Permanent magnet coupling design optimization method and system based on physical information neural network

Abstract

The application discloses a permanent magnet coupler design optimization method and system based on a physical information neural network, relates to the technical field of permanent magnet coupler optimization, and comprises the following steps: according to the value range of each to-be-optimized parameter of a permanent magnet coupler, the parameters are divided into multiple data combinations; each data combination is input into a trained model to predict the magnetic potential of each region of the permanent magnet coupler under each data combination; the magnetic potential of the label of the trained model is calculated according to corresponding training data combinations, a magnetic potential partial differential equation and a magnetic potential boundary condition; according to the magnetic potential of each region of the permanent magnet coupler under each data combination, corresponding output torque and torque density are solved, and the optimal value of each to-be-optimized parameter is determined according to the data combination corresponding to the maximum output torque and torque density. The application integrates the physical information satisfied by the permanent magnet coupler into the neural network, calculates the torque according to the output solution, reduces the solution time of the to-be-optimized parameters, and improves the optimization efficiency.

Description

Technical Field

[0001] This invention relates to the field of permanent magnet coupler optimization technology, and in particular to a method and system for permanent magnet coupler design optimization based on Physics-informed Neural Networks (PINN). Background Technology

[0002] In recent years, with continuous breakthroughs in science and technology, permanent magnet technology has become a popular technology. A permanent magnet coupler is a product that uses permanent magnet technology and is a mechanical device used to transmit power. To conduct performance research and design optimization of permanent magnet couplers, it is necessary to establish accurate and reliable analytical models.

[0003] However, the design and optimization process of permanent magnet couplers faces the following problems: establishing an analytical model requires profound mathematical and physical knowledge, involving multiple integrations and derivations of numerous tedious and complex calculus formulas or partial differential equations before a final analytical result can be obtained. Therefore, when using existing finite element software to simulate permanent magnet couplers, the calculation time often takes several days or even a week, making the design and optimization process of permanent magnet couplers extremely slow. Summary of the Invention

[0004] The purpose of this invention is to provide a highly efficient design optimization method and system for permanent magnet couplers based on physical information neural networks.

[0005] This invention provides a design optimization method for permanent magnet couplers based on physical information neural networks, comprising the following steps:

[0006] Step 1: Obtain the value range of each parameter to be optimized for the permanent magnet coupler; the parameters to be optimized include the number of pole pairs, pole arc coefficient, thickness of permanent magnet yoke, thickness of permanent magnet, thickness of copper layer, thickness of copper layer yoke, and air gap thickness;

[0007] Step 2: Based on the value range of each parameter to be optimized, divide the parameter to be optimized into multiple data combinations; each data combination is composed of a number of magnetic pole pairs, pole arc coefficient, permanent magnet yoke thickness, permanent magnet thickness, copper layer thickness, copper layer yoke thickness and air gap thickness, and at least one parameter to be optimized has a different value between any two data combinations;

[0008] Step 3: Input each of the data combinations into the trained PINN model to predict the magnetic potential of each region of the permanent magnet coupler under each data combination; the trained PINN model is a model trained with the training data combination as input and the magnetic potential of each region of the permanent magnet coupler established based on the training data combination as a label; the training data combination is composed of a number of magnetic pole pairs, pole arc coefficient, permanent magnet yoke thickness, permanent magnet thickness, copper layer thickness, copper layer yoke thickness, and air gap thickness, and the magnetic potential as a label is calculated from the corresponding training data combination, the magnetic potential partial differential equation of the permanent magnet coupler, and the magnetic potential boundary conditions;

[0009] Step 4: Based on the predicted magnetic potential of each region of the permanent magnet coupler under each of the data combinations, solve for the output torque and torque density corresponding to each of the data combinations;

[0010] Step 5: Compare the output torque and torque density corresponding to each data combination, and determine the optimal value of each parameter to be optimized based on the data combination corresponding to the maximum output torque and torque density.

[0011] Optionally, the loss function during training of the trained PINN model includes magnetic potential loss and magnetic potential boundary loss, wherein the magnetic potential boundary loss is determined according to the magnetic potential boundary conditions.

[0012] Optionally, the permanent magnet coupler includes a permanent magnet yoke region, a permanent magnet region, an air gap region, a copper layer region, and a copper layer yoke region.

