A method for dynamic modeling of temperature field of cable connector and overheating risk prediction

Abstract

This invention discloses a method for dynamic modeling of the temperature field and prediction of overheating risk in cable connectors, relating to the field of electrical equipment condition monitoring and thermal management technology. The method includes constructing the connector's geometric domain and establishing a fully coupled electro-magnetic-thermal-mechanical initial value model containing Lorentz force correction terms and eddy current loss heat source terms; jointly assembling the Lorentz force and eddy current loss terms to form a magneto-thermal coupling correction matrix, calculating the equivalent heat source field of a strong magnetic field; solving the temperature field and updating the conductivity and permeability distributions in reverse, forming a bidirectional coupled iterative loop until a converged temperature field is output; extracting hot spot trajectories and temperature gradient vector fields based on the converged temperature field, inputting them into the thermal aging kinetic model of the insulation material to generate a multidimensional indicator surface for overheating risk, determining the risk level and outputting a warning signal. This invention improves the accuracy of connector temperature field prediction and the reliability of overheating risk warning under strong magnetic field environments through bidirectional coupled iterative correction and fully coupled modeling.

Description

Technical Field

[0001] This invention relates to the field of electrical equipment condition monitoring and thermal management technology, and in particular to a method for dynamic modeling of temperature field and overheating risk prediction of cable connectors. Background Technology

[0002] Traditional technical solutions fail to incorporate the Lorentz force correction term exerted by the magnetic field on the current density distribution during modeling, resulting in an inaccurate description of the current redistribution phenomenon caused by the Lorentz force. Traditional models also lack quantitative characterization of the eddy current loss heat source term induced by time-varying magnetic fields, leading to the systematic omission of eddy current heating effects in scenarios with strong background magnetic fields, such as nuclear fusion devices, large motors, or electromagnetic catapults. Traditional industrial-grade temperature field simulation models fail under strong magnetic field conditions, with their predicted temperature field distribution deviating from measured values. In particular, they cannot capture local current concentration and overheating distortion phenomena caused by magnetohydrodynamic effects, leading to distorted assessments of insulation material aging and failing to provide reliable risk warnings for equipment operation and maintenance.

[0003] Furthermore, existing technologies generally lack a unified modeling framework capable of achieving bidirectional strong coupling iteration of multiple physical fields (electromagnetic, thermal, and mechanical). Current solutions often perform unidirectional weak coupling between the electromagnetic and temperature fields or only steady-state calculations, without establishing a dynamic feedback mechanism for the changes in material conductivity and permeability with temperature. During the drastic temperature rise caused by a strong magnetic field, the electromagnetic properties of conductors and ferromagnetic materials evolve in real time. Traditional methods cannot update the conductivity and permeability distributions in reverse based on the iterative solution of the temperature field to correct the electromagnetic field distribution. This unidirectionality in the model not only leads to insufficient accuracy in calculating the equivalent heat source field but also hinders the dynamic tracking of the migration patterns of hot spots inside the connector, making it difficult to quantitatively assess the degree of erosion of connector insulation life by strong magnetic field environments. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method for dynamic modeling of the temperature field and prediction of overheating risks in cable connectors. It aims to solve the technical problems of temperature field prediction distortion, hot spot location deviation, and inaccurate insulation aging risk assessment caused by existing cable connector temperature field simulation technologies in strong magnetic field environments, which neglect the Lorentz force correction of the magnetic field on the current distribution and the thermal effect of eddy current loss, and lack a bidirectional coupling iteration mechanism of electromagnetism-thermal-mechanical.

[0005] To achieve the above objectives, the present invention provides a method for dynamic modeling of the temperature field and prediction of overheating risk in cable connectors, comprising the following steps: S1. Obtain the geometric structure parameters, material electromagnetic property parameters, excitation parameters and boundary condition parameters of the cable connector in a strong magnetic field environment, and construct the connector geometric domain; S2. An initial value model of full electro-magnetic-thermal-mechanical coupling is established based on the connector geometric domain. The initial value model of full electro-magnetic-thermal-mechanical coupling includes a Lorentz force correction term characterizing the magnetic field applied to the current density distribution and an eddy current loss heat source term characterizing the time-varying magnetic field induced by the eddy current loss. S3. In the fully coupled electromagnetic-thermal-mechanical initial value model, the Lorentz force correction term and the eddy current loss heat source term are jointly assembled to form the magnetothermal coupling correction matrix. S4. Calculate the equivalent heat source field under strong magnetic field based on the magnetothermal coupling correction matrix and the initial current density distribution in the connector geometry. S5. Substitute the equivalent heat source field into the transient heat conduction equation to solve the temperature field iterative solution, and update the conductivity distribution and magnetic permeability distribution in reverse according to the temperature field iterative solution. Use the updated conductivity distribution and magnetic permeability distribution to correct the magnetothermal coupling correction matrix, forming a two-way coupling iterative loop until the temperature field iterative solution meets the preset convergence tolerance, and output the converged temperature field. S6. Extract the hot spot trajectory and temperature gradient vector field inside the connector based on the convergent temperature field, and input the hot spot trajectory and temperature gradient vector field into the pre-constructed thermal aging dynamics model of the insulation material to generate a multi-dimensional indicator surface for connector overheating risk. S7. Determine the risk level of the connector under its current operating state based on the multi-dimensional indicator surface for overheating risk, and output a risk warning signal.

[0006] Furthermore, the acquisition of the geometric structural parameters, material electromagnetic property parameters, excitation parameters, and boundary condition parameters of the cable connector in a strong magnetic field environment, and the construction of the connector's geometric domain, includes: Based on the design drawings and engineering specifications of the cable connector, the cross-sectional shape of the connector conductor, conductor diameter, insulation layer thickness, shielding layer structure and connector axial length are extracted to generate the geometric parameters of the cable connector. The conductivity and relative permeability of the connector conductor are measured by an impedance analyzer within a preset strong magnetic field environment operating frequency range. The magnetization curve and permeability temperature coefficient of the ferromagnetic material in the connector under different magnetic field intensities are measured by a magnetic material testing system to generate material electromagnetic property parameters. An AC excitation current with a preset frequency and amplitude is applied to the excitation winding port of the cable connector using a magnetic field measuring device, and the waveform and effective value of the excitation current are recorded to generate excitation parameters. Based on the working environment of the cable connector, the convective heat transfer coefficient between the outer surface of the connector and the surrounding medium, the ambient temperature, and the current inflow and outflow surfaces at the connector ends are determined to generate boundary condition parameters. Finite element meshes are generated for the spatial region constrained by geometric parameters, and material electromagnetic property parameters, excitation parameters, and boundary condition parameters are assigned as physical field properties to the meshed mesh elements and mesh nodes to generate a connector geometric domain containing the distribution of physical properties.

[0007] Furthermore, the electro-magnetic-thermal-mechanical fully coupled initial value model established based on the connector geometric domain includes a Lorentz force correction term characterizing the magnetic field's effect on the current density distribution and an eddy current loss heat source term characterizing the time-varying magnetic field-induced eddy current loss, including: Based on the connector geometry domain, electromagnetic field control equations are defined, which include Faraday's law of electromagnetic induction, Ampere's circuital law, and the current continuity equation in Maxwell's equations. Vector magnetic potential and scalar potential are used as solution variables to generate an electromagnetic field boundary value problem description. The Galerkin finite element method is used to spatially discretize the description of the electromagnetic field boundary value problem, generating a set of discrete finite element equations for the electromagnetic field. The excitation parameters are applied as the excitation source to the electromagnetic field finite element discrete equations. The initial vector magnetic potential distribution of each grid node in the connector geometry is obtained by solving the initial vector magnetic potential distribution. The initial magnetic field strength distribution and the initial current density distribution are derived from the initial vector magnetic potential distribution to generate the initial electromagnetic field distribution. In the initial electromagnetic field distribution, the Lorentz force vector field is calculated based on the initial current density distribution and the initial magnetic field strength distribution. The Lorentz force vector field is then used as the volume force source term to be applied to the mechanical equilibrium equation in the connector geometry domain to generate the Lorentz force correction term. In the initial electromagnetic field distribution, the eddy current loss power density of each grid cell is calculated from the initial current density distribution and conductivity distribution, and the eddy current loss power density is used as an internal heat source term to be loaded into the transient heat conduction equation to generate the eddy current loss heat source term. The mechanical equilibrium equations containing the Lorentz force correction term, the transient heat conduction equations containing the eddy current loss heat source term, and the electromagnetic field finite element discrete equations are combined to form a fully coupled electromagnetic-thermal-mechanical initial value model.

