MBSE-based electrical equipment electromagnetic field finite element simulation method

Abstract

The invention provides an MBSE-based electrical equipment electromagnetic field finite element simulation method. The MBSE-based electrical equipment electromagnetic field finite element simulation method comprises the following steps: establishing a numerical simulation-artificial intelligence bidirectional coupling relationship; an electromagnetic field finite element simulation software architecture is constructed by selecting a modeling method, an open source modeling tool and a modeling language based on a bidirectional coupling relationship, and a four-layer overall architecture of an interface layer, a control layer, an engine layer and a core module layer is constructed by adopting a method based on MBSE; and establishing an electromagnetic field finite element simulation software prototype IFEM integrated with artificial intelligence, and calculating and verifying a two-dimensional electrostatic field and electromagnetic optimization. According to the method, the defects existing in a traditional document-based system engineering method are effectively overcome, it is guaranteed that the requirements and the architecture are closely combined, and the consistency of the requirements and the design is improved.

Description

Technical Field

[0001] The present application belongs to the technical field of electromagnetic field calculation of electromagnetic equipment, and in particular, relates to a finite element simulation method of electromagnetic field of electrical equipment based on MBSE. Background Art

[0002] As a key tool for electromagnetic analysis and design, electromagnetic finite element simulation software undertakes multi-level and multi-dimensional tasks such as electromagnetic field simulation, data processing and user interaction. In today's increasingly complex field of electromagnetic field finite element simulation software development, the use of advanced modeling methods is crucial to improving software quality, development efficiency and knowledge inheritance. At the same time, with the rapid development of artificial intelligence, the combination of deep learning and numerical simulation to simulate and analyze electromagnetic fields has also become an important development direction.

[0003] Large-scale commercial software is fully functional and highly accurate, but while providing versatility and ease of use, it also brings problems such as high barriers to use, high costs, and redundant functions for specific projects. Commercial software is usually expensive and has a large installation package. When solving specific problems, companies often only need a small part of the software to provide. From the perspective of usage barriers and costs, it is not cost-effective to choose commercial software. In addition, commercial software is regarded as a "black box", and it is difficult to accurately determine the cause if problems are encountered during use. As a result, many companies and researchers have carried out secondary development based on foreign commercial software in order to achieve rapid calculations for specific projects, but the kernel of the secondary development tools is ultimately dependent. In order to provide end-to-end services to enterprises and assist in the performance analysis and optimization of electrical equipment, it is urgent to develop electromagnetic field simulation software that is autonomous, controllable, lightweight, and customized for enterprises.

[0004] In the context of AI for Science, studying the construction method of electromagnetic field simulation software integrated with AI is an opportunity to develop customized electromagnetic field simulation software for enterprises. Since Hinton proposed deep learning in 2006, AI has experienced a series of landmark developments from AlphaGo to ChatGPT, and then to the video generation model Sora in 2024. These developments have opened the era of "AI for Science". Many researchers have begun to explore the use of AI algorithms for electromagnetic field simulation, and have achieved initial results in improving calculation accuracy and optimizing efficiency. In the context of the rapid development of artificial intelligence, joint simulation of deep learning algorithms and traditional numerical simulation algorithms is common, such as using the improved Linknet model to predict the magnetic field cloud map of the motor, predicting the magnetic field distribution of the coil and the motor through deep learning, and the motor drive efficiency diagram. However, traditional numerical simulation and artificial intelligence algorithms run on different platforms, and there are differences in code languages. It is difficult to interact when multiple algorithms are mixed, which is not conducive to the deep integration of the two.

[0005] The continuous development and update process of electromagnetic field finite element simulation software reflects the typical characteristics of complex software systems - continuous adaptive evolution. Traditional electromagnetic field finite element simulation software uses natural language and is based on document carriers. It has shortcomings such as difficulty in ensuring information consistency, ambiguity in description content, and difficulty in structural changes. Summary of the invention

[0006] In view of this, the present application aims to propose an MBSE-based electromagnetic field finite element simulation method for electrical equipment to solve the problems of electromagnetic field finite element simulation software, such as difficulty in ensuring information consistency, ambiguity in description content, and difficulty in structural changes.

[0007] To achieve the above purpose, the technical solution of this application is implemented as follows:

[0008] This application provides a finite element simulation method for electromagnetic fields of electrical equipment based on MBSE, including:

[0009] Establish a bidirectional coupling relationship between numerical simulation and artificial intelligence;

[0010] By selecting modeling methods, open source modeling tools and modeling languages, and building an electromagnetic field finite element simulation software architecture based on a bidirectional coupling relationship, a four-layer overall architecture of the interface layer, control layer, engine layer and core module layer is built using an MBSE-based method;

[0011] A prototype of electromagnetic field finite element simulation software IFEM with integrated artificial intelligence was established, and two-dimensional electrostatic fields and electromagnetic optimization were calculated and verified.

