A method for reconstructing the physical field of high-voltage bushings based on multi-field reconstruction networks

Abstract

This invention discloses a method for reconstructing the physical field of a high-voltage bushing based on a multi-field reconstruction network, belonging to the field of physical field reconstruction technology. The method includes the following steps: placing sensors on the high-voltage bushing to acquire its physical data and establishing a simplified bushing model; determining key physical processes and boundary conditions, constructing control equations and a total loss function; constructing a multi-field reconstruction network based on the control equations and loss function; inputting the physical data into the multi-field reconstruction network for training to obtain a trained multi-field reconstruction network; and inputting the high-voltage bushing data to be reconstructed into the trained multi-field reconstruction network to generate the temperature and stress fields of the high-voltage bushing. This invention combines experimental data with electrothermal-mechanical physical constraints to achieve accurate reconstruction of the internal temperature and stress fields, effectively reproducing the internal state under complex multi-physics conditions.

Description

Technical Field

[0001] This invention relates to the field of physical field reconstruction technology, and in particular to a method for physical field reconstruction of high-voltage bushings based on a multi-field reconstruction network. Background Technology

[0002] With the increasing complexity of modern power systems and the ever-increasing energy demands, ensuring the operational reliability of critical components such as high-voltage bushings has become a significant challenge. Advanced technologies such as multiphysics simulation, digital twins, and physical information machine learning are becoming important tools for improving fault detection, enhancing equipment transparency, and optimizing energy efficiency.

[0003] High-voltage bushings are among the most common fault points in power systems due to their susceptibility to complex electrothermal-mechanical coupling effects. As a critical component connecting high-voltage terminals and grounding terminals, high-voltage bushings are essential for ensuring the stability and reliability of power systems. However, their performance is often compromised by thermal and mechanical faults. Thermal faults are primarily caused by Joule heating and repeated thermal cycling, leading to overheating and accelerated insulation aging. Mechanical faults stem from thermal stress generated by thermal expansion and vibration caused by repeated mechanical loads, both of which weaken the structural integrity of the bushing. Particularly at terminal connections, thermal stress concentration often leads to deformation, adversely affecting contact resistance. Studies show that bushing faults account for approximately 30% of transformer fire accidents. Therefore, accurately reconstructing the internal temperature and stress field is crucial for early fault detection, improving the transparency of bushing conditions, and enabling more reliable diagnostics and preventative maintenance.

[0004] Currently, casing monitoring and diagnostic methods primarily rely on external measurements such as temperature, vibration, and acoustic signals. However, due to the sealed structure of the casing and its inherent multiphysics coupling characteristics, it is difficult to establish a reliable mapping between external measurements and the internal physical state. This challenge is even more pronounced under harsh operating conditions, as external signals often fail to accurately reflect the true temperature and stress distribution inside the casing. Furthermore, while finite element method (FEM) simulations are widely used for forward modeling to simulate casing behavior, they have inherent limitations in solving inverse problems because they rely on predefined input parameters and cannot directly infer the internal state from experimental measurements. Therefore, FEM lacks the ability to reconstruct the internal physical field based on actual data. Developing methods to reconstruct the internal physical field from external measurements has become an urgent research task. Accurately reconstructing these fields is crucial for improving the transparency of casing operating conditions, enhancing fault diagnosis capabilities, and overcoming the limitations of traditional FEM-based methods.

[0005] In recent years, Physical Information Neural Networks (PINNs) have emerged as a promising approach for solving inverse reconstruction problems. PINNs directly integrate the governing equations into the loss function of the neural network, seamlessly integrating initial conditions, boundary conditions, and multiphysics constraints. Studies have shown that PINNs achieve high accuracy in physical field reconstruction across various fields, including fluid dynamics, heat transfer, and solid mechanics. Despite progress in these areas, most existing research focuses on single-physics systems or simplified multiphysics couplings, with limited attention paid to integrating real-world experimental data to reconstruct complex coupled fields. Furthermore, challenges related to noise interference and sparse measurements in practical applications remain largely unresolved.

