A low-rank physical constraint surrogate modeling method and system for insulation structures of switchgears

Abstract

The application discloses a kind of low rank physical constraint agent modeling method and system of switchgear insulation structure, high-precision and low-precision finite element model is established for different structure parameters, and through material partition in-mapping, material interface two sides independent sampling and electric field vector local coordinate transformation, potential and electric field response are mapped to unified observation space.Utilize high-precision parameter point that has been solved to construct high-precision field state snapshot matrix, select skeleton sample column and skeleton observation degree of freedom row, form high-precision column skeleton matrix and cross sub-matrix;Based on high-low precision matching sample, establish cross-precision correction model.For the point to be predicted, low-precision skeleton observation response is input, high-precision equivalent skeleton observation response is obtained by cross-precision correction, and low-rank coefficient is solved by combining skeleton observation consistency, finite element physical residual and low-rank coefficient regularization term, to restore high-precision equivalent prediction full-field state;Through leaving out high-precision sample verification and updating agent model when error is over threshold.

Description

Technical Field

[0001] This invention relates to the field of insulation structure design and electric field finite element simulation technology for switchgear, and particularly to a low-rank physical constraint proxy modeling method and system for insulation structure of switchgear. Background Technology

[0002] During the insulation structure design phase, metal-armored switchgear, metal-enclosed switchgear, gas-insulated switchgear, and low-voltage switchgear assemblies require finite element analysis of the electric field for structures such as busbars, contact boxes, insulating supports, shielding covers, bushings, grounding supports, and cabinet gaps. Common design variables include conductor phase-to-phase distance, conductor-to-grounding cabinet distance, insulation thickness, creepage path length, shielding cover radius of curvature, dielectric constant of insulating material, bushing location, and the arrangement of grounding metal components.

[0003] Current design processes typically begin by providing multiple sets of candidate structural parameters, then establish a high-precision finite element model for each set of parameters and solve for the full field distribution to obtain indicators such as maximum electric field strength, peak field location, interphase insulation margin, ground insulation margin, surface electric field, and internal electric field of the material. When there are many design variables, multi-dimensional parameter scanning is required, or structural optimization needs to be performed, the high-precision three-dimensional finite element solver is repeatedly invoked, resulting in high computation time and storage costs. Directly reducing mesh accuracy or the number of sampling points may lead to the omission of local field strength peaks near the sharp corners of insulating components, shield edges, minimum air gaps, and material interfaces, thus causing misjudgments of insulation safety.

[0004] The potential and electric field distributions of the insulation structure of the same type of switchgear under adjacent parameters typically exhibit spatial correlation and parameter continuity. Therefore, a low-rank surrogate model can be constructed using the relevant information between solved samples. However, some low-rank recovery methods assume that the row and column data used for recovery come from the same complete matrix. In engineering applications, unsolved parameter points usually only yield low-precision meshes or local solution results, while skeleton columns typically come from high-precision finite element results. If low-precision observation rows are directly substituted into the skeleton matrix formed by high-precision samples, a systematic bias exists between the low-precision observations and the high-precision skeleton, failing to form a strictly high-precision full-field recovery closed loop.

[0005] Furthermore, variations in structural parameters can lead to changes in the node positions, local mesh density, and number of degrees of freedom of the finite element mesh. If only ordinary spatial interpolation is used to map the field responses of different meshes to a unified mesh, interpolation may be performed across the interfaces of conductors, air, and solid insulating materials, thus smoothing out jumps in the normal electric field or electric displacement at points of abrupt changes in dielectric constant and weakening local field strength peaks. For vector electric fields, if the coordinate definitions of the normal and tangential components are not unified when the structural orientation changes, it is also not conducive to modeling low-rank correlations between different parameter points.

[0006] Some surrogate models only calculate the finite element residuals after prediction and use these residuals for result evaluation or subsequent sampling. The physical equations are not involved in solving the surrogate coefficients, so the prediction results may still deviate from Gauss's law, irrotational conditions, material interface conditions, and electrode boundary conditions. Some surrogate models also only fit a single maximum field strength scalar and do not retain the full-field spatial structure. Therefore, a high-precision equivalent full-field proxy modeling method for switchgear insulation structure is needed. This method can clearly distinguish between solved high-precision parameter points and parameter points to be predicted, perform interface-aware unified mapping of field responses with different geometries and meshes, use high- and low-precision paired samples to correct low-precision skeleton observations, enable finite element physical constraints to directly participate in the solution of low-rank coefficients, and verify and update the proxy model by reserving high-precision samples. Summary of the Invention

[0007] This invention aims to address the problems in existing methods for scanning and continuously optimizing insulation structure parameters of switchgear, such as the high number of repeated calls to high-precision finite element methods, the difficulty in unifying the modeling of field solutions for different parameter points, the lack of a correction closed loop between low-precision observations and high-precision skeletons, the fact that surrogate predictions are not directly constrained by the finite element physical equations, the insufficient reliability of predictions near insulation boundaries, and the repeated evaluation of a large number of local field point constraints by general optimizers. The invention provides a method and system for surrogate modeling of low-rank physical constraints for switchgear insulation structures.