[0012] Furthermore, the establishment of a numerical simulation-artificial intelligence bidirectional coupling relationship includes:

[0013] Numerical solutions to electromagnetic problems are obtained by finite element method to generate training data;

[0014] Training an artificial intelligence model based on the training data, comparing the results predicted by the artificial intelligence model with the numerical simulation results, analyzing the deviation between the two, and optimizing the artificial intelligence model using the deviation information feedback;

[0015] A bidirectional coupling framework is integrated into the simulation software to establish a numerical simulation-artificial intelligence bidirectional coupling relationship.

[0016] Furthermore, the Arcadia modeling method, the open source modeling tool Capella, and the implicitly defined modeling language Arcadia / Capella improved based on SysML and embedded in Capella were selected to complete the establishment of the electromagnetic field finite element simulation software architecture.

[0017] Furthermore, the method for calculating and verifying the two-dimensional electrostatic field includes:

[0018] The finite element method and PINN deep learning model are used to calculate the two-dimensional electric field distribution between electrodes.

[0019] The PINN deep learning model includes three hidden layers, and defines the number of neurons in each layer. The activation function is Tanh, and the node coordinates after the domain grid is divided are used as the input of the PINN deep learning model, and the potential discrete value of the node is obtained as the output.

[0020] Furthermore, the calculation and verification of the solenoid interface magnetic field optimization process includes:

[0021] A two-dimensional control area is selected inside the solenoid, and the design variable is the solenoid radius. The first optimization goal is to minimize the difference between the actual value of the magnetic flux density in the control area and the specified value of the magnetic flux density; the second optimization goal is to minimize the power loss of the solenoid. The coil is set to be powered by a constant current, and the coil radius reflects the power loss. The expressions of the two optimization objective functions are as follows:

[0022]

[0023] Where P is power loss, I is current value, ρ is resistivity, l is wire length, S is wire cross-sectional area, n is t is the number of turns of the solenoid, f1 is the first objective function value, B0=2mT is the target magnetic flux density value, B j is the actual value of magnetic flux density in the control area, n p is the number of sampling points;

[0024]

[0025] Where f2 is the second objective function value;

[0026] Specify multiple radii and calculate the magnetic field around the solenoid. Then compare it with COMSOL to verify the correctness of the IFEM calculation.

[0027] Furthermore, 1 / 4 of the cross section through the center is selected, and the solution domain is specified as a square of fixed length, the left, right, and upper boundaries are first-class boundary conditions, and the lower boundary is a natural boundary condition;

[0028] In a two-dimensional plane field, the current density J is parallel to the vector magnetic potential A and parallel to the z-axis, that is, Ax = Ay = 0, Jx = Jy = 0, and the z-component of the vector magnetic potential A is taken as z is a field variable function, and the boundary value problem is expressed as:

[0029]

[0030] Where v is the magnetic reluctance;

[0031] The weighted residual method is used for discretization, and the finite element discretization equation is obtained:

[0032] KA = F;

[0033] In the formula, the coefficient matrix K = [K ij ], the right-hand end array F = [F i ], which is composed of the corresponding terms of each unit cell, among which, i and j represent the local numbers of all nodes in unit e;

[0034] According to the weighted residual method, the finite element discretization formula is:

[0035]

[0036] F i =∫ Ω N i J z dΩ;

[0037] Where N i and N j is the basis function, i,j = K, M, N, representing the numbers of the three nodes of the triangular element e;

[0038] Using triangular elements for meshing, the contribution of the elements to the coefficient matrix and the right-hand side terms is:

[0039]

[0040] Calculate the vector magnetic potential component A z Draw the amplitude distribution diagram and contour lines of discrete values ​​of

[0041] The error analysis was carried out between the calculation results of the finite element simulation software prototype IFEM and the COMSOL results.

[0042] Furthermore, the error values ​​of the magnetic flux density values ​​of the finite element simulation software prototype IFEM and COMSOL are calculated by the mean absolute error, mean absolute percentage error and mean square error respectively.

