Magnetic gear magnetic field simulation method based on physical information neural network and sub-domain method

Abstract

The application provides a magnetic gear magnetic field simulation method based on a physical information neural network and a subdomain method, and the purpose of the application is to divide the magnetic gear into eight subdomains based on the subdomain division idea in the subdomain method, in combination with the structural characteristics and material properties of the magnetic gear. Control equations, boundary conditions and initial values met by each subdomain are taken as neural network loss items, a neural network model based on physical information is established, a problem of directly solving the control equations is converted into an optimization problem of a loss function to find a solution of the Maxwell equation set, and the magnetic field simulation of each subdomain of the magnetic gear is realized. The application can reduce the error caused by model simplification in the current analytical method, and avoid the problems of high calculation cost and long time under the extremely fine grid of the finite element simulation.

Description

Technical Field

[0001] This invention relates to the field of magnetic field simulation, and more particularly to a method for simulating the magnetic field of a magnetic gear based on a physical information neural network and a subdomain method. Background Technology

[0002] With the widespread application of high-performance rare-earth permanent magnet materials and the emergence of novel magnetic gear topologies, magnetic field-modulated magnetic gears are increasingly being used in aerospace, military, medical devices, food processing, chemical equipment, and clean energy development due to their advantages such as high utilization rate of permanent magnets, high torque density, low vibration and noise, contactless transmission, and no need for lubrication. Accurate solution of the magnetic field of magnetic gears is crucial. Currently, finite element simulation and analytical methods are commonly used to solve the magnetic field of magnetic gears, and both methods achieve high accuracy. However, problems remain, including high computational cost and time for simulations with extremely fine meshes, and errors caused by model simplification in analytical methods. With the rapid development of artificial intelligence, neural networks, with their powerful learning capabilities, are being applied in various fields. By embedding the latent physical information in partial differential equations into neural networks, the partial differential equations can be solved, thereby enabling the solution of the physical field. Using a neural network based on physical information to solve the magnetic field can reduce errors caused by model simplification and avoid the high computational cost associated with extremely fine meshes. Summary of the Invention

[0003] To address the issues of high computational cost, long processing time, and errors caused by model simplification in analytical methods under extremely fine mesh conditions, this invention proposes a magnetic field simulation method for magnetic gears based on a physical information neural network and the subdomain method. This invention primarily utilizes the subdomain partitioning concept, introducing a deep neural network. The governing equations, boundary conditions, and initial values ​​satisfied by each subdomain are used as loss terms. The underlying physical knowledge from Maxwell's equations is embedded into the deep neural network to solve the equations, thus achieving the magnetic field simulation of the magnetic gears. The proposed method is meshless and requires no model simplification, reducing errors caused by model simplification and avoiding the high computational cost associated with extremely fine meshes.

[0004] The technical means employed in this invention are as follows:

[0005] A magnetic field simulation method for magnetic gears based on physical information neural networks and subdomain methods is characterized by the following steps:

[0006] Step 1: Based on the structural characteristics and material parameters of the magnetic gear, the magnetic gear is divided into subdomains;

[0007] Step 2: Establish the governing equations and boundary conditions satisfied by each subdomain of the magnetic gear;

[0008] Step 3: Establish training and test datasets for each subdomain based on the magnetic gear; the training and test datasets include: sampling point data of the solution domain in each subdomain, boundary data of the solution domain, and initial data of the simulation domain;

[0009] Step 4: Build deep neural network models for each subdomain of the magnetic gear;

[0010] Step 5: Based on the control equations and boundary conditions of each subdomain of the magnetic gear, a loss function is generated, and a neural network model embedding physical information is built.

[0011] Step Six: Normalize the training dataset and the test dataset;

[0012] Step 7: Train a neural network embedding physical information based on a normalized training dataset, and optimize the parameters of the neural network embedding physical information;

[0013] Step 8: Test the training effect of the neural network embedding physical information based on the normalized test dataset to obtain the magnetic vectors of each subdomain of the magnetic gear;

[0014] Step 9: Simulate the magnetic field of the magnetic gear based on the magnetic vectors of each subdomain.

[0015] Preferably, the magnetic gear includes: an inner back iron subdomain, an inner permanent magnet subdomain, an inner air gap subdomain, a magnetically conductive subdomain, a non-magnetically conductive subdomain, an outer air gap subdomain, an outer permanent magnet subdomain, and an outer back iron subdomain.

[0016] Preferably, the sampling method for each subdomain coordinate point is: random sampling, uniform sampling of an arithmetic sequence, or importance-adaptive sampling.