[0008] Furthermore, the method of jointly assembling the Lorentz force correction term and the eddy current loss heat source term in the fully coupled electro-magnetic-thermal-mechanical initial value model to form a magnetothermal coupling correction matrix includes: The volume force density of the Lorentz force correction term in each mesh node within the connector geometry domain is extracted from the fully coupled electro-magnetic-thermal-mechanical initial value model, and the Lorentz force node load vector is generated. The internal heat source power density of each mesh element in the connector geometry domain is extracted from the eddy current loss heat source term in the fully coupled electro-magnetic-thermal-mechanical initial value model to generate the eddy current loss element thermal load vector. Based on the principle of virtual work, the Lorentz force nodal load vector is transformed into an equivalent heat source contribution term in the heat conduction control equation, thereby generating the Lorentz force thermal coupling contribution vector. The thermal load vector of the eddy current loss element is assembled into the finite element discretization scheme of the heat conduction control equation to generate the thermal coupling contribution vector of eddy current loss. The Lorentz force thermal coupling contribution vector and the eddy current loss thermal coupling contribution vector are superimposed on the right-hand source term of the heat conduction control equation to generate the magnetothermal coupling correction matrix.

[0009] Furthermore, the calculation of the equivalent heat source field under a strong magnetic field based on the magnetothermal coupling correction matrix and the initial current density distribution within the connector's geometric domain includes: The initial current density distribution of each grid node in the connector geometry is extracted from the initial electromagnetic field distribution of the fully coupled electromagnetic-thermal-mechanical initial value model, and the initial current density vector is generated. The initial eddy current loss power density of each grid cell in the connector geometry domain is extracted from the initial electromagnetic field distribution of the fully coupled electromagnetic-thermal-mechanical initial value model to generate the initial eddy current loss heat source field. The magnetothermal coupling correction matrix is ​​applied to the source term on the right-hand side of the heat conduction equation corresponding to the initial eddy current loss heat source field to obtain the corrected eddy current loss power density of each grid element in the connector geometry domain, thereby generating the corrected eddy current loss heat source field. The heat source values ​​of each grid element in the corrected eddy current loss heat source field are converted into equivalent nodal heat source values ​​of each grid node using the finite element shape function integration method, thereby generating an equivalent heat source field under the action of a strong magnetic field.

[0010] Furthermore, the step of substituting the equivalent heat source field into the transient heat conduction equation to solve the iterative solution of the temperature field, and updating the conductivity and permeability distributions in reverse according to the iterative solution of the temperature field, and correcting the magnetothermal coupling correction matrix with the updated conductivity and permeability distributions, forming a bidirectional coupling iterative loop until the iterative solution of the temperature field satisfies the preset convergence tolerance, and outputting the converged temperature field, includes: The equivalent heat source field is applied as an internal heat source load term to the transient heat conduction finite element equation in the connector geometry domain. The transient heat conduction finite element equation is solved by the time step method to obtain the current iteration step temperature value of each mesh node in the connector geometry domain and generate the temperature field iterative solution. Based on the temperature values ​​of each grid node in the iterative solution of the temperature field, the conductivity temperature coefficient in the electromagnetic property parameters of the material is called to calculate the updated conductivity values ​​of each grid node and generate the updated conductivity distribution. Based on the temperature values ​​of each grid node in the iterative solution of the temperature field, the temperature coefficient of permeability in the electromagnetic property parameters of the material is called to calculate the updated relative permeability value of each grid node and generate the updated permeability distribution. The conductivity parameters in the fully coupled electro-magnetic-thermal-mechanical model are updated with the updated conductivity distribution, and the magnetic permeability parameters in the fully coupled electro-magnetic-thermal-mechanical model are updated with the updated magnetic permeability distribution. The Lorentz force correction term and the eddy current loss heat source term are recalculated to obtain the updated magnetothermal coupling correction matrix. Calculate the maximum norm of the difference between the temperature values ​​of each grid node in the temperature field iterative solution and the temperature values ​​of each grid node in the temperature field of the previous iteration step. Determine whether the maximum norm is less than the preset convergence tolerance. If the maximum norm is greater than or equal to the preset convergence tolerance, use the updated magnetothermal coupling correction matrix as the magnetothermal coupling correction matrix for the next iteration step and return to the equivalent heat source field calculation step to continue the iterative loop. If the maximum norm is less than the preset convergence tolerance, terminate the iterative loop and output the current temperature field iterative solution as the converged temperature field.

[0011] Furthermore, the conductivity parameters in the fully coupled electro-magnetic-thermal-mechanical model are updated with the updated conductivity distribution, and the magnetic permeability parameters in the fully coupled electro-magnetic-thermal-mechanical model are updated with the updated magnetic permeability distribution. The Lorentz force correction term and the eddy current loss heat source term are recalculated to obtain the updated magnetothermal coupling correction matrix, as follows: The updated conductivity distribution is configured as the conductivity value of each grid cell in the connector geometry domain of the fully coupled electro-magnetic-thermal-mechanical initial value model, and the updated magnetic permeability distribution is configured as the magnetic permeability value of each grid cell, thus generating the updated electromagnetic material parameter distribution.

[0012] Based on the updated electromagnetic material parameter distribution, the electromagnetic field finite element discrete equations are solved again to obtain the updated current density distribution and the updated magnetic field strength distribution, and thus generate the updated electromagnetic field distribution. In the updated electromagnetic field distribution, the Lorentz force vector field is recalculated based on the updated current density distribution and the updated magnetic field strength distribution to obtain the updated Lorentz force nodal load vector. In the updated electromagnetic field distribution, the eddy current loss power density of each grid element is recalculated from the updated current density distribution and the updated conductivity distribution to obtain the updated eddy current loss element thermal load vector. Based on the principle of virtual work, the updated Lorentz force nodal load vector is transformed into the updated Lorentz force thermal coupling contribution vector. The updated eddy current loss element thermal load vector is assembled into the finite element discretization scheme of the heat conduction control equation to obtain the updated eddy current loss thermal coupling contribution vector. The updated Lorentz force thermal coupling contribution vector and the updated eddy current loss thermal coupling contribution vector are superimposed on the source term of the right-hand side of the heat conduction control equation to generate the updated magnetothermal coupling correction matrix.

[0013] Furthermore, the process involves extracting the hot spot trajectory and temperature gradient vector field inside the connector based on the convergent temperature field, and inputting these two parameters into a pre-constructed thermal aging kinetic model of the insulation material to generate a multi-dimensional indicator surface for connector overheating risk, including: In the convergent temperature field, based on the temperature value of each grid node in the connector geometry at each time step, the coordinates and time labels of grid nodes with temperature values ​​higher than the preset hotspot threshold are extracted to generate the hotspot trajectory inside the connector. Spatial gradient calculation is performed on the temperature values ​​of each grid node in the connector geometric domain of the convergent temperature field to obtain the temperature gradient vector of each grid node and generate a temperature gradient vector field. The time series of temperature values ​​at the coordinates of each grid node in the hot spot trajectory and the time series of temperature gradient vectors at the coordinates of each grid node in the temperature gradient vector field are input into the thermal aging dynamics model of the insulating material to calculate the aging rate of the insulating material at each grid node and generate the aging rate field of the insulating material. By integrating the aging rate field of the insulation material in the time dimension, the cumulative aging factor of each grid node is obtained, and a multi-dimensional indicator surface for connector overheating risk is generated.

[0014] Furthermore, the method of determining the risk level of the connector under its current operating state based on the multi-dimensional indicator surface for overheating risk and outputting a risk warning signal includes: In the multidimensional indicator surface for connector overheating risk, the cumulative aging factor value of each mesh node in the connector geometry is extracted at the current time step to generate the current spatial distribution of the cumulative aging factor. The cumulative aging factor value of each grid node in the current spatial distribution of cumulative aging factor is compared with the preset classification threshold to determine the risk level label corresponding to each grid node and generate a node-level risk level distribution map. Perform connectivity analysis on the node-level risk level distribution map, extract the connected regions and their spatial ranges corresponding to the highest risk level, and generate the overall risk level and risk area location information of the connector in its current operating state. The overall risk level and risk area location information are encoded into early warning signals, which are then output through a communication interface.

