor, and gas density distribution field, the first parameter correction amount for the nonlinear optical parameters is determined. The gas density distribution field is mapped to a theoretical linear refractive index distribution based on the refractive index correction factor and path integral processing is performed to obtain the theoretical linear optical response prediction value. Based on the theoretical linear optical response prediction value and optical parameter variation information, the theoretical nonlinear response curve is obtained. The response curve and the theoretical nonlinear response curve are compared using a difference comparison process to obtain a nonlinear residual sequence. Based on the optical parameter variation information, the nonlinear sensitivity coefficient is obtained. The nonlinear residual sequence and the nonlinear sensitivity coefficient are compared and inverted to obtain the first parameter correction amount. An observation vector is constructed based on the nonlinear residual sequence, and a sensitivity matrix is ​​obtained based on the nonlinear sensitivity coefficient. Based on the observation vector and the sensitivity matrix, a mapping equation is obtained. Using the mapping equation as a constraint, the pre-constructed regularized objective function is iteratively optimized using the conjugate gradient technique to obtain the optimal parameter deviation solution. The optimal parameter deviation solution is then subjected to grid mapping processing to obtain the first parameter correction amount for the nonlinear optical parameters.

[0037] The first parameter correction amount, determined based on the response curve, refractive index correction factor, and gas density distribution field, is crucial for correcting deviations in nonlinear optical parameters caused by dispersion effects and gas density distribution. This provides accurate nonlinear parameter input for optimizing the electric field strength measurement model. The first parameter correction amount is a value used to correct deviations in the original nonlinear optical parameters, ensuring they align with actual equipment operating conditions. The theoretical linear refractive index distribution is a three-dimensional refractive index spatial distribution containing only linear dispersion effects, obtained by mapping the gas density distribution field through the refractive index correction factor. Path integration is the process of integrating the theoretical linear refractive index distribution along the incident laser propagation path. The theoretical linear optical response prediction value is a simulated optical response value obtained through path integration, considering only linear effects. The theoretical nonlinear response curve is the response relationship curve generated solely by nonlinear effects after subtracting the theoretical linear optical response prediction value. The nonlinear residual sequence is the deviation data sequence obtained by comparing the response curve and the theoretical nonlinear response curve point by point. The nonlinear sensitivity coefficient... The coefficients characterize the degree of influence of changes in nonlinear optical parameters on the optical response. The observation vector is a vector constructed based on the nonlinear residual sequence for iterative optimization. The sensitivity matrix is ​​a matrix composed of all nonlinear sensitivity coefficients. The mapping equation is a linear equation describing the relationship between the observation vector, the sensitivity matrix, and the parameter deviation solution. The regularization objective function is a mathematical function used to avoid overfitting during the iterative optimization process and to ensure the stability of the solution. The conjugate gradient technique is an iterative optimization algorithm used to solve for the optimal solution of the regularization objective function. The optimal parameter deviation solution is the nonlinear optical parameter deviation value that minimizes the residual obtained after iterative optimization. The mesh mapping process is a method of mapping the optimal parameter deviation solution to the three-dimensional voxel mesh of the device to obtain a spatially uniform correction amount.

