A transformer bushing magnetic-thermal deduction method and system based on MC-PINN

Abstract

The application provides a transformer bushing magnetic and thermal deduction method and system based on MC-PINN, relates to the technical field of transformers, and comprises the following steps: a bushing geometric model of a transformer bushing sample is constructed, and the bushing geometric model is divided into a plurality of physical subdomains with different thermal conduction parameters and / or electromagnetic parameters; a plurality of sampling points are respectively generated at the geometric range of each physical subdomain, the position with a clear physical boundary along the boundary curve, and the common interface between any two adjacent physical subdomains along the interface direction; a thermal conduction control equation and an electromagnetic field control equation are constructed based on the sampling data of the sampling points; the thermal conduction control equation and the electromagnetic field control equation are embedded into a preset MC-PINN network; the MC-PINN network is trained in combination with the sampling data and the position information of each type of sampling point; the loss function of each subdomain neural network is determined; iterative optimization is completed; the target MC-PINN network is obtained; and the temperature field distribution and the hoop magnetic flux density field distribution of the transformer bushing to be measured are deduced.

Description

Technical Field

[0001] This invention relates to the field of transformer technology, and in particular to a method and system for magnetothermal deduction of transformer bushings based on MC-PINN. Background Technology

[0002] Transformer bushings are key components in power systems, providing insulation between conductors and external lines. Their early operational reliability directly impacts the safe and stable operation of the transformer and the power system. During long-term operation, the flow of power frequency current through the bushing's internal conductors generates electromagnetic losses and Joule heating, while simultaneously creating complex magnetic field distributions and temperature gradients within the insulation medium and shielding structure. Excessive internal temperature rise or abnormal magnetic field distribution can easily lead to insulation aging, localized overheating, and even breakdown. Therefore, accurate modeling and evaluation of the internal temperature field and circumferential magnetic flux density field of the bushing are crucial research areas in equipment condition monitoring and operational safety analysis.

[0003] Currently, the analysis of the magnetic and temperature fields inside bushings mainly relies on numerical simulation methods such as the finite element method. While establishing a refined geometric model and combining it with electromagnetic and heat conduction theories for multi-physics joint modeling and calculation offers high physical accuracy, it typically suffers from high modeling and computation costs, strong dependence on parameter acquisition, and long computation times. It struggles to simultaneously achieve computational efficiency and physical consistency under conditions of multiple materials and multi-interface structures. Furthermore, in engineering settings where only limited measurement data is available, it is difficult to reliably extrapolate the continuous magneto-thermal physical fields inside bushings. Similarly, data-driven machine learning methods also usually rely on large amounts of measurement data and struggle to guarantee that predictions conform to fundamental physical laws. In complex media and multi-structure transformer bushing scenarios, they are prone to insufficient generalization ability or lack of physical consistency. Summary of the Invention

[0004] In view of this, the present invention proposes a method and system for magnetothermal deduction of transformer bushings based on MC-PINN.

[0005] The technical solution of this invention is implemented as follows: The first aspect of this invention provides a method for magnetocaloric deduction of transformer bushings based on MC-PINN, comprising: A bushing geometric model of a transformer bushing sample is constructed, and the bushing geometric model is divided into multiple physical subdomains with different thermal conductivity parameters and / or electromagnetic parameters based on the differences in physical properties of different regions. Multiple intra-domain sampling points are generated within the geometric range of each physical subdomain; multiple boundary sampling points are generated along the boundary curve at the location with a clear physical boundary on the sleeve geometric model; and multiple interface sampling points are generated along the interface direction at the common interface of any two adjacent physical subdomains. Based on the sampling data of the sampling points within the domain, the sampling points at the boundary, and the sampling points at the interface, heat conduction control equations and electromagnetic field control equations are constructed. These equations are then embedded into a preset MC-PINN network. The preset MC-PINN network is then trained by combining the sampling data and the location information of each type of sampling point to determine the loss function for each sub-domain neural network. The loss function includes a physical residual loss function, a boundary condition loss function, and an interface continuity loss function. The subdomain neural network is iteratively optimized based on the loss function to obtain the target MC-PINN network, and the temperature field distribution and circumferential magnetic flux density field distribution of the bushing of the transformer under test are deduced using the target MC-PINN network.

[0006] Based on the above technical solutions, preferably, the construction of the bushing geometric model for the transformer bushing sample, and the division of the bushing geometric model into multiple physical subdomains with different thermal conductivity parameters and / or electromagnetic parameters based on the differences in physical properties of different regions, includes: The transformer bushing sample was modeled using a two-dimensional axisymmetric modeling method to construct a bushing geometric model; Based on the differences in material parameters and physical field variation patterns in different regions, the bushing geometric model is divided into a conductor subdomain, a capacitor screen subdomain, an insulating dielectric subdomain, and an external dielectric subdomain.

[0007] Based on the above technical solutions, preferably, the sampling points within the domain, the boundary sampling points, and the interface sampling points all include temperature sampling points and electromagnetic sampling points; The temperature sampling points are measured using thermocouples or fiber optic temperature sensors, and temperature data during steady-state or heating processes are acquired through a multi-channel data acquisition device. The electromagnetic sampling points are equipped with a Hall magnetic field sensor array arranged along the axial direction of the sleeve to measure the circumferential magnetic flux density, so as to obtain circumferential magnetic flux density data at different axial positions.