[0015] The present invention provides a method for dynamic modeling of the temperature field and prediction of overheating risk of cable connectors, the beneficial effects of which are mainly reflected in the following aspects: 1. This invention overcomes the limitations of traditional simplified models by establishing a fully coupled electro-magnetic-thermal-mechanical initial value model and introducing a bidirectional coupling iterative correction mechanism, significantly improving the realism and accuracy of temperature field simulation and risk prediction under strong magnetic field conditions. This invention successfully incorporates the magnetohydrodynamic effects and additional eddy current heat generation generated by strong magnetic fields into a unified calculation framework by explicitly defining the Lorentz force correction term representing the effect of the magnetic field on the current density distribution and the eddy current loss heat source term representing the time-varying magnetic field induced within the connector's geometric domain. This invention constructs a magnetothermal coupling correction matrix, superimposing the Lorentz force thermal coupling contribution vector and the eddy current loss thermal coupling contribution vector onto the source term of the heat conduction equation, thereby accurately calculating the equivalent heat source field under strong magnetic fields. This approach effectively solves the technical problem of inaccurate temperature field "distortion" caused by neglecting the macroscopic effects of the magnetic field in traditional models, and can truly reflect the profound impact of strong magnetic fields on the redistribution of current density and the hot spot formation mechanism within the connector.

[0016] 2. This invention updates the conductivity and permeability distributions in reverse based on the iterative solution of the temperature field. Using the updated electromagnetic parameters, it recalculates the Lorentz force correction term and eddy current loss heat source term to update the magnetothermal coupling correction matrix, forming a bidirectional coupled iterative loop until convergence. This ensures the model accurately captures the feedback effect of changes in the material's electrical and magnetic conductivity due to temperature increases on the heating mechanism. Furthermore, by extracting the hot spot trajectory and temperature gradient vector field from the converged temperature field and inputting them into the thermal aging kinetic model of the insulating material, a multi-dimensional indicator surface for connector overheating risk is generated. This surface integrates temperature amplitude, spatial gradient, and cumulative aging effects, accurately determining the risk level under the current operating state and outputting early warning signals. This provides solid data support for condition-based maintenance and lifespan management of cable connectors in strong magnetic field environments. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the method for dynamic modeling of the temperature field and prediction of overheating risk of a cable connector according to the present invention. Figure 2 This is a flowchart of the process of constructing the connector geometry in step S1 of the present invention; Figure 3 This is a flowchart of the process of establishing the fully coupled electro-magnetic-thermal-mechanical initial value model in step S2 of the present invention; Figure 4 This is a flowchart of the process of forming the magnetothermal coupling correction matrix in step S3 of the present invention; Figure 5 This is a flowchart of the bidirectional coupling iterative loop in step S5 of the present invention; Figure 6 This is a flowchart of the process of generating the multidimensional indicator surface for overheating risk in step S6 of the present invention; Figure 7This is a flowchart of risk assessment and early warning output in step S7 of the present invention. Detailed Implementation

[0018] 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.

[0019] like Figures 1-7 As shown, this invention provides a method for dynamic modeling of the temperature field and prediction of overheating risk in cable connectors, comprising the following steps: S1. Obtain the geometric structure parameters, material electromagnetic property parameters, excitation parameters and boundary condition parameters of the cable connector in a strong magnetic field environment, and construct the connector geometric domain; In this embodiment, obtaining the geometric structural parameters, material electromagnetic property parameters, excitation parameters, and boundary condition parameters of the cable connector in a strong magnetic field environment, and constructing the connector's geometric domain, includes: Based on the design drawings and engineering specifications of the cable connector, the cross-sectional shape of the connector conductor, conductor diameter, insulation layer thickness, shielding layer structure and connector axial length are extracted to generate the geometric parameters of the cable connector.

[0020] Specifically, design drawings are mechanical drawings that indicate component dimensions and assembly relationships. Engineering specifications refer to technical documents that record rated parameters and material grades. Cross-sectional shape refers to the transverse geometric profile of the body. Conductor diameter refers to the outer edge dimension of the metal conductor. Insulation layer thickness refers to the radial dimension of the insulating medium. Shielding layer structure refers to the arrangement of the metal braided mesh or tape layers. Connector axial length refers to the total extension distance along the central axis. Geometric parameters refer to the numerical set of the above spatial dimensions that describe the connector configuration.

[0021] The conductivity and relative permeability of the connector conductor are measured using an impedance analyzer within a preset strong magnetic field operating frequency range. The magnetization curves and permeability temperature coefficients of ferromagnetic materials under different magnetic field intensities are measured using a magnetic material testing device to generate electromagnetic property parameters of the materials.

[0022] Specifically, an impedance analyzer is an instrument that obtains material parameters by analyzing complex impedance through frequency sweeping. The operating frequency range of a strong magnetic field refers to the main frequency interval of the actual operating excitation current. Conductivity reflects the conductor's ability to conduct electricity. Relative permeability is the ratio of a material's permeability to the permeability of free space. A magnetic material testing device refers to an experimental platform composed of an excitation coil and a data acquisition unit. A magnetization curve is a nonlinear curve showing the change in magnetic induction intensity with magnetic field strength. The temperature coefficient of permeability is the rate of change of permeability with temperature. The electromagnetic property parameters of a material refer to the collection of the above-mentioned conductivity, permeability, magnetization curve, and temperature dependence.

[0023] An AC excitation current with a preset frequency and amplitude is applied to the excitation winding port of the cable connector, and the waveform and effective value of the excitation current are recorded to generate excitation parameters.

[0024] Specifically, the excitation winding port refers to the coil terminal where excitation current is introduced to simulate a strong magnetic field environment. The preset frequency and amplitude are determined based on actual operating conditions. The excitation current waveform refers to the instantaneous change of the current value over time. The effective value refers to the current value equivalent to DC heating. Excitation parameters refer to a description of the excitation conditions, including frequency, amplitude, and waveform characteristics.

[0025] Based on the working environment of the cable connector, the convective heat transfer coefficient between the outer surface and the surrounding medium, the ambient temperature, and the positions of the current inflow and outflow surfaces are determined to generate boundary condition parameters.

[0026] Specifically, the operating environment refers to the physical state of the connector's operating space. The convective heat transfer coefficient refers to the heat transfer capacity per unit area and unit temperature difference between the surface and the fluid medium. Ambient temperature refers to the reference temperature of the medium far from the connector surface. Current inflow and outflow surfaces refer to the end-face regions in the model that define the direction of current inflow and outflow. Boundary condition parameters refer to the set of the aforementioned thermal and electrical constraints.

[0027] Finite element meshes are generated for the spatial region constrained by geometric parameters, and material electromagnetic property parameters, excitation parameters and boundary condition parameters are assigned to the meshed mesh elements and nodes to generate a connector geometric domain containing the distribution of physical properties.

[0028] Specifically, the spatial region refers to the three-dimensional area enclosed by the guide body, insulation layer, and shielding layer. Finite element mesh generation refers to discretizing a continuous region into a set of tetrahedral or hexahedral elements. Assignment refers to assigning physical parameters such as electrical conductivity, magnetic permeability, and thermal coefficient to the corresponding mesh entities according to the material domain and boundary position. The connector geometry refers to a discretized digital model loaded with all electromagnetic, thermal, and constraint information, serving as the direct input for subsequent multiphysics coupling calculations.

[0029] S2. An initial value model of full electro-magnetic-thermal-mechanical coupling is established based on the connector geometric domain. The initial value model of full electro-magnetic-thermal-mechanical coupling includes a Lorentz force correction term characterizing the magnetic field applied to the current density distribution and an eddy current loss heat source term characterizing the time-varying magnetic field induced by the eddy current loss. In this embodiment, the electro-magnetic-thermal-mechanical fully coupled initial value model established based on the connector geometric domain includes a Lorentz force correction term characterizing the magnetic field's effect on the current density distribution and an eddy current loss heat source term characterizing the time-varying magnetic field-induced eddy current loss. The electromagnetic field control equations are defined based on the connector geometry domain. These equations include Faraday's law of electromagnetic induction, Ampere's circuital law, and the current continuity equation from Maxwell's equations. Vector magnetic potential and scalar potential are used as solution variables to generate a description of the electromagnetic field boundary value problem.