[0038] The first parameter correction for determining nonlinear optical parameters based on response curves, refractive index correction factors, and gas density distribution fields refers to first using the refractive index correction factor determined in the previous steps as a physical mapping bridge to convert each voxel density value in the inverted high-resolution three-dimensional gas density distribution field into the corresponding local theoretical linear refractive index value, thereby constructing a theoretical linear refractive index distribution field that reflects the non-uniformity of the actual medium inside the device. Then, a ray tracing algorithm is used to perform line integral operations on this theoretical linear refractive index distribution field along the propagation path of each selected incident laser beam, calculating the phase delay and intensity attenuation rate that the laser should produce under ideal conditions, considering only the non-uniform gas density distribution and ignoring nonlinear effects. This is the theoretical linear optical response prediction value, which represents the model's best estimate of the linear background effect. Subsequently, the theoretical linear optical response prediction value is subtracted from the measured optical parameter variation information, and the remaining part is the nonlinear optical response residual purely induced by strong light fields or high electric fields. Simultaneously, the theoretical linear optical response prediction value is combined with the peak intensity distribution of the incident laser, based on nonlinear optical polarization theory... The theoretical nonlinear response curve expected by the model under the current density distribution is derived. This curve describes the ideal trajectory of the nonlinear signal as the light intensity changes when the nonlinear parameters in the pre-constructed electric field strength measurement model are completely accurate. Then, the measured nonlinear optical parameter response curve obtained by fitting the measured data in the previous section is compared point by point with the theoretical nonlinear response curve. The difference sequence between the two in terms of slope, curvature and saturation threshold is calculated, which is the nonlinear residual sequence. This sequence quantifies the degree of mismatch between the existing model parameters and the actual physical conditions. At the same time, based on multiple sets of test data with different light intensities in the optical parameter change information, the rate of change of the response signal caused by the unit change of the nonlinear optical parameters is calculated, which is the nonlinear sensitivity coefficient. This coefficient constitutes the Jacobian matrix element connecting the parameter deviation and the signal residual, reflecting the sensitivity of the system to parameter disturbances. Then, the nonlinear residual sequence is assembled into a multidimensional observation vector, and the nonlinear sensitivity coefficients under all optical paths and wavelengths are assembled into a large sparse sensitivity matrix, thereby establishing a mapping equation describing the linear approximate relationship between the parameter deviation and the observation residual.This equation explicitly characterizes the linear response mechanism between parameter bias and observation residuals, and is directly embedded as a core constraint into the gradient calculation term of the pre-constructed regularized objective function. Since this inversion problem is typically ill-conditioned and susceptible to measurement noise, direct inversion would lead to severe oscillations in the solution. Therefore, a regularized objective function containing a data fidelity term and a spatial smoothing regularization term is constructed. The mapping equation serves as the constraint. The data fidelity term minimizes the residual norm between the observation vector and the model prediction, while the spatial smoothing regularization term constrains the continuity of parameter corrections between adjacent grid points to conform to the physical reality distribution. A conjugate gradient technique is introduced to efficiently iteratively optimize this pre-constructed regularized objective function. In each iteration, the search direction is dynamically calculated and the optimal step size is determined. Simultaneously, physical constraints such as parameter non-negativity and maximum rate of change are applied to prevent solution divergence until the objective function value converges to a preset threshold or the parameter update approaches zero, ultimately yielding the solution. The optimal parameter deviation solution, which minimizes the global residual, represents the correction requirements of the nonlinear optical parameters at various points in space. Finally, this optimal parameter deviation solution is remapped back to the 3D computational model mesh of the electrical equipment under test according to the mesh index, generating the first parameter correction field of the nonlinear optical parameters with the same resolution as the original model. This determination method, based on the deviation analysis of measured and theoretical curves and regularized iterative inversion, can accurately remove the linear interference caused by density nonuniformity and directly deduce the spatial distribution error of microscopic nonlinear parameters from macroscopic signal differences. It effectively solves the problem that traditional single-point calibration cannot adapt to complex nonuniform fields. By introducing regularization constraints, the physical rationality and spatial smoothness of the correction amount are ensured, avoiding model distortion caused by overfitting noise. It significantly improves the characterization accuracy of the electric field strength measurement model for nonlinear physical processes such as the Kerr effect, laying a solid parameter foundation for subsequent high-fidelity electric field strength reconstruction.

[0039] Next, each linear optical parameter in the optical parameter variation information is extracted, and a second parameter correction amount is determined for each linear optical parameter based on the gas environment parameters. Each linear optical parameter extracted from the optical parameter variation information includes at least the gas molecule density, phase mismatch coefficient, and focusing Rayleigh length. The gas environment parameters are processed to obtain a first correction amount for the gas molecule density. Based on the optical parameter variation information, a second correction amount for the phase mismatch coefficient and a correction wavelength value are obtained, and a third correction amount for the focusing Rayleigh length is obtained based on the correction wavelength value. Based on the first, second, and third correction amounts, the second parameter correction amount for each linear optical parameter is determined.

[0040] The system extracts the linear optical parameters from the optical parameter variation information and determines the second parameter correction amount for each linear optical parameter based on the gas environment parameters. The core is to correct the deviation of the linear optical parameters affected by the gas environment. Together with the first parameter correction amount, it completes the comprehensive parameter optimization of the electric field intensity measurement model. Linear optical parameters are physical quantities that describe the linear effects produced when laser propagates in a gas. They include at least gas molecule density, phase mismatch coefficient, and focused Rayleigh length. Gas molecule density is the number of gas molecules per unit volume, which directly affects the absorption and scattering effects of the laser. The phase mismatch coefficient is a coefficient characterizing the deviation of the laser's phase change from the ideal state during propagation, affecting laser interference and propagation stability. The focused Rayleigh length is the propagation distance when the laser spot radius is increased to √2 after focusing, reflecting the laser focusing characteristics. The second parameter correction is a correction value used to correct the deviations of each linear optical parameter to make it conform to the actual gas environment of the equipment. The first correction, namely the gas molecule density correction, is a correction value for the deviation calculated for the gas molecule density. The second correction, namely the phase mismatch coefficient correction, is a value for correcting the deviation of the phase mismatch coefficient. The correction wavelength value is the incident laser wavelength after correction based on the gas environment parameters. The third correction, namely the focused Rayleigh length correction, is a correction value for the deviation calculated for the focused Rayleigh length.

