CN117709170B - Magnetic field rapid calculation method based on improved depth operator network - Google Patents
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Abstract
The invention relates to the technical field of depth operator networks, and discloses a magnetic field rapid calculation method based on an improved depth operator network, which comprises the steps of determining a model and parameters: first, the type and structure parameters of the established finite element model are determined, mesh generation is performed based on the parameters, and boundary conditions including magnetic field conditions and material parameters are determined when the finite element model is established. According to the magnetic field rapid calculation method based on the improved depth operator network, relative permeability information is extracted by utilizing a U-net convolutional neural network on the basis of the depth operator network, boundary conditions and grid point coordinate information are extracted by utilizing two fully-connected neural networks, relative permeability and grid point coordinates are fused in a Hadamard product mode, prediction accuracy is further improved, a training set is constructed by utilizing the changed boundary conditions, grid vertex coordinates and corresponding finite element solutions, and electromagnetic field distribution under the untrained boundary conditions can be rapidly predicted by the trained network.
Description
Technical Field
The invention relates to the technical field of depth operator networks, in particular to a magnetic field rapid calculation method based on an improved depth operator network.
Background
In order to improve the design and manufacturing level of the power equipment and the reliability of the operation stage, a finite element method is often adopted in the industrial production process to analyze the internal complex electric field and magnetic field distribution of the power equipment, but the finite element method generally needs to discretize a calculation area into a finite number of units, the finite element theory is used in each unit to solve the problem, as the complexity of the calculation area and the number of units are increased, the number of matrix operation increases, and the calculation time also increases, so that in the scene needing real-time calculation, such as a transformer hot temperature problem and a generator temperature rise problem, the real-time of evaluation is difficult to ensure if the finite element method is used for calculation, but the main methods for solving the two problems at present comprise a reduced order model method, a Kriging method, a response surface method, a U-net neural network method and the like, the reduced order model method needs to be deduced for specific equations and boundary conditions, once an object is replaced or a geometric model is changed, the Kriging method and the response surface method needs to be deduced again for the geometric problem of two-dimensional simplicity, but the error convolution in three-dimensional complex geometric problem is larger, the error is calculated, the error convolution method is a large, the error is studied in the map between the complex image block and the complex image is a high, and the position of the complex image is difficult to be lost, and the image is difficult to be studied, and the image is lost in the position of the complex image is difficult to be calculated, and the image is a complex, and the image is prone to be lost.
Disclosure of Invention
This section is intended to outline some aspects of embodiments of the application and to briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section as well as in the description of the application and in the title of the application, which may not be used to limit the scope of the application.
In view of the limitations of the above-mentioned or prior art magnetic field rapid calculation methods in specific situations, it is not possible to solve the complex problem well or adapt to the changes of different situations.
In order to achieve the above purpose, the present invention provides the following technical solutions:
A magnetic field rapid calculation method based on an improved depth operator network comprises the following operation steps:
s1, determining a model and parameters: firstly, determining the type and the structural parameters of an established finite element model, and performing mesh subdivision based on the parameters;
s2, setting boundary conditions: determining boundary conditions, including magnetic field conditions and material parameters, when establishing a finite element model;
s3, solving a magnetic field by a finite element method: solving magnetic fields under various working conditions by adopting a finite element method to obtain a magnetic field distribution result;
s4, data export and arrangement: deriving the grid point coordinates, the relative magnetic permeability, the magnetic induction intensity, the constant C and the current density J s data on each finite element grid point, and dividing the data into a training set and a testing set;
S5, data filling and preprocessing: processing the derived data, filling the data into square size to ensure proper format of the input data, and preparing for input of a subsequent neural network model, wherein the filled data adopts the value of the 0 th data point in the original data;
S6, designing a neural network: according to the design shown in fig. 2, constructing structures of a branch network 1, a branch network 2 and a main network, wherein the structures comprise a fully connected neural network and a U-net convolutional neural network, and determining the number of neurons and parameter configuration of each layer;
S7, training a neural network: training the neural network by using the training set, and selecting a loss function, an optimizer and an activation function parameter;
S8, model evaluation: after training is completed, the model is applied to the test set and the accuracy of the model is assessed by Normalized Mean Absolute Error (NMAE).