[0008] This invention discloses a low-rank physical constraint proxy modeling method for the insulation structure of switchgear, comprising the following steps: S01: Obtain the finite element basic model of the insulation structure of the switchgear, the set of design variables, the range of design variable values, the insulation constraint conditions, and the set of candidate parameter points, and define the set of solved high-precision parameter points and the set of unsolved parameter points under the current iteration.

[0009] S02. For candidate parameter points, establish high-precision finite element models and low-precision finite element models, establish a field response post-processing model including potential and electric field components, and establish an interface perception unified observation mapping model that combines material partitioning, independent sampling on both sides of the interface, and vector local coordinate transformation to obtain high-precision field state vectors and low-precision field state vectors in the unified observation space.

[0010] S03: Select initial high-precision parameter points from the candidate parameter point set, and obtain the high-precision field state and the corresponding low-precision field state for each initial high-precision parameter point to form a high-low precision paired sample.

[0011] S04 uses only the unified field state vector of the solved high-precision parameter points to estimate the normalized parameters and construct a high-precision field state snapshot matrix; the low-rank order is determined based on the singular value energy, cross-validation error or a predetermined rank threshold.

[0012] S05, select skeleton parameter points and skeleton observation degrees of freedom from the high-precision field state snapshot matrix, and construct a high-precision column skeleton matrix and cross submatrix; the selection of skeleton observation degrees of freedom simultaneously satisfies the requirements of low-rank identifiability, cross submatrix condition number, and insulation critical area coverage.

[0013] S06, using high and low precision paired samples, establish a cross-precision correction model from low precision skeleton observation response to high precision equivalent skeleton observation response. The cross-precision correction model is divided into blocks according to material region, electric field component or insulation evaluation region, and the ill-conditioned amplification of the correction model is limited by regularization.

[0014] S07. For unsolved parameter points, first call low-precision finite element method, local mesh solution or physical interpolation to obtain low-precision response on skeleton observation degrees of freedom. After cross-precision correction, obtain high-precision equivalent skeleton observation response. Then solve the low-rank coefficients through the objective function that simultaneously includes skeleton observation consistency term, finite element physical residual term and coefficient regularization term to restore the high-precision equivalent full-field state.

[0015] S08: Select reserved verification parameter points from the currently solved high-precision parameter point set; reconstruct the surrogate model using high-precision samples that do not include the reserved verification parameter points; and predict the high-precision equivalent full-field state of the reserved verification parameter points. Compare the surrogate prediction result with the high-precision finite element true result of the reserved verification parameter points in terms of the degrees of freedom of the verification observation to obtain the verification error of the current surrogate model. When the verification error is not greater than a preset verification threshold, output the parameter points to be predicted obtained in step S07. The high-precision equivalent prediction of the full-field response; when the verification error is greater than the preset verification threshold, select a new high-precision parameter point from the current unsolved parameter point set, and obtain its high-precision field state and low-precision field state at the same time, update the solved high-precision parameter point set, and re-execute steps S04 to S08.

[0016] In the preferred technical solution, step S01 includes: the candidate structure parameter vector is represented as: in, This indicates the number of structural parameters involved in the optimization, determined by the design task. Indicates the first The design variables are defined by their physical units, which are determined by the variable type. These include length parameters, angle parameters, material parameters, and positional parameters. The range of design variables is determined by the equipment structural dimensions, electrical clearance requirements, manufacturing capabilities, and assembly constraints. This represents the design space jointly defined by structural boundaries, manufacturing constraints, and insulation coordination requirements. The set of candidate parameter points is defined as follows: The set of high-precision parameter points has been solved as follows: The set of unsolved parameter points is ,in Indicates the number of candidate parameter points. Indicates the number of adaptive iterations. This indicates the number of high-precision parameter points that have been solved. Therefore, subsequent high-precision snapshot matrices are only derived from... The high-precision field state is actually obtained in the construction, and the high-precision full-field response that has not yet been obtained is not taken as a known quantity.

[0017] In the preferred technical solution, step S02 includes: targeting the candidate structure parameter vector The high-precision finite element discretization equation and the low-precision finite element discretization equation are expressed as follows: Among them, superscript and These represent high precision and low precision, respectively. This represents the matrix of the finite element system determined by the current structural parameters, material dielectric constant, boundary conditions, mesh, and element order. The number of degrees of freedom in a finite element method is represented by the number of degrees of freedom in the system matrix for a finite element discretization of an electrostatic field. Each element can be represented as: in, This represents the total number of finite element elements. Indicates the first The spatial integration region corresponding to each finite element element. For the entire electric field solution domain, Indicates the first Each unit corresponds to the dielectric constant of the material. , Represents the shape function of the finite element. Representation of spatial gradient operator , is used to describe the rate of change of shape functions in the spatial coordinate direction.

[0018] Represents the electric potential degree of freedom vector; Represents the load vector. Low-precision models include at least one of the following: coarse mesh models, low-order element models, geometrically simplified models, local region models, or low convergence accuracy models.

[0019] The electric field response is expressed as: in, This represents the electric field post-processing matrix formed by the gradient of the unit shape function, coordinate transformation, and field post-processing rules.