[0013] Optionally, the magnetic potential partial differential equation is as follows:

[0014]

[0015] Where A1-A5 are the dependent variables, A1 is the magnetic potential of the permanent magnet yoke region, A2 is the magnetic potential of the permanent magnet region, A3 is the magnetic potential of the air gap region, A4 is the magnetic potential of the copper layer region, and A5 is the magnetic potential of the copper layer yoke region. x∈[-0.072, 0.072], y is the sum of the thicknesses of the permanent magnet yoke, permanent magnet, copper layer, copper layer yoke, and air gap, and α=nπ / τ p ω1=2πn1p / 60, μ0 is the free permeability, μ eq Where is the equivalent permeability of the copper-layered yoke, s is the slip, n is the harmonic order, n1 is the input rotational speed, p is the number of pole pairs, and B is the number of pole pairs. r τ is the remanent magnetic field strength. p τ is the average pole spacing. m σ is the average polar arc length. b The conductivity of the copper layer yoke iron is σ. cI represents the conductivity of the copper layer, II represents the permanent magnet yoke region, III represents the air gap region, IV represents the copper layer region, and V represents the copper layer yoke region.

[0016] Optionally, the magnetic potential boundary conditions are as follows:

[0017]

[0018] Where, μ av μ is the equivalent permeability of the permanent magnet yoke iron. x μ is the equivalent permeability of the permanent magnet, μ0 is the permeability of free space, and μ eq Let be the equivalent magnetic permeability of the copper-layer yoke, x and y be the independent variables, and A1-A5 be the dependent variables. A1 is the magnetic potential of the permanent magnet yoke region, A2 is the magnetic potential of the permanent magnet region, A3 is the magnetic potential of the air gap region, A4 is the magnetic potential of the copper layer region, A5 is the magnetic potential of the copper-layer yoke region, y is the sum of the thicknesses of the permanent magnet yoke, permanent magnet, copper layer, copper-layer yoke and air gap, y1 is the outer boundary of the permanent magnet yoke region, y2 is the overlapping boundary of the permanent magnet yoke region and the permanent magnet region, y3 is the overlapping boundary of the permanent magnet region and the air gap region, y4 is the overlapping boundary of the air gap region and the copper layer region, y5 is the overlapping boundary of the copper layer region and the copper-layer yoke region, and y6 is the outer boundary of the copper-layer yoke region.

[0019] Optionally, the output torque is calculated according to the following formula:

[0020]

[0021] Where T is the output torque, r mean k is the average radius. s w is the correction factor. m denoted as ω1 = 2πn1p / 60, where n1 is the input rotational speed, σ is the activation function, y is the sum of the thicknesses of the permanent magnet yoke, permanent magnet, copper layer, copper layer yoke, and air gap, y4 is the overlapping boundary between the air gap region and the copper layer region, y5 is the overlapping boundary between the copper layer region and the copper layer yoke region, y6 is the outer boundary of the copper layer yoke region, A4 is the magnetic potential of the copper layer region, and A5 is the magnetic potential of the copper layer yoke region.

[0022] Optionally, the torque density is calculated according to the following formula:

[0023] T V =T / V;

[0024] Among them, T V Where is the torque density, T is the output torque of the permanent magnet coupler, and V is the volume of the permanent magnet coupler.

[0025] This invention also provides a permanent magnet coupler design optimization system based on a physical information neural network, comprising:

[0026] The parameter acquisition module is used to acquire the value range of each parameter to be optimized in the permanent magnet coupler; the parameters to be optimized include the number of pole pairs, pole arc coefficient, permanent magnet yoke thickness, permanent magnet thickness, copper layer thickness, copper layer yoke thickness, and air gap thickness.

[0027] The parameter division module is used to divide the parameters to be optimized into multiple data combinations according to the value range of each parameter to be optimized; each data combination is composed of a number of magnetic pole pairs, pole arc coefficient, permanent magnet yoke thickness, permanent magnet thickness, copper layer thickness, copper layer yoke thickness and air gap thickness, and at least one parameter to be optimized has a different value between any two data combinations.

[0028] The parameter calculation module is used to input each of the data combinations into the trained PINN model to predict the magnetic potential of each region of the permanent magnet coupler under each data combination. The trained PINN model is a model trained with the training data combination as input and the magnetic potential of each region of the permanent magnet coupler established based on the training data combination as a label. The training data combination is composed of a number of magnetic pole pairs, pole arc coefficient, permanent magnet yoke thickness, permanent magnet thickness, copper layer thickness, copper layer yoke thickness, and air gap thickness. The magnetic potential as a label is calculated from the corresponding training data combination, the magnetic potential partial differential equation of the permanent magnet coupler, and the magnetic potential boundary conditions.

[0029] The torque calculation module is used to calculate the output torque and torque density corresponding to each data combination based on the magnetic potential of each region of the permanent magnet coupler under each predicted data combination.