As still further aspects of the invention: in steps S1 and S2, the calculation formulas for solving the equations and boundary conditions are as follows:
；
Wherein the method comprises the steps of Is a conductor region,/>Is a non-conductor region, A is a vector magnetic potential (Wb/m),/>Is the magnetic permeability (H/m) of the conductor region,/>Permeability (H/m) for the conductor region; j s is the current density (A/m 2);
The calculation formula of the vector magnetic bit is as follows: ；
Wherein C is a constant value, and wherein, Is a boundary;
The magnetic induction intensity is used for describing the strength of a magnetic field in engineering, and the relation formula of the magnetic field strength and the vector magnetic position is as follows:
；
wherein B is magnetic induction intensity (T).
As still further aspects of the invention: in steps S3 and S4, coordinates of the grid point on each finite element grid point, coordinates of the material region, magnetic induction intensity, and coordinates of the center of gravity position of the conductor region are derived, andThe material region refers to the number of the material corresponding to each finite element lattice point derived by firstly labeling different materials, and dividing the derived data into a training set and a testing set.
As still further aspects of the invention: in step S5, since the grid points obtained by the grid division under each working condition are different, and when the convolution operation is performed, in order to facilitate the "scanning" operation performed by the convolution kernel, the input data will be kept as square or square, so the grid point coordinates, the relative permeability and the magnetic induction intensity need to be filled as square dimensions, and the filled data is the value of the 0 th data point of the original data.
As still further aspects of the invention: as shown in fig. 2, the constant C and the current density J s are used as the input of the branch network 1 in fig. 2, the relative permeability at each finite element lattice point is used as the input of the branch network 2, the lattice point coordinates are used as the input of the main network, the branch network 1 adopts a fully-connected neural network structure, the branch network 2 adopts a U-net convolutional neural network structure for extracting key information of the geometric model and the material, the main network adopts a fully-connected neural network structure, and the branch network 1 and the branch network 2 are connected by using hadamard products, and the formula is as follows:
；
Wherein Ba is the total output of the branch network, ba 1 is the output of the branch network 1, ba 2 is the output of the branch network 2, and As indicated by Hadamard product;
the number of neurons in the last layer of the two branch networks should be kept consistent, and the main network T and the branch network Ba are connected by matrix multiplication, and the formula is as follows:
；
Wherein G (y) is the output of the neural network, y is the grid point coordinates, ba and The meaning of the term is consistent, namely the total output of the branch network, and T is the output of the branch network.
As still further aspects of the invention: in step S6, since the relative permeability and the lattice point coordinates on the lattice points are in one-to-one correspondence, in order to accelerate the convergence speed of the network, the relative permeability is fused into the calculation of each layer of the backbone network, the relative permeability and the lattice point coordinates are first kept consistent by a linear layer, and then are embedded into the backbone network in the hadamard product manner, where the formula is as follows:
；
Where x is the input of the branch network 2, i.e. the relative permeability, y is the input of the backbone network, i.e. the lattice point coordinates, are the linear layers, U is the output of x after passing through a linear layer, H (k) is the output of lattice point coordinates after passing through the kth linear layer, L is the total number of linear layers of the backbone network, and as such, is the Hadamard product.
As still further aspects of the invention: in step S7, where the optimizer selects Adam, the linear layer activation function selects LeakyRelu, and the loss function formula is as follows:
；
Wherein the method comprises the steps of For the constant C and the current density J s, the passing parameter is/>The value of the sampling point y i, s i is the magnetic induction intensity calculated by the finite element, and n is the number of the sampling points.
As still further aspects of the invention: in step S8, the trained model evaluates accuracy by the normalized mean absolute error of the test set (NMAE), which is specifically formulated as follows:
；
Wherein the method comprises the steps of For the constant C and the current density J s, the passing parameter is/>The value of the sampling point y i, s i is the magnetic induction intensity calculated by the finite element, and n is the number of the sampling points.