[0020] In the preferred technical solution, step S03 further includes: dividing the unified observation space into multiple physical regions: in, This refers to an observation sub-region within the conductor edge, air gap, interior of solid insulation, surface path, phase-to-phase path, or ground path; and Representing materials With materials The observation points are located on both sides of the interface. The interface-aware unified observation mapping performs spatial interpolation only within the same material sub-region, retaining the observation degrees of freedom on both sides of the material interface, and does not perform smooth interpolation across interfaces with abrupt changes in dielectric constant.

[0021] For a vector electric field, for each observation point in the unified observation space, a local orthogonal coordinate system is established, where the first basis vector is the normal direction of the material interface, and the second and third basis vectors are the tangential directions of the interface. A local orthogonal transformation matrix is ​​constructed from these three unit orthogonal basis vectors: in , , These represent the current structure parameter vectors respectively. The local normal unit vector and two tangential unit vectors corresponding to the next observation point satisfy the following: This matrix is ​​used to convert the global electric field obtained by the finite element method into local physical coordinates: The unified observation field state vector is represented as: in, The potential unified observation mapping matrix, its elements Indicates the first A unified observation point is composed of finite element nodes. The weights obtained from the differences; The unified observation mapping matrix of the electric field is determined by the unit gradient matrix, the coordinate rotation matrix, and the difference weights. This represents the number of degrees of freedom in a unified field state. The unified field state includes at least one of the following: electric potential, normal electric field, tangential electric field, field strength magnitude, or electric displacement component. (Function) This represents the column vector concatenation operation, which involves concatenating vectors... with vector Combine them into a new vector along the column direction.

[0022] In the preferred technical solution, step S04 includes: using only the first The high-precision sample estimate mean vector and scaling matrix are solved in the next iteration: in, For high-precision sample size, For the first The standard deviation of the unified field state degrees of freedom in the already solved high-precision sample: in This is the standard deviation function. To prevent low-degree-of-freedom scales from approaching zero, a preset minimum scale value is determined based on measurement accuracy. The normalized high-precision field state vector and high-precision snapshot matrix are as follows: When new high-precision samples are added, the estimation is recalculated. and The updated normalization parameters are then used to renormalize all historical high-precision samples and paired low-precision samples.

[0023] Because the potential distribution is continuous under adjacent structural parameters, the electric field distribution is correlated, and the changes in the insulation structure take precedence, a high-precision snapshot matrix is ​​necessary. It exhibits low-rank properties. (Regarding...) Perform singular value decomposition, low rank order It can be determined according to the following formula: in, This represents singular values ​​arranged in descending order. , The singular value energy threshold is determined through historical model validation and is typically set between 0.95 and 0.999. The low-rank order can also be adjusted by incorporating leave-one-out cross-validation error or engineering peak error.

[0024] In the preferred technical solution, step S05 includes: determining the skeleton parameter point index set using at least one of the following methods: column pivoting QR decomposition, maximum volume selection, lever fraction selection, or residual greedy selection. Construct a high-precision column skeleton matrix: in, and Adopting the approach The set of skeleton observation degrees of freedom indexes is determined by column pivoting QR decomposition, discrete empirical interpolation, maximum volume selection, or a greedy method with forced keypoints. ,structure: in, , This represents the skeleton observation degree of freedom selection matrix, used to further extract from the column skeleton matrix. The skeleton observation degrees of freedom cover at least one of the following: conductor edge, shield edge, insulator sharp corner, minimum air gap, both sides of material interface, surface path, phase-to-phase path, and ground path. The selection of the skeleton observation degrees of freedom simultaneously satisfies low-rank identifiability, cross-submatrix condition number requirements, and insulation critical region coverage requirements. If... Greater than the predetermined threshold number Then, increase or replace the skeleton observation degrees of freedom until the stable solution requirements are met.

[0025] In the preferred technical solution, step S06 includes: simultaneously performing low-precision solution for each solved high-precision parameter point to obtain the normalized low-precision field state. The low-precision skeleton observation response and the high-precision skeleton observation response are expressed as follows: For the parameter points to be predicted From the currently solved high-precision parameter point set Select high- and low-precision paired samples from the nearest neighbor to form a neighboring paired sample set. Each parameter point in the set All have high-precision skeleton observation response and the corresponding low-precision skeleton observation response Based on the weighted fitting of the paired samples, the parameters to be predicted are... Local cross-precision correction matrix and local bias vector Specifically, this involves solving the following locally weighted cross-precision correction model: in, This represents the non-negative weights determined based on parameter distance or local element relationships. , This represents the coefficient by which the correction matrix deviates from the constraint of the identity matrix. This represents the Frobenius norm.

[0026] In the preferred technical solution, step S07 includes: for the parameter points to be predicted First, a low-precision model is called to obtain... Then, the high-precision equivalent skeleton observation response of the parameter points to be predicted is calculated: When the correlation between high and low precision is strong and the number of samples is small, the calibration matrix It can be simplified to a regional diagonal scaling factor; when there is a stable nonlinear deviation, the correction model can also use low-dimensional kernel regression, local polynomial or a neural network constrained by monotonicity, but its input and output are limited to low-dimensional responses on the skeleton observation degrees of freedom.