[0030] The parameter output module is used to compare the output torque and torque density corresponding to each data combination, and determine the optimal value of each parameter to be optimized based on the data combination corresponding to the maximum output torque and torque density.

[0031] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0032] This invention provides a design optimization method for permanent magnet couplers based on a physical information neural network. The method includes: first, obtaining the value range of each parameter to be optimized in the permanent magnet coupler; the parameters to be optimized include the number of pole pairs, pole arc coefficient, permanent magnet yoke thickness, permanent magnet thickness, copper layer thickness, copper layer yoke thickness, and air gap thickness; then, according to the value range of each parameter to be optimized, dividing the parameters to be optimized into multiple data combinations; each data combination is composed of a combination of the number of pole pairs, pole arc coefficient, permanent magnet yoke thickness, permanent magnet thickness, copper layer thickness, copper layer yoke thickness, and air gap thickness, and at least one parameter to be optimized differs between any two data combinations; finally, inputting each data combination into a trained PINN model to predict the magnetic properties of each region of the permanent magnet coupler under each data combination. The trained PINN model is a model trained using training data combinations as input and the magnetic potential of each region of the permanent magnet coupler established based on the training data combinations as labels. The training data combinations consist of a combination of the number of pole pairs, pole arc coefficient, permanent magnet yoke thickness, permanent magnet thickness, copper layer thickness, copper layer yoke thickness, and air gap thickness. The magnetic potentials used as labels are calculated from the corresponding training data combinations, the partial differential equation of magnetic potential of the permanent magnet coupler, and the magnetic potential boundary conditions. Then, based on the predicted magnetic potentials of each region of the permanent magnet coupler under each data combination, the output torque and torque density corresponding to each data combination are solved. Finally, the output torque and torque density corresponding to each data combination are compared, and the optimal values ​​of each parameter to be optimized are determined based on the data combination corresponding to the maximum output torque and torque density.

[0033] This invention divides the parameters to be optimized into multiple data combinations based on the value range of each parameter in the permanent magnet coupler. Each data combination is input into a trained PINN model, and the magnetic potential of each region of the permanent magnet coupler under each data combination is quickly solved. Due to the rapid solution of the magnetic potential, the solution speed of the output torque and torque density is also accelerated. The solution time of the optimal value of each parameter in the parameters to be optimized is shortened due to the accelerated solution speed of the output torque and torque density. Therefore, this invention accelerates the solution speed of the parameters to be optimized and improves the optimization efficiency of the permanent magnet coupler by optimizing the design of the permanent magnet coupler through the neural network method. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] Figure 1 A flowchart of a permanent magnet coupler design optimization method based on a physical information neural network provided in an embodiment of the present invention;

[0036] Figure 2 This is a structural diagram of a disc-type permanent magnet coupler provided in an embodiment of the present invention;

[0037] Figure 3 This is a schematic diagram of a two-dimensional model of a permanent magnet coupler provided in an embodiment of the present invention;

[0038] Figure 4 A schematic diagram of the parameters to be optimized for a permanent magnet coupler provided in an embodiment of the present invention;

[0039] Figure 5 This is a network structure diagram of the PINN model provided in an embodiment of the present invention;

[0040] Figure 6 A comparison diagram of the analytical solution and the PINN predicted solution of the permanent magnet coupler provided in this embodiment of the invention; wherein, Figure 6 (a) is the analytical solution. Figure 6 (b) is the predicted solution of the PINN model;

[0041] Figure 7 The PINN loss function result diagram provided in this embodiment of the invention. Detailed Implementation

[0042] 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.

[0043] The purpose of this invention is to provide a highly efficient design optimization method and system for permanent magnet couplers based on physical information neural networks.

[0044] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0045] This invention provides a design optimization method for permanent magnet couplers based on physical information neural networks, comprising the following steps:

[0046] Step 1: Obtain the value range of each parameter to be optimized for the permanent magnet coupler; the parameters to be optimized include the number of pole pairs, pole arc coefficient, permanent magnet yoke thickness, permanent magnet thickness, copper layer thickness, copper layer yoke thickness, and air gap thickness.

[0047] Step 2: Based on the value range of each parameter to be optimized, divide the parameter to be optimized into multiple data combinations; each data combination is composed of a number of magnetic pole pairs, pole arc coefficient, permanent magnet yoke thickness, permanent magnet thickness, copper layer thickness, copper layer yoke thickness and air gap thickness, and at least one parameter to be optimized has a different value between any two data combinations.