[0030] Specifically, the connector geometric domain refers to a discrete model that has been meshed and loaded with the electromagnetic properties of the material and boundary conditions. The electromagnetic field governing equations refer to a set of partial differential equations describing the spatial coupling relationship between the electric and magnetic fields. Faraday's law of electromagnetic induction characterizes the vortex electric field induced by a time-varying magnetic field, Ampere's circuital law characterizes the magnetic field jointly induced by conduction and displacement currents, and the current continuity equation characterizes charge conservation. Vector magnetic potential is an auxiliary vector function that satisfies the curl relationship of magnetic induction intensity, and scalar potential is a scalar function describing the Coulomb electric field. The description of the electromagnetic field boundary value problem refers to a deterministic solution proposition formed under the constraints of boundary conditions in a given region.

[0031] The Galerkin finite element method is used to spatially discretize the description of the electromagnetic field boundary value problem, generating a set of discrete finite element equations for the electromagnetic field.

[0032] Specifically, the Galerkin finite element method is a numerical method that transforms partial differential equations into weak integral forms using weighted residuals and employs shape functions as weighting functions. Spatial discretization refers to dividing a continuous domain into finite elements and approximating field variables using nodal interpolation. The discrete equations of the electromagnetic field finite element method refer to a system of algebraic equations with nodal vector magnetic potential and scalar potential as unknowns, and their coefficient matrix reflects material properties and geometric constraints.

[0033] The excitation parameters are applied as the excitation source to the electromagnetic field finite element discrete equations. The initial vector magnetic potential distribution of each grid node in the connector geometry is obtained by solving the initial vector magnetic potential distribution. The initial magnetic field strength distribution and the initial current density distribution are derived from the initial vector magnetic potential distribution to generate the initial electromagnetic field distribution.

[0034] Specifically, excitation parameters refer to the excitation conditions including frequency, amplitude, and waveform. The applied excitation source refers to the source term corresponding to the excitation current introduced on the right-hand side of the equations. The initial vector magnetic potential distribution refers to the vector magnetic potential values ​​at each node obtained under the steady-state assumption. The initial magnetic field strength is obtained from the curl of the vector magnetic potential, and the initial current density is derived from the electric field strength and constitutive relations. The initial electromagnetic field distribution is the spatial distribution state of the aforementioned magnetic field and current density fields.

[0035] In the initial electromagnetic field distribution, the Lorentz force vector field is calculated based on the initial current density distribution and the initial magnetic field strength distribution. The Lorentz force vector field is then used as the volume force source term and applied to the mechanical equilibrium equations in the connector geometry domain to generate the Lorentz force correction term.

[0036] formula:

[0037] In the formula, The Lorentz force is a volume force density vector, with units of Newtons per cubic meter, representing the electromagnetic force per unit volume of a current-carrying conductor in a magnetic field. The current density vector, in amperes per square meter, is provided by the initial current density distribution; This is a magnetic flux density vector, measured in Tesla, determined by the initial magnetic field strength distribution and the material's permeability; operators This represents the vector cross product, with the force direction following the left-hand rule. The Lorentz force vector field is... Spatial distribution throughout the entire solution domain. The mechanical equilibrium equations are partial differential equations describing the displacement field of an elastic body, which... When added to the right-hand side of the equation as a volume force source term, it constitutes the Lorentz force correction term, which is used to reflect the influence of electromagnetic force on structural deformation.

[0038] In the initial electromagnetic field distribution, the eddy current loss power density of each grid cell is calculated from the initial current density distribution and conductivity distribution, and the eddy current loss power density is used as an internal heat source term to be loaded into the transient heat conduction equation to generate the eddy current loss heat source term.

[0039] formula:

[0040] In the formula, Eddy current loss power density, expressed in watts per cubic meter, represents the thermal power generated per unit volume due to eddy current heating. The eddy current density vector is generated by the time-varying magnetic field; here, the induced component in the initial current density is taken. This indicates the magnitude of the vector; The electrical conductivity of the material, measured in Siemens per meter, is given by the material's electromagnetic properties. This formula originates from the differential form of Joule's law. The transient heat conduction equation refers to the partial differential equation describing the spatiotemporal evolution of the temperature field. When loaded onto the right-hand side of the equation as an internal heat source term, it constitutes the eddy current loss heat source term, serving as the core internal thermal excitation for temperature field calculation.

[0041] The mechanical equilibrium equations containing the Lorentz force correction term, the transient heat conduction equations containing the eddy current loss heat source term, and the electromagnetic field finite element discrete equations are combined to form a fully coupled electromagnetic-thermal-mechanical initial value model.

[0042] Specifically, the simultaneous solution refers to solving the governing equations of the electromagnetic field, temperature field, and displacement field within the same spatial discrete grid and time-progression framework. Field variables are bidirectionally coupled and data is transferred through the Lorentz force correction term and the eddy current loss heat source term. The fully coupled electro-magnetic-thermal-mechanical initial value model refers to a multiphysics numerical computation framework that integrates the above-mentioned interaction mechanisms. Starting from given excitation and boundary conditions, it can directly solve the dynamic evolution of the temperature field of cable connectors in a strong magnetic field environment, providing quantitative simulation basis for overheating risk prediction.

[0043] S3. In the fully coupled electromagnetic-thermal-mechanical initial value model, the Lorentz force correction term and the eddy current loss heat source term are jointly assembled to form the magnetothermal coupling correction matrix. In this embodiment, the step of jointly assembling the Lorentz force correction term and the eddy current loss heat source term in the fully coupled electro-magnetic-thermal-mechanical initial value model to form a magnetothermal coupling correction matrix includes: The volume force density of the Lorentz force correction term at each mesh node in the connector geometry domain is extracted from the fully coupled electro-magnetic-thermal-mechanical initial value model, and the Lorentz force node load vector is generated.

[0044] Specifically, the Lorentz force correction term refers to the volume force contribution introduced by the interaction between current density and magnetic field in the mechanical equilibrium equations. Volume force density refers to the electromagnetic force vector per unit volume. The Lorentz force nodal load vector refers to the discrete force vector set formed after equivalently condensing the volume force density to each node according to the finite element shape function interpolation rules.

[0045] The internal heat source power density of each mesh element in the connector geometry domain is extracted from the eddy current loss heat source term in the fully coupled electro-magnetic-thermal-mechanical initial value model to generate the eddy current loss element thermal load vector.

[0046] Specifically, the eddy current loss heat source term refers to the internal heating contribution generated by the Joule effect of eddy currents induced by the time-varying magnetic field in the transient heat conduction equation. The internal heat source power density refers to the heating power per unit volume, which is directly proportional to the square of the eddy current density modulus and inversely proportional to the electrical conductivity. The eddy current loss element heat load vector refers to the discrete vector that transforms the heat source power density within the element into the equivalent heat flux contribution at the nodes according to the finite element volume integral rule.

[0047] Based on the principle of virtual work, the Lorentz force nodal load vector is transformed into an equivalent heat source contribution term in the heat conduction control equation, thereby generating the Lorentz force thermal coupling contribution vector.

[0048] Specifically, the principle of virtual work refers to a variational transformation method that maps volume forces in the mechanical domain to temperature field source terms in the thermal domain through the energy conservation relation satisfied by virtual displacements. The equivalent heat source contribution term refers to the internal energy increment converted from the mechanical work consumed by the Lorentz force during the infinitesimal deformation of the conductor. The Lorentz force thermal coupling contribution vector is the additional heat source vector obtained by projecting the force load vector onto the discretized scheme of the heat conduction equation using the principle of virtual work.

[0049] The thermal load vector of the eddy current loss element is assembled into the finite element discretization scheme of the heat conduction control equation to generate the thermal coupling contribution vector of eddy current loss.

[0050] Specifically, assembly refers to the process of superimposing the thermal load vectors of each element into the global thermal load vector according to the grid node connectivity. The eddy current loss thermal coupling contribution vector is the global heat source vector component formed after element assembly, which directly reflects the excitation effect of electromagnetic induction heating on the temperature field.