[0027] Let the normalized global state of the parameter points to be predicted be written as: in, This represents the low-rank coefficients to be solved.

[0028] from Potential observations were extracted from the samples respectively. and electric field observation : in, Extraction matrix for potential observation, Extracting the matrix for electric field observations, Indicates based on the current low-rank coefficient The predicted high-precision potential field in the unified observation space is recovered. This represents the predicted high-precision electric field vector recovered based on the low-rank coefficients.

[0029] Define Gauss's law residual, irrotational condition residual, interface tangential residual, interface normal electric displacement residual, boundary condition residual, and potential gradient uniformity residual: The above residuals are combined as follows: in, This represents a discrete divergence operator that includes the dielectric constant. Represents volume charge terms or zero charge constraint terms; Represents the discrete curl operator; This indicates the extraction operator for the continuous condition of the tangential electric field at the material interface; The operator for extracting the condition of normal electric displacement jump is represented. Represents the surface charge term at the interface; Operators representing electrode potential, grounding, or equipotential boundary extraction. Indicates the boundary target value; This represents the potential gradient operator in a unified observation space. The physical residuals mentioned above can be calculated at all observation points, or at physical check points selected based on element residuals, critical insulation regions, and boundary coverage.

[0030] The low-rank coefficients are solved by the following formula: in, Represents the physical constraint weights. This represents the coefficient regularization parameter. This represents the skeleton observation weight matrix, used to describe the importance of different skeleton observation degrees of freedom in the low-rank coefficient solution. The weight matrix is ​​in diagonal form: in, Indicates the number of degrees of freedom observed in the skeleton. Indicates the first The weights of the skeleton observation degrees of freedom are determined based on the insulation evaluation area to which the observation point belongs, the field strength sensitivity, and the normalization scale; higher weights are assigned to critical observation degrees of freedom near conductor edges, shield edges, minimum air gaps, and material interfaces.

[0031] The dimensionally normalized and weighted matrix representing the different physical residual components is given by Gauss's law for the total residual. Irrotational conditional weights Interface condition weights Boundary condition weights Gradient consistency weights Determination of normalized statistical variance or project importance level: Therefore, the inverse normalized high-precision equivalent full-field prediction is obtained as follows: Compared to the method of using only the generalized inverse for posterior recovery, the above coefficient solution allows Gauss's law, irrotational condition, material interface condition, electrode boundary condition, and potential gradient relationship to directly participate in the determination of the final field state.

[0032] In the preferred technical solution, step S08 includes: from the first The set of high-precision parameter points solved in the next iteration Selecting outflow verification parameter points technique For any point where verification parameters are left out. Without using the high-precision field state of the parameter point to construct the high-precision snapshot matrix, column skeleton matrix, and cross-precision correction model, the high-precision equivalent prediction of the entire field state is obtained by following steps S04 to S07. subscript This indicates that no parameter points were used during the proxy model construction process. High-precision results.

[0033] Set the set of degrees of freedom for skeleton observation Incompletely overlapping set of verification observation degrees of freedom And use the verification observation degrees of freedom to select the matrix. Calculate the validation error of the current proxy model: in, Indicates leaving verification parameter points High-precision finite element method for real-time full-field conditions; and These represent the responses of the surrogate prediction results and the high-precision real results to the degrees of freedom of the verification observations, respectively. To prevent tiny constants with a denominator of zero; Indicates the current number The maximum relative verification error among the reserved verification parameter points in each iteration.

[0034] when Compared with the preset verification error threshold Between satisfy When the current proxy model meets the preset accuracy requirement, output: in This represents the current parameter point to be predicted.

[0035] when In this case, it is preferable to select the set of unsolved parameter points within the neighborhood of the parameter points with the largest verification error. Select a parameter point for which high-precision results have not yet been obtained. Simultaneously perform high-precision and low-precision finite element solutions on it to form new high- and low-precision paired samples, and update: Then, the normalization parameters are re-estimated using the updated sample set, a high-precision snapshot matrix and row and column skeleton are constructed, and the cross-precision correction model is updated, and steps S04 to S08 are re-executed.

[0036] The present invention also provides a low-rank physical constraint proxy modeling system for the insulation structure of switchgear, including an input data acquisition module, a high- and low-precision finite element modeling module, an interface-aware unified observation mapping module, a high-precision sample and low-rank skeleton module, a cross-precision correction module, a physical constraint full-field reconstruction module, a verification and update module, and a result output and data storage module.