[0048] Step 3: Input each of the data combinations into the trained PINN model to predict the magnetic potential of each region of the permanent magnet coupler under each data combination; the trained PINN model is a model trained with the training data combination as input and the magnetic potential of each region of the permanent magnet coupler established based on the training data combination as a label; the training data combination is composed of a number of magnetic pole pairs, pole arc coefficient, permanent magnet yoke thickness, permanent magnet thickness, copper layer thickness, copper layer yoke thickness and air gap thickness, and the magnetic potential as a label is calculated by the corresponding training data combination, the magnetic potential partial differential equation of the permanent magnet coupler and the magnetic potential boundary conditions.

[0049] Step 4: Based on the predicted magnetic potential of each region of the permanent magnet coupler under each of the data combinations, solve for the output torque and torque density corresponding to each of the data combinations.

[0050] Step 5: Compare the output torque and torque density corresponding to each data combination, and determine the optimal value of each parameter to be optimized based on the data combination corresponding to the maximum output torque and torque density.

[0051] Before obtaining the value range of each parameter to be optimized in the permanent magnet coupler, a system is first established as follows: Figure 2 The permanent magnet coupler structure model is shown.

[0052] Specifically, a permanent magnet coupler structural model is established using a disc-type model. The permanent magnet coupler mainly consists of five parts: a permanent magnet yoke, permanent magnets, an air gap, a copper layer, and a copper-layer yoke. The conductor rotor consists of a copper-layer yoke and a copper layer. The permanent magnet rotor consists of a permanent magnet yoke and permanent magnets. The conductor rotor and the permanent magnet rotor are separated by an air gap. The permanent magnets are surface-mounted, attached to the outer surface of the permanent magnet yoke. Adjacent permanent magnets are arranged with alternating N and S poles.

[0053] To simplify the computational complexity, for example... Figure 2 The three-dimensional permanent magnet coupler model shown is reduced in dimension by flattening it into a two-dimensional model from the central axis, resulting in the model shown below. Figure 3The simplified two-dimensional model of the permanent magnet coupler in Cartesian coordinates is shown below. The model consists of five regions and six boundaries. The five regions are: Permanent Magnet Yoke Region I, Permanent Magnet Region II, Air Gap Region III, Copper Layer Region IV, and Copper Layer Yoke Region V. The six boundaries are: outer boundary y1 of the Permanent Magnet Yoke Region, coincident boundary y2 of the Permanent Magnet Yoke Region and the Permanent Magnet Region, coincident boundary y3 of the Permanent Magnet Region and the Air Gap Region, coincident boundary y4 of the Air Gap Region and the Copper Layer Region, coincident boundary y5 of the Copper Layer Region and the Copper Layer Yoke Region, and outer boundary y6 of the Copper Layer Yoke Region.

[0054] In some embodiments, the range of values ​​for the number of pole pairs, pole arc coefficient, permanent magnet yoke thickness, permanent magnet thickness, copper layer thickness, copper layer yoke thickness, and air gap thickness of the permanent magnet coupler can be obtained as follows:

[0055] Find: θ = [h] i ,h m ,h c ,h o ,g,p,a]

[0056] St: 0.012 ≤ h i ≤0.018

[0057] 0.018≤h m ≤0.022

[0058] 0.0045≤h c ≤0.0085

[0059] 0.012≤h o ≤0.018.

[0060] 0.002≤g≤0.023

[0061] 4≤p≤8, where p is an integer

[0062] 0.4≤a≤0.8

[0063] In the formula, θ represents the vector of parameters to be optimized, and there are 7 parameters to be optimized, namely h i Permanent magnet yoke thickness, h m Permanent magnet thickness, h c Copper layer thickness, h o The thickness of the copper yoke, the air gap thickness (g), the number of p pole pairs, and the a pole arc coefficient are all given, along with their value ranges. Figure 4 As shown, the polar arc coefficient a = τ m / τ p .

[0064] In this embodiment, based on the two-dimensional structural model of the permanent magnet coupler, the partial differential equation of magnetic potential and the magnetic potential boundary conditions of the permanent magnet coupler are obtained using the vector magnetic potential method, as follows:

[0065] In constructing the vector partial differential equations for the permanent magnet coupler, starting from the constitutive relations of magnetic induction and magnetic field strength, and based on Ampere's law and the definition of magnetic potential, the time-harmonic analysis method is used to perform a Fourier transform on the remanent magnetization, deriving the vector partial differential equations (magnetic potential partial differential equations) for the permanent magnet yoke region I, permanent magnet region II, air gap region III, copper layer region IV, and copper layer yoke region V in the permanent magnet coupler. The partial derivatives in the equations can be obtained through automatic differentiation. The specific equations are as follows:

[0066]