[0051] The Lorentz force thermal coupling contribution vector and the eddy current loss thermal coupling contribution vector are superimposed on the right-hand source term of the heat conduction control equation to generate the magnetothermal coupling correction matrix.

[0052] Specifically, superposition refers to summing the contribution vectors of the two heat sources on the right-hand side of the linear algebraic equations. The magnetothermal coupling correction matrix refers to the coefficient correction term expressed in matrix form of the combined heat source contribution after superposition. The product of this matrix and the temperature vector gives the total thermal input of the electromagnetic field to the temperature field. Through this joint assembly process, the temperature field solution can simultaneously take into account the dual thermal effects of electromagnetic force work and eddy current Joule heating, providing an accurate heat source characterization basis for predicting the overheating risk of cable connectors in strong magnetic field environments.

[0053] S4. Calculate the equivalent heat source field under strong magnetic field based on the magnetothermal coupling correction matrix and the initial current density distribution in the connector geometry. In this embodiment, the step of calculating the equivalent heat source field under a strong magnetic field based on the magnetothermal coupling correction matrix and the initial current density distribution within the connector's geometric domain includes: The initial current density distribution of each grid node in the connector geometry is extracted from the initial electromagnetic field distribution of the fully coupled electromagnetic-thermal-mechanical initial value model, and the initial current density vector is generated.

[0054] Specifically, the initial electromagnetic field distribution refers to the spatial state of the electromagnetic field before thermal feedback correction. The initial current density distribution refers to the current density vector of each node obtained by solving under excitation parameters, including conduction current and induced eddy current components. The initial current density vector refers to the discrete vector formed by arranging the current densities of each node according to the finite element shape function, which serves as the basic input for subsequent heat source calculations.

[0055] The initial eddy current loss power density of each grid cell in the connector geometry is extracted from the initial electromagnetic field distribution of the fully coupled electromagnetic-thermal-mechanical initial value model to generate the initial eddy current loss heat source field.

[0056] Specifically, the initial eddy current loss power density refers to the heat generated per unit volume by induced eddy currents under the Joule effect in the initial electromagnetic field. Its value is equal to the square of the eddy current density modulus divided by the conductivity. The initial eddy current loss heat source field is the distribution of this power density on a spatial cell.

[0057] The magnetothermal coupling correction matrix is ​​applied to the source term on the right-hand side of the heat conduction equation corresponding to the initial eddy current loss heat source field to obtain the corrected eddy current loss power density of each grid element in the connector geometry domain, thereby generating the corrected eddy current loss heat source field.

[0058] Specifically, the magnetothermal coupling correction matrix refers to the coefficient correction term formed by superimposing the thermal coupling contribution of Lorentz force and the thermal coupling contribution of eddy current loss. The source term on the right-hand side of the heat conduction equation refers to the known heat load vector in the heat dissipation and conduction algebraic equation. Multiplying the correction matrix by the initial heat source vector yields the comprehensive heat source intensity that takes into account the heating effect of electromagnetic force. The corrected eddy current loss power density is the actual internal heat source value of each element after correction.

[0059] The heat source values ​​of each grid element in the corrected eddy current loss heat source field are converted into equivalent nodal heat source values ​​of each grid node using the finite element shape function integration method, thereby generating an equivalent heat source field under the action of a strong magnetic field.

[0060] Specifically, the finite element shape function integration method refers to the numerical integration process of transforming the continuously distributed heat source density within an element into concentrated nodal heat loads using element interpolation functions. The equivalent nodal heat source value is the nodal heat flux contribution distributed to each vertex of the element according to the principle of energy conservation. The equivalent heat source field refers to the comprehensive spatial distribution of heat sources, expressed in the form of nodal heat loads and incorporating both electromagnetic induction Joule heating and electromagnetic force heating effects, serving as the heat load input for subsequent transient temperature field solutions.

[0061] S5. Substitute the equivalent heat source field into the transient heat conduction equation to solve the temperature field iterative solution, and update the conductivity distribution and magnetic permeability distribution in reverse according to the temperature field iterative solution. Use the updated conductivity distribution and magnetic permeability distribution to correct the magnetothermal coupling correction matrix, forming a two-way coupling iterative loop until the temperature field iterative solution meets the preset convergence tolerance, and output the converged temperature field. In this embodiment, the step of substituting the equivalent heat source field into the transient heat conduction equation to solve the iterative solution of the temperature field, and updating the conductivity and permeability distributions in reverse according to the iterative solution of the temperature field, and correcting the magnetothermal coupling correction matrix with the updated conductivity and permeability distributions, forming a bidirectional coupling iterative loop until the iterative solution of the temperature field satisfies the preset convergence tolerance, and outputting the converged temperature field, includes: The equivalent heat source field is applied as an internal heat source load term to the transient heat conduction finite element equation within the connector geometry. The time-stepping method is used to solve the equation, obtaining the current iteration step temperature value of each mesh node within the connector geometry, and generating the temperature field iterative solution.

[0062] Specifically, the equivalent heat source field refers to the comprehensive heat source distribution expressed in the form of nodal thermal loads after processing with the magnetocaloric coupling correction matrix. The transient heat conduction finite element equation refers to a system of ordinary differential equations with nodal temperatures as unknowns after discretizing the Fourier heat conduction equation using the Galerkin method. The time-stepping method refers to a numerical method that discretizes the time domain into small intervals and solves them recursively. The iterative solution of the temperature field is the spatial distribution vector composed of all nodal temperatures obtained in the current iteration step.

[0063] Based on the temperature values ​​of each grid node in the iterative solution of the temperature field, the conductivity temperature coefficient in the electromagnetic property parameters of the material is called to calculate the updated conductivity values ​​of each grid node and generate the updated conductivity distribution.

[0064] Specifically, the conductivity temperature coefficient refers to the pre-measured rate of change of conductivity with temperature. The reference conductivity is calculated by multiplying the difference between the current node temperature and the reference temperature by this coefficient and then summing it to the reference conductivity. The updated conductivity distribution is the spatial distribution of the temperature-corrected conductivity across all nodes.

[0065] Based on the temperature values ​​of each grid node in the iterative solution of the temperature field, the permeability temperature coefficient in the electromagnetic property parameters of the material is called to calculate the updated relative permeability value of each grid node and generate the updated permeability distribution.

[0066] Specifically, the temperature coefficient of permeability refers to the rate of change of the relative permeability of a ferromagnetic material with temperature. The updated permeability distribution is the spatial distribution of the relative permeability at all nodes after temperature correction.

[0067] The conductivity parameters in the fully coupled electro-magnetic-thermal-mechanical model are updated with the updated conductivity distribution, and the magnetic permeability parameters in the fully coupled electro-magnetic-thermal-mechanical model are updated with the updated magnetic permeability distribution. The Lorentz force correction term and the eddy current loss heat source term are recalculated to obtain the updated magnetothermal coupling correction matrix.

[0068] Specifically, replacement refers to reassigning the electromagnetic parameter node distribution obtained in the previous step to the material properties of the fully coupled model. Recalculation refers to solving the electromagnetic field equations again based on the new parameters to generate new current density, magnetic field strength, and corresponding eddy current loss power density, which are then assembled into an updated magnetothermal coupling correction matrix. This matrix reflects the true electromagnetic response of the material at the current temperature.

[0069] Calculate the maximum norm of the temperature difference between the iterative solution of the temperature field and the temperature field of the previous iteration at each grid node, and determine whether it is less than the preset convergence tolerance. If the maximum norm is greater than or equal to the preset convergence tolerance, substitute the updated magnetothermal coupling correction matrix into the next iteration step and return to the equivalent heat source field calculation step to continue the loop; if the maximum norm is less than the preset convergence tolerance, terminate the loop and output the current iterative solution of the temperature field as the converged temperature field.