[0008] Based on the above technical solutions, preferably, the step of constructing the heat conduction control equation and the electromagnetic field control equation based on the sampling data of the sampling points within the domain, the boundary sampling points, and the interface sampling points includes: Physical residual constraints for the heat conduction equation and the electromagnetic field control equation are constructed based on the sampling data of the sampling points within the domain. Based on the sampling data of the boundary sampling points, thermal and electromagnetic boundary condition constraints are constructed for the heat conduction equation and the electromagnetic field control equation. Based on the sampling data from the interface sampling points, the field variable continuity constraints of the heat conduction equation and the electromagnetic field control equation are constructed.

[0009] Based on the above technical solutions, preferably, the step of training each subdomain neural network of the preset MC-PINN network by combining the sampling data and the location information of each type of sampling point, and determining the loss function of each subdomain neural network, includes: An initial neural network for each of the physical subdomains is created based on thermal conductivity parameters and electromagnetic parameters; By embedding the corresponding heat conduction control equation and electromagnetic field control equation into each initial neural network, an optimized subdomain neural network is obtained. Using the spatial coordinates of each type of sampling point as input, and the temperature data and circumferential magnetic flux density data within the corresponding physical subdomain as prediction results, the subdomain neural network is trained to determine the loss function of each subdomain neural network.

[0010] Based on the above technical solutions, preferably, the loss function further includes a data consistency loss function; before iteratively optimizing the subdomain neural network based on the loss function to obtain the target MC-PINN network, the following is also included: Sparse sampling points are generated at local locations in the sleeve geometry model; the sparse sampling points include temperature sampling points and electromagnetic sampling points. The data consistency loss function is determined based on the measured parameters of the sparse sampling points and the output parameters of the subdomain neural network.

[0011] Based on the above technical solutions, preferably, the iterative optimization of the subdomain neural network based on the loss function to obtain the target MC-PINN network includes: The parameter gradients of each of the subdomain neural networks are calculated based on the loss function. The parameter gradients are iteratively optimized using the AdamW optimization algorithm until the loss function is less than a preset threshold, thus obtaining the target MC-PINN network.

[0012] Furthermore, a second aspect of the present invention provides a transformer bushing magnetocaloric deduction system based on MC-PINN, comprising: a subdomain partitioning module, a sampling point generation module, a function determination module, and a data deduction module; wherein, The subdomain partitioning module is configured to construct a bushing geometric model of a transformer bushing sample, and divide the bushing geometric model into multiple physical subdomains with different thermal conductivity parameters and / or electromagnetic parameters based on the differences in physical properties of different regions. The sampling point generation module is configured to generate multiple intra-domain sampling points within the geometric range of each physical subdomain, generate multiple boundary sampling points along the boundary curve at a location with a clear physical boundary on the sleeve geometric model, and generate multiple interface sampling points along the interface direction at the common interface of any two adjacent physical subdomains. The function determination module is configured to construct heat conduction control equations and electromagnetic field control equations based on sampling data from sampling points within the domain, boundary sampling points, and interface sampling points; embed the heat conduction control equations and electromagnetic field control equations into a preset MC-PINN network; and train each subdomain neural network of the preset MC-PINN network by combining the sampling data and the location information of each type of sampling point, thereby determining the loss function for each subdomain neural network; the loss function includes a physical residual loss function, a boundary condition loss function, and an interface continuity loss function. The data extrapolation module is configured to iteratively optimize the subdomain neural network based on the loss function to obtain a target MC-PINN network, and then use the target MC-PINN network to extrapolate the temperature field distribution and circumferential magnetic flux density field distribution of the bushing of the transformer under test.

[0013] More preferably, a third aspect of the present invention provides an electronic device, including a processor and a memory; the memory has a computer program stored thereon, wherein the computer program, when executed by the processor, implements the transformer bushing magnetocaloric deduction method based on MC-PINN described in the first aspect.

[0014] More preferably, the fourth aspect of the present invention provides a non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the transformer bushing magnetocaloric deduction method based on MC-PINN described in the first aspect.

[0015] The transformer bushing magnetocaloric deduction method and system based on MC-PINN of the present invention have the following advantages over the prior art: 1. Addressing the multi-material structure of the casing, physical subdomains are established for different material regions, and continuity constraints are applied at the interfaces, effectively solving the problem of balancing accuracy and stability in complex media structures. Simultaneously, by explicitly embedding the heat conduction control equations, electromagnetic field control relationships, and subdomain interface continuity conditions during network training, the model can still obtain continuous field distribution results that conform to physical laws even under sparse measurement data conditions, avoiding the instability of pure data-driven models in the extrapolation region. Training is constrained by a triple loss function of physical residuals, boundary conditions, and interface continuity. This retains the advantages of the finite element method—rigorous physical mechanisms and results conforming to the objective laws of electromagnetic-thermal conduction—while avoiding the shortcomings of pure data-driven machine learning, such as deviating from physical rules, predicting results that violate field distribution laws, and poor generalization. This achieves continuous and high-precision extrapolation of the temperature field and circumferential magnetic flux density field within the casing.

[0016] 2. By adopting two-dimensional axisymmetric modeling and abandoning the redundant three-dimensional spatial dimension, the workload of model construction, the number of meshes and solution variables are greatly reduced while fully conforming to the actual structural field distribution law. This significantly reduces the computational power consumption and computation time. Furthermore, it accurately matches the actual hierarchical structure of the casing, conforms to the engineering entity to divide subdomains, and fits the inherent physical properties of different material levels. This avoids model structure distortion from the source and accurately restores the real characteristics of electromagnetic field conduction and heat transfer in each region, ensuring that the subsequent physical field evolution logic is more in line with the actual working conditions.