[0006] Therefore, providing a high-voltage bushing physical field reconstruction method based on a multi-field reconstruction network to solve the difficulties existing in the prior art is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0007] In view of this, the present invention provides a high-voltage bushing physical field reconstruction method based on a multi-field reconstruction network, which combines experimental data with electrothermal-mechanical physical constraints to achieve accurate reconstruction of internal temperature and stress fields, effectively reproducing the internal state under complex multi-physics field conditions.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] A method for reconstructing the physical field of a high-voltage bushing based on a multi-field reconstruction network includes the following steps:

[0010] Sensors are placed on the high-voltage bushing to acquire physical data of the high-voltage bushing and to establish a simplified bushing model.

[0011] Key physical processes and boundary conditions are identified, and governing equations including electrical conductivity, thermal field and mechanical field are constructed. The governing equations are then used to spatially expand the physical data.

[0012] Construct a total loss function that includes the control equation loss, experimental data loss, and known boundary and initial condition loss, and use the total loss function to iteratively optimize the model parameters.

[0013] A multi-field reconstruction network is constructed based on the control equation and loss function. Physical data is input into the multi-field reconstruction network for training to obtain a well-trained multi-field reconstruction network.

[0014] The high-pressure bushing data to be reconstructed is input into a trained multi-field reconstruction network to generate the temperature field and stress field of the high-pressure bushing.

[0015] Optionally, the boundary conditions in the conductance field of the governing equations are set to a specified applied current density, representing the current density and Joule heat, corresponding to the electrostatic field equations expressing the electric field distribution in the inner and outer regions of the bushing:

[0016] ,

[0017] in, , These are electric field strength and charge density, respectively. It is the nabla operator.

[0018] Optionally, the boundary conditions for the thermal field are convective heat transfer in the simulated thermal field, and the initial temperature is set as the ambient temperature, expressed as:

[0019] ,

[0020] in, Where J is temperature and J is current density.

[0021] Optionally, the flange interface is fixed in the mechanical field; therefore, the tensor form of the three-dimensional steady-state thermoelastic coupling equation is expressed as:

[0022] ,

[0023] in, It is the thermal strain vector. Represents volume force. It is a fourth-order constitutive tensor. This is the strain vector.

[0024] Optionally, the governing equation loss is used to ensure that the reconstructed stress and temperature fields at the sampling points within the domain conform to the relevant physical laws, the measurement data loss term ensures that the reconstruction results of PINN at the measurement points are consistent with the experimental data, and the loss functions for initial and boundary conditions specify the temperature and displacement fields at the initial time points and corresponding boundaries.

[0025] Optionally, the total loss function is constructed as a weighted sum of different loss functions, with the weight coefficients defined as follows: , and An adaptive adjustment method based on gradient magnitude is used to adjust the weights of different loss functions, expressed as follows:

[0026] ,

[0027] in, To control the loss of the equation, To measure data loss, The loss function is used for the initial and boundary conditions.

[0028] As can be seen from the above technical solutions, compared with the prior art, the present invention provides a high-pressure bushing physical field reconstruction method based on multi-field reconstruction network, which has the following beneficial effects: 1) The present invention uses PEG-MFRN to demonstrate the ability to accurately reconstruct the field in the critical top flange area, effectively captures multi-physics interactions using sparse experimental data, and generates reliable stress and temperature distributions; 2) The present invention exhibits stronger robustness under coupled noise conditions through the joint optimization mechanism and adaptive weight compensation in the loss function, and has a lower relative error compared with single noise input scenarios. Attached Figure Description

[0029] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0030] Figure 1 This is a flowchart of a high-voltage bushing physical field reconstruction method based on a multi-field reconstruction network disclosed in this invention.

[0031] Figure 2 This is a schematic diagram of the physical field reconstruction principle of a high-voltage bushing based on a multi-field reconstruction network disclosed in this invention.

[0032] Figure 3 The images show the reconstruction results under different load conditions disclosed in the embodiments of the present invention. Detailed Implementation

[0033] 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. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0034] Reference Figure 1 and Figure 2 As shown, this invention discloses a method for reconstructing the physical field of a high-voltage bushing based on a multi-field reconstruction network, comprising the following steps:

[0035] Sensors are placed on the high-voltage bushing to acquire physical data of the high-voltage bushing and to establish a simplified bushing model.