[0070] Specifically, the maximum norm of the difference refers to the maximum absolute value of the temperature change at each node. The preset convergence tolerance refers to the temperature change threshold preset based on engineering precision. The judgment logic is as follows: if the maximum temperature change exceeds the tolerance, it indicates that the material parameter changes still affect the temperature field, and the equivalent heat source field needs to be recalculated and the temperature field solved again using the updated magnetothermal coupling correction matrix, forming a two-way coupling iteration; if it is less than the tolerance, the temperature field has tended to stabilize. The converged temperature field is the final temperature distribution when thermal equilibrium is reached under this strong coupling mechanism. The overall effect is that by correcting electromagnetic parameters through temperature field feedback and iteratively solving, the nonlinear influence of material temperature change characteristics on the electromagnetic heat source can be accurately captured, and a steady-state temperature field that truly reflects the strong electro-magnetic-thermal coupling effect can be output, providing a reliable data foundation for overheating risk prediction.

[0071] In this embodiment, the conductivity parameters in the fully coupled electro-magnetic-thermal-mechanical model are updated with the updated conductivity distribution, and the magnetic permeability parameters in the fully coupled electro-magnetic-thermal-mechanical model are updated with the updated magnetic permeability distribution. The Lorentz force correction term and the eddy current loss heat source term are recalculated to obtain the updated magnetothermal coupling correction matrix, as follows: The updated conductivity distribution is configured as the conductivity value of each grid cell in the connector geometry domain of the fully coupled electro-magnetic-thermal-mechanical initial value model, and the updated magnetic permeability distribution is configured as the magnetic permeability value of each grid cell, thus generating the updated electromagnetic material parameter distribution.

[0072] Specifically, the updated conductivity and permeability distributions refer to the set of nodal material parameters corrected by temperature field feedback. Configuration refers to mapping the nodal parameters to element integration points via shape functions, enabling the electromagnetic field solution to utilize material properties matched to the current temperature. The updated electromagnetic material parameter distributions are thus spatially differentiated conductivity and permeability fields.

[0073] Based on the updated electromagnetic material parameter distribution, the electromagnetic field finite element discrete equations are solved again to obtain the updated current density distribution and the updated magnetic field strength distribution, thus generating the updated electromagnetic field distribution.

[0074] Specifically, the discrete equations of the electromagnetic field finite element method use vector magnetic potential and scalar potential as unknowns. Resolving the equations involves solving them again with new electromagnetic parameters, while keeping the excitation and boundary conditions unchanged. The updated current density distribution is obtained by multiplying the electric field strength and conductivity, and the updated magnetic field strength distribution is obtained by the curl of the vector magnetic potential.

[0075] In the updated electromagnetic field distribution, the Lorentz force vector field is recalculated based on the updated current density distribution and the updated magnetic field strength distribution to obtain the updated Lorentz force nodal load vector.

[0076] Specifically, the updated Lorentz force nodal load vector refers to the discrete force vector formed by condensing the updated electromagnetic volume force density to each node according to the shape function.

[0077] In the updated electromagnetic field distribution, the eddy current loss power density of each grid element is recalculated from the updated current density distribution and the updated conductivity distribution to obtain the updated eddy current loss element thermal load vector.

[0078] formula:

[0079] In the formula, The updated eddy current loss power density is expressed in watts per cubic meter, representing the eddy current heating power per unit volume under the updated electromagnetic material parameters. The updated eddy current density vector is determined by the induced electric field in the updated electromagnetic field distribution and the updated conductivity. This represents the magnitude of the current density vector; The updated conductivity value is obtained by correcting the conductivity temperature coefficient from the iterative solution of the temperature field. This formula originates from the differential form of Joule's law. The updated eddy current loss element heat load vector refers to the discrete vector that transforms the power density into the nodal equivalent heat flux contribution according to the finite element volume integral rule.

[0080] Based on the principle of virtual work, the updated Lorentz force nodal load vector is transformed into the updated Lorentz force thermal coupling contribution vector. The updated eddy current loss element thermal load vector is assembled into the finite element discretization scheme of the heat conduction control equation to obtain the updated eddy current loss thermal coupling contribution vector. The updated Lorentz force thermal coupling contribution vector and the updated eddy current loss thermal coupling contribution vector are superimposed on the source term of the right-hand side of the heat conduction control equation to generate the updated magnetothermal coupling correction matrix.

[0081] Specifically, the virtual work principle refers to the variational transformation method that maps volume forces in the mechanical domain to temperature field source terms in the thermal domain. Assembly refers to superimposing the element thermal load vectors into a global vector based on node connectivity. The updated magnetothermal coupling correction matrix, which is the comprehensive heat source contribution coefficient expressed in matrix form, is used for the next round of temperature field solving to ensure that the thermal load is synchronized with the material's temperature change characteristics.

[0082] S6. Extract the hot spot trajectory and temperature gradient vector field inside the connector based on the convergent temperature field, and input the hot spot trajectory and temperature gradient vector field into the pre-constructed thermal aging dynamics model of the insulation material to generate a multi-dimensional indicator surface for connector overheating risk. In this embodiment, the step of extracting the hot spot trajectory and temperature gradient vector field inside the connector based on the convergent temperature field, and inputting the hot spot trajectory and temperature gradient vector field into a pre-constructed thermal aging kinetic model of the insulating material to generate a multi-dimensional indicator surface for connector overheating risk includes: In the convergent temperature field, based on the temperature value of each grid node in the connector geometry at each time step, the coordinates and time labels of grid nodes with temperature values ​​higher than the preset hotspot threshold are extracted to generate the hotspot trajectory inside the connector.

[0083] Specifically, the convergent temperature field refers to the final spatial temperature distribution that reaches thermal equilibrium after bidirectional coupling iteration. The preset hotspot threshold refers to the critical temperature value preset based on the heat resistance grade of the insulation material. The hotspot trajectory refers to the spatiotemporal sequence data composed of the spatial coordinates and time labels of the overheated nodes, used to describe the migration path and duration of the high-temperature concentration area inside the connector.

[0084] Spatial gradient calculations are performed on the temperature values ​​of each grid node within the connector geometry domain in the convergent temperature field to obtain the temperature gradient vector of each grid node, thereby generating a temperature gradient vector field.

[0085] Specifically, spatial gradient calculation refers to the mathematical operation of taking partial derivatives of the temperature scalar field along three spatial directions to form a vector field. The temperature gradient vector points in the direction of the fastest temperature increase, and its magnitude represents the amount of temperature change per unit distance. The temperature gradient vector field is the spatial distribution of temperature gradient vectors at each node, used to characterize the conduction path and intensity of heat within the connector.

[0086] The time series of temperature values ​​at the coordinates of each grid node in the hot spot trajectory and the time series of temperature gradient vectors at the coordinates of each grid node in the temperature gradient vector field are input into the thermal aging dynamics model of the insulating material to calculate the aging rate of the insulating material at each grid node and generate the aging rate field of the insulating material.

[0087] Specifically, a temperature time series refers to the sequence of temperature changes at the same spatial coordinates over time steps. A temperature gradient vector time series refers to the sequence of temperature gradient changes at the same spatial coordinates over time steps. An insulation material thermal aging kinetic model is a mathematical model established based on the Arrhenius equation to describe the rate of performance degradation of insulation materials under thermal stress. The aging rate of insulation materials refers to the amount of aging damage accumulated per unit time under given temperature and temperature gradient conditions. The aging rate field of insulation materials is the spatial distribution of the aging rate at each node.

[0088] By integrating the aging rate field of the insulation material in the time dimension, the cumulative aging factor of each grid node is obtained, and a multi-dimensional indicator surface for connector overheating risk is generated.

[0089] Specifically, time-dimensional integration refers to the operation of accumulating the aging rate at each node along the time axis from the initial moment to the current moment. The cumulative aging factor refers to the total amount of thermal aging damage suffered by the insulation material at each node after the entire calculation time, with a value ranging from zero to one, where zero indicates no aging and one indicates the end of life. The connector overheating risk multidimensional indicator surface refers to a three-dimensional surface constructed with spatial coordinates as the base and the cumulative aging factor as the ordinate, or a two-dimensional cloud map presented using chromatographic mapping. Its height or color depth intuitively represents the overheating failure risk level at various locations within the connector. The overall effect is that, through the joint analysis of hotspot spatiotemporal trajectories and temperature gradient fields, and by substituting them into a thermal aging kinetic model for aging rate calculation and time integration, a multidimensional risk indicator surface integrating spatial location, temperature amplitude, temperature change rate, and time cumulative effects is generated.

[0090] S7. Determine the risk level of the connector under its current operating state based on the multi-dimensional indicator surface for overheating risk, and output a risk warning signal.