[0017] 3. By constructing residual constraints for the equations using in-domain sampling data, the model output is forced to strictly obey the fundamental control equations of classical heat conduction and electromagnetic fields, ensuring that the changing trend of the field across the entire domain conforms to objective physical laws. Boundary sampling points are used to establish thermal and electromagnetic dual-class boundary constraints, accurately reproducing actual boundary conditions such as heat dissipation from the outer wall of the casing, end electrical constraints, environmental heat exchange, and external electromagnetic effects. This ensures that the model's derivation results closely match the actual operating environment, eliminating overall field distribution shifts and calculation errors caused by missing boundary conditions. Interface sampling points are used to build continuous constraints for field variables, ensuring a smooth transition of physical quantities such as temperature, magnetic flux density, and field strength at the interfaces of different subdomains such as conductors, capacitor screens, and insulating media. This avoids abrupt changes in field quantities and logical breaks in interlayer field transmission under multi-material layered structures. These three elements form a complete constraint system, significantly improving the reliability and accuracy of the derivation results. Attached Figure Description

[0018] 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 some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 A flowchart illustrating a transformer bushing magnetocaloric deduction method based on MC-PINN provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the casing geometry model provided in an embodiment of the present invention; Figure 3 A schematic diagram of the structure of a transformer bushing magnetocaloric deduction system based on MC-PINN provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0020] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. 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.

[0021] In some embodiments, such as Figure 1 As shown, Figure 1 The flowchart illustrates a transformer bushing magnetothermal deduction method based on MC-PINN provided in this embodiment of the invention; the transformer bushing magnetothermal deduction method based on MC-PINN provided by this invention includes: S110, construct the bushing geometric model of the transformer bushing sample, and divide the bushing geometric model into multiple physical subdomains with different thermal conductivity parameters and / or electromagnetic parameters based on the differences in physical properties of different regions.

[0022] S120 generates multiple intra-domain sampling points within the geometric range of each physical subdomain, generates multiple boundary sampling points along the boundary curve at locations with clear physical boundaries on the sleeve geometric model, and generates multiple interface sampling points along the interface direction at the common interface of any two adjacent physical subdomains.

[0023] S130: Based on the sampling data of sampling points within the domain, boundary sampling points, and interface sampling points, construct the heat conduction control equation and the electromagnetic field control equation. Embed the heat conduction control equation and the electromagnetic field control equation into a preset MC-PINN network. Combine the sampling data and the location information of each type of sampling point to train each sub-domain neural network of the preset MC-PINN network and determine the loss function of each sub-domain neural network. The loss function includes the physical residual loss function, the boundary condition loss function, and the interface continuity loss function.

[0024] S140. The subdomain neural network is iteratively optimized based on the loss function to obtain the target MC-PINN network. The temperature field distribution and circumferential magnetic flux density field distribution of the bushing of the transformer under test are then deduced using the target MC-PINN network.

[0025] In this embodiment, a geometric model of the transformer bushing is established to closely match the actual shape and hierarchical structure of the bushing, preserving the core characteristics of the field distribution. Based on the material properties, thermal conductivity, electromagnetic conductivity and magnetic permeability, and physical field variation characteristics of different parts of the bushing, the overall geometric model is divided into regions. Each divided physical subdomain is independently configured with exclusive thermal conductivity and electromagnetic parameters, realizing differentiated assignment of physical property parameters for different structural regions and restoring the true physical property distribution of the bushing.

[0026] For all the divided physical subdomains, sampling points are deployed within the internal geometric space of each subdomain to characterize the distribution and variation of field quantities within the subdomain. Boundary sampling points are deployed along the boundary curves at clearly defined physical boundaries such as the overall outer contour of the bushing, its ends, heat dissipation surfaces, and electrical action surfaces to collect information on external operating conditions and boundary field quantities. Interface sampling points are deployed along the interface at the common interface between two adjacent different physical subdomains to capture the field quantity transfer and energy interaction characteristics at the interface of multi-layer structures.

[0027] Based on the spatial location information and field quantity sampling data of sampling points within the domain, boundary sampling points, and interface sampling points, heat conduction control equations and electromagnetic field control equations suitable for the piping operation are established, and the physical constraint relationship of magnetic-thermal coupling is established. These two types of physical control equations are embedded into a pre-built multi-domain physical information neural network (MC-PINN), with independent sub-domain neural networks set up according to the number of physical sub-domains to achieve precise domain-specific learning. Combining the sampling data and the spatial location of the sampling points, domain-specific neural network training is carried out, and physical residual loss functions, boundary condition loss functions, and interface continuity loss functions are constructed simultaneously. Specifically, the physical residual loss function uses the sampling points within the domain to calculate the control equations and solve for the residuals, constraining the network prediction results to obey fundamental physical laws; the boundary condition loss function uses the boundary sampling points to fit the actual thermal and electromagnetic boundary conditions, constraining the model to fit the on-site operating boundary conditions; and the interface continuity loss function uses the interface sampling points to constrain the continuous and smooth transition of field quantities such as temperature and magnetic flux density at the interface between adjacent sub-domains.

[0028] Using physical residual loss function, boundary condition loss function, and interface continuity loss function as optimization objectives, backpropagation iterative training is performed on all subdomain neural networks in MC-PINN, continuously adjusting network weights and bias parameters until the loss values ​​converge and stabilize, resulting in the trained target MC-PINN network. By inputting the bushing structural parameters and operating conditions of the transformer under test into the target MC-PINN network, the global temperature field distribution and circumferential magnetic flux density field distribution of the bushing can be obtained, achieving accurate integrated prediction of internal multi-physics fields.