[0036] Key physical processes and boundary conditions are identified, and governing equations including electrical conductivity, thermal field and mechanical field are constructed. The governing equations are then used to spatially expand the physical data.

[0037] Construct a total loss function that includes the control equation loss, experimental data loss, and known boundary and initial condition loss, and use the total loss function to iteratively optimize the model parameters.

[0038] A multi-field reconstruction network is constructed based on the control equation and loss function. Physical data is input into the multi-field reconstruction network for training to obtain a well-trained multi-field reconstruction network.

[0039] The high-pressure bushing data to be reconstructed is input into a trained multi-field reconstruction network to generate the temperature field and stress field of the high-pressure bushing.

[0040] Furthermore, the boundary conditions in the conductance field of the governing equations are set to a specified applied current density, representing the current density and Joule heat, which are expressed as the electrostatic field equations for the electric field distribution inside and outside the bushing:

[0041] ,

[0042] in, , These are electric field strength and charge density, respectively. It's the Nabla operator, electric field. and current density The relationship between them is as follows, and it also generates a large amount of heat per unit volume. This is the main heat source for the bushing.

[0043] ,in The electrical conductivity of the material.

[0044] Furthermore, in a three-dimensional Cartesian coordinate system, the heat conduction equation is expressed as follows:

[0045] ,

[0046] in, , and These are the material's density, specific heat capacity, and thermal conductivity. It's temperature. It is the heat per unit volume obtained from an electrostatic field.

[0047] Furthermore, the boundary conditions of the thermal field are to simulate convective heat transfer in the thermal field, and the initial temperature is set as the environmental condition, expressed as:

[0048] ,

[0049] in, Here, J is temperature, and J is current density. In the heat transfer model, the initial temperature is set to the ambient temperature. Due to the regular cylindrical shape of the contact area between the wall-mounted pipe and the surrounding cooling medium, the fluid flow remains relatively stable, and its characteristics do not change significantly. To simplify the calculation, the influence of the flow field on the convective heat transfer coefficient can be neglected, and it can be regarded as a Neumann boundary condition acting on the temperature field:

[0050] , ,

[0051] in, , and These represent the convective heat transfer coefficient, the normal vector, and the corresponding boundary, respectively.

[0052] Furthermore, in a mechanical field with a fixed flange interface, under thermoelastic effects, the relationship between stress and strain is typically described by the generalized Hooke's law, which considers both thermal expansion and mechanical deformation. This equation is usually expressed as:

[0053] ,

[0054] in, For strain vector, and These are the thermal strain vector and the coefficient of thermal expansion, respectively. It's a temperature change. It is a fourth-order constitutive tensor.

[0055] Since the material is isotropic, the stress vector and strain vector The relationship between them can be further simplified into component form:

[0056] ,

[0057] and These represent Lamé constants, which are related to the Young's modulus of the material. Compared to Poisson related:

[0058] , ,

[0059] Under steady-state conditions, the high-voltage bushing is in mechanical equilibrium and therefore satisfies the momentum balance equation:

[0060] ,

[0061] in, This refers to volume force, specifically gravity, which only exists in... The direction has components, and the component form of the equilibrium equations is as follows:

[0062] ,

[0063] strain vector The following kinematic equations and generalized displacement vectors can be used to solve the problem. Related:

[0064] Therefore, the tensor form of the three-dimensional steady-state thermoelastic coupling equation is expressed as:

[0065] ,

[0066] in, It represents volume force.

[0067] Furthermore, the governing equation loss is used to ensure that the reconstructed stress and temperature fields at the sampling points within the domain conform to the relevant physical laws, the measurement data loss term ensures that the reconstruction results of PINN at the measurement points are consistent with the experimental data, and the loss functions for initial and boundary conditions specify the temperature and displacement fields at the initial time points and corresponding boundaries.