[0041] The second parameter correction for extracting each linear optical parameter from the optical parameter variation information and determining it based on the gas environment parameters refers to first accurately separating each linear optical parameter related only to gas density and linear refractive index from the optical parameter variation information containing multiple wavelengths and polarization states. These parameters specifically include gas molecule density, which characterizes the number of gas molecules per unit volume; phase mismatch coefficient, which describes the phase accumulation error caused by the difference in propagation speed between the fundamental frequency light and the second harmonic light in the medium; and focusing Rayleigh length, which characterizes the propagation distance of the laser beam to maintain high energy density in the focusing region. Then, the previously acquired gas environment... The absolute pressure and thermodynamic temperature values ​​in the parameters are processed using the ideal gas law, converting the measured pressure and temperature data into accurate gas number densities under the current operating conditions. These are then compared with the gas density distribution field obtained from a previous inversion to calculate the gas molecule density correction. This correction is used to correct density reference deviations caused by macroscopic sensor errors or local microclimate fluctuations. Subsequently, using phase delay difference data at different wavelengths from the optical parameter variation information, combined with the phase matching condition formula in nonlinear optics, the wave vector mismatch in the actual optical path is calculated, thus obtaining the phase mismatch coefficient correction. Simultaneously, through... The center wavelength shift of the second harmonic signal acquired by the analytical spectrometer is used to obtain a corrected wavelength value. This value reflects the change in the effective working wavelength caused by gas dispersion and inhomogeneity. Then, based on Gaussian beam propagation theory, the focusing Rayleigh length correction is recalculated using the corrected wavelength value and the measured beam waist radius to correct for beam focusing position drift and depth of focus changes caused by the refractive index gradient of the medium. Finally, the calculated gas molecule density correction, phase mismatch coefficient correction, and focusing Rayleigh length correction are weighted, fused, and spatially mapped to determine the second parameter correction for each linear optical parameter on the three-dimensional computational grid. The correction method based on the joint solution of multiple physical parameters can comprehensively cover the main physical factors affecting the linear optical response. By correcting the gas density, phase matching conditions and beam propagation characteristics in real time, it effectively eliminates the linear measurement errors caused by environmental parameter fluctuations and beam distortion, ensuring the accuracy of the linear background model. This makes the subsequent separation of nonlinear effects from the total signal purer and more reliable, avoiding misjudgment of nonlinear parameters due to inaccurate linear parameters. It significantly improves the robustness and calculation accuracy of the electric field strength measurement model under complex dynamic conditions, providing a solid linear physical foundation for the accurate reconstruction of the internal electric field of high-voltage electrical equipment.

[0042] Furthermore, based on the first parameter correction amount and each of the second parameter correction amounts, the parameters of the pre-constructed electric field strength measurement model of the electrical equipment under test are optimized to obtain the optimized electric field strength measurement model.

[0043] Based on the first parameter correction and various second parameter corrections, the pre-constructed electric field strength measurement model of the electrical equipment under test is optimized to obtain the optimized electric field strength measurement model. The core is to correct the deviations of nonlinear and linear optical parameters in the model, so that the model calculation results closely match the actual electric field state of the equipment. The pre-constructed electric field strength measurement model is a mathematical model based on electromagnetic theory and optical propagation laws, used to calculate the internal electric field strength distribution of the electrical equipment under test. Its initial parameters include the initial values ​​of nonlinear and linear optical parameters, but it does not consider the deviations caused by the gas environment and optical effects. The optimized electric field strength measurement model, after parameter correction, has higher calculation accuracy and can truly reflect the actual electric field distribution of the equipment.