[0029] In some embodiments, a bushing geometric model of a transformer bushing sample is constructed, and the bushing geometric model is divided into multiple physical subdomains with different thermal conductivity parameters and / or electromagnetic parameters based on the differences in physical properties of different regions, including: A two-dimensional axisymmetric modeling method was used to model the transformer bushing sample and construct the bushing geometric model; Based on the differences in material parameters and physical field variation patterns in different regions, the bushing geometric model is divided into a conductor subdomain, a capacitor screen subdomain, an insulating dielectric subdomain, and an external dielectric subdomain.

[0030] In this embodiment, please refer to Figure 2 , Figure 2 This is a schematic diagram of the bushing geometric model provided in an embodiment of the present invention. The axisymmetric geometric model of the transformer bushing may include a conductor subdomain, a capacitor shield subdomain, an insulating medium subdomain, and an external medium subdomain. Further detailed subdomain divisions are possible, such as: Subdomain G1: Conductor subdomain, representing the current-carrying conductors and their connecting components inside the bushing, including the top connecting seat, primarily responsible for current transmission and being the main source of magnetic field and Joule heat; Subdomain G2: Metal shield subdomain, representing the metal support and connecting structures such as the bottom flange of the bushing, which participates in the heat conduction process and affects the local magnetic field distribution; Subdomain B: External insulating sheath, representing the external insulating sheath and shed structure of the bushing, primarily exchanging heat with the external air or ambient medium, and affecting... The distribution of the external magnetic field has a certain influence; Subdomain O: Internal capacitor screen, used to represent the capacitor screen structure inside the bushing, usually composed of multiple layers of conductive foil or metal layers, which plays a role in equalizing voltage and shielding the electric field distribution, and also participates in the joint modeling process of magnetic-thermal multiphysics fields; Subdomain Y: Main insulating medium, used to represent the oil-paper insulation or oil-impregnated composite insulation material region located between the conductor and the capacitor screen and between each capacitor screen. This subdomain has low electrical conductivity and strong thermal conductivity characteristics, and is the key medium for heat diffusion and electric field homogenization inside the bushing; Subdomain OIL: Internal oil region of the bushing, used to represent the insulating oil region inside and around the bushing, undertaking the function of heat convection and heat diffusion, and is an important channel for heat dissipation of the bushing. The physical subdomains are separated by clear geometric interfaces, and the boundary positions of the subdomains are determined according to the actual bushing structure dimensions.

[0031] In some embodiments, the domain sampling points, boundary sampling points, and interface sampling points all include temperature sampling points and electromagnetic sampling points; Temperature sampling points are measured using thermocouples or fiber optic temperature sensors, and temperature data during steady-state or heating processes are acquired through a multi-channel data acquisition device. Electromagnetic sampling points are equipped with a Hall magnetic field sensor array arranged along the axial direction of the sleeve to measure the circumferential magnetic flux density, so as to obtain circumferential magnetic flux density data at different axial positions.

[0032] In this embodiment, to avoid training imbalance caused by differences in geometric dimensions between different physical subdomains, sampling points within the domain are allocated according to the area ratio of each physical subdomain, thereby ensuring reasonable weights of multi-domain physical constraints during the training process.

[0033] In some embodiments, heat conduction control equations and electromagnetic field control equations are constructed based on sampling data from intra-domain sampling points, boundary sampling points, and interface sampling points, including: Physical residual constraints are constructed based on the sampling data of sampling points within the domain to construct the heat conduction equation and the electromagnetic field control equation. Thermal and electromagnetic boundary condition constraints are constructed based on the sampling data of boundary sampling points to form the heat conduction equation and the electromagnetic field control equation; The continuity constraints of field variables are constructed based on the sampling data of the interface sampling points to form the heat conduction equation and the electromagnetic field control equation.

[0034] In this selected embodiment, for physical residual constraints, within subdomain m, the number of sampling points within the subdomain is determined based on the geometric area ratio of the subdomain to the overall computational region. The specific steps are as follows:

[0035] First, calculate the geometric area of ​​each subdomain. And calculate its proportion of the total area; Based on the preset total number of sampling points within the domain The following is distributed proportionally: ; Within the geometric range of subdomain m, a uniform random sampling method is used to generate [the data] in the (r,z) coordinate space. Sampling points within the domain .

[0036] It should be noted that in MC-PINN, the actual temperature field is predicted by the subdomain neural network. Instead, this allows for the construction of thermal physical residual constraints: ; The residual term reflects the degree to which the network-predicted temperature field violates the physical laws of heat conduction.

[0037] Under axisymmetric and quasi-steady-state conditions, the magnetic field generated by the current-carrying conductor inside the bushing is mainly characterized by a circumferential magnetic flux density distribution. This magnetic field should satisfy the magnetic field control relationship obtained by simplifying Maxwell's equations. The predicted circumferential magnetic flux density within the subdomain... Electromagnetic residual constraints are constructed by incorporating the magnetic field control relationship:

[0038] ; in, For the equivalent current density term, m is the subdomain index, and (r,z) are the coordinates of the sampling point.

[0039] Within the subdomain m, the thermal and electromagnetic residuals are summed by squares to construct the corresponding domain physical residual loss function: ; This loss function is used to constrain the network to simultaneously satisfy the thermal and electromagnetic control equations within the subdomain.

[0040] For thermal and electromagnetic boundary condition constraints, a deviation between the predicted temperature and the given boundary temperature or convective heat transfer relationship is constructed at the temperature boundary sampling point; an error term for the circumferential magnetic flux density or magnetic field strength satisfying the boundary conditions is constructed at the magnetic field boundary sampling point.