[0017] Preferably, the number of regions divided by the magnetic gear is equal to the number of deep neural networks.

[0018] Preferably, the governing equations for the inner back iron subdomain, the inner air gap subdomain, the magnetic conductor subdomain, the non-magnetic conductor subdomain, the outer air gap subdomain, and the outer back iron subdomain should satisfy the following relationship:

[0019]

[0020] Where (r, α) represents the coordinates of any point within the subdomain, A i This represents a magnetic vector.

[0021] Preferably, the governing equations of the inner permanent magnet subdomain and the outer permanent magnet subdomain should satisfy the following relationship:

[0022]

[0023] Where M represents magnetization, A iLet r represent the magnetic vector, and α represent the coordinates of any point within the subdomain.

[0024] Preferably, the magnetization method of the magnetic gear can be: radial magnetization, parallel magnetization, and Halbach array magnetization.

[0025] Preferably, the boundary conditions satisfy the continuity of the magnetic medium surface, i.e., the following relationship:

[0026] B in (r,α)=B jn (r,α);

[0027] H it (r,α)=H jt (r,α);

[0028] Among them, B n H represents the normal component of magnetic flux density. t Let (r, α) represent the tangential component of the magnetic field strength, (r, α) represent the coordinates of any point within the subdomain, and i and j represent the subdomain numbers.

[0029] Preferably, the boundary conditions at the inner diameter of the inner back iron subdomain and the outer diameter of the outer back iron subdomain satisfy the following relationship:

[0030] A i =0;

[0031] Among them, A i This represents a magnetic vector.

[0032] Preferably, the deep neural network includes: an input layer, a hidden layer, an output layer, and a non-linear activation function.

[0033] Preferably, the neural network embedding physical information includes: the deep neural network of each subdomain of the magnetic gear, the loss function embedding physical information, and the training dataset.

[0034] Preferably, the loss function for embedding physical information can be selected as: mean squared error (MSE) loss, mean absolute error (MAE) loss, or Smooth L1 loss.

[0035] Preferably, the loss term embedding physical information includes: governing equation loss (MSE). P Boundary condition loss MSE B and initial value loss MSE IS The loss term embedding physical information should satisfy the following relationship:

[0036] MSE=ω1MSE B +ω2MSE P +ω3MSE IS ;

[0037] Where, ω i This represents the adaptive weights of each loss term. Compared with existing technologies, this invention has the following advantages:

[0038] The magnetic field simulation method for magnetic gears provided by this invention, based on physical information neural networks and the subdomain method, leverages the subdomain partitioning concept in the subdomain method and the powerful learning ability of neural networks. Compared with traditional analytical methods, it eliminates the need for model simplification, effectively reducing errors caused by model simplification in current analytical methods. Furthermore, as a novel meshless magnetic field simulation method, it avoids the problems of high computational cost and long solution time in current finite element electromagnetic simulations with extremely fine meshes.

[0039] Based on the above reasons, this invention can be widely applied in fields such as magnetic field simulation. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 This is a flowchart of the magnetic field simulation method for magnetic gears based on physical information neural networks and subdomain methods according to the present invention.

[0042] Figure 2 This is a schematic diagram of the neural network model based on physical information of the present invention.

[0043] Figure 3 This is a schematic diagram of the magnetic gear structure described in this invention.

[0044] Figure 4 This is a schematic diagram of the magnetic gear subdomain model of the present invention.

[0045] Figure 5 These are comparative diagrams of radial magnetic flux density in the inner and outer air gaps according to an embodiment of the present invention. (a) is a comparative diagram of radial magnetic flux density in the inner air gap; (b) is a comparative diagram of radial magnetic flux density in the outer air gap.

[0046] Figure 6 This is a comparison diagram of the tangential magnetic flux density of the inner and outer air gaps in an embodiment of the present invention. (a) is a comparison diagram of the tangential magnetic flux density of the inner air gap; (b) is a comparison diagram of the tangential magnetic flux density of the outer air gap. In the diagrams: 1, back iron; 2, permanent magnet; 3, magnetic conductor; 4, non-magnetic conductor; 5, air gap; 6, inner back iron sub-domain 1; 7, inner magnet sub-domain 2; 8, inner air gap sub-domain 3; 9, magnetic conductor sub-domain 4; 10, non-magnetic conductor sub-domain 5; 11, outer air gap sub-domain 6; 12, outer permanent magnet sub-domain 7; 13, outer back iron sub-domain 8. Detailed Implementation

[0047] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. 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 should fall within the scope of protection of the present invention.