[0044] The optimization of the electric field strength measurement model of the pre-constructed electrical equipment under test based on the first parameter correction and various second parameter corrections involves mapping and superimposing the first parameter correction, which characterizes the nonlinear refractive index coefficient error obtained through nonlinear residual inversion in the previous steps, and various second parameter corrections, which characterize the gas molecule density error, phase mismatch coefficient error, and focusing Rayleigh length error obtained through linear parametric calculation, one by one according to the spatial grid index, into the corresponding physical parameter fields of the pre-constructed electric field strength measurement model. This pre-constructed electric field strength measurement model is an inversion calculation model specifically built based on the physical mechanism of electric field-induced second harmonic effect. Its core algorithm is based on the third nonlinear... Polarization theory establishes a quantitative conversion relationship between the second harmonic light intensity and the square of the external DC electric field intensity. Then, the dielectric property matrix and phase matching factor in the model are reinitialized using updated physical parameters. The fixed nonlinear polarizability constant and linear refractive index constant, originally based on the assumption of an ideal homogeneous gas, are replaced with a modified parameter field that dynamically varies with spatial location. This constructs an adaptive inversion environment that can realistically reflect the non-uniform gas distribution inside the device, the phase mismatch caused by dispersion, and the nonlinear saturation effect of the strong light field. Subsequently, the inversion solver is started to iteratively solve the modified electric field-induced second harmonic effect equations. During the solution process, the Newton-Raphson method is used to handle the nonlinear coupling convergence problem between the electric field intensity and the second harmonic signal. This method utilizes multigrid technology to accelerate the solution speed of the spatial electric field distribution until the relative error between two consecutive iterations of key physical quantities such as the inverted electric field intensity distribution, second harmonic conversion efficiency, and phase-matching integral value is less than a preset convergence threshold. The final output is an optimized electric field intensity measurement model containing high-precision spatial electric field distribution data, local field strength extremum coordinates, and the contribution rate of nonlinear effects. This parameter closed-loop optimization method based on multi-source optical feedback can directly convert laser-measured inversion data into correction instructions for the electric field inversion model, effectively solving the problem of electric field inversion distortion caused by the inability of traditional calculation models based on electric field-induced second harmonic effects to adapt to complex actual working conditions due to reliance on idealized gas parameters. Through real-time... Correcting the nonlinear polarizability background affecting the second harmonic generation efficiency and the linear phase matching condition affecting signal propagation significantly improves the model's prediction accuracy for the gas breakdown critical electric field, the partial discharge initiation field strength, and the electric field distortion region. This ensures a high degree of consistency between the electric field strength calculation results based on the second harmonic signal inversion and the actual physical field inside the equipment. It provides a highly confident digital basis for insulation status assessment, fault early warning, and optimized design of high-voltage electrical equipment. At the same time, this optimization process achieves a technological leap from offline static estimation to online dynamic correction, enabling the electric field strength measurement model based on the electric field-induced second harmonic effect to automatically evolve with changes in the gas environment, greatly enhancing the proactive defense capability of power system security monitoring.

[0045] Finally, the electric field strength results output by the electric field strength measurement model are obtained. Obtaining the electric field strength results output by the electric field strength measurement model is the final data acquisition step in completing the entire optical detection and electric field inversion process. The electric field strength measurement model is an electric field strength calculation model optimized by the first and second parameter corrections. It can accurately reflect the electric field distribution state in the three-dimensional space inside the electrical equipment under test. The electric field strength results are a complete dataset containing the electric field strength amplitude, electric field vector direction, and electric field uniformity index at each voxel grid position inside the equipment. In practice, the optimized electric field strength measurement model is first launched. Acquired gas environment parameters, incident laser parameters, and gas density distribution field are input into the model's calculation interface to load boundary conditions and initial field quantities before calculation. Then, the model's numerical solution module is activated, using the finite-difference time-domain method or the finite element method to iteratively solve the electric field across the entire space. The electric field strength is calculated point-by-point according to a pre-defined voxel grid, simultaneously recording the spatial coordinates of each voxel and the corresponding scalar and vector components of the electric field strength. After calculation, the model automatically performs data post-processing, interpolating and smoothing the spatially discrete electric field strength data, removing outliers and eliminating abrupt changes beyond reasonable limits. The data is then organized into a structured electric field strength dataset according to spatial coordinates and output as a matrix or 3D field diagram through the data interface, ultimately completing the acquisition of the complete electric field strength results. This approach directly obtains reliable electric field distribution data within the equipment, providing a direct basis for insulation condition assessment and fault identification.