[0041] For any physical subdomain m, its thermal conductivity is set. ,density Specific heat capacity Under steady-state conditions, the temperature field within the subdomain satisfies the heat conduction governing equation:

[0042] ; in, This represents the temperature field distribution within the subdomain m. This is the equivalent heat source term within this subdomain, used to characterize conductor Joule losses and the effects of other heat sources.

[0043] At the boundary of the subdomain, set either convective heat transfer or isothermal boundary conditions according to the actual operating conditions: ; Where h is the convective heat transfer coefficient. This refers to the air environment or oil temperature.

[0044] For the electromagnetic field component, the focus is on the circumferential magnetic flux density distribution formed by the bushing under the action of power frequency alternating current. Conductivity is set for each subdomain. and permeability .

[0045] Under axisymmetric conditions, circumferential magnetic flux density The control relationship, which is obtained by simplifying Maxwell's equations, has the following basic form: ; Where A is the magnetic vector potential and J is the current density. Under axisymmetric conditions, the correspondence between the circumferential magnetic flux density and the current-carrying current can be directly obtained through variable elimination, which can be used to construct physical constraints.

[0046] In the set of boundary sampling points Above, known temperature value Construct the thermal boundary loss function: ; In the set of boundary sampling points Above, given the circumferential magnetic flux density Construct the electromagnetic boundary loss function: ; The overall boundary condition loss function can be expressed as: .

[0047] For the continuity constraints of field variables, the following continuity constraints are constructed at the interface sampling points: temperature continuity, the predicted temperature values ​​of adjacent subdomains are equal; heat flux continuity, the normal heat flux density of adjacent subdomains is equal; magnetic field continuity, the circumferential magnetic flux density of adjacent subdomains satisfies the continuity condition.

[0048] By constructing a squared error term based on the above continuity conditions and summarizing it at the interface sampling points, a subdomain interface continuity loss function is formed to ensure the continuous transmission of physical fields at the subdomain boundaries in a multi-medium structure.

[0049] At the subdomain interface, temperature continuity and heat flow continuity constraints are introduced: ; The corresponding interfacial thermal loss function is defined as: ; Under quasi-static conditions at power frequency, neglecting the influence of displacement current, the magnetic diffusion equation is processed under the time-harmonic steady-state assumption, and the electromagnetic field distribution is modeled using an equivalent steady-state magnetic field, with its circumferential magnetic flux density... Satisfies the magnetic diffusion control equation: ; in, For the permeability corresponding to a physical subdomain, Let be the electrical conductivity. Under steady-state power frequency operation conditions, the magnetic field tends to stabilize over time, and the above equation can be simplified to a steady-state magnetic field control form:

[0050] ; Predicting the circumferential magnetic flux density output by the neural network Automatic differentiation is performed to calculate the residuals of the above electromagnetic control equations at sampling points in each physical subdomain, and the corresponding electromagnetic physical residual loss function is constructed.

[0051] At the interface between adjacent physical subdomains, a magnetic field continuity constraint is introduced to ensure the physical consistency of the magnetic field solution across different material regions. The continuity condition is expressed as follows: ; Where the subscripts i and j represent the adjacent physical subdomains on both sides of the interface, and n is the interface normal direction.

[0052] The corresponding interface electromagnetic loss function is defined as: ; in, This is the set of interface sampling points.

[0053] The interface continuity loss function can be expressed as: .

[0054] The above loss functions are weighted and summed to form the overall joint loss function of the magnetic-thermal multiphysics field: ; Where M is the total number of physical subdomains. These are weighting coefficients used to balance the impact of different physical and data constraints on the training process, and can be determined through experience or current needs.

[0055] In some embodiments, the subdomain neural networks of a preset MC-PINN network are trained by combining sampling data and location information of various types of sampling points, and the loss function of each subdomain neural network is determined, including: An initial neural network for each physical subdomain is created based on thermal conductivity and electromagnetic parameters; By embedding the corresponding heat conduction control equation and electromagnetic field control equation into each initial neural network, the optimized subdomain neural network is obtained. Using the spatial coordinates of various types of sampling points as input, and the temperature data and circumferential magnetic flux density data within the corresponding physical subdomain as prediction results, the subdomain neural network is trained to determine the loss function of each subdomain neural network.

[0056] In this embodiment, an independent sub-network structure is configured for each physical subdomain. While the sub-networks maintain a consistent structural form, their network parameters are independent to accommodate the differences in physical characteristics within different subdomains. By introducing continuity constraints at the interface, collaborative work between the multi-subdomain networks is achieved, thereby forming a holistic, continuous multi-domain physical information neural network model.

[0057] Each subdomain network is a feedforward fully connected neural network, with its input layer taking axisymmetric spatial coordinates (r, z) as input and its output layer simultaneously providing the predicted temperature value within that subdomain. and circumferential flux density prediction , can be represented as: ; in, This represents the neural network mapping function corresponding to the m-th physical subdomain. It is its set of network parameters.

[0058] Each sub-domain network adopts the same network structure, including: one input layer, four hidden layers, each containing 32 neurons; tanh is used as the activation function between the hidden layers; and one output layer with an output dimension of 2, corresponding to the predicted values ​​of the temperature field and the circumferential magnetic flux density field, respectively. This structure, while ensuring the network's expressive power, can approximate the continuous and smooth physical field distribution function well, and is beneficial for automatic differentiation calculation of higher-order spatial derivatives. During the model's forward extrapolation or training process, for any input sampling point coordinates... First, the physical subdomain number m to which the sample point belongs is determined based on its spatial location. This determination process can be implemented using a predefined geometric discriminant function or a subdomain mask. Once the subdomain is determined, the sample point is only input into the corresponding subdomain subnetwork. The input sample is forward-computed without participating in the computation of other subdomains or subnetworks. This method enables automatic forwarding of input samples between multiple subdomains, avoiding the aliasing of physical properties between different material regions and improving the model's ability to represent multi-medium structures. It should be noted that in this embodiment, each subdomain or subnetwork simultaneously outputs predicted values ​​for both the temperature field and the circumferential magnetic flux density field, achieving joint modeling of the magnetic-thermal dual physics fields.