Compared with the prior art, the invention has the beneficial effects that:
1. According to the invention, on the basis of a depth operator network, the relative permeability information is extracted by utilizing a U-net convolutional neural network, the boundary condition and the grid point coordinate information are extracted by utilizing two fully connected neural networks, the relative permeability and the grid point coordinate are fused in a Hadamard product mode, the prediction precision is further improved, a training set is constructed by utilizing the changed boundary condition, grid vertex coordinate and corresponding finite element solution, and the trained network can rapidly predict the electromagnetic field distribution under the untrained boundary condition.
Drawings
FIG. 1 is a FEM model diagram of a magnetic field fast computation method based on an improved depth operator network;
FIG. 2 is a block diagram of a neural network in a magnetic field fast computation method based on an improved depth operator network;
Fig. 3 is a diagram of magnetic induction intensity, neural network solution and point-by-point error calculated by finite elements in a magnetic field rapid calculation method based on an improved depth operator network.
Detailed Description
The foregoing objects, features and advantages of the invention will be more readily apparent from the following detailed description of the embodiments of the invention taken in conjunction with the accompanying drawings.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways other than those described herein, and persons skilled in the art will readily appreciate that the present invention is not limited to the specific embodiments disclosed below.
Further, reference herein to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic can be included in at least one implementation of the invention. The appearances of the phrase "in one embodiment" in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments.
Examples:
Referring to fig. 1-3, a first embodiment of the present invention provides a method for quickly calculating a magnetic field based on an improved depth operator network, which includes two parts of circular areas, wherein the circle center of the first part is fixed at (0, 0), the radius is 0.1m, the relative permeability is set to be 1.5, a current with a current density of 10A/m2 is introduced, the radius of the second part is fixed at 0.1m, and the position of the circle center and the size of the introduced current density are changed as follows:
Specifically, the relative permeability is set to 1.5, the outer edge is provided with an air area with a radius of 1m, the relative permeability is set to 1, the outer boundary loss magnetic potential is set to 0, and the FEM model is shown in figure 1 by taking the circle center coordinates as (-0.3, -0.27) as an example.
Further, 13 sets of circular center abscissas x,6 sets of circular center ordinates y and 6 sets of current densities J s are equidistantly selected, and parameterization calculation is performed by using a finite element method under the condition that 13×6×6=468 sets are summed to obtain a data set.
Further, the grid point coordinates, relative permeability, magnetic induction, and current density on each finite element grid point of the square region of fig. 1 were derived.
Further, since the derived data has 3100 rows at most, a square with a size of 56×56 is selected, the grid point coordinates, the material parameters and the magnetic induction intensity are filled into the square, the filled data is the value of the 0 th data point of the original data, 400 groups of the whole data set are selected as training sets, and the rest are selected as test sets.
Further, as shown in fig. 2, the current density J s is used as the input of the branch network 1 in fig. 2, the relative permeability at each lattice point is used as the input of the branch network 2, the coordinates of the lattice points are used as the input of the main network, the branch network 1 adopts a fully connected neural network structure, the branch network 2 adopts a U-net convolutional neural network structure for extracting key information of the geometric model and the material, the main network adopts the fully connected neural network structure, the optimizer selects Adam, and the loss function isAnd trains the neural network.
Further, the accuracy is evaluated by adopting a normalized average absolute error, the average value of the test set is 0.98%, the maximum relative error is 2.68%, the accuracy meets the requirements, a group of data is randomly acquired in the test set, and the magnetic induction intensity, the neural network solution and the point-by-point error which are calculated by the finite element are shown in figure 3.
When the model is used, firstly, the type and the structure parameters of the established finite element model are determined, mesh subdivision is carried out based on the parameters, boundary conditions including magnetic field conditions and material parameters are determined when the finite element model is established, a finite element method is adopted to solve magnetic fields under various working conditions, a magnetic field distribution result is obtained, lattice point coordinates, relative permeability, magnetic induction intensity, constant C and current density J s data on each finite element lattice point are exported and divided into a training set and a test set, the exported data are processed and filled into square sizes, the proper format of input data is ensured, the input of a subsequent neural network model is prepared, the filled data adopt the value of the 0 th data point in original data, the structures of a branch network 1, a branch network 2 and a main network are established according to the design shown in fig. 2, the structures including a fully connected neural network and a U-net convolutional neural network are determined, training of the neural network of each layer is carried out by utilizing the training set, a loss function, an optimizer and an activation function parameter are selected, and after the training is completed, the model is applied to the test set, and the average precision (NMAE) of the model is estimated.