[0046] It should be noted that the above embodiments provide an electric field strength measurement method applicable to general gas environments. By acquiring gas environment parameters and optical parameter variation information, and combining the hierarchical correction of nonlinear and linear optical parameters, the parameter optimization of the electric field strength measurement model and the output of electric field strength results are achieved. The following embodiments are further concretizations and application extensions based on the above embodiments. The optical parameter correction framework based on gas environment parameters proposed in the above embodiments is applied to actual physical modeling. Based on the overall measurement process of steps S2 to S9 of the first embodiment, the following embodiments further focus on the nonlinear optical effect of electric field-induced second harmonics. The "first parameter correction amount of nonlinear optical parameters" and the "refractive index correction factor based on gas dispersion difference" in the above embodiments are analyzed in depth, and an innovative "decoupling analysis and hierarchical compensation" strategy applicable to SF6 gas environments is proposed. Therefore, the following embodiments are essentially specific application examples and physical deepenings of the first embodiment in SF6 gas environments. Together, they constitute a complete technical solution from a general measurement method to adaptation to special gas environments.

[0047] Another embodiment of this invention discloses a method for constructing and correcting the electric field calculation model for electric field-induced second harmonics (HHMs) in SF6 gas environments. This method aims to address the measurement error problem caused by neglecting changes in medium properties in existing measurement models under the complex SF6 gas environment. Firstly, based on the nonlinear optical physics principle of HHMs, this method deeply analyzes the original calculation model. The original model describes the quantitative relationship between the HHM output power, incident laser power, external induced electric field strength, and medium property parameters. By systematically analyzing the source, physical meaning, and formation mechanism of each physical quantity in the model, key correlation parameters directly related to the gas medium properties are clearly identified, mainly including gas molecule number density, third-order nonlinear polarizability, focusing Rayleigh length, and phase mismatch coefficient. These parameters characterize the number of molecules participating in the nonlinear response, the ability of gas molecules to generate nonlinear polarization, the effective range of the laser in the medium, and the phase matching relationship between the fundamental frequency light and the HHM light, and are the core factors determining the HHM signal intensity.

[0048] To address the unique characteristics of the SF6 gas environment, this invention further establishes the physical relationship between the aforementioned key correlation parameters and gas operating state parameters (i.e., gas pressure, temperature, and refractive index). Research shows that the pressure and temperature of SF6 gas directly regulate the gas molecule density by altering the molecular distribution characteristics per unit volume, thereby affecting the number of effective molecules participating in the nonlinear polarization process. Simultaneously, changes in the gas's refractive index correct the laser propagation wavelength in the medium, thus changing the focusing Rayleigh length and the effective interaction region. Furthermore, the difference in refractive index at different frequencies determines the phase-matching condition, directly affecting the value of the phase mismatch coefficient. For the third-order nonlinear polarizability, its equivalent value is not only related to the electronic structure and polarization characteristics of the gas molecules but is also indirectly affected by the density changes caused by pressure and temperature, as well as the changes in polarization capability reflected by the refractive index. Therefore, fluctuations in gas environment parameters significantly alter the nonlinear optical response characteristics through a multi-physics coupling mechanism.

[0049] To accurately characterize the complex effects of this nonlinear, strongly coupled, and multi-parameter correlation, this invention innovatively proposes a "decoupling analysis and hierarchical compensation" strategy, decomposing the environmental impact into four levels for structured correction. The first level, based on the ideal gas law, uses pressure and temperature for explicit basic compensation of gas molecule density. The second level, based on the gas refractive index and its dispersion characteristics, performs analytical calculations to correct the laser propagation wavelength, focusing Rayleigh length, and phase mismatch coefficient. The third level, targeting the most difficult-to-analyze third-order nonlinear polarizability, constructs a specific nonlinear mapping function with the compensated density and refractive index as input, employing a lightweight neural network or empirical formula for targeted compensation. The fourth level introduces a lightweight coupling correction network to fine-tune the combined output after the first three levels of compensation, capturing residual coupling effects not covered by the explicit model. This hierarchical strategy preserves the clarity of the physical mechanism while using a data-driven approach to solve the fitting problem of complex nonlinear relationships.

[0050] First, a dynamic reconstruction mechanism of gas molecule number density based on thermodynamic state.

[0051] Instead of treating the number of gas molecules participating in the nonlinear response as a fixed constant, this approach establishes a direct mapping between molecular density and the macroscopic environmental state based on the physical laws of the ideal gas law. The core principle is that gas pressure represents the momentum transfer intensity of molecular collisions per unit area, while temperature reflects the intensity of molecular thermal motion. When pressure increases or temperature decreases, the number of SF6 molecules compressed and contained per unit volume inevitably increases. Therefore, by correcting the molecular density to a function of pressure and temperature, it is possible to accurately and in real-time characterize the change in the total number of effective molecules actually participating in the electric field-induced second harmonic generation process under different operating conditions, thus eliminating signal amplitude errors caused by changes in gas density at a material level.