[0059] In some embodiments, the loss function further includes a data consistency loss function; before iteratively optimizing the subdomain neural network based on the loss function to obtain the target MC-PINN network, the following is also included: Sparse sampling points are generated at local locations in the casing geometry model; the sparse sampling points include temperature sampling points and electromagnetic sampling points. The data consistency loss function is determined based on the measured parameters of sparse sampling points and the output parameters of the subdomain neural network.

[0060] In this embodiment, to enhance the model's constraint capability under real engineering conditions, a small number of temperature measurement points and circumferential magnetic flux density measurement points are introduced at local locations on the sleeve. Temperature measurement points are placed near the conductor, in the capacitor screen area, or inside the insulation layer, and steady-state or quasi-steady-state temperature data are acquired using thermocouples or fiber optic temperature sensors. Circumferential magnetic flux density measurement points are preferably placed on the outer surface of the sleeve, and circumferential magnetic flux density data at the corresponding locations are acquired using a Hall sensor array. The collected data is introduced into the network training process in discrete point form to construct consistency loss constraints for the measurement data.

[0061] ; in, The temperature output parameters of the subdomain neural network, These are measured temperature parameters. The output parameters of the circumferential magnetic flux density of the subdomain neural network are: These are the measured parameters of the circumferential magnetic flux density. This represents the total amount of data collected.

[0062] In some embodiments, the subdomain neural network is iteratively optimized based on a loss function to obtain the target MC-PINN network, including: The parameter gradients of each subdomain neural network are calculated based on the loss function; The AdamW optimization algorithm is used to iteratively optimize the parameter gradients until the loss function is less than a preset threshold, thus obtaining the target MC-PINN network.

[0063] In this embodiment, an adaptive optimization algorithm based on first-order gradients is used to jointly optimize the parameters of each sub-domain sub-network. The AdamW optimization algorithm is adopted, which introduces a weight decay term into the Adam algorithm, which helps to suppress network overfitting and improve generalization ability.

[0064] In each training iteration, the specific steps include: inputting all types of sampling points into the corresponding subdomain subnetwork according to their subdomain and category; calculating the temperature field and circumferential magnetic flux density field predicted by the network through forward propagation; calculating various physical residuals, boundary errors, interface continuity errors, and measurement data errors using automatic differentiation; and calculating the joint total loss function. Calculate the gradients of the network parameters for each subdomain and update the parameters using the AdamW optimization algorithm. Repeat this process until the change in the joint total loss function over several consecutive training epochs is less than a preset threshold, or the physical residual losses of each subdomain decrease to a preset physical tolerance range, or the preset maximum number of training epochs is reached. During training, the convergence curves of various loss terms changing with training epochs can be recorded simultaneously for analyzing the model training status and adjusting weight parameter settings.

[0065] In some embodiments, please refer to Figure 3 , Figure 3 This is a schematic diagram of a transformer bushing magnetothermal deduction system based on MC-PINN, provided in an embodiment of the present invention. The present invention provides a transformer bushing magnetothermal deduction system 300 based on MC-PINN, comprising: a subdomain partitioning module 310, a sampling point generation module 320, a function determination module 330, and a data deduction module 340; wherein,

[0066] The subdomain partitioning module 310 is configured to construct the bushing geometric model of the transformer bushing sample and divide the bushing geometric model into multiple physical subdomains with different thermal conductivity parameters and / or electromagnetic parameters based on the differences in physical properties of different regions. The sampling point generation module 320 is configured to generate multiple intra-domain sampling points within the geometric range of each physical subdomain, generate multiple boundary sampling points along the boundary curve at the location with a clear physical boundary on the sleeve geometric model, and generate multiple interface sampling points along the interface direction at the common interface of any two adjacent physical subdomains. The function determination module 330 is configured to construct heat conduction control equations and electromagnetic field control equations based on sampling data from in-domain sampling points, boundary sampling points, and interface sampling points. It embeds these equations into a preset MC-PINN network and trains each subdomain neural network of the preset MC-PINN network using the sampling data and the location information of each type of sampling point. The module then determines the loss function for each subdomain neural network. The loss functions include a physical residual loss function, a boundary condition loss function, and an interface continuity loss function. The data extrapolation module 340 is configured to iteratively optimize the subdomain neural network based on the loss function to obtain the target MC-PINN network, and use the target MC-PINN network to extrapolate the temperature field distribution and circumferential magnetic flux density field distribution of the bushing of the transformer under test.

[0067] In some embodiments, the subdomain partitioning module 310 is specifically configured as follows: A two-dimensional axisymmetric modeling method was used to model the transformer bushing sample and construct the bushing geometric model; Based on the differences in material parameters and physical field variation patterns in different regions, the bushing geometric model is divided into a conductor subdomain, a capacitor screen subdomain, an insulating dielectric subdomain, and an external dielectric subdomain.

[0068] In some embodiments, the domain sampling points, boundary sampling points, and interface sampling points all include temperature sampling points and electromagnetic sampling points; Temperature sampling points are measured using thermocouples or fiber optic temperature sensors, and temperature data during steady-state or heating processes are acquired through a multi-channel data acquisition device. Electromagnetic sampling points are equipped with a Hall magnetic field sensor array arranged along the axial direction of the sleeve to measure the circumferential magnetic flux density, so as to obtain circumferential magnetic flux density data at different axial positions.