[0067] Where A1-A5 are the dependent variables, A1 is the magnetic potential of the permanent magnet yoke region, A2 is the magnetic potential of the permanent magnet region, A3 is the magnetic potential of the air gap region, A4 is the magnetic potential of the copper layer region, and A5 is the magnetic potential of the copper layer yoke region. x∈[-0.072, 0.072], y is the sum of the thicknesses of the permanent magnet yoke, permanent magnet, copper layer, copper layer yoke, and air gap, and α=nπ / τ p ω1=2πn1p / 60, μ0 is the free permeability, μ eq Where is the equivalent permeability of the copper-layered yoke, s is the slip, n is the harmonic order, n1 is the input rotational speed, p is the number of pole pairs, and B is the number of pole pairs. r τ is the remanent magnetic field strength. p τ is the average pole spacing. m σ is the average polar arc length. b The conductivity of the copper layer yoke iron is σ. c I represents the conductivity of the copper layer, II represents the permanent magnet yoke region, III represents the air gap region, IV represents the copper layer region, and V represents the copper layer yoke region.

[0068] When constructing the magnetic potential boundary conditions for the permanent magnet coupler, due to the continuity of magnetic field strength and magnetic flux density, the following relationship exists at the boundaries of each region:

[0069]

[0070] Where, μ av μ is the equivalent permeability of the permanent magnet yoke iron. xLet be the equivalent permeability of the permanent magnet, x and y be the independent variables, and A1-A5 be the dependent variables. A1 is the magnetic potential of the permanent magnet yoke region, A2 is the magnetic potential of the permanent magnet region, A3 is the magnetic potential of the air gap region, A4 is the magnetic potential of the copper layer region, A5 is the magnetic potential of the copper layer yoke region, y is the sum of the thicknesses of the permanent magnet yoke, permanent magnet, copper layer, copper layer yoke and air gap, y1 is the outer boundary of the permanent magnet yoke region, y2 is the overlapping boundary of the permanent magnet yoke region and the permanent magnet region, y3 is the overlapping boundary of the permanent magnet region and the air gap region, y4 is the overlapping boundary of the air gap region and the copper layer region, y5 is the overlapping boundary of the copper layer region and the copper layer yoke region, and y6 is the outer boundary of the copper layer yoke region.

[0071] In some embodiments, the PINN model can be established as follows:

[0072] The network structure diagram of the PINN model is as follows: Figure 5 As shown, the PINN model is based on the TensorFlow deep learning framework. A fully connected neural network is constructed on the PyCharm platform using the Python programming language. It includes an input layer, hidden layers, and an output layer. The parameters to be optimized, θ, and spatial variables x and y are used as the input layer of the deep neural network. The fully connected neural network outputs torque T and torque density T0. V The output layer is used as an example. For instance, using seven parameters to be optimized (permanent magnet yoke thickness, permanent magnet thickness, copper layer thickness, copper layer yoke thickness, air gap thickness, number of pole pairs, and pole arc coefficient) and spatial variables x and y as the input layer of a deep neural network, three hidden layers are set up with 20 neurons per layer, outputting torque T and torque density T0. V This is the output layer. The output of each layer of the neural network is shown in the following formula:

[0073]

[0074] In the formula, W i-1 b i-1 Z represents the weight matrix and bias vector of the (i-1)th layer, respectively. i-1 Let σ be the output of layer i-1, and σ be the activation function. Each layer in the neural network has a corresponding weight W and bias b. In this example, the sigmoid function, which is suitable for this model, is chosen as the activation function. It has significant advantages in expressing the partial differential equation of magnetic potential in the model, making the optimization of the neural network easier. Its expression is:

[0075] The loss function for calculating magnetic potential is obtained through mean square error, and the calculation formula is as follows:

[0076] MSE = MSE u +MSE r

[0077]

[0078]

[0079] In the formula, the loss MSE is divided into two parts, MSE u MSE represents the loss obtained through magnetic potential boundary conditions. r This represents the loss obtained from the partial differential equation of magnetic potential, with the loss being included as a regularization term in the loss function, N. u N r The number of data points This corresponds to the predicted value (magnetic potential).

[0080] The loss function is calculated by finding the difference between the predicted and actual values. In this scheme, the loss includes the mean squared error (MSE). r and MSE u Two parts, MSE r It is the loss corresponding to the partial differential equation, that is, the previous governing equation (vector partial differential equation), MSE. u This is the loss corresponding to the boundary conditions; calculate the MSE. r The expressions for both the predicted and actual values ​​are the left-hand sides of the preceding partial differential equation. However, the right-hand side is 0, meaning the left-hand side of the equation for the actual value is also 0. Substituting this into the loss function, the actual value becomes 0. Therefore, here the MSE... r The expression only contains the predicted value, because the true value is 0, so the MSE is calculated. u The same principle applies.

