A fast method for calculating magnetic field in electromagnetic pulse welding

Abstract

The application relates to a magnetic field rapid calculation method for electromagnetic pulse welding, which takes circuit parameters and structural geometric parameters as input variables and takes the spatial magnetic field distribution of the inner ring of a magnet collector as an output quantity; optimal Latin hypercube sampling is carried out in the input parameter space, a finite element model is called to calculate the magnetic field distribution under each sample point, principal component analysis (PCA) is used to carry out data dimension reduction on the magnetic field calculation result, eigenvalues and eigenvectors are obtained, a radial basis function (RBF) is used to construct a mapping relationship between the input parameters and the eigenvalues, and finally a calculation model between the input parameters and the magnetic field can be obtained; the method solves the problems that the analytic method used in the current electromagnetic field analysis is insufficient in precision and the numerical method is large in calculation amount.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic pulse welding and relates to a method for rapid calculation of magnetic field for electromagnetic pulse welding. Background Technology

[0002] Electromagnetic pulse welding (EMP) is a high-speed impact welding technology. Its basic principles include pulse power technology and electromagnetic induction. The welding process consists of three stages: 1. Charging stage: A DC power supply charges the capacitor bank; 2. Discharging stage: The charged capacitor rapidly discharges to the welding coil, generating a pulsed induced magnetic field; 3. Welding stage: A magnetizer focuses and amplifies the magnetic field to generate a high-frequency, strong magnetic field, inducing eddy currents on the workpiece surface. These eddy currents interact with the strong magnetic field to generate pulsed electromagnetic force, driving the workpiece to collide at high speed and achieving a strong bond between the workpiece materials. After more than fifty years of research, EMP welding technology has made significant progress in theory, but it only began industrial application at the end of the last century. Compared with traditional arc welding, laser welding, and flame brazing, EMP welding has superior advantages in welding dissimilar metals and can also weld between metallic and non-metallic materials. It is widely applicable to welding tubular, plate-shaped, and irregularly shaped structural parts. The welding process does not produce substances harmful to humans or the environment, and automated large-scale production can be achieved by adjusting the welding electrical parameters.

[0003] Electromagnetic fields, acting as a bridge between circuits and structural fields, play a decisive role in welding quality. Circuit analysis yields the voltage and current in the coil, which in turn induces an electromagnetic field within the coil. This electromagnetic field then acts on the structural field formed by the workpiece to be welded, ultimately driving the workpiece to high-speed motion. Therefore, analyzing the magnetic field is crucial for circuit design, magnet collector design, and structural field analysis. Magnetopulse welding involves complex multi-physics coupling, including circuits, electromagnetic fields, structural fields, and temperature fields. The high-speed movement of the workpiece during welding alters circuit parameters, further increasing the analysis difficulty. Common methods for electromagnetic field analysis include analytical and numerical methods. Analytical methods, as a loosely coupled calculation approach, first simplify the system and then calculate the spatial magnetic field distribution using electromagnetic field theory and structural parameters. This method is fast but lacks accuracy, serving only as an approximation. Numerical methods, on the other hand, construct finite element models. Finite element analysis can effectively handle multi-physics coupling problems during welding, providing high-precision results, but it requires significant computational resources and time. Summary of the Invention

[0004] In view of this, in order to solve the problems of insufficient accuracy of analytical methods and large computational load of numerical methods currently used in electromagnetic field analysis, this invention provides a rapid magnetic field calculation method for electromagnetic pulse welding, which reduces the computational load while meeting the requirements of calculation accuracy.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A method for rapid calculation of magnetic field for electromagnetic pulse welding includes the following steps:

[0007] S1, Training Sample Sampling

[0008] In the input variable space consisting of circuit parameters and structural geometric parameters, m sample points are extracted using the optimal Latin hypercube method, denoted as X. m×q , where q represents the number of circuit parameters and structural geometric parameters;

[0009] S2, Call the finite element model

[0010] The finite element model of the electromagnetic pulse welding system is represented by G(·). The electromagnetic pulse welding finite element model is called once at each sample point to obtain the spatial distribution of the magnetic field strength of the magnetizer, denoted as M=G(X). i ), i = 1, 2, ..., m;

[0011] S3. Construct the RBF proxy model

[0012] Each sample point X i A magnetic flux density curve with respect to time is obtained. Taking a time interval [0, t], it is discretized into d time points, resulting in an m×d magnetic flux density matrix, denoted as .

[0013]

[0014] Center matrix B

[0015]

[0016] Calculate the centered matrix B * covariance matrix

[0017] Perform eigenvalue decomposition on the covariance matrix C, and arrange the eigenvalues ​​in descending order as λ1, λ2, ..., λ3. d The corresponding feature vector

[0018] The contribution rate of the i-th principal component is

[0019] The cumulative contribution rate of the first k principal components is

[0020] Select and determine the cumulative contribution rate according to the actual situation, obtain the first k (k<<d) principal components, and the projection coordinates of the original d-dimensional magnetic induction intensity data B in the k-dimensional coordinate system are

[0021]

[0022]

[0023] corresponding eigenvectors Thus, the magnetic induction intensity B is equivalently represented in the low-dimensional space as

[0024] It can be seen that the mapping relationship between the input variable X m×q and the magnetic induction intensity B is transformed into the mapping relationship between the input variable X m×q and the projection coordinate α m×k , and k sets of interpolation nodes are obtained

[0025] S4. Magnetic field prediction

[0026] Construct the RBF proxy model between the input variable X m×q and the projection coefficient α based on the k sets of interpolation nodes respectively i

[0027]

[0028] where ω i denotes the interpolation weight value, φ denotes the radial basis kernel function, and ||X-X i || denotes the Euclidean distance from the prediction point X to the sample point X i

[0029] The mapping relationship between the input variable X m×q and the magnetic induction intensity B is expressed as

[0030]

[0031] The time-varying curve of the input variable X m×q and the magnetic induction intensity B is expressed as {t, B(X)}.

[0032] Further, in step S2, the finite element model is called to calculate the magnetic field distribution at each sample point.

[0033] Further, in step S3, principal component analysis (PCA) is adopted to perform data dimensionality reduction on the magnetic field calculation results to obtain eigenvalues and eigenvectors, and a radial basis function (RBF) is adopted to construct the mapping relationship between the input parameters and the eigenvalues.

[0034] ​​Furthermore, in step S3, PCA dimensionality reduction reduces the dimensionality of the initial samples by reprojecting these redundant data into mutually orthogonal coordinate systems. In the new coordinate system, the data is sorted according to the size of the contribution value. While ensuring data accuracy, the top few features are selected to replace the original high-dimensional data, generating new low-dimensional samples. These new samples are then used as inputs to the training model of the RBF neural network to construct the RBF model.

[0035] Furthermore, in step S4, the radial basis kernel function φ is one of the following: Gaussian kernel function, cubic kernel function, or polynomial kernel function.

[0036] Furthermore, in steps S3 and S4, the magnetic induction intensity B can be in the form of a curve, a two-dimensional cloud map, or a