[0052] Second, an adaptive correction mechanism for light wave propagation scale and phase matching based on the optical properties of the medium.

[0053] To address the wave optical behavior of lasers propagating in gaseous media, the refractive index and its dispersion characteristics are used to explicitly correct the light wave parameters. The underlying physical principle is that the speed of light in a medium is lower than in a vacuum, causing the effective wavelength to shorten as the refractive index of the medium increases. This change in wavelength directly triggers two chain reactions: First, the focusing characteristics are changed. Due to the shortened wavelength, the divergence angle of the laser beam after focusing becomes smaller, which correspondingly extends the focusing depth (i.e., Rayleigh length) of high energy density, thereby expanding the effective spatial range for nonlinear interaction between the laser and gas molecules. Secondly, there is the drift in phase matching conditions. Because the fundamental frequency light and the second harmonic light have different frequencies, their corresponding refractive indices also differ (dispersion effect). This difference determines the difference in the phase accumulation velocity of the two light waves during propagation. By calculating the refractive index difference at different frequencies to correct the phase mismatch coefficient, it is possible to accurately reflect how changes in the gas environment disrupt or improve the coherent superposition conditions of light waves, thereby accurately predicting the signal interference enhancement or cancellation effect caused by phase mismatch.

[0054] Third, a special mapping mechanism for nonlinear response capability based on micro-polarization mechanism.

[0055] For the complex parameter of third-order nonlinear polarizability, which cannot be described by a simple linear formula, a data-driven nonlinear mapping relationship is constructed. The underlying physical principle is that the nonlinear polarizability of a gas depends not only on the electron cloud distortion characteristics of individual molecules, but also strongly on the density-determined distance between molecules and the local electric field environment reflected by the refractive index. In high-density SF6 gas, intermolecular collisions, dipole interactions, and local field enhancement effects cause the macroscopic polarizability to exhibit complex nonlinear variations. By using the corrected molecular density and refractive index as input, a nonlinear mapping function such as a neural network is used to fit this polarizability variation under multi-factor coupling, aiming to capture the dynamic drift of equivalent polarizability caused by microscopic intermolecular interactions that cannot be covered by traditional analytical formulas.

[0056] Fourth, a fine-tuning mechanism based on the residual coupling effect of the overall system behavior.

[0057] After completing the independent corrections for density, propagation scale, and polarization capability, a lightweight coupled correction network or empirical factor is introduced for final fine-tuning. The principle behind this is to acknowledge the complexity of the physical world: while the aforementioned layered corrections cover the main influencing factors, higher-order, nonlinear cross-coupling effects still exist between parameters (for example, temperature changes may simultaneously and slightly affect the refractive index dispersion curve and molecular collision cross-section, thus generating superposition errors). This step is equivalent to performing a "system-level calibration" of the entire measurement system, learning and compensating for residual errors that are not fully decoupled from the explicit physical model through a data-driven approach, ensuring that the final output second harmonic power prediction highly matches the comprehensive response characteristics in the real physical scenario.

[0058] Another embodiment of the present invention provides a system for measuring electric field strength; for details, please refer to [link to relevant documentation]. Figure 2 , Figure 2 The diagram shown illustrates the structure of an electric field strength measurement system according to one embodiment of the present invention, comprising: Acquisition module 11 is used to acquire the gas environment parameters of the electrical equipment under test; Test module 12 is used to obtain the optical parameter change information of each incident laser in the electrical device under test during the simulation test using each selected incident laser; Inversion module 13 is used to invert the gas density distribution field of the electrical equipment under test based on the optical parameter change information; The determination module 14 is used to extract nonlinear optical parameters from the optical parameter change information and determine the response curve of the nonlinear optical parameters; Dispersion module 15 is used to determine the refractive index correction factor based on the gas dispersion differences of gas environment parameters; The first module 16 is used to determine the first parameter correction amount of the nonlinear optical parameters based on the response curve, refractive index correction factor and gas density distribution field. The second module 17 is used to extract each linear optical parameter from the optical parameter change information, and to determine the second parameter correction amount for each linear optical parameter based on the gas environment parameters. The optimization module 18 is used to optimize the parameters of the pre-constructed electric field strength measurement model of the electrical equipment under test based on the first parameter correction amount and each of the second parameter correction amounts, so as to obtain the optimized electric field strength measurement model. Result module 19 is used to obtain the electric field strength results output by the electric field strength measurement model.