[0043] Compared with the prior art, the MBSE-based finite element simulation method for electromagnetic field of electrical equipment described in this application has the following beneficial effects:

[0044] The present application describes an MBSE-based finite element simulation method for electromagnetic fields of electrical equipment, which effectively overcomes the shortcomings of traditional document-based system engineering methods, ensures a close integration of requirements and architecture, and improves the consistency of requirements and design. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0046] Figure 1 This is a flow chart of electromagnetic field finite element simulation of electrical equipment based on MBSE as described in an embodiment of the present application;

[0047] Figure 2 This is the operation architecture diagram described in the embodiment of the present application;

[0048] Figure 3 A system task capability diagram described in an embodiment of the present application;

[0049] Figure 4 This is a system function data flow diagram described in an embodiment of the present application;

[0050] Figure 5 This is a system architecture diagram described in an embodiment of the present application;

[0051] Figure 6 This is a logical architecture diagram described in the embodiment of the present application;

[0052] Figure 7 This is a general architecture diagram of software interaction described in the embodiments of the present application;

[0053] Figure 8 This is a diagram of the inter-electrode electric field calculation model described in the embodiment of the present application;

[0054] Fig. 9 This is a simulation diagram of the finite element method calculation results described in the embodiment of the present application;

[0055] Fig.10 A loss function curve diagram of the PINN model described in the embodiment of the present application;

[0056] Fig.11 This is a simulation diagram of the calculation results of the PINN model described in the embodiment of the present application;

[0057] Fig.12 The TEAM Workshop 35th benchmark problem model described in the embodiment of the present application;

[0058] Fig.13 The amplitude distribution diagram and contour diagram described in the embodiments of the present application;

[0059] Fig.14 It is the component value of each direction of magnetic flux density and the amplitude diagram of the synthetic quantity described in the embodiment of the present application;

[0060] Fig.15 The optimization roadmap described in the embodiment of this application;

[0061] Fig.16 This is an expanded diagram of the guidance optimization module described in an embodiment of the present application. DETAILED DESCRIPTION

[0062] In order to make the objectives, technical solutions and advantages of the present application more clearly understood, the present application is further described in detail below in combination with specific embodiments and with reference to the accompanying drawings.

[0063] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the embodiments of the present application should be the usual meanings understood by people with ordinary skills in the field to which the present application belongs. The "first", "second" and similar words used in the embodiments of the present application do not represent any order, quantity or importance, but are only used to distinguish different components. "Including" or "comprising" and similar words mean that the elements or objects appearing in front of the word cover the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0064] The embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0065] See also Figure 1 As shown, this embodiment provides an MBSE-based finite element simulation method for electromagnetic fields of electrical equipment, which specifically includes the following steps:

[0066] Step S101, establishing a numerical simulation-artificial intelligence bidirectional coupling relationship.

[0067] Specifically, in this embodiment, "bidirectional coupling" refers to two aspects: bidirectional coupling between numerical simulation and AI; and bidirectional coupling between software designers and users.

[0068] Establish the coupling between numerical simulation and artificial intelligence. To go further, first of all, the training of artificial intelligence often requires a large amount of data, which comes from experimental measurements or numerical simulations. The experimental data is affected by the experimental conditions. It is difficult to obtain experimental data for some extreme working conditions. Numerical simulation can simulate the operating state of equipment that is difficult to achieve in simulation experiments, and is used to generate training sets for artificial intelligence models. Secondly, the calculation amount and cost of obtaining data using traditional numerical simulation are large, and the cost of using artificial intelligence instead of numerical simulation methods is low and more efficient.

[0069] Basic idea: There are many ways to combine finite element (numerical simulation) with neural network (artificial intelligence). For example, for the modeling problem of dynamic system of complex nonlinear structure, the linear part can be modeled by finite element, and the nonlinear part can be described by neural network (such as inputting the state variable of nonlinear component and outputting its restoring force). Then, the finite element model part and the neural network part are combined through boundary conditions and connection conditions to obtain a hybrid model. Another method is to first establish a variety of different models through finite element, and then use the modal characteristics (that is, the final design requirements to be achieved) as output variables, and the corresponding model structure parameters as input variables to train the neural network, and use the generalization characteristics of the neural network to obtain the corrected values ​​of the design parameters. Combined with the Monte Carlo method to perform multiple groups of finite element analysis, the data is input into the neural network for training, which can be used to analyze the reliability of the structure.

[0070] Implementation steps: Guided by numerical simulation, first, the finite element method is used to accurately numerically solve electromagnetic problems. In this stage, the focus is on building a comprehensive and accurate physical model to provide training data and verification benchmarks for AI; AI enhancement, using the data generated in the first stage to train machine learning models. These models are designed to learn the behavior patterns of electromagnetic fields to predict new scenario responses. After training, AI models can quickly provide solutions in new designs or quickly scan possible configurations in parameter studies; coupled iterative optimization, compare the results predicted by AI with numerical simulations, analyze the deviations between the two, and use deviation information feedback to optimize the AI ​​model. In addition, AI can guide numerical simulations to focus on possible key areas, thereby making more efficient use of computing resources; integrated applications, integrating a bidirectional coupling framework in the simulation software, users can choose precise mode (numerical simulation) or fast mode (AI-driven) as needed. Such integration not only improves the flexibility of the software and user experience, but also greatly enhances the adaptability of simulation tasks.