[0037] The input data acquisition module is used to acquire the finite element basic model of the insulation structure of the switchgear, design variables, the range of design variable values, the set of candidate parameter points, and boundary conditions. The high-precision and low-precision finite element modeling module is used to establish high-precision finite element models and low-precision finite element models based on parameter points, and obtain potential response and electric field response respectively. The interface-aware unified observation mapping module is used to map high-precision field response and low-precision field response within the same material sub-region. It sets observation degrees of freedom on both sides of the material interface and converts the electric field vector in the global coordinate system into local normal and tangential components, forming high-precision field state vector and low-precision field state vector in the unified observation space. The high-precision sample and low-rank skeleton module is used to maintain the set of solved high-precision parameter points, use the high-precision field state vector of the solved high-precision parameter points to estimate the normalized parameters and construct the high-precision field state snapshot matrix, determine the low-rank order, select skeleton parameter samples and skeleton observation degrees of freedom, and form a high-precision column skeleton matrix and cross submatrix. The cross-precision correction module is used to establish a cross-precision correction model from the low-precision skeleton observation response to the high-precision equivalent skeleton observation response based on the high- and low-precision paired samples corresponding to the solved parameter points. The physical constraint full-field reconstruction module is used to obtain low-precision skeleton observation response for the parameter point to be predicted, obtain high-precision equivalent skeleton observation response through the cross-precision correction model, and solve the low-rank coefficient through the objective function containing skeleton observation consistency term, finite element physical residual term and low-rank coefficient regularization term to restore the high-precision equivalent prediction full-field state of the parameter point to be predicted. The verification and update module is used to select high-precision verification parameter points, obtain the high-precision equivalent predicted full-field state of the high-precision verification parameter points according to the physical constraint full-field reconstruction module, and compare it with the corresponding high-precision finite element real full-field state; when the verification error exceeds the preset verification threshold, high- and low-precision paired samples are added and the normalization parameters, high-precision field state snapshot matrix, low-rank order, high-precision column skeleton matrix and cross-precision correction model are updated. The result output and data storage module is used to output and store the parameter points to be predicted, the high-precision equivalent prediction of the entire field state, the potential response, the electric field response, the low-rank coefficients, and the model verification error.

[0038] Compared with the prior art, the present invention has at least the following beneficial effects.

[0039] First, this invention clearly distinguishes between all candidate parameter points, solved high-precision parameter points, and unsolved parameter points, and constructs a high-precision snapshot matrix using only the available high-precision samples, thus avoiding mistaking the unsolved high-precision full field as a known matrix row or column.

[0040] Second, this invention achieves interface-aware mapping for different geometries and mesh states by interpolating within material partitions, independently sampling both sides of the material interface, and unifying the electric field normal / tangential components. This can reduce the impact of ordinary cross-interface interpolation on the smoothing of abrupt changes in dielectric constant and local peaks.

[0041] Third, this invention utilizes high- and low-precision paired samples of the same parameter point to establish a cross-precision correction relationship, so that low-precision skeleton observations are first converted into high-precision equivalent skeleton observations, and then participate in the full-field reconstruction together with high-precision column skeletons, thus fixing the problem of inconsistent precision levels when directly substituting low-precision observations into high-precision skeletons to restore the relationship.

[0042] Fourth, this invention does not only calculate the physical residual after prediction, but also directly writes Gauss's law, irrotational condition, material interface condition, electrode boundary condition and potential gradient relationship into the low-rank coefficient solution objective, so that the physical constraints and the consistency of low-rank observation jointly determine the final global state.

[0043] Fifth, this invention independently verifies the full-field prediction error of the surrogate model by verifying the degrees of freedom of observation that do not completely overlap with the degrees of freedom of skeleton observation and by reserving high-precision samples, thus avoiding the use of training samples involved in model construction to self-verify the model; when the verification error exceeds a preset threshold, the normalization parameters, low-rank skeleton and cross-precision correction model are updated by supplementing high- and low-precision paired samples, thereby improving the reliability of the high-precision equivalent full-field prediction results.

[0044] Sixth, the result restored by this invention is a high-precision equivalent full-field state in a unified observation space, rather than a single maximum field strength scalar. It can simultaneously output the potential, electric field normal component, electric field tangential component, and field strength modulus, and retain the spatial distribution and local peak position of the field response, providing a complete field data basis for subsequent insulation verification and structural design.

[0045] The aforementioned technical features are not simply listed side-by-side. Interface-aware unified observation mapping provides unified physical coordinates for field responses with different geometries, meshes, and precision levels; the cross-precision correction model established by high- and low-precision paired samples ensures that the low-precision skeleton observations of the parameter points to be predicted are at a matching precision level with the high-precision column skeleton; finite element physical constraints directly participate in the low-rank coefficient solution, suppressing non-physical solutions caused by cross-precision correction errors and low-rank truncation; and the reserved high-precision sample verification and paired sample updates are used to evaluate and improve the overall prediction reliability of the surrogate model. These steps together form a complete technical closed loop: low-precision input—high-precision equivalent skeleton correction—physical constraint full-field reconstruction—independent verification and update. Attached Figure Description

[0046] Figure 1 This is a schematic diagram of the overall process of the low-rank physical constraint proxy modeling method for the insulation structure of switching equipment according to the present invention. Detailed Implementation

[0047] The present invention will be further described below with reference to the accompanying drawings. It should be noted that the specific embodiments described below are used to illustrate the technical concept and feasible path of the present invention, and are not intended to limit the scope of protection of the present invention. Where there is no conflict, the following technical features can be combined with each other.

[0048] Specifically, the following uses the busbar compartment of a metal-clad switchgear as an example to illustrate the multi-precision low-rank physical constraint proxy modeling process.