[0048] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0049] like Figure 1-5 As shown, this invention provides a method for dividing subdomains based on the structural characteristics and material properties of magnetic gears, and establishing a magnetic gear subdomain model: the magnetic field modulation type magnetic gear is a coaxial structure and can be modeled in a polar coordinate system. The inner and outer back irons and magnetic conductors of the magnetic gear are mostly made of silicon steel, while the inner and outer permanent magnets are mostly high-performance neodymium iron boron permanent magnets. The air gap can be considered as air, and the non-magnetic materials are made of epoxy resin. The magnetic field modulation type magnetic gear adopts a coaxial distribution, including: an inner magnetic ring, an outer magnetic ring, and a tuning ring. The three rings are separated by two extremely narrow air gaps. The tuning ring uses alternating arrangements of magnetic and non-magnetic materials to modulate the magnetic field at the inner and outer air gaps, realizing the movement and power transmission of the three rings. The materials used in the magnetic gear include: permanent magnets, magnetic silicon steel sheets, non-magnetic epoxy resin, and air, each with different magnetic permeabilities.

[0050] Based on the different magnetic permeability of the four materials and the characteristics of the coaxial structure, the magnetic gear is divided into the inner back iron subdomain 1, the inner magnet subdomain 2, the inner air gap subdomain 3, the magnetic permeable body subdomain 4, the non-magnetic permeable body subdomain 5, the outer air gap subdomain 6, the outer permanent magnet subdomain 7, and the outer back iron subdomain 8.

[0051] Based on the magnetic gear subdomain model, the governing equations, boundary conditions, and initial values ​​that each subdomain should satisfy are constructed: The magnetic vector potentials of the inner magnet subdomain 2 and the outer permanent magnet subdomain 7 satisfy the following Poisson equation: The inner magnet subdomain 2 and the outer permanent magnet subdomain 7 satisfy the magnetic medium continuity condition at their boundaries with other subdomains: B in (r,α)=B jn (r,α), H it (r,α)=H jt (r, α). The inner back iron subdomain 1, inner air gap subdomain 3, magnetic conductor subdomain 4, non-magnetic conductor subdomain 5, outer air gap subdomain 6, and outer back iron subdomain 8 satisfy the following Laplace equation: The inner back iron subdomain 1, inner air gap subdomain 3, magnetic conductor subdomain 4, non-magnetic conductor subdomain 5, outer air gap subdomain 6, and outer back iron subdomain 8 satisfy the magnetic medium continuity condition at their boundaries with other subdomains: B in (r,α)=B jn (r,α), H it (r,α)=H jt (r,α).

[0052] Based on the control equations, boundary conditions, and initial values ​​of each subdomain of the magnetic gear, arbitrary coordinate points within each subdomain are sampled: According to the control equations, boundary conditions, and initial values ​​of each subdomain, the coordinates of any point within each subdomain are randomly sampled to form a training dataset and a test dataset. The ratio of the training set to the test set in the dataset is 8:2, and Min-Max normalization is performed.

[0053] Building a deep neural network model: A separate deep neural network model is built for each subdomain of the magnetic gear. The neural network type is a fully connected neural network, with one input layer, four hidden layers, and one output layer. The activation function is a non-linear function such as the tanh function. The neural networks of each subdomain are connected through boundary conditions between subdomains, enabling simultaneous training of multiple neural networks.

[0054] By embedding the governing equations, boundary conditions, and initial values ​​of each subdomain into the loss term of a deep neural network for that subdomain, implicit physical information is introduced into the equations, thus constructing a physical information-embedded neural network model (PINN). PINN is trained using a training dataset, and its hyperparameters are optimized. For a physical information-based neural network model, see [link to documentation]. Figure 2 The loss term for the physics-based neural network model includes: governing equation loss, boundary condition loss, and initial value loss. The mean squared error (MSE) function is chosen as the loss function, and the loss term in the example must satisfy the following relationship: MSE = ω1MSE B +ω2MSE P +ω3MSE IS , where ω iAdaptive weights are assigned to each loss term, which are dynamically adjusted as the loss value changes during training. The optimizer is set to the Adaptive Moment Estimation (Adam) algorithm, with 2000 training data points fed in each time, and a total of 50,000 forward and backpropagation iterations are performed. The initial learning rate is set to 0.003, and it is dynamically adjusted using cosine annealing, with the period of the cosine function being twice the training cycle. Within a complete training cycle, the learning rate decays with the cosine function until it reaches 0 after 50,000 iterations. After 50,000 iterations, the model parameter file with the lowest loss value on the training set is selected and saved, thus obtaining the optimal model parameter file.