[0071] In the design process of complex software systems, the information gap between designers and users often leads to incoordination between design and implementation. To overcome this problem, a two-way coupling approach can be used to enable the two departments to play a balanced role and ensure that the design and use of the software are coordinated with each other.

[0072] The target design adopts a top-down model, transforming theories and concepts into specific tasks and capabilities according to strategic goals, decomposing tasks layer by layer through scenario-based design, forming a capability tree of task levels, and designing the support and collaboration relationship between capabilities. Multiple designs are carried out under different external influence conditions to discover relatively stable high-level capabilities and system application forms. Software design adopts a bottom-up model. Based on existing software and technology trends, by building typical application scenarios, the expected goals are reversely decomposed into capability trees of tasks of different complexity to guide the design and implementation of specific software.

[0073] The key is to establish a mechanism to ensure effective information interaction between target design and software design. By refining the scenarios in the target design, forming a capability tree and system application form for each scenario, both the target design and software design will obtain a capability tree, and group the leaf node capabilities into basic business capability sets and basic system capability sets. Through coupling analysis, the capability requirements of the target design, the expected capability requirements of the technology, and the current capability requirements are compared to determine the capabilities that need to be developed and their key directions, and then make other related design decisions.

[0074] Through two-way coupling analysis, designers and users analyze and refine basic capabilities in their respective fields, and conduct coupling analysis when necessary, ultimately determining the capabilities that need to be developed and the corresponding equipment systems, effectively solving the information gap between design and user departments. This approach ensures that the designs of complex software systems can support each other and be coordinated, improving the overall effectiveness and reliability of the system.

[0075] Step S102, by selecting modeling methods, open source modeling tools and modeling languages, and constructing an electromagnetic field finite element simulation software architecture based on a bidirectional coupling relationship, wherein a four-layer overall architecture of an interface layer, a control layer, an engine layer and a core module layer is constructed using an MBSE-based method.

[0076] Specifically, in this embodiment, by comparing and analyzing the three elements of MBSE: modeling method, modeling language and modeling tool, guided by the above software requirement analysis and design plan, the Arcadia modeling method, the open source modeling tool Capella, and the modeling language Arcadia / Capella improved based on SysML and embedded in Capella, which is implicitly defined, are selected to complete the design of the electromagnetic field finite element simulation software architecture.

[0077] The modeling process of electromagnetic field simulation software based on MBSE is as follows:

[0078] Level 1: Operational analysis and modeling

[0079] Run the analysis level to determine the needs and goals of the system's users and gain a clear understanding of the problem domain rather than providing solutions. The modeling process can be divided into three stages.

[0080] Define operational entities (OE): Define "user" and "simulation software" as operational entities, which are used in various subsequent model diagrams, making each model element strongly associated.

[0081] Capture operational capabilities (OC): Operational capabilities are used to describe the capabilities provided by one or more operational entities and establish an interactive relationship with the operational entities. "Electromagnetic field calculation" is an operational capability that the software should have, which requires the joint action of the operational entity "user" and "simulation software", and the connection between them is established through interactive "operations".

[0082] Describe the activities corresponding to the operation capability and assign each operation entity: multiple activities are required to complete an operation capability. The "electromagnetic field calculation" operation capability consists of five interactive activities. "Input data and instructions" are assigned to the user, "display interface", "front-end and back-end interaction", "solution of electromagnetic field", and "import and export data" are assigned to the simulation software, and the operation architecture diagram is obtained, as shown in the figure. Figure 2 The boxes represent running activities, and the arrow lines represent the interactions between running activities.

[0083] Level 2: System Analysis and Modeling

[0084] The purpose of the system analysis level is to define the functions provided by the system. The system architecture design defines the system capabilities and tasks in turn, identifies and decomposes the system functions and their interactions, and finally allocates these functions to specific system elements to form a complete system architecture diagram to ensure the full realization of the system function requirements. The modeling process can be divided into three stages.

[0085] Define System Capability (SC) and System Mission (SM): System Capability refers to the capabilities that the system should provide, corresponding to the functional requirements of the software. System Mission represents the goal achieved by the combined efforts of system capabilities. System Actor (SA) is an external element that interacts with the system. Figure 3 It shows the system task "electromagnetic field calculation" that the software needs to complete, and this system task is realized by five system capabilities.