[0049] The finite element model includes three-phase busbars, contact boxes, insulating supports, shielding covers, cabinet panels, and grounding brackets. Design variables may include the phase-to-phase distance of the three-phase busbars. Distance from busbar to grounding cabinet Thickness of insulating support components Radius of curvature of the shield Dielectric constant of insulating materials and casing position At least one of the following. The range of design variables is determined by the product's external dimensions, electrical clearances, creepage distances, minimum wall thickness, assembly space, and machining tolerances.

[0050] The high-precision model employs locally refined meshes and higher-order elements in key field strength regions, and the solver residual threshold meets the accuracy requirements for product insulation verification. The low-precision model uses coarse meshes, lower-order elements, or simplified models in local regions. Low-precision results are calculated simultaneously for each high-precision sample, thus forming a one-to-one pairing of high- and low-precision samples. When different meshes are used in the high-precision and low-precision models, a mapping is established using unified observation point identification numbers and material partition identification numbers.

[0051] The unified observation space is established according to the following regions: the conductor edge and the mother box conductor edge are the first observation region; the rounded corners of the shield and the grounding metal edge are the second observation region; the interior of the insulating support is the third observation region; the minimum air gap and its neighborhood are the fourth observation region; the conductor-air interface and the sides of the insulating component-air interface are the fifth and sixth observation regions, respectively; parameterized observation points are set for the phase-to-phase path, the ground path, and the surface path. The observation points on both sides of the material interface have different material side identifiers and are not smoothed across the interface using the same interpolation unit.

[0052] The initial high-precision parameter points can be composed of the parameter space center point, boundary points of each major design variable, historical typical structural parameters, and Latin hypercube samples. To ensure the identifiability of cross-precision corrections, the initial number of paired samples should not be less than the larger of the low-rank order and the number of correction block parameters. After each new high-precision sample is added, the system saves the high-precision potential, high-precision electric field, low-precision potential, low-precision electric field, engineering peak position, engineering peak value of each region, and regional insulation margin.

[0053] The system only uses currently solved high-precision samples to build In one embodiment, candidate low-rank orders can be determined first according to the singular value energy threshold, and then the engineering peak error can be checked by leave-one-out cross-validation; if the energy threshold has been met but the engineering peak error is still higher than the requirement, the low-rank order can be increased or the skeleton observation degrees of freedom near the peak position can be forcibly added.

[0054] Skeleton parameter points can be selected by performing column-pivoting QR decomposition on the high-precision snapshot matrix. The skeleton observation degrees of freedom can first be obtained by performing column-pivoting QR decomposition on the transpose of the high-precision column skeleton matrix to obtain numerically identifiable points. Then, forced key points for conductor fillets, shield edges, minimum air gaps, and both sides of the material interface are added to the set. If highly correlated observation rows exist after adding forced key points, redundant observation points are replaced using the condition number and maximum volume criterion.

[0055] For points with unsolved parameters, the low-precision finite element model outputs the low-precision field states on the skeleton observation degrees of freedom and the verification observation degrees of freedom. Cross-precision correction is divided into blocks based on conductor edge regions, air gap regions, solid insulation regions, interface normal components, interface tangential components, and along the surface path. If the low-precision model in a certain region mainly exhibits amplitude deviation, a diagonal scaling factor and bias can be used; if stable coupling deviation exists, a small-scale block matrix is ​​used; if local samples are insufficient, the regularization strength is increased and the correction matrix is ​​limited to approach the identity matrix.

[0056] In solving for the physical constraint coefficients, the Gaussian law residuals are calculated separately on the observation units inside the air and solid insulating materials; the continuous residuals of the tangential electric field and the jump residuals of the normal electric displacement at the material interface are calculated on the paired observation points on both sides of the interface; the residuals of the electrode equipotential and grounding boundary are calculated on the observation points of the conductor and the cabinet; the potential gradient consistency residual is used to establish the relationship between the constraint potential prediction and the electric field prediction. Each residual is first normalized to engineering dimensions and then combined using a weight matrix.

[0057] During the model validation phase, at least one validation parameter point is selected from the currently solved high-precision parameter point set. This parameter point's high-precision field state is temporarily not used when constructing the high-precision snapshot matrix, column skeleton matrix, and cross-precision correction model. The parameter point is then reconstructed across the entire field according to step S07. Using the validation observation degrees of freedom that do not completely overlap with the skeleton observation degrees of freedom, the surrogate prediction results are compared with their actual high-precision finite element results. If the validation error exceeds a preset threshold, high- and low-precision paired samples are added, and the surrogate model is reconstructed.

[0058] This invention's system can be deployed on workstations, servers, or cloud computing platforms. The input data acquisition module receives parametric geometric models, material libraries, boundary conditions, mesh rules, design variable ranges, and insulation evaluation rules. The high- and low-precision finite element modeling modules generate high-precision and low-precision models through finite element software interfaces, script interfaces, or a self-developed solver.

[0059] The interface-aware unified observation mapping module stores the material region, interface side, local normal and tangential basis vectors, original finite element index, and interpolation weights for each unified observation point. The high-precision sample and low-rank skeleton module stores the high-precision snapshot matrix, low-rank order, skeleton parameter point set, skeleton observation degrees of freedom set, verification observation degrees of freedom set, and cross submatrix condition number.