[0059] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc.

[0060] Accordingly, embodiments of the present invention provide a computer-readable storage medium, the computer-readable storage medium including a stored computer program, wherein, when the computer program is executed, it controls the device where the computer-readable storage medium is located to perform steps in the electric field strength measurement method of the above embodiments, for example... Figure 1 Steps S1 to S9 as described above.

[0061] This invention abandons traditional static parameter assumptions and instead acquires gas environment parameters in real time and performs multiple incident laser tests. It reconstructs the true gas density distribution field and nonlinear optical parameter response curves from the optical parameter variation information, calculates the refractive index correction factor using gas dispersion differences, and then precisely isolates errors caused by density non-uniformity and nonlinear effects by fitting the deviation between the measured response curve and the theoretical prediction. The first and second parameter correction amounts are then determined to optimize the pre-constructed electric field strength measurement model. This significantly improves the adaptability and anti-interference robustness of the electric field strength measurement model to complex operating conditions, ensuring high-precision output of true electric field strength values ​​even in mixed gas and non-uniform field environments. It effectively eliminates the risk of protection failure due to falsely low monitoring data, providing a reliable technical barrier for preventing SF6 gas breakdown, avoiding equipment explosions, and large-scale power outages.

[0062] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A method for measuring electric field strength, characterized in that, include: Obtain the gas environment parameters of the electrical equipment under test; During the simulation test using selected incident lasers, information on the changes in optical parameters of each incident laser in the electrical device under test is obtained. The gas density distribution field of the electrical equipment under test is obtained by inversion based on the optical parameter change information; Extract the nonlinear optical parameters from the optical parameter change information, and determine the response curve of the nonlinear optical parameters; Based on the differences in gas dispersion of the aforementioned gas environment parameters, a refractive index correction factor is determined; Based on the response curve, the refractive index correction factor, and the gas density distribution field, the first parameter correction amount of the nonlinear optical parameter is determined; Extract each linear optical parameter from the optical parameter change information, and determine the second parameter correction amount for each linear optical parameter based on the gas environment parameters; Based on the first parameter correction amount and each of the second parameter correction amounts, the parameters of the pre-constructed electric field strength measurement model of the electrical equipment under test are optimized to obtain the optimized electric field strength measurement model. Obtain the electric field strength result output by the electric field strength measurement model.

2. The method for measuring electric field strength as described in claim 1, characterized in that, The process of obtaining optical parameter variation information of each incident laser in the electrical device under test during simulation testing using selected incident lasers includes: Based on the gas components in the gas environment parameters, the dispersion curve corresponding to each gas component is determined, and the dispersion curve is selected based on a preset threshold to determine the wavelength gradient. Based on the gas density and preset nonlinear refractive index coefficient in the gas environment parameters, the critical light intensity is obtained, and the light intensity gradient is determined based on the critical light intensity. Based on the topology of the electrical device under test, determine the polarization state combination; Based on the wavelength gradient, the light intensity gradient, and the polarization state combination, each incident laser is selected; Simulation tests were performed based on the various incident lasers to obtain information on the changes in the optical parameters.

3. The method for measuring electric field strength as described in claim 2, characterized in that, The process of testing based on each incident laser to obtain the optical parameter variation information includes: Each incident laser is introduced into the electrical device under test to obtain the relationship between each incident laser and the corresponding detection optical path. Differential calculations are performed on each incident laser and its corresponding detection optical path to obtain the optical parameter variation information of each incident laser in the electrical device under test.

4. The method for measuring electric field strength as described in claim 1, characterized in that, The process of inverting the gas density distribution field of the electrical equipment under test based on the optical parameter variation information includes: Extract the optical response features from the optical parameter change information; Construct a linear integral equation relating the optical response characteristics and the local gas density; The electrical device under test is divided into a three-dimensional voxel mesh, and a system weight matrix of the propagation path trajectory and the three-dimensional voxel mesh is constructed based on the propagation path trajectory of the incident laser. The pre-constructed initial gas density distribution field is processed based on the system weight matrix and the linear integral relationship equation to obtain the predicted optical response characteristics; The initial gas density distribution field is corrected based on the optical response characteristics and the predicted optical response characteristics to obtain the gas density distribution field.