[0086] Identify system functions (SF) and their interactions: Mapping the operation activities to system functions not only retains the objects involved in the operation activities, but also inherits the various data flows involved in the interaction process. In order to reflect the functional requirements of the software in more detail, the system functions converted from the operation analysis layer are decomposed. Taking the user's "input data and instructions" as an example, it can be decomposed into five specific functions such as "login software" and "input geometric model information". The system functions and interactions can be described by the system function data flow diagram, such as Figure 4 shown.

[0087] Assigning system functions to system elements: After identifying all system functions, assign them to system elements to obtain a system architecture diagram that provides all the information at the system level, e.g. Figure 5 shown.

[0088] Level 3: Logical Architecture Modeling

[0089] The logical architecture level is the beginning of the modeling process from the problem domain to the solution. It aims to explain how the system achieves expectations through the association of internal logical components, without paying too much attention to the technical details of the implementation. The system model is transformed and inherited to the logical architecture layer, and the system executor is converted to the logical executor (Logical Actor, LA). The modeling process is: analyze logical functions, define logical components, and assign logical functions to logical components. First, define logical functions (LogicalFunction, LF) based on system functions, and further subdivide them to clarify the specific functions of internal components. For example, the "post-processing" logical function can be subdivided into three sub-functions: "electromagnetic quantity calculation", "data visualization", and "error analysis". Secondly, use logical components (LogicalComponent, L) to undertake logical functions. Convert the users and simulation software in the system architecture into logical components, and add logical components such as "interface layer", "control layer", "engine layer", and "core module layer" to this layer according to the specific logical functions decomposed. Finally, assign logical functions to logical components, and establish a complete logical architecture diagram through the interaction between logical components and logical functions, such as Figure 6 shown.

[0090] Level 4: Software Architecture Modeling

[0091] The goal of the software architecture level is similar to that of the logical architecture level, except that it defines the final architecture of the system. At this level, the software is decomposed to the smallest design granularity, and the abstract modeling elements in the logical architecture layer are converted into specific technologies. The corresponding software development is to convert the module design into specific class implementations and assign the modules to the software function layer. The detailed modeling process can be divided into three stages.

[0092] Define software functions: Define software functions based on the transformation and decomposition of logical functions at the logical architecture level.

[0093] Define software components: Components are divided into node components (software function modules) and behavior components (software function layers). Among them, the behavior component is responsible for completing specific functions, and the node component is responsible for scheduling related behavior components. Defining software components can build a specific solution to implement the logical architecture.

[0094] Allocate software functions to components: first assign the behavior components to the node components, and then assign the functions to the behavior components to form a software architecture diagram, which is not shown in the attached figure.

[0095] Finally, the complex interaction relationships between software components drawn using Visio software, such as Figure 7 As shown. It can show the relationship between components, but it is more difficult to draw, and it is difficult to change the relationship between modules or add new modules. In contrast, MBSE modeling tools provide the function of highlighting model elements and interaction paths, making it efficient and convenient to draw and view complex models. When changes occur, linkage modification is supported, that is, changes in the element at other locations at the same level are automatically modified. Using the MBSE method to describe software requirements, design, and implementation with models will help promote collaborative software development, inheritance, and expansion.

[0096] Step S103, establishing an electromagnetic field finite element simulation software prototype IFEM integrating artificial intelligence, and calculating and verifying the two-dimensional electrostatic field and electromagnetic optimization.

[0097] Guided by the construction method of electromagnetic field finite element simulation software with integrated AI, the software prototype IFEM was developed. After the user enters the data of the electromagnetic simulation task, the parameter viewing area of ​​the main window is automatically updated, which is convenient for the user to browse and check the correctness of the input at each step and after the completion of the parameter setting. "Start calculation" starts the backend program, solves the field, and displays the potential function distribution diagram in the result display area of ​​the main window. The calculation results are stored in the default result storage folder, and the bottom status bar outputs the mesh division status and prompt information.

[0098] In order to realize the integrated development of AI and numerical simulation, this embodiment adopts Python programming language and PyCharm integrated development environment to unify the development and debugging of finite element modules and AI modules, reducing compatibility issues between different development tools; uses scientific computing libraries such as SciPy and NumPy to provide efficient data structure and operation support for AI models, while ensuring accurate numerical simulation and ensuring the efficiency of large-scale data processing; through Python's Pandas library, data transmission is realized on a unified platform to ensure that finite element simulation data can be directly used for AI model training and prediction; the software adopts object-oriented programming methods and modular ideas, realizes layer and module connection through import mechanism, completes interface development and jump, front-end and back-end data interaction, front-end and back-end processing, node finite element discrete equation group matrix assembly, boundary condition processing and linear equation group solution, as well as physical information neural network (Physics-informed Neural Networks, PINN) and improved LinkNet deep learning model integration.