[0091] In this embodiment, the step of determining the risk level of the connector under its current operating state based on the multi-dimensional indicator surface for overheating risk and outputting a risk warning signal includes: In the multidimensional indicator surface for connector overheating risk, the cumulative aging factor value of each mesh node in the connector geometry is extracted at the current time step, and the spatial distribution of the current cumulative aging factor is generated.

[0092] Specifically, the overheating risk multidimensional indicator surface refers to a surface or cloud map with spatial coordinates as the base and cumulative aging factor as the height or chromatogram. The cumulative aging factor value refers to the total amount of thermal aging damage accumulated at each node from the initial time to the current time, with a value between zero and one. The current spatial distribution of the cumulative aging factor is the spatial set of aging factors for all nodes at the current time, reflecting the degree of spatial differentiation of thermal aging damage.

[0093] The cumulative aging factor value of each grid node in the current spatial distribution of cumulative aging factor is compared with the preset classification threshold to determine the risk level label corresponding to each grid node and generate a node-level risk level distribution map.

[0094] Specifically, the preset grading threshold refers to the numerical boundary that divides the continuous aging factor value into multiple risk level intervals. The risk level label refers to the discrete risk category identifier assigned to each node. The node-level risk level distribution map is a node distribution map presented using color-coded risk level labels.

[0095] Connectivity analysis is performed on the node-level risk level distribution map to extract the connected regions and their spatial ranges corresponding to the highest risk level, and to generate the overall risk level and risk area location information of the connector under its current operating status.

[0096] Specifically, connected component analysis refers to identifying sets of spatially adjacent nodes with the same risk level label. The highest risk level refers to the highest risk category currently appearing in the distribution. A connected region refers to a spatially continuous area composed of nodes with the highest risk level. The overall risk level refers to the global risk level determined comprehensively based on the size of the highest risk region. Risk region location information refers to the three-dimensional location and boundary description of this region within the connector.

[0097] The overall risk level and risk area location information are encoded into early warning signals, which are then output through a communication interface.

[0098] Specifically, encoding refers to converting risk level and location information into data frames suitable for transmission according to communication protocols. External monitoring devices refer to terminal equipment that receives and displays connector status information. Risk warning signals are coded data streams containing risk level and fault location information, used to trigger alarms or generate maintenance work orders. The overall effect is to transform multiphysics simulation results into clear risk level and spatial location information and output them in real time, providing timely and accurate early warning basis for condition monitoring and preventative maintenance of cable connectors in strong magnetic field environments.

[0099] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0100] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0101] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for dynamic modeling of the temperature field and prediction of overheating risk in cable connectors, characterized in that, Includes the following steps: S1. Obtain the geometric structure parameters, material electromagnetic property parameters, excitation parameters and boundary condition parameters of the cable connector in a strong magnetic field environment, and construct the connector geometric domain; S2. An initial value model of full electro-magnetic-thermal-mechanical coupling is established based on the connector geometric domain. The initial value model of full electro-magnetic-thermal-mechanical coupling includes a Lorentz force correction term characterizing the magnetic field applied to the current density distribution and an eddy current loss heat source term characterizing the time-varying magnetic field induced by the eddy current loss. S3. In the fully coupled electromagnetic-thermal-mechanical initial value model, the Lorentz force correction term and the eddy current loss heat source term are jointly assembled to form the magnetothermal coupling correction matrix. S4. Calculate the equivalent heat source field under strong magnetic field based on the magnetothermal coupling correction matrix and the initial current density distribution in the connector geometry. S5. Substitute the equivalent heat source field into the transient heat conduction equation to solve the temperature field iterative solution, and update the conductivity distribution and magnetic permeability distribution in reverse according to the temperature field iterative solution. Use the updated conductivity distribution and magnetic permeability distribution to correct the magnetothermal coupling correction matrix, forming a two-way coupling iterative loop until the temperature field iterative solution meets the preset convergence tolerance, and output the converged temperature field. S6. Extract the hot spot trajectory and temperature gradient vector field inside the connector based on the convergent temperature field, and input the hot spot trajectory and temperature gradient vector field into the pre-constructed thermal aging dynamics model of the insulation material to generate a multi-dimensional indicator surface for connector overheating risk. S7. Determine the risk level of the connector under its current operating state based on the multi-dimensional indicator surface for overheating risk, and output a risk warning signal.

2. The method for dynamic modeling of temperature field and overheating risk prediction of cable connectors according to claim 1, characterized in that, The process of acquiring the geometric structural parameters, material electromagnetic property parameters, excitation parameters, and boundary condition parameters of the cable connector in a strong magnetic field environment, and constructing the connector's geometric domain, includes: Based on the design drawings and engineering specifications of the cable connector, the cross-sectional shape of the connector conductor, conductor diameter, insulation layer thickness, shielding layer structure and connector axial length are extracted to generate the geometric parameters of the cable connector. The conductivity and relative permeability of the connector conductor are measured by an impedance analyzer within a preset strong magnetic field environment operating frequency range. The magnetization curve and permeability temperature coefficient of the ferromagnetic material in the connector under different magnetic field intensities are measured by a magnetic material testing system to generate material electromagnetic property parameters. An AC excitation current with a preset frequency and amplitude is applied to the excitation winding port of the cable connector using a magnetic field measuring device, and the waveform and effective value of the excitation current are recorded to generate excitation parameters. Based on the working environment of the cable connector, the convective heat transfer coefficient between the outer surface of the connector and the surrounding medium, the ambient temperature, and the current inflow and outflow surfaces at the connector ends are determined to generate boundary condition parameters. Finite element meshes are generated for the spatial region constrained by geometric parameters, and material electromagnetic property parameters, excitation parameters, and boundary condition parameters are assigned as physical field properties to the meshed mesh elements and mesh nodes to generate a connector geometric domain containing the distribution of physical properties.

3. The method for dynamic modeling of temperature field and overheating risk prediction of cable connectors according to claim 1, characterized in that, The electro-magnetic-thermal-mechanical fully coupled initial value model established based on the connector geometry domain includes a Lorentz force correction term characterizing the magnetic field's effect on the current density distribution and an eddy current loss heat source term characterizing the time-varying magnetic field-induced eddy current loss. Based on the connector geometry domain, electromagnetic field control equations are defined, which include Faraday's law of electromagnetic induction, Ampere's circuital law, and the current continuity equation in Maxwell's equations. Vector magnetic potential and scalar potential are used as solution variables to generate an electromagnetic field boundary value problem description. The Galerkin finite element method is used to spatially discretize the description of the electromagnetic field boundary value problem, generating a set of discrete finite element equations for the electromagnetic field. The excitation parameters are applied as the excitation source to the electromagnetic field finite element discrete equations. The initial vector magnetic potential distribution of each grid node in the connector geometry is obtained by solving the initial vector magnetic potential distribution. The initial magnetic field strength distribution and the initial current density distribution are derived from the initial vector magnetic potential distribution to generate the initial electromagnetic field distribution. In the initial electromagnetic field distribution, the Lorentz force vector field is calculated based on the initial current density distribution and the initial magnetic field strength distribution. The Lorentz force vector field is then used as the volume force source term to be applied to the mechanical equilibrium equation in the connector geometry domain to generate the Lorentz force correction term. In the initial electromagnetic field distribution, the eddy current loss power density of each grid cell is calculated from the initial current density distribution and conductivity distribution, and the eddy current loss power density is used as an internal heat source term to be loaded into the transient heat conduction equation to generate the eddy current loss heat source term. The mechanical equilibrium equations containing the Lorentz force correction term, the transient heat conduction equations containing the eddy current loss heat source term, and the electromagnetic field finite element discrete equations are combined to form a fully coupled electromagnetic-thermal-mechanical initial value model.