[0068] Specifically, the governing equation loss requires the temperature field The heat conduction equation and stress field must be satisfied. The force balance equations must be satisfied, and both fields must obey the thermoelastic constitutive equations:

[0069] ,

[0070] in, Let the temperature loss function be... Let be the stress loss function. Let thermal strain loss function be used. It is the number of sampling points. and Representation domain The internal temperature and stress distribution are reconstructed. The physical equation loss can be expressed as:

[0071] ,

[0072] The measurement data loss term ensures that the reconstruction results of PINN at the measurement points are consistent with the experimental data:

[0073] ,

[0074] in, For temperature measurement loss, For stress measurement loss; and These are the number of measurement points for temperature and deformation, respectively. The value of the temperature field reconstructed by the neural network at the j-th measurement point. Let be the temperature value actually measured by the experiment at the j-th temperature measurement point. The stress value actually measured experimentally at the k-th stress measurement point. The stress field reconstructed by the neural network at the k-th measurement point has the measurement data loss as follows:

[0075] ,

[0076] The loss functions for the initial and boundary conditions specify the temperature and displacement fields at the initial time point and the corresponding boundary:

[0077] ,

[0078] ,

[0079] ,

[0080] in, For displacement field loss, For temperature field loss, , , and Representing boundaries respectively , , and The number of sampling points in the data is determined by the initial and boundary conditions of the displacement and temperature fields. , , and These data are derived from experimental data.

[0081] Furthermore, the total loss function is constructed as a weighted sum of different loss functions, and the weight coefficients are defined as follows: , and An adaptive adjustment method based on gradient magnitude is used to adjust the weights of different loss functions, expressed as follows:

[0082] ,

[0083] in, To control the loss of the equation, To measure data loss, The loss function is used for the initial and boundary conditions.

[0084] Specifically, during neural network training, the weights in the loss function significantly influence the relative importance of different loss components, thus affecting the overall model optimization process. To dynamically adjust these weights and better balance the contribution of each loss component, an adaptive adjustment method based on gradient magnitude can be used. In this method, the weight of each loss term is updated according to its gradient norm relative to the model parameters. The weight update formula is:

[0085] ,

[0086] in, Indicates at time step No. The gradient norm of each loss term, express The number of loss components. In this approach, the magnitude of the gradient for each loss component is reflected in its corresponding weight. A larger gradient indicates that the loss component contributes significantly to the total loss, and therefore its weight should be reduced to prevent it from unduly influencing model updates. Conversely, a smaller gradient leads to an increase in weights to ensure that all loss components are adequately optimized during training.

[0087] In one specific embodiment, an experimental platform was constructed, comprising a current source, a 110kV bushing sample, strain gauges, an infrared thermal imager, a data acquisition system, and a constant-temperature oil tank. The bushing was vertically inserted into the tank and maintained at 353.15K, with current applied through its top flange. By adjusting the current source, different current levels could be applied to simulate actual operating conditions under different loads. The strain gauges and infrared thermal imager were strategically placed in key locations, such as the bushing's flange base and top cap, to monitor thermal stress and temperature in real time. For consistency and ease of comparison, all stress measurements were converted to Von der ... Mises stress.

[0088] Set three different loads, with 60%... 80% For light load, 100% A continuous temperature rise test was conducted under different load conditions at rated load. Starting from zero, the current was gradually increased to 60%. The current is kept constant until thermal equilibrium is reached, defined as a temperature change of less than 1 K per hour. At thermal equilibrium, stress-strain and temperature data are recorded and transmitted to a computer via a data acquisition system for storage and preliminary processing. Subsequently, the current is further increased, and at 80%... and 100% The same procedure is followed under thermal equilibrium conditions under load. The collected data is then preprocessed using denoising, normalization, and interpolation techniques to improve data quality.

[0089] Reconstruction results as follows Figure 3 As shown, it demonstrates the performance of a 110kV high-voltage bushing under three load conditions. Mises stress axial displacement and temperature field The reconstruction distribution is: 60%, 80%, and 100% of the rated load. The first line shows Feng's... The Mises stress distribution shows maximum stresses of 18.8 MPa, 24.6 MPa, and 34.3 MPa under 60%, 80%, and 100% loads, respectively. Stress concentration is mainly observed in the contact area and intensifies with increasing load. The second line depicts the axial displacement distribution, with maximum displacements of 0.375 mm, 0.597 mm, and 0.884 mm under 60%, 80%, and 100% loads, respectively. These results indicate that axial deformation increases with increasing load, particularly in the middle of the sleeve. The third line presents the temperature field distribution, with maximum temperatures of 307 K, 328 K, and 351 K under 60%, 80%, and 100% loads, respectively. Higher temperatures are concentrated near the central connection point of the mandrel, especially under full load conditions, consistent with the larger axial displacements.