In sum, the relative permeability information is extracted by utilizing the U-net convolutional neural network on the basis of the depth operator network, the boundary condition and the grid point coordinate information are extracted by utilizing the two fully connected neural networks, and the relative permeability and the grid point coordinate are fused in a Hadamard product mode, so that the prediction precision is further improved. The training set is constructed by using the changed boundary conditions, the grid vertex coordinates and the corresponding finite element solutions, and the trained network can rapidly predict the electromagnetic field distribution under the untrained boundary conditions.
It is important to note that the construction and arrangement of the application as shown in the various exemplary embodiments is illustrative only. Although only a few embodiments have been described in detail in this disclosure, those skilled in the art who review this disclosure will readily appreciate that many modifications are possible (e.g., variations in sizes, dimensions, structures, shapes and proportions of the various elements, values of parameters (e.g., temperature, pressure), mounting arrangements, use of materials, colors, orientations, etc.) without materially departing from the novel teachings and advantages of the subject matter described in this application. For example, elements shown as integrally formed may be constructed of multiple parts or elements, the position of elements may be reversed or otherwise varied, and the nature or number of discrete elements or positions may be altered or varied. Accordingly, all such modifications are intended to be included within the scope of present application. The order or sequence of any process or method steps may be varied or re-sequenced according to alternative embodiments. In the claims, any means-plus-function clause is intended to cover the structures described herein as performing the recited function and not only structural equivalents but also equivalent structures. Other substitutions, modifications, changes and omissions may be made in the design, operating conditions and arrangement of the exemplary embodiments without departing from the scope of the present applications. Therefore, the application is not limited to the specific embodiments, but extends to various modifications that nevertheless fall within the scope of the appended claims.
Furthermore, in order to provide a concise description of the exemplary embodiments, all features of an actual implementation may not be described (i.e., those not associated with the best mode presently contemplated for carrying out the invention, or those not associated with practicing the invention).
It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions may be made. Such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure.
It should be noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solution of the present invention may be modified or substituted without departing from the spirit and scope of the technical solution of the present invention, which is intended to be covered in the scope of the claims of the present invention.
Claims (7)
1. A magnetic field rapid calculation method based on an improved depth operator network is characterized by comprising the following steps of: the operation steps are as follows:
s1, determining a model and parameters: firstly, determining the type and the structural parameters of an established finite element model, and performing mesh subdivision based on the parameters;
s2, setting boundary conditions: determining boundary conditions, including magnetic field conditions and material parameters, when establishing a finite element model;
s3, solving a magnetic field by a finite element method: solving magnetic fields under various working conditions by adopting a finite element method to obtain a magnetic field distribution result;
s4, data export and arrangement: deriving the grid point coordinates, the relative magnetic permeability, the magnetic induction intensity, the constant C and the current density J s data on each finite element grid point, and dividing the data into a training set and a testing set;
S5, data filling and preprocessing: processing the derived data, filling the data into square size to ensure proper format of the input data, and preparing for input of a subsequent neural network model, wherein the filled data adopts the value of the 0 th data point in the original data;
s6, designing a neural network: building structures of a branch network 1, a branch network 2 and a backbone network, wherein the structures comprise a fully-connected neural network and a U-net convolutional neural network, and determining the number of neurons and parameter configuration of each layer;
S7, training a neural network: training the neural network by using the training set, and selecting a loss function, an optimizer and an activation function parameter;
S8, model evaluation: after training is completed, the model is applied to a test set, and the accuracy of the model is evaluated through a normalized average absolute error (NMAE);
taking a constant C and a current density J s as inputs of a branch network 1, taking the relative magnetic permeability on each finite element lattice point as inputs of a branch network 2, taking the lattice point coordinates as inputs of a main network, wherein the branch network 1 adopts a fully-connected neural network structure, the branch network 2 adopts a U-net convolutional neural network structure for extracting key information of a geometric model and materials, the main network adopts the fully-connected neural network structure, and the branch network 1 and the branch network 2 are connected by using Hadamard products, wherein the formula is as follows:
；
Wherein Ba is the total output of the branch network, ba 1 is the output of the branch network 1, ba 2 is the output of the branch network 2, and As indicated by Hadamard product;
the number of neurons in the last layer of the two branch networks should be kept consistent, and the main network T and the branch network Ba are connected by matrix multiplication, and the formula is as follows:
；
Wherein G (y) is the output of the neural network, y is the grid point coordinates, ba and The meaning of the term is consistent, namely the total output of the branch network, and T is the output of the branch network.