[0099] Next, we will use the calculation of the two-dimensional electric field distribution between electrodes and the 35th benchmark problem of TEAM Workshop to carry out case verification.

[0100] 3.1 Calculation of the electric field between electrodes

[0101] This embodiment uses two solvers, the finite element method and the PINN deep learning model, to calculate the two-dimensional electric field distribution between electrodes. Figure 8 The square (1m×1m) solution domain shown has thin plate conductors on the left and right boundaries, and the left end is given a potential of 0V, the right end is given a potential of 10V, and the two conductors are between a uniform linear dielectric with a relative dielectric constant of 5. It is assumed that there is no free charge in the region.

[0102] The domain shape of this example is simple, and a custom regularized meshing method is used. The number of meshes in the x and y directions is 20, with a total of 441 nodes and 800 units. When the finite element method is used for solution, the calculation results are as follows: Fig. 9 shown.

[0103] Change the solver to the deep learning model PINN (Physics-informed Neural Networks). The neural network contains 3 hidden layers, each with 150 neurons, and the activation function is Tanh. The corresponding training loss function curve is as follows: Fig.10 As shown in the figure, the node coordinates after the domain mesh is divided as the input of the PINN model, and the potential discrete value of the node can be obtained. The distribution diagram is shown in the figure. Fig.11 shown.

[0104] In order to verify the post-processing function of IFEM, the potential contours are visualized, the electric field strength is calculated, and its discrete value file and amplitude distribution diagram are obtained. In order to verify the correctness of the solver developed based on the finite element method, the overall error analysis of the node potential and electric field strength amplitude calculated by IFEM is carried out based on the COMSOL results, as shown in Table 1.

[0105] Table 1 COMSOL and IFEM errors for two-dimensional electrostatic field examples

[0106] name MAE MAPE(%) MSE Potential 1.132e-12 2.735e-11 1.763e-24 Electric field strength 4.185e-12 4.185e-11 2.730e-23

[0107] The availability of IFEM simulation functions such as pre-processing, solving, and post-processing, as well as the accuracy of two-dimensional electrostatic field calculations, are demonstrated through the software operation process, the error values ​​of IFEM calculation results and COMSOL, as well as the comparison of scalar potential and electric field intensity data.

[0108] 3.2 Optimization of solenoid interface magnetic field

[0109] The 35th benchmark problem of the TEAM Workshop proposed by the International Society for Computational Electromagnetism is a multi-objective, multi-variable optimization problem. The research object is an axisymmetric hollow solenoid, which consists of 20 turns of series coils symmetrically connected in an upper and lower direction. The width of each coil is w = 1 mm, the height is h = 1.5 mm, and the radius is Ri The variation range is 5-50mm and the input excitation current is 3A.

[0110] A 5×5 mm two-dimensional control area is selected inside the solenoid, and the design variable is the solenoid radius R. i The first optimization goal is to minimize the difference between the actual value of the magnetic flux density in the control area and the specified value of the magnetic flux density, that is, the magnetic field distribution is as uniform as possible; the second optimization goal is to minimize the power loss of the solenoid. The coil is set to be powered by a constant current. It can be deduced from formula (1) that the power loss is proportional to the coil radius. Therefore, the coil radius is used to reflect the power loss, which reduces the complexity of the objective function.

[0111] The two optimization objective function expressions are shown in equations (2) and (3).

[0112]

[0113] Where P is power loss; I is current value; ρ is resistivity; l is wire length; S is wire cross-sectional area; n t is the number of turns of the solenoid; f1 is the first objective function value; B0=2mT is the target magnetic flux density value; B j is the actual value of magnetic flux density in the control area, n p is the number of sampling points, which is taken as 66.

[0114]

[0115] Where f2 is the second objective function value.

[0116] Specify 10 radii of [5, 6, 7, 8, 9, 10, 11, 12, 13, 14] mm, calculate the magnetic field around the solenoid, and compare it with COMSOL to verify the correctness of the IFEM calculation. Due to the symmetrical distribution of the geometric model and material parameter boundaries, 1 / 4 of the cross section through the center is selected, and the solution domain is specified as a square with a length of 40 mm. The left, right, and upper boundaries are first-class boundary conditions, and the lower boundary is a natural boundary condition. In order to facilitate comparison and avoid errors caused by interpolation, the division results of the COMSOL physical field control grid with a finer division are directly imported, with 1168 grid nodes and 2224 grid units. The calculation model is as follows Fig.12 shown.