5. The method for measuring electric field strength as described in claim 1, characterized in that, The step of extracting the nonlinear optical parameters from the optical parameter change information and determining the response curve of the nonlinear optical parameters includes: The optical parameter variation information is processed based on the gas density distribution field and the refractive index correction factor to obtain the nonlinear optical response residual; The peak intensity of the incident laser in the optical parameter variation information is extracted as the excitation variable, and the nonlinear optical response residual is correlated and matched to obtain a set of optical response residual pairs. The optical response residual pair is fitted to determine the response curve of the nonlinear optical parameter.

6. The method for measuring electric field strength as described in claim 1, characterized in that, The determination of the refractive index correction factor based on the gas dispersion differences in the gas environment parameters includes: Based on the gas environment parameters, the theoretical refractive index values ​​of each incident laser are obtained. A reference incident laser is selected, and the refractive index deviation of each of the other incident lasers relative to the reference incident laser is calculated. Based on each of the refractive index deviations, the corresponding spectral dispersion characteristics are obtained. The refractive index correction factor is obtained by normalizing each of the aforementioned spectral dispersion characteristics.

7. The method for measuring electric field strength as described in claim 1, characterized in that, The determination of the first parameter correction amount for the nonlinear optical parameters based on the response curve, the refractive index correction factor, and the gas density distribution field includes: Based on the refractive index correction factor, the gas density distribution field is mapped to a theoretical linear refractive index distribution, and the theoretical linear refractive index distribution is processed by path integration to obtain the theoretical linear optical response prediction value. Based on the theoretical linear optical response prediction and the optical parameter variation information, the theoretical nonlinear response curve is obtained; The response curve and the theoretical nonlinear response curve are compared by difference to obtain a nonlinear residual sequence; Based on the optical parameter variation information, the nonlinear sensitivity coefficient is obtained; The nonlinear residual sequence and the nonlinear sensitivity coefficient are compared and inverted to obtain the first parameter correction amount.

8. The method for measuring electric field strength as described in claim 7, characterized in that, The step of comparing and inverting the nonlinear residual sequence with the nonlinear sensitivity coefficient to obtain the first parameter correction includes: An observation vector is constructed based on the nonlinear residual sequence, and a sensitivity matrix is ​​obtained based on the nonlinear sensitivity coefficient. Based on the observation vector and the sensitivity matrix, the mapping equation is obtained; Using the aforementioned mapping equation as a constraint, the pre-constructed regularized objective function is iteratively optimized based on the conjugate gradient technique to obtain the optimal parameter deviation solution; The optimal parameter deviation solution is subjected to mesh mapping processing to obtain the first parameter correction amount of the nonlinear optical parameter.

9. The method for measuring electric field strength as described in claim 1, characterized in that, The step of extracting each linear optical parameter from the optical parameter change information and determining a second parameter correction amount for each linear optical parameter based on the gas environment parameters includes: Extract each linear optical parameter from the optical parameter change information, wherein each linear optical parameter includes at least gas molecule density, phase mismatch coefficient and focusing Rayleigh length; The gas environment parameters are processed to obtain a first correction value for the gas molecule density; Based on the optical parameter change information, a second correction amount and a correction wavelength value for the phase mismatch coefficient are obtained, and based on the correction wavelength value, a third correction amount for the focusing Rayleigh length is obtained; Based on the first correction amount, the second correction amount, and the third correction amount, a second parameter correction amount is determined for each of the linear optical parameters.

10. A system for measuring electric field strength, characterized in that, include: The acquisition module is used to acquire the gas environment parameters of the electrical equipment under test; The test module is used to obtain information on the changes in optical parameters of each incident laser in the electrical device under test during the simulation test using each selected incident laser. The inversion module is used to invert the gas density distribution field of the electrical equipment under test based on the optical parameter change information; The determination module is used to extract nonlinear optical parameters from the optical parameter change information and determine the response curve of the nonlinear optical parameters; The dispersion module is used to determine the refractive index correction factor based on the gas dispersion differences of the gas environment parameters. The first module is used to determine the first parameter correction amount of the nonlinear optical parameter based on the response curve, the refractive index correction factor and the gas density distribution field; The second module is used to extract each linear optical parameter from the optical parameter change information, and determine the second parameter correction amount for each linear optical parameter based on the gas environment parameters. An optimization module is used to optimize the parameters of the pre-constructed electric field strength measurement model of the electrical equipment under test based on the first parameter correction amount and each of the second parameter correction amounts, so as to obtain the optimized electric field strength measurement model. The results module is used to obtain the electric field strength results output by the electric field strength measurement model.

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