[0060] The cross-precision correction module saves paired samples, neighborhood selection rules, correction block structure, regularization parameters, and correction residuals. The physical constraint full-field reconstruction module saves discrete divergence, discrete curl, interface jumps, boundary conditions, and potential gradient operators, and updates the dielectric constant and local geometric correlation coefficients based on candidate parameter points.

[0061] The verification and update module is used to select and retain high-precision verification parameter points, calculate the verification error between the surrogate prediction of the entire field and the high-precision finite element real field, and update the solved high-precision parameter point set, normalized parameters, high-precision snapshot matrix, low-rank skeleton, and cross-precision correction model when the verification error exceeds a preset threshold. The results output module is used to output the high-precision equivalent prediction of the entire field state, potential response, electric field response, and current model verification error for the parameter points to be predicted.

[0062] Those skilled in the art can make equivalent substitutions or combinations of the candidate parameter point generation method, low-precision model form, low-rank order determination method, skeleton parameter sample selection method, skeleton observation degree of freedom selection method, cross-precision correction model form, physical residual discretization method, and reserved verification sample selection method without departing from the technical concept of the present invention; as long as the interface-aware unified observation, high- and low-precision paired correction, high-precision row and column skeleton construction, and physical constraint low-rank coefficient solution to recover the high-precision equivalent full-field response of the parameter point to be predicted are still adopted, they are all implementation methods of the technical concept of the present invention.

Claims

1. A method for low-rank physical constraint proxy modeling of the insulation structure of switchgear, characterized in that, Includes the following steps: S01, obtain the finite element basic model of the insulation structure of the switchgear, design variables, the range of values ​​of design variables and the set of candidate parameter points, and define the set of solved high-precision parameter points and the set of unsolved parameter points under the current iteration; S02, establish parameterized high-precision finite element model and low-precision finite element model, perform post-processing on potential response and electric field response, and form high-precision field state vector and low-precision field state vector in unified observation space through mapping within material sub-regions, independent sampling on both sides of material interface and local orthogonal coordinate transformation of electric field vector. S03, select initial high-precision parameter points from the candidate parameter point set, and perform high-precision finite element solution and low-precision finite element solution on each initial high-precision parameter point to form high- and low-precision paired samples; S04, use only the high-precision field state vector of the solved high-precision parameter points to estimate the normalized parameters and construct a high-precision field state snapshot matrix, and determine the low-rank order based on the high-precision field state snapshot matrix; S05, Select the skeleton parameter sample column and skeleton observation degree of freedom row from the high-precision field state snapshot matrix to form a high-precision column skeleton matrix and cross submatrix; S06, Using the high- and low-precision paired samples, establish a cross-precision correction model from the low-precision skeleton observation response to the high-precision equivalent skeleton observation response; S07. For the parameter points to be predicted in the set of unsolved parameter points, the low-precision finite element model is called to obtain the low-precision skeleton observation response. The high-precision equivalent skeleton observation response is obtained through the cross-precision correction model. The low-rank coefficient is used as the variable to be solved. The low-rank coefficient is solved through an objective function that includes a skeleton observation consistency term, a finite element physical residual term, and a low-rank coefficient regularization term to restore the high-precision equivalent prediction of the entire field state of the parameter points to be predicted. S08: Select reserved verification parameter points from the set of solved high-precision parameter points, exclude the reserved verification parameter points when constructing the surrogate model, and obtain the high-precision equivalent predicted full-field state of the reserved verification parameter points according to step S07. Compare it with the corresponding high-precision finite element real full-field state. When the verification error is not greater than the preset verification threshold, output the high-precision equivalent predicted full-field state of the parameter point to be predicted. When the verification error is greater than the preset verification threshold, add high- and low-precision paired samples and re-execute steps S04 to S08.

2. The low-rank physical constraint proxy modeling method for the insulation structure of switchgear according to claim 1, characterized in that, The high-precision finite element model and the low-precision finite element model respectively satisfy: in, Represents a structure parameter vector, with superscripts and These represent high precision and low precision, respectively. and They represent the matrices of the finite element system, and These represent the electric potential degree of freedom vectors, and Let each represent a load vector; the electric field response satisfies: The low-precision finite element model is at least one of the following: coarse mesh model, low-order element model, geometrically simplified model, local region model, or model with reduced convergence accuracy.

3. The low-rank physical constraint proxy modeling method for the insulation structure of switchgear according to claim 2, characterized in that, In step S02, a local orthogonal transformation matrix consisting of a local normal unit vector and two local tangential unit vectors is established at each unified observation point: The high-precision field state vector and the low-precision field state vector are represented as follows: in, This represents the unified observation mapping matrix of potential. This represents the unified observation mapping matrix for the electric field. The unified observation mapping is performed only within the same material sub-region, and the observation degrees of freedom are retained on both sides of the material interface.