[0117] For this two-dimensional plane field (xy plane), the current density J is parallel to the vector magnetic potential A and is also parallel to the z-axis, i.e. A x =A y =0, J x =J y = 0. Take the z-direction component A of the vector magnetic potential z is a function of field variables, and the boundary value problem is described as:

[0118]

[0119] Γ1: A z =0

[0120]

[0121] In the formula, v is the magnetic resistivity.

[0122] The weighted residual method is used for discretization, and the finite element discretization equation is obtained:

[0123] KA=F (5)

[0124] In the formula, the coefficient matrix K = [K ij ], the right-hand end array F = [F i ], which is composed of the corresponding terms of each unit cell, among which, i and j represent the local numbers of all nodes in unit e.

[0125] According to the weighted residual method, the finite element discretization formula is:

[0126]

[0127] F i =∫ Ω N i J z dΩ (7)

[0128] Where N i and N j is the basis function, i,j=K,M,N, representing the numbers of the three nodes of the triangular element e.

[0129] Using triangular elements for meshing, the contribution of the elements to the coefficient matrix and the right-hand side term is:

[0130]

[0131]

[0132] After calculation, we get the vector magnetic potential component A z Draw the amplitude distribution diagram and contour lines of the discrete values ​​of Fig.13 shown.

[0133] After error analysis, it was found that the error value MAE between the vector magnetic potential calculation results of the self-compiled electromagnetic field finite element simulation software and COMSOL is 3.211e -9 , MAPE is 0.054%, MSE is 6.310 e-17 .

[0134] The vector magnetic potential node discrete value calculation unit and node magnetic flux density in each direction and the synthetic amplitude can be used. Its distribution is as follows: Fig.14 shown.

[0135] Comparison of the calculation error values ​​of magnetic flux density between IFEM and COMSOL is shown in Table 2.

[0136] Table 2. Magnetic flux density error between COMSOL and IFEM

[0137] name MAE MAPE MSE Bx 7.861e-06 2.034％ 9.711e-10 By 1.646e-05 3.215％ 4.288e-09 B amplitude 1.526e-05 2.889％ 3.615e-09

[0138] By comparing the error values ​​of IFEM calculation results with those of COMSOL, as well as the distribution diagrams of vector magnetic potential and magnetic flux density, it can be seen that IFEM can realize the numerical simulation function of two-dimensional constant magnetic field. Among them, the error of IFEM calculation of vector magnetic potential is small, and the error of magnetic flux density is enlarged compared with the vector magnetic potential. The reason is that the vector magnetic potential A obtained by the IFEM solver only has piecewise linear approximation accuracy, and its curl needs to be calculated to obtain the magnetic flux density. After taking the first-order derivative of A in the grid unit, the piecewise constant will be obtained, resulting in insufficient approximation accuracy for B. In order to improve the approximation accuracy of B, the corresponding code of the solver module can be changed, and A can be expanded using a high-order finite element basis function.

[0139] According to the above process, IFEM calculates the magnetic flux density values ​​under multiple radius combinations as the training data set of the improved LinkNet model. The guided optimization algorithm is applied to use the trained improved LinkNet model as the proxy model. The input of the model is the geometric structure diagram of the solenoid. Based on the particle swarm optimization algorithm, the magnetic field distribution of the solenoid is optimized. The implementation route is as follows Fig.15 shown.

[0140] In the process of IFEM development, the Arcadia modeling method, the open source modeling tool Capella, and the Arcadia / Capella modeling language were adopted, and the guided optimization module was integrated into the electromagnetic field finite element simulation software architecture under the guidance of the bidirectional coupling demonstration design method. MBSE supports multi-level modeling. After integrating the LinkNet module in the system architecture, the LinkNet module can be directly expanded in the overall architecture and detailed modeling can be performed, as shown in 16, which is more conducive to the development of complex software.

[0141] The method described in this embodiment introduces the MBSE modeling concept into the design of electromagnetic field finite element simulation software, and proposes a two-way coupling decision-making mechanism by building the relationship between requirements, functions and architecture. Under this mechanism, an example of the modeling method of electromagnetic field simulation software is carried out with the requirements of electromagnetic field finite element simulation as the guide, which effectively overcomes the shortcomings of the traditional document-based system engineering method, ensures the close integration of requirements and architecture, and improves the consistency of requirements and design.