[0081] Specifically, the variable x takes values ​​in the range [-0.072, 0.072], and the value range of y in each layer is determined by the thickness. Both spatial variables x and y take 100 sample points, therefore each layer has 100 × 100 sample points, totaling 10,000 sample points. The loss function MSE is obtained through mean squared error. Following the above formula, substituting the magnetic potential partial differential equation and the magnetic potential boundary conditions, the specific expression for the loss is as follows:

[0082]

[0083]

[0084] In the formula, the total loss MSE = MSE1 + ... + MSE 15 The total loss is divided into two parts: one part represents the loss obtained through the boundary conditions, and the other part represents the loss obtained through the magnetic potential partial differential equation. The loss is included in the loss function as a regularization term.

[0085] In this formula, the loss corresponding to the governing equation is calculated. The value in parentheses is the predicted value, which is the left-hand side of the previous vector partial differential equation. However, the left-hand side of the partial differential equation for the true value is equal to the right-hand side, which is 0. Therefore, only the predicted value is left. The reason for substituting the value into the governing equation to calculate the loss is that when the loss function is minimized to a very small number, we can assume that the predicted value is approximately equal to the true value. That is, the expression for the predicted value is also equal to 0, and we can assume that the magnetic potential in the predicted value is the solution to the previous governing equation.

[0086] Specifically, after obtaining the loss function, this approach selects the Adam optimizer suitable for this model for training. The set of parameters to be optimized is trained 35,000 times. During the optimization process, the loss function value gradually decreases, while the weight matrix and bias vector of the fully connected neural network are updated. When the loss function value decreases to a minimum, the PINN framework satisfies both the magnetic potential partial differential equation and the given boundary conditions, accurately simulating the electromagnetic field process of the permanent magnet coupler. The training result of the PINN model is considered a solution to the magnetic potential partial differential equation system, from which the output torque and torque density can be calculated.

[0087] After calculating the output torque and torque density of the current data combination, the data combination is changed, and the values ​​of the parameters to be optimized are changed. The parameters to be optimized are continuous variables within the range of values. The change of each set of parameters to be optimized corresponds to the change of the shape of the permanent magnet coupler. The data combination is continued to be input into the PINN model until all data combinations are trained.

[0088] Finally, from all the output results, find the output torque T and torque density T. V The maximum value is obtained, and then the optimal set of parameters to be optimized is obtained, and the optimization is completed.

[0089] Based on the training results, training a set of parameters to be optimized can be completed within 5 minutes, while a single finite element simulation of the same model takes 3-4 hours, demonstrating a significant improvement in PINN's computational efficiency. Figure 6 (a) and Figure 6 As shown in (b), the magnetic potential predicted by PINN is highly consistent with the analytical solution; Figure 7 As shown, the loss of this scheme is very small and the effect is excellent, which proves the effectiveness and feasibility of the PINN model. It can replace the analytical solution and the simulation solution, and lay a good foundation for design optimization.

[0090] In some embodiments, the output torque and torque density of the permanent magnet coupler can be calculated according to the following formula:

[0091] Specifically, according to the formula Calculate the output torque of the permanent magnet coupler. Where T is the output torque, and r... mean k is the average radius. s w is the correction factor. m denoted as ω1 = 2πn1p / 60, where n1 is the input rotational speed, σ is the activation function, y is the sum of the thicknesses of the permanent magnet yoke, permanent magnet, copper layer, copper layer yoke, and air gap, y4 is the overlapping boundary between the air gap region and the copper layer region, y5 is the overlapping boundary between the copper layer region and the copper layer yoke region, y6 is the outer boundary of the copper layer yoke region, A4 is the magnetic potential of the copper layer region, and A5 is the magnetic potential of the copper layer yoke region.

[0092] Specifically, according to formula T V The torque density of the permanent magnet coupler is calculated using the formula T / V. Where T... V Where is the torque density, T is the output torque of the permanent magnet coupler, and V is the volume of the permanent magnet coupler.

[0093] The specifications for the permanent magnet coupler can be found in the following parameter table:

[0094] Table 1 Specifications of Permanent Magnet Couplers

[0095]

[0096] This invention also provides a permanent magnet coupler design optimization system based on a physical information neural network, comprising:

[0097] The parameter acquisition module is used to acquire the value range of each parameter to be optimized in the permanent magnet coupler; the parameters to be optimized include the number of magnetic pole pairs, the pole arc coefficient, the thickness of the permanent magnet yoke, the thickness of the permanent magnet, the thickness of the copper layer, the thickness of the copper layer yoke, and the air gap thickness.