4. The low-rank physical constraint proxy modeling method for the insulation structure of switchgear according to claim 1, characterized in that, In step S04, the first The mean vector, scaling matrix, and normalized high-precision field state vector for each iteration are as follows: in, Indicates the first The set of high-precision parameter points solved in the next iteration. This indicates the number of high-precision samples in the set. Indicates the first The scale values ​​of the unified field state degrees of freedom in the high-precision sample. The scale lower bound is represented; a high-precision field state snapshot matrix is ​​constructed from normalized high-precision field state vectors. Its lower rank order is determined by the following formula: in, This represents singular values ​​arranged in descending order. , This represents the singular value energy threshold.

5. The low-rank physical constraint proxy modeling method for the insulation structure of switchgear according to claim 4, characterized in that, In step S05, based on the skeleton parameter sample index set Columns are extracted from the high-precision field state snapshot matrix to form a high-precision column skeleton matrix: Based on the skeleton observation degree of freedom index set Construct the skeleton observation degree of freedom selection matrix Then, row extraction is performed on the high-precision column skeleton matrix to form a cross submatrix: The skeleton parameter samples are determined using at least one of the following methods: column pivot QR decomposition, maximum volume selection, lever fraction selection, or residual greedy selection; the skeleton observation degrees of freedom simultaneously satisfy the requirements of low-rank identifiability, cross submatrix condition number, and insulation critical area coverage.

6. The low-rank physical constraint proxy modeling method for the insulation structure of switchgear according to claim 5, characterized in that, In step S06, the low-precision skeleton observation response and the high-precision skeleton observation response are respectively: For the parameter points to be predicted Select a set of neighboring paired samples from the set of already solved high-precision parameter points. The local cross-precision correction matrix and local bias vector are solved by the following formula: in, Indicates the weight of neighboring paired samples. This represents the constraint coefficient that causes the correction matrix to deviate from the identity matrix.

7. The low-rank physical constraint proxy modeling method for the insulation structure of switchgear according to claim 6, characterized in that, In step S07, the parameter points to be predicted The high-precision equivalent skeleton observation response is: For any candidate low-rank coefficient, the normalized candidate global state is: Extract the potential prediction from the normalized candidate full-field states. and electric field prediction And the finite element physical residual is expressed as: in The finite element physical residuals include Gauss's law residuals, irrotational condition residuals, material interface tangential electric field continuity residuals, material interface normal electric displacement jump residuals, boundary condition residuals, and potential gradient consistency residuals.

8. The low-rank physical constraint proxy modeling method for the insulation structure of switchgear according to claim 7, characterized in that, In step S07, the parameter points to be predicted The corresponding optimal low-rank coefficients are solved by the following formula: $ $ in, Represents the skeleton observation weight matrix. This represents the normalized dimensions and weight matrix of the physical residuals. Represents the physical constraint weights. The low-rank coefficient regularization parameter is represented; the inverse normalized high-precision equivalent prediction of the entire field state for the parameter points to be predicted is: 。 9. The low-rank physical constraint proxy modeling method for the insulation structure of switchgear according to claim 8, characterized in that, In step S08, the set of high-precision parameter points that have already been solved is... Select a set of validation parameter points from the middle. The verification error is expressed as: in, This represents the matrix for selecting the degrees of freedom of the verification observations. This indicates that parameter points are excluded when constructing the proxy model. After obtaining the high-precision results, the high-precision equivalent prediction of the entire field state is obtained according to step S07. Represents the stability constant; when When the value exceeds the preset verification threshold, select a new parameter point from the set of unsolved parameter points. And update the sample set according to the following formula: 。 10. A low-rank physical constraint proxy modeling system for the insulation structure of switchgear, characterized in that, It includes an input data acquisition module, a high- and low-precision finite element modeling module, an interface-aware unified observation mapping module, a high-precision sample and low-rank skeleton module, a cross-precision correction module, a physical constraint full-field reconstruction module, a verification and update module, and a result output and data storage module. The input data acquisition module is used to acquire the finite element basic model, design variables, the range of design variable values, and the set of candidate parameter points; The high-precision and low-precision finite element modeling module is used to establish high-precision finite element models and low-precision finite element models, and to obtain potential response and electric field response. The interface-sensing unified observation mapping module is used to perform field response mapping in the material sub-region, independently set the observation degrees of freedom on both sides of the material interface, and unify the electric field normal component and tangential component. The high-precision sample and low-rank skeleton module is used to construct a high-precision field state snapshot matrix, determine the low-rank order, select skeleton parameter samples and skeleton observation degrees of freedom, and form a high-precision column skeleton matrix and cross submatrix. The cross-precision correction module is used to convert the low-precision skeleton observation response of the parameter point to be predicted into a high-precision equivalent skeleton observation response based on the high- and low-precision paired samples. The physical constraint full-field reconstruction module is used to jointly solve the low-rank coefficient by the skeleton observation consistency term, the finite element physical residual term and the low-rank coefficient regularization term, and to restore the high-precision equivalent prediction of the full-field state of the parameter points to be predicted. The verification and update module is used to calculate the verification error by reserving high-precision parameter points, and to add high- and low-precision paired samples and update the proxy model when the verification error exceeds a preset verification threshold. The result output and data storage module is used to output and store the high-precision equivalent prediction of the overall field state, potential response, electric field response, low-rank coefficient, and verification error of the parameter points to be predicted.

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