2. The method for quickly calculating the magnetic field based on the improved depth operator network according to claim 1, wherein the method comprises the following steps: in steps S1 and S2, the calculation formulas for solving the equations and boundary conditions are as follows:
；
Wherein the method comprises the steps of Is a conductor region,/>Is a non-conductor region, A is a vector magnetic potential (Wb/m),/>Is the magnetic permeability (H/m) of the conductor region,/>Permeability (H/m) for the conductor region; j s is the current density (A/m 2);
The calculation formula of the vector magnetic bit is as follows: ；
Wherein C is a constant value, and wherein, Is a boundary;
The magnetic induction intensity is used for describing the strength of a magnetic field in engineering, and the relation formula of the magnetic field strength and the vector magnetic position is as follows:
；
wherein B is magnetic induction intensity (T).
3. The method for quickly calculating the magnetic field based on the improved depth operator network according to claim 2, wherein the method comprises the following steps of: in steps S3 and S4, coordinates of the grid point on each finite element grid point, coordinates of the material region, magnetic induction intensity, and coordinates of the center of gravity position of the conductor region are derived, andThe material region refers to the number of the material corresponding to each finite element lattice point derived by firstly labeling different materials, and dividing the derived data into a training set and a testing set.
4. The method for quickly calculating the magnetic field based on the improved depth operator network according to claim 1, wherein the method comprises the following steps: in step S5, since the grid points obtained by the grid division under each working condition are different, and when the convolution operation is performed, in order to facilitate the "scanning" operation performed by the convolution kernel, the input data will be kept as square or square, so the grid point coordinates, the relative permeability and the magnetic induction intensity need to be filled as square dimensions, and the filled data is the value of the 0 th data point of the original data.
5. The method for quickly calculating the magnetic field based on the improved depth operator network according to claim 1, wherein the method comprises the following steps: in step S6, since the relative permeability and the lattice point coordinates on the lattice points are in one-to-one correspondence, in order to accelerate the convergence speed of the network, the relative permeability is fused into the calculation of each layer of the backbone network, the relative permeability and the lattice point coordinates are first kept consistent by a linear layer, and then are embedded into the backbone network in the hadamard product manner, where the formula is as follows:
；
Where x is the input of the branch network 2, i.e. the relative permeability, y is the input of the backbone network, i.e. the lattice point coordinates, are the linear layers, U is the output of x after passing through a linear layer, H (k) is the output of lattice point coordinates after passing through the kth linear layer, L is the total number of linear layers of the backbone network, and as such, is the Hadamard product.
6. The method for quickly calculating the magnetic field based on the improved depth operator network according to claim 1, wherein the method comprises the following steps: in step S7, where the optimizer selects Adam, the linear layer activation function selects LeakyRelu, and the loss function formula is as follows:
；
Wherein the method comprises the steps of For the constant C and the current density J s, the passing parameter is/>The value of the sampling point y i, s i is the magnetic induction intensity calculated by the finite element, and n is the number of the sampling points.
7. The method for quickly calculating the magnetic field based on the improved depth operator network according to claim 1, wherein the method comprises the following steps: in step S8, the trained model evaluates accuracy by the normalized mean absolute error of the test set (NMAE), which is specifically formulated as follows:
；
Wherein the method comprises the steps of For the constant C and the current density J s, the passing parameter is/>The value of the sampling point y i, s i is the magnetic induction intensity calculated by the finite element, and n is the number of the sampling points.
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