[0098] The parameter partitioning module is used to divide the parameters to be optimized into multiple data combinations according to the value range of each parameter to be optimized; each data combination is composed of a number of magnetic pole pairs, pole arc coefficient, permanent magnet yoke thickness, permanent magnet thickness, copper layer thickness, copper layer yoke thickness and air gap thickness, and at least one parameter to be optimized has a different value between any two data combinations.

[0099] The parameter calculation module is used to input each of the data combinations into the trained PINN model to predict the magnetic potential of each region of the permanent magnet coupler under each data combination. The trained PINN model is a model trained with the training data combination as input and the magnetic potential of each region of the permanent magnet coupler established based on the training data combination as a label. The training data combination is composed of a number of magnetic pole pairs, pole arc coefficient, permanent magnet yoke thickness, permanent magnet thickness, copper layer thickness, copper layer yoke thickness, and air gap thickness. The magnetic potential as a label is calculated from the corresponding training data combination, the magnetic potential partial differential equation of the permanent magnet coupler, and the magnetic potential boundary conditions.

[0100] The torque calculation module is used to calculate the output torque and torque density corresponding to each data combination based on the magnetic potential of each region of the permanent magnet coupler under each predicted data combination.

[0101] The parameter output module is used to compare the output torque and torque density corresponding to each data combination, and determine the optimal value of each parameter to be optimized based on the data combination corresponding to the maximum output torque and torque density.

[0102] In summary, the present invention has the following advantages:

[0103] This invention provides a design optimization method for permanent magnet couplers based on Physics-informed Neural Networks (PINN). It integrates prior knowledge such as partial differential equations and physical constraints that satisfy the practical problem into the loss function of the neural network, training a convergent solution that can be considered as a solution to the partial differential equation. This allows for easy calculation of the performance parameters of the permanent magnet coupler, replacing analytical and simulation models and facilitating subsequent optimization. This solves the problems of difficulty in obtaining sample points and poor optimization results in permanent magnet coupler design optimization.

[0104] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0105] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A design optimization method for permanent magnet couplers based on physical information neural networks, characterized in that, Includes the following steps: Step 1: Obtain the value range of each parameter to be optimized for the permanent magnet coupler; the parameters to be optimized include the number of pole pairs, pole arc coefficient, thickness of permanent magnet yoke, thickness of permanent magnet, thickness of copper layer, thickness of copper layer yoke, and air gap thickness; Step 2: Based on the value range of each parameter to be optimized, divide the parameter to be optimized into multiple data combinations; each data combination is composed of a number of magnetic pole pairs, pole arc coefficient, permanent magnet yoke thickness, permanent magnet thickness, copper layer thickness, copper layer yoke thickness and air gap thickness, and at least one parameter to be optimized has a different value between any two data combinations; Step 3: Input each of the data combinations into the trained PINN model to predict the magnetic potential of each region of the permanent magnet coupler under each data combination; the trained PINN model is a model trained with the training data combination as input and the magnetic potential of each region of the permanent magnet coupler established based on the training data combination as a label; the training data combination is composed of a number of magnetic pole pairs, pole arc coefficient, permanent magnet yoke thickness, permanent magnet thickness, copper layer thickness, copper layer yoke thickness, and air gap thickness, and the magnetic potential as a label is calculated from the corresponding training data combination, the magnetic potential partial differential equation of the permanent magnet coupler, and the magnetic potential boundary conditions; Step 4: Based on the predicted magnetic potential of each region of the permanent magnet coupler under each of the data combinations, solve for the output torque and torque density corresponding to each of the data combinations; Step 5: Compare the output torque and torque density corresponding to each data combination, and determine the optimal value of each parameter to be optimized based on the data combination corresponding to the maximum output torque and torque density.

2. The permanent magnet coupler design optimization method according to claim 1, characterized in that, The loss function during PINN model training includes magnetic potential loss and magnetic potential boundary loss, wherein the magnetic potential boundary loss is determined based on the magnetic potential boundary conditions.

3. The permanent magnet coupler design optimization method according to claim 1, characterized in that, The permanent magnet coupler includes a permanent magnet yoke region, a permanent magnet region, an air gap region, a copper layer region, and a copper layer yoke region.