[0055] The training effect of PINN was tested using a test training set to obtain the magnetic vectors of each subdomain. The accuracy of the PINN simulation results was compared to achieve the goal of simulating the magnetic field of this gear. Based on the above optimal model parameter file, the test dataset was fed into the optimal model to obtain the optimal result of the neural network, thus verifying the accuracy of the PINN simulation results. The accuracy calculation method is as follows: Where A net For the PINN magnetic vector simulation results, A fea The results are from the finite element simulation. Based on the magnetic vector results of each subdomain simulated by PINN, the magnetic flux density, magnetic field line distribution, and torque at various positions of the magnetic gear can be further obtained. This embodiment takes the radial and tangential magnetic flux density at the inner and outer air gaps as examples, see... Figure 5 , 6 It can be seen that the method described in this invention is comparable to the finite element simulation results under extremely fine mesh in terms of accuracy, and it is meshless.

[0056] In summary, this invention can simulate the magnetic field of a magnetic gear with high accuracy.

[0057] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments. In the above embodiments of the present invention, the descriptions of each embodiment have their own emphasis; parts not described in detail in a certain embodiment can be referred to in the relevant descriptions of other embodiments. It should be understood that the disclosed technical content in the several embodiments provided in this application can be implemented in other ways.

[0058] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A magnetic field simulation method for magnetic gears based on physical information neural networks and subdomain methods, characterized in that, Includes the following steps: Step 1: Divide the magnetic gear into subdomains based on its structural characteristics and material parameters; Step 2: Establish the governing equations and boundary conditions satisfied by each subdomain of the magnetic gear; Step 3: Establish training and testing datasets for each subdomain based on the magnetic gear; The training and test datasets include: sampling point data of the solution domain in each subdomain, boundary data of the solution domain, and initial data of the simulation domain; Step 4: Build deep neural network models for each subdomain of the magnetic gear; Step 5: Based on the control equations and boundary conditions of each subdomain of the magnetic gear, a loss function is generated, and a neural network model embedding physical information is built. Step Six: Normalize the training dataset and the test dataset; Step 7: Train a neural network embedding physical information based on a normalized training dataset, and optimize the parameters of the neural network embedding physical information; Step 8: Test the training effect of the neural network embedding physical information based on the normalized test dataset to obtain the magnetic vectors of each subdomain of the magnetic gear; Step 9: Simulate the magnetic field of the magnetic gear based on the magnetic vectors of each subdomain; The magnetic gear includes: an inner back iron sub-domain (1), an inner permanent magnet sub-domain (2), an inner air gap sub-domain (3), a magnetic conductor sub-domain (4), a non-magnetic conductor sub-domain (5), an outer air gap sub-domain (6), an outer permanent magnet sub-domain (7), and an outer back iron sub-domain (8). The governing equations for the inner back iron subdomain (1), the inner air gap subdomain (2), the magnetic conductor subdomain (4), the non-magnetic conductor subdomain (5), the outer air gap subdomain (6), and the outer back iron subdomain (8) should satisfy the following relationship: in,( r , α () represents the coordinates of any point within the subdomain. A i Represents a magnetic vector; The governing equations for the inner permanent magnet subdomain (2) and the outer permanent magnet subdomain (7) should satisfy the following relationship: in, M Indicates magnetization intensity. A i Represents the magnetic vector, ( r , α () represents the coordinates of any point within the subdomain; The boundary conditions satisfy the continuity of the magnetic medium surface, i.e., the following relationship: ； ； in, Represents the normal component of magnetic flux density. Represents the tangential component of the magnetic field strength, ( r , α () represents the coordinates of any point within the subdomain. i and j Indicates the subdomain number to which it belongs; The boundary conditions at the inner diameter of the inner back iron subdomain (1) and the outer diameter of the outer back iron subdomain (8) satisfy the following relationship: ； in, A i This represents a magnetic vector.

2. The magnetic field simulation method for magnetic gears based on physical information neural networks and subdomain method according to claim 1, characterized in that, The sampling methods for the coordinate points of each subdomain are: random sampling, uniform sampling of an arithmetic sequence, or importance-adaptive sampling.

3. The magnetic field simulation method for magnetic gears based on physical information neural networks and subdomain method according to claim 1, characterized in that, The number of subdomains of the magnetic gear is equal to the number of deep neural networks.

4. The magnetic field simulation method for magnetic gears based on physical information neural networks and subdomain method according to claim 1, characterized in that, The loss term embedded with physical information includes: the governing equation loss MSE. P Boundary condition loss MSE B and initial value loss MSE IS The loss term embedding physical information should satisfy the following relationship: ； in, ω i This represents the adaptive weights of each loss term.

Images