[0090] In addition, a FEM model was developed using COMSOL 6.2 for comparative validation. This model includes solid mechanics, circuit, and heat transfer modules. The FEM model is configured with the same geometry, material, and boundary parameters as the PEG-MFRN model, but does not include experimental data. Comparison of the FEM results at the corresponding geometric locations with experimental measurements and PEG-MFRN reconstructions shows that, for the stress field, the maximum absolute error decreased from 1.22 MPa (FEM) to 0.37 MPa (PEG-MFRN), a reduction of 69.67%. Similarly, the mean absolute error of stress decreased from 0.86 MPa to 0.25 MPa, a reduction of 70.93%. In the temperature field, the maximum absolute error of PEG-MFRN was 1.1 K, an improvement of 59.41% compared to 2.71 K of FEM. The mean absolute error of temperature also decreased from 1.47 K (FEM) to 0.47 K (PEG-MFRN), a reduction of 68.03%.

[0091] These results demonstrate that PEG-MFRN, which integrates experimental data, consistently outperforms FEM in the accuracy of stress and temperature reconstruction. In summary, the integration of experimental data allows PEG-MFRN to achieve significantly more accurate results compared to FEM, particularly in the region near the data supervision points, and even in other regions.

[0092] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A high-voltage bushing physical field reconstruction method based on a multi-field reconstruction network, characterized in that, The method comprises the following steps: arranging a sensor on the high-voltage bushing, acquiring physical data of the high-voltage bushing, and establishing a simplified bushing model; determining key physical processes and boundary conditions, constructing control equations including electric field, thermal field and mechanical field, and using the control equations to extend the physical data in space; constructing a total loss function including loss of the control equation, loss of experimental data and loss of known boundary and initial conditions, and using the total loss function to iteratively optimize model parameters, wherein the loss of the control equation is used to ensure that the reconstructed stress and temperature fields at the sampling points in the domain meet the relevant physical laws; constructing a multi-field reconstruction network based on the control equations and the loss function, inputting the physical data into the multi-field reconstruction network for training, and obtaining the trained multi-field reconstruction network; inputting the data of the high-voltage bushing to be reconstructed into the trained multi-field reconstruction network to generate the temperature field and the stress field of the high-voltage bushing; wherein the boundary condition in the electric field is set as a specified applied current density, representing the current density and the Joule heat, and the corresponding expression is an electrostatic field equation representing the electric field distribution in the internal and external regions of the bushing: ， wherein , are the electric field strength, the charge density, respectively, is the nabla operator; the boundary condition of the thermal field is to simulate the convective heat transfer in the thermal field, and the initial temperature is set as the environmental condition, and the expression is: ， wherein is the temperature, J is the current density; the flange interface is fixed in the mechanical field, therefore, the tensor form expression of the three-dimensional steady-state thermoelastic coupling equation is: ， wherein is the thermal strain vector, denotes the volume force, is the fourth order constitutive tensor, is the strain vector.

2. The high-voltage bushing physical field reconstruction method based on the multi-field reconstruction network according to claim 1, wherein the measurement data loss term ensures that the reconstruction result of the PINN at the measurement point is consistent with the experimental data, and the loss function of the initial and boundary conditions specifies the temperature and displacement fields at the initial time point and the corresponding boundary.

3. The high-voltage bushing physical field reconstruction method based on the multi-field reconstruction network according to claim 2, wherein The total loss function is constructed as a weighted sum of different loss functions, and the weight coefficients are defined as , and An adaptive adjustment method based on gradient size is used to adjust the weights of different loss functions, and the expression is ， where, is the loss for the control equation, is the loss for the measurement data, is the loss function for initial and boundary conditions.

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