[0142] It should be noted that the above describes some embodiments of the present application. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in an order different from that in the above embodiments and still achieve the desired results. In addition, the processes depicted in the accompanying drawings do not necessarily require the specific order or continuous order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0143] The embodiments of the present application are intended to cover all such substitutions, modifications and variations that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the embodiments of the present application should be included in the scope of protection of the present application.

Claims

1. A finite element simulation method for electromagnetic field of electrical equipment based on MBSE, characterized in that: include: Establish a bidirectional coupling relationship between numerical simulation and artificial intelligence; By selecting modeling methods, open source modeling tools and modeling languages, and building an electromagnetic field finite element simulation software architecture based on a bidirectional coupling relationship, a four-layer overall architecture of the interface layer, control layer, engine layer and core module layer is built using an MBSE-based method; A prototype of electromagnetic field finite element simulation software IFEM with integrated artificial intelligence was established, and two-dimensional electrostatic fields and electromagnetic optimization were calculated and verified.

2. The method according to claim 1, characterized in that The establishing of a numerical simulation-artificial intelligence bidirectional coupling relationship includes: Numerical solutions to electromagnetic problems are obtained by finite element method to generate training data; Training an artificial intelligence model based on the training data, comparing the results predicted by the artificial intelligence model with the numerical simulation results, analyzing the deviation between the two, and optimizing the artificial intelligence model using the deviation information feedback; A bidirectional coupling framework is integrated into the simulation software to establish a numerical simulation-artificial intelligence bidirectional coupling relationship.

3. The method according to claim 1, characterized in that: The Arcadia modeling method, the open source modeling tool Capella, and the implicitly defined modeling language Arcadia / Capella improved based on SysML and embedded in Capella were selected to complete the establishment of the electromagnetic field finite element simulation software architecture.

4. The method according to claim 1, characterized in that The method for calculating and verifying the two-dimensional electrostatic field comprises: The two solvers, finite element method and PINN deep learning model, are used to calculate the two-dimensional electric field distribution between electrodes; The PINN deep learning model includes three hidden layers, and defines the number of neurons in each layer. The activation function is Tanh, and the node coordinates after the domain grid is divided are used as the input of the PINN deep learning model, and the potential discrete value of the node is obtained as the output.

5. The method according to claim 1, characterized in that The calculation and verification of the solenoid interface magnetic field optimization process includes: A two-dimensional control area is selected inside the solenoid, and the design variable is the solenoid radius. The first optimization goal is to minimize the difference between the actual value of the magnetic flux density in the control area and the specified value of the magnetic flux density; the second optimization goal is to minimize the power loss of the solenoid. The coil is set to be powered by a constant current, and the coil radius reflects the power loss. The expressions of the two optimization objective functions are as follows: Where P is power loss, I is current value, ρ is resistivity, l is wire length, S is wire cross-sectional area, n is t is the number of turns of the solenoid, f1 is the first objective function value, B0=2mT is the target magnetic flux density value, B j is the actual value of magnetic flux density in the control area, n p is the number of sampling points; Where f2 is the second objective function value; Specify multiple radii and calculate the magnetic field around the solenoid. Then compare it with COMSOL to verify the correctness of the IFEM calculation.

6. The method according to claim 5, characterized in that: Select 1 / 4 of the cross-section through the center, and specify the solution domain as a square of fixed length. The left, right, and upper boundaries are first-class boundary conditions, and the lower boundary is a natural boundary condition. In a two-dimensional plane field, the current density J is parallel to the vector magnetic potential A and parallel to the z-axis, that is, Ax = Ay = 0, Jx = Jy = 0, and the z-direction component A of the vector magnetic potential is taken as z is a field variable function, and the boundary value problem is expressed as: Where v is the magnetic reluctance; The weighted residual method is used for discretization, and the finite element discretization equation is obtained: KA = F; In the formula, the coefficient matrix K = [K ij ], the right-hand end array F = [F i ], which is composed of the corresponding terms of each unit cell, among which, i and j represent the local numbers of all nodes in unit e; According to the weighted residual method, the finite element discretization formula is: F i =∫ Ω N i J z dΩ; Where N i and N j is the basis function, i,j = K, M, N, representing the numbers of the three nodes of the triangular element e; Using triangular elements for meshing, the contribution of the elements to the coefficient matrix and the right-hand side terms is: Calculate the vector magnetic potential component A z Draw the amplitude distribution diagram and contour lines of discrete values ​​of The error analysis was carried out between the calculation results of the finite element simulation software prototype IFEM and the COMSOL results.

7. The method according to claim 6, characterized in that: The error values ​​of the magnetic flux density values ​​of the finite element simulation software prototype IFEM and COMSOL are calculated by the mean absolute error, mean absolute percentage error and mean square error respectively.

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