[0069] In some embodiments, the function determination module 330 is specifically configured as follows: Physical residual constraints are constructed based on the sampling data of sampling points within the domain to construct the heat conduction equation and the electromagnetic field control equation. Thermal and electromagnetic boundary condition constraints are constructed based on the sampling data of boundary sampling points to form the heat conduction equation and the electromagnetic field control equation; The continuity constraints of field variables are constructed based on the sampling data of the interface sampling points to form the heat conduction equation and the electromagnetic field control equation.

[0070] In some embodiments, the function determination module 330 is specifically configured as follows: An initial neural network for each physical subdomain is created based on thermal conductivity and electromagnetic parameters; By embedding the corresponding heat conduction control equation and electromagnetic field control equation into each initial neural network, the optimized subdomain neural network is obtained. Using the spatial coordinates of various types of sampling points as input, and the temperature data and circumferential magnetic flux density data within the corresponding physical subdomain as prediction results, the subdomain neural network is trained to determine the loss function of each subdomain neural network.

[0071] In some embodiments, the loss function further includes a data consistency loss function; the function determination module 330 is further configured to: Sparse sampling points are generated at local locations in the casing geometry model; the sparse sampling points include temperature sampling points and electromagnetic sampling points. The data consistency loss function is determined based on the measured parameters of sparse sampling points and the output parameters of the subdomain neural network.

[0072] In some embodiments, the data extrapolation module 340 is specifically configured as follows: The parameter gradients of each subdomain neural network are calculated based on the loss function; The AdamW optimization algorithm is used to iteratively optimize the parameter gradients until the loss function is less than a preset threshold, thus obtaining the target MC-PINN network.

[0073] It should be noted that the transformer bushing magnetothermal deduction system based on MC-PINN provided in this application embodiment and the transformer bushing magnetothermal deduction method based on MC-PINN provided in this application embodiment are based on the same application concept. Therefore, the specific implementation of this embodiment can refer to the implementation of the aforementioned transformer bushing magnetothermal deduction method based on MC-PINN, and the repeated parts will not be described again.

[0074] In some embodiments, please refer to Figure 4, Figure 4 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. The electronic device 400 provided in this embodiment includes a processor 410 and a memory 420; the memory 420 stores a computer program, wherein the computer program, when executed by the processor, implements the aforementioned transformer bushing magnetothermal deduction method based on MC-PINN.

[0075] Specifically, processor 410 may include, for example, a general-purpose microprocessor, an instruction set processor and / or an associated chipset and / or a special-purpose microprocessor (e.g., an application-specific integrated circuit (ASIC)), etc. Processor 410 may also include onboard memory for caching purposes. Processor 410 may be a single processing unit or multiple processing units for performing different actions of the method flow according to embodiments of this application.

[0076] Memory 420 may be any medium capable of containing, storing, transmitting, propagating, or transmitting instructions. For example, memory 420 may include, but is not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, instruments, or propagation media. Specific examples of memory 420 include: magnetic storage devices such as magnetic tape or hard disk drives (HDDs); optical storage devices such as optical discs (CD-ROMs); and may also be random access memory (RAM) or flash memory; and / or wired / wireless communication links.

[0077] This application also provides a non-transitory computer-readable storage medium storing a computer program thereon. When executed by a processor, this program implements the above-described method for magnetothermal deduction of transformer bushings based on MC-PINN. This computer-readable medium may be included in the device / apparatus / system described in the above embodiments; or it may exist independently and not assembled into that device / apparatus / system. The aforementioned computer-readable medium carries one or more programs, which, when executed, implement the method according to the embodiments of this application.

[0078] According to embodiments of this application, a computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. A computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this application, a computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. In this application, a computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media can also be any computer-readable medium other than computer-readable storage media, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium can be transmitted using any suitable medium, including but not limited to: wireless, wired, optical fiber, radio frequency signals, etc., or any suitable combination thereof.

[0079] Those skilled in the art will understand that the features described in the various embodiments and / or claims of this application can be combined and / or combined in various ways, even if such combinations or combinations are not explicitly described in this application. In particular, the features described in the various embodiments and / or claims of this application can be combined and / or combined in various ways without departing from the spirit and teachings of this application. All such combinations and / or combinations fall within the scope of this application. Therefore, the scope of this application should not be limited to the above embodiments, but should be defined not only by the appended claims, but also by their equivalents. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this invention should be included within the protection scope of this invention.

Claims

1. A method for magnetocaloric deduction of transformer bushings based on MC-PINN, characterized in that, include: A bushing geometric model of a transformer bushing sample is constructed, and the bushing geometric model is divided into multiple physical subdomains with different thermal conductivity parameters and / or electromagnetic parameters based on the differences in physical properties of different regions. Multiple intra-domain sampling points are generated within the geometric range of each physical subdomain; multiple boundary sampling points are generated along the boundary curve at the location with a clear physical boundary on the sleeve geometric model; and multiple interface sampling points are generated along the interface direction at the common interface of any two adjacent physical subdomains. Based on the sampling data of the sampling points within the domain, the sampling points at the boundary, and the sampling points at the interface, heat conduction control equations and electromagnetic field control equations are constructed. These equations are then embedded into a preset MC-PINN network. The preset MC-PINN network is then trained by combining the sampling data and the location information of each type of sampling point to determine the loss function for each sub-domain neural network. The loss function includes a physical residual loss function, a boundary condition loss function, and an interface continuity loss function. The subdomain neural network is iteratively optimized based on the loss function to obtain the target MC-PINN network, and the temperature field distribution and circumferential magnetic flux density field distribution of the bushing of the transformer under test are deduced using the target MC-PINN network.