4. The method for dynamic modeling of temperature field and overheating risk prediction of cable connectors according to claim 1, characterized in that, The process of jointly assembling the Lorentz force correction term and the eddy current loss heat source term in the fully coupled electro-magnetic-thermal-mechanical initial value model to form a magneto-thermal coupling correction matrix includes: The volume force density of the Lorentz force correction term in each mesh node within the connector geometry domain is extracted from the fully coupled electro-magnetic-thermal-mechanical initial value model, and the Lorentz force node load vector is generated. The internal heat source power density of each mesh element in the connector geometry domain is extracted from the eddy current loss heat source term in the fully coupled electro-magnetic-thermal-mechanical initial value model to generate the eddy current loss element thermal load vector. Based on the principle of virtual work, the Lorentz force nodal load vector is transformed into an equivalent heat source contribution term in the heat conduction control equation, thereby generating the Lorentz force thermal coupling contribution vector. The thermal load vector of the eddy current loss element is assembled into the finite element discretization scheme of the heat conduction control equation to generate the thermal coupling contribution vector of eddy current loss. The Lorentz force thermal coupling contribution vector and the eddy current loss thermal coupling contribution vector are superimposed on the right-hand source term of the heat conduction control equation to generate the magnetothermal coupling correction matrix.

5. The method for dynamic modeling of temperature field and overheating risk prediction of cable connectors according to claim 4, characterized in that, The calculation of the equivalent heat source field under a strong magnetic field based on the magnetothermal coupling correction matrix and the initial current density distribution within the connector's geometric domain includes: The initial current density distribution of each grid node in the connector geometry is extracted from the initial electromagnetic field distribution of the fully coupled electromagnetic-thermal-mechanical initial value model, and the initial current density vector is generated. The initial eddy current loss power density of each grid cell in the connector geometry domain is extracted from the initial electromagnetic field distribution of the fully coupled electromagnetic-thermal-mechanical initial value model to generate the initial eddy current loss heat source field. The magnetothermal coupling correction matrix is ​​applied to the source term on the right-hand side of the heat conduction equation corresponding to the initial eddy current loss heat source field to obtain the corrected eddy current loss power density of each grid element in the connector geometry domain, thereby generating the corrected eddy current loss heat source field. The heat source values ​​of each grid element in the corrected eddy current loss heat source field are converted into equivalent nodal heat source values ​​of each grid node using the finite element shape function integration method, thereby generating an equivalent heat source field under the action of a strong magnetic field.

6. The method for dynamic modeling of temperature field and overheating risk prediction of cable connectors according to claim 1, characterized in that, The process involves substituting the equivalent heat source field into the transient heat conduction equation to solve the iterative solution of the temperature field, and then updating the conductivity and permeability distributions in reverse based on the iterative solution. The updated conductivity and permeability distributions are then used to correct the magnetothermal coupling correction matrix, forming a bidirectional coupling iterative loop until the iterative solution of the temperature field satisfies the preset convergence tolerance, and finally outputting a converged temperature field. This includes: The equivalent heat source field is applied as an internal heat source load term to the transient heat conduction finite element equation in the connector geometry domain. The transient heat conduction finite element equation is solved by the time step method to obtain the current iteration step temperature value of each mesh node in the connector geometry domain and generate the temperature field iterative solution. Based on the temperature values ​​of each grid node in the iterative solution of the temperature field, the conductivity temperature coefficient in the electromagnetic property parameters of the material is called to calculate the updated conductivity values ​​of each grid node and generate the updated conductivity distribution. Based on the temperature values ​​of each grid node in the iterative solution of the temperature field, the temperature coefficient of permeability in the electromagnetic property parameters of the material is called to calculate the updated relative permeability value of each grid node and generate the updated permeability distribution. The conductivity parameters in the fully coupled electro-magnetic-thermal-mechanical model are updated with the updated conductivity distribution, and the magnetic permeability parameters in the fully coupled electro-magnetic-thermal-mechanical model are updated with the updated magnetic permeability distribution. The Lorentz force correction term and the eddy current loss heat source term are recalculated to obtain the updated magnetothermal coupling correction matrix. Calculate the maximum norm of the difference between the temperature values ​​of each grid node in the temperature field iterative solution and the temperature values ​​of each grid node in the temperature field of the previous iteration step. Determine whether the maximum norm is less than the preset convergence tolerance. If the maximum norm is greater than or equal to the preset convergence tolerance, use the updated magnetothermal coupling correction matrix as the magnetothermal coupling correction matrix for the next iteration step and return to the equivalent heat source field calculation step to continue the iterative loop. If the maximum norm is less than the preset convergence tolerance, terminate the iterative loop and output the current temperature field iterative solution as the converged temperature field.

7. The method for dynamic modeling of temperature field and overheating risk prediction of cable connectors according to claim 6, characterized in that, The conductivity parameters in the fully coupled electro-magnetic-thermal-mechanical model are updated with the updated conductivity distribution, and the magnetic permeability parameters in the fully coupled electro-magnetic-thermal-mechanical model are updated with the updated magnetic permeability distribution. The Lorentz force correction term and the eddy current loss heat source term are recalculated to obtain the updated magnetothermal coupling correction matrix, as follows: The updated conductivity distribution is configured as the conductivity value of each grid cell in the connector geometry domain of the fully coupled electro-magnetic-thermal-mechanical initial value model, and the updated magnetic permeability distribution is configured as the magnetic permeability value of each grid cell, thus generating the updated electromagnetic material parameter distribution.

8. Based on the updated electromagnetic material parameter distribution, the electromagnetic field finite element discrete equations are solved again to obtain the updated current density distribution and the updated magnetic field strength distribution, and the updated electromagnetic field distribution is generated. In the updated electromagnetic field distribution, the Lorentz force vector field is recalculated based on the updated current density distribution and the updated magnetic field strength distribution to obtain the updated Lorentz force nodal load vector. In the updated electromagnetic field distribution, the eddy current loss power density of each grid element is recalculated from the updated current density distribution and the updated conductivity distribution to obtain the updated eddy current loss element thermal load vector. Based on the principle of virtual work, the updated Lorentz force nodal load vector is transformed into the updated Lorentz force thermal coupling contribution vector. The updated eddy current loss element thermal load vector is assembled into the finite element discretization scheme of the heat conduction control equation to obtain the updated eddy current loss thermal coupling contribution vector. The updated Lorentz force thermal coupling contribution vector and the updated eddy current loss thermal coupling contribution vector are superimposed on the source term of the right-hand side of the heat conduction control equation to generate the updated magnetothermal coupling correction matrix.

9. The method for dynamic modeling of temperature field and prediction of overheating risk of cable connectors according to claim 1, characterized in that, The process involves extracting the hot spot trajectory and temperature gradient vector field inside the connector based on the convergent temperature field, inputting the hot spot trajectory and temperature gradient vector field into a pre-constructed thermal aging kinetic model of the insulation material, and generating a multi-dimensional indicator surface for connector overheating risk, including: In the convergent temperature field, based on the temperature value of each grid node in the connector geometry at each time step, the coordinates and time labels of grid nodes with temperature values ​​higher than the preset hotspot threshold are extracted to generate the hotspot trajectory inside the connector. Spatial gradient calculation is performed on the temperature values ​​of each grid node in the connector geometric domain of the convergent temperature field to obtain the temperature gradient vector of each grid node and generate a temperature gradient vector field. The time series of temperature values ​​at the coordinates of each grid node in the hot spot trajectory and the time series of temperature gradient vectors at the coordinates of each grid node in the temperature gradient vector field are input into the thermal aging dynamics model of the insulating material to calculate the aging rate of the insulating material at each grid node and generate the aging rate field of the insulating material. By integrating the aging rate field of the insulation material in the time dimension, the cumulative aging factor of each grid node is obtained, and a multi-dimensional indicator surface for connector overheating risk is generated.

10. The method for dynamic modeling of temperature field and overheating risk prediction of cable connectors according to claim 8, characterized in that, The method for determining the risk level of the connector under its current operating state based on the multi-dimensional indicator surface for overheating risk and outputting a risk warning signal includes: In the multidimensional indicator surface for connector overheating risk, the cumulative aging factor value of each mesh node in the connector geometry is extracted at the current time step to generate the current spatial distribution of the cumulative aging factor. The cumulative aging factor value of each grid node in the current spatial distribution of cumulative aging factor is compared with the preset classification threshold to determine the risk level label corresponding to each grid node and generate a node-level risk level distribution map. Perform connectivity analysis on the node-level risk level distribution map, extract the connected regions and their spatial ranges corresponding to the highest risk level, and generate the overall risk level and risk area location information of the connector in its current operating state. The overall risk level and risk area location information are encoded into early warning signals, which are then output through a communication interface.

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