4. The permanent magnet coupler design optimization method according to claim 1, characterized in that, The specific partial differential equation for magnetic potential is as follows: ； in, As the dependent variable, A 1 This refers to the magnetic potential of the yoke region of the permanent magnet. A 2 This refers to the magnetic potential of the permanent magnet region. A 3 The magnetic potential of the air gap region. A 4 The magnetic potential of the copper layer region, A 5 Let x represent the magnetic potential of the copper-layer yoke region, x∈[-0.072, 0.072], and y represent the sum of the thicknesses of the permanent magnet yoke, the permanent magnet, the copper layer, the copper-layer yoke, and the air gap. , , , The permeability of free space, ρ is the equivalent permeability of the copper-layered yoke, s is the slip, and n is the harmonic order. Input speed, p The number of magnetic pole pairs Residual magnetic flux density The average pole spacing, The average polar arc length, The conductivity of the copper layer yoke iron is given by... I represents the conductivity of the copper layer, II represents the permanent magnet yoke region, III represents the air gap region, IV represents the copper layer region, and V represents the copper layer yoke region.

5. The permanent magnet coupler design optimization method according to claim 1, characterized in that, The specific magnetic potential boundary conditions are as follows: ； in, The equivalent permeability of the permanent magnet yoke iron. Let be the equivalent permeability of the permanent magnet, and x and y be the independent variables. As the dependent variable, A 1 This refers to the magnetic potential of the yoke region of the permanent magnet. A 2 This refers to the magnetic potential of the permanent magnet region. A 3 The magnetic potential of the air gap region. A 4 The magnetic potential of the copper layer region, A 5 Let be the magnetic potential of the copper-layer yoke region, and y be the sum of the thicknesses of the permanent magnet yoke, the permanent magnet, the copper layer, the copper-layer yoke, and the air gap. y 1 represents the outer boundary of the permanent magnet yoke region. y 2 represents the boundary where the permanent magnet yoke region and the permanent magnet region coincide. y 3 represents the boundary between the permanent magnet region and the air gap region. y 4 represents the boundary where the air gap region and the copper layer region overlap. y 5 represents the overlapping boundary between the copper layer region and the copper layer yoke region. y 6 represents the outer boundary of the copper layer yoke region.

6. The permanent magnet coupler design optimization method according to claim 1, characterized in that, The output torque of the permanent magnet coupler is calculated according to the following formula: ； in, The average radius, As a correction factor, The width of the permanent magnet. p denoted by , where is the number of pole pairs and s is the slip. , Input speed, σ Let be the electrical conductivity, and y be the sum of the thicknesses of the permanent magnet yoke, the permanent magnet, the copper layer, the copper layer yoke, and the air gap. y 4 represents the boundary where the air gap region and the copper layer region overlap. y 5 represents the overlapping boundary between the copper layer region and the copper layer yoke region. y 6 represents the outer boundary of the copper-layer yoke region. A 4 The magnetic potential of the copper layer region, A 5 This represents the magnetic potential of the copper-layer yoke region.

7. The permanent magnet coupler design optimization method according to claim 1, characterized in that, The torque density of the permanent magnet coupler is calculated according to the following formula: ； in, T This refers to the output torque of the permanent magnet coupler. V The volume of the permanent magnet coupler.

8. A permanent magnet coupler design optimization system based on a physical information neural network, characterized in that, include: The parameter acquisition module is used to acquire the value range of each parameter to be optimized in the permanent magnet coupler; the parameters to be optimized include the number of pole pairs, pole arc coefficient, permanent magnet yoke thickness, permanent magnet thickness, copper layer thickness, copper layer yoke thickness, and air gap thickness. The parameter division module is used to divide the parameters to be optimized into multiple data combinations according to the value range of each parameter to be optimized; each data combination is composed of a number of magnetic pole pairs, pole arc coefficient, permanent magnet yoke thickness, permanent magnet thickness, copper layer thickness, copper layer yoke thickness and air gap thickness, and at least one parameter to be optimized has a different value between any two data combinations. The parameter calculation module is used to input each of the data combinations into the trained PINN model to predict the magnetic potential of each region of the permanent magnet coupler under each data combination. The trained PINN model is a model trained with the training data combination as input and the magnetic potential of each region of the permanent magnet coupler established based on the training data combination as a label. The training data combination is composed of a number of magnetic pole pairs, pole arc coefficient, permanent magnet yoke thickness, permanent magnet thickness, copper layer thickness, copper layer yoke thickness, and air gap thickness. The magnetic potential as a label is calculated from the corresponding training data combination, the magnetic potential partial differential equation of the permanent magnet coupler, and the magnetic potential boundary conditions. The torque calculation module is used to calculate the output torque and torque density corresponding to each data combination based on the magnetic potential of each region of the permanent magnet coupler under each predicted data combination. The parameter output module is used to compare the output torque and torque density corresponding to each data combination, and determine the optimal value of each parameter to be optimized based on the data combination corresponding to the maximum output torque and torque density.

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