2. The transformer bushing magnetocaloric deduction method based on MC-PINN as described in claim 1, characterized in that, The process involves constructing a bushing geometric model for a transformer bushing sample, and dividing the bushing geometric model into multiple physical subdomains with different thermal conductivity parameters and / or electromagnetic parameters based on the differences in physical properties of different regions, including: The transformer bushing sample was modeled using a two-dimensional axisymmetric modeling method to construct a bushing geometric model; Based on the differences in material parameters and physical field variation patterns in different regions, the bushing geometric model is divided into a conductor subdomain, a capacitor screen subdomain, an insulating dielectric subdomain, and an external dielectric subdomain.

3. The transformer bushing magnetocaloric deduction method based on MC-PINN as described in claim 1, characterized in that, The sampling points within the domain, the boundary sampling points, and the interface sampling points all include temperature sampling points and electromagnetic sampling points; The temperature sampling points are measured using thermocouples or fiber optic temperature sensors, and temperature data during steady-state or heating processes are acquired through a multi-channel data acquisition device. The electromagnetic sampling points are equipped with a Hall magnetic field sensor array arranged along the axial direction of the sleeve to measure the circumferential magnetic flux density, so as to obtain circumferential magnetic flux density data at different axial positions.

4. The transformer bushing magnetocaloric deduction method based on MC-PINN as described in claim 1, characterized in that, The construction of heat conduction control equations and electromagnetic field control equations based on sampling data from the domain sampling points, the boundary sampling points, and the interface sampling points includes: Physical residual constraints for the heat conduction equation and the electromagnetic field control equation are constructed based on the sampling data of the sampling points within the domain. Based on the sampling data of the boundary sampling points, thermal and electromagnetic boundary condition constraints are constructed for the heat conduction equation and the electromagnetic field control equation. Based on the sampling data from the interface sampling points, the field variable continuity constraints of the heat conduction equation and the electromagnetic field control equation are constructed.

5. The transformer bushing magnetocaloric deduction method based on MC-PINN as described in claim 1, characterized in that, The step of training each subdomain neural network of the preset MC-PINN network by combining the sampled data and the location information of each type of sample point, and determining the loss function of each subdomain neural network, includes: An initial neural network for each of the physical subdomains is created based on thermal conductivity parameters and electromagnetic parameters; By embedding the corresponding heat conduction control equation and electromagnetic field control equation into each initial neural network, an optimized subdomain neural network is obtained. Using the spatial coordinates of each type of sampling point as input, and the temperature data and circumferential magnetic flux density data within the corresponding physical subdomain as prediction results, the subdomain neural network is trained to determine the loss function of each subdomain neural network.

6. The transformer bushing magnetocaloric deduction method based on MC-PINN as described in claim 5, characterized in that, The loss function further includes a data consistency loss function; before iteratively optimizing the subdomain neural network based on the loss function to obtain the target MC-PINN network, the following is also included: Sparse sampling points are generated at local locations in the sleeve geometry model; the sparse sampling points include temperature sampling points and electromagnetic sampling points. The data consistency loss function is determined based on the measured parameters of the sparse sampling points and the output parameters of the subdomain neural network.

7. The transformer bushing magnetocaloric deduction method based on MC-PINN as described in claim 6, characterized in that, The iterative optimization of the subdomain neural network based on the loss function to obtain the target MC-PINN network includes: The parameter gradients of each of the subdomain neural networks are calculated based on the loss function. The parameter gradients are iteratively optimized using the AdamW optimization algorithm until the loss function is less than a preset threshold, thus obtaining the target MC-PINN network.

8. A transformer bushing magnetocaloric deduction system based on MC-PINN, characterized in that, include: The system comprises a subdomain partitioning module, a sampling point generation module, a function determination module, and a data derivation module; among which... The subdomain partitioning module is configured to construct a bushing geometric model of a transformer bushing sample, and divide the bushing geometric model into multiple physical subdomains with different thermal conductivity parameters and / or electromagnetic parameters based on the differences in physical properties of different regions. The sampling point generation module is configured to generate multiple intra-domain sampling points within the geometric range of each physical subdomain, generate multiple boundary sampling points along the boundary curve at a location with a clear physical boundary on the sleeve geometric model, and generate multiple interface sampling points along the interface direction at the common interface of any two adjacent physical subdomains. The function determination module is configured to construct heat conduction control equations and electromagnetic field control equations based on sampling data from sampling points within the domain, boundary sampling points, and interface sampling points; embed the heat conduction control equations and electromagnetic field control equations into a preset MC-PINN network; and train each subdomain neural network of the preset MC-PINN network by combining the sampling data and the location information of each type of sampling point, thereby determining the loss function for each subdomain neural network; the loss function includes a physical residual loss function, a boundary condition loss function, and an interface continuity loss function. The data extrapolation module is configured to iteratively optimize the subdomain neural network based on the loss function to obtain a target MC-PINN network, and then use the target MC-PINN network to extrapolate the temperature field distribution and circumferential magnetic flux density field distribution of the bushing of the transformer under test.

9. An electronic device, characterized in that, It includes a processor and a memory; the memory stores a computer program, wherein the computer program, when executed by the processor, implements the transformer bushing magnetocaloric deduction method based on any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium, characterized in that, It stores a computer program, wherein when the computer program is executed by a processor, it implements the transformer bushing magnetothermal deduction method based on any one of claims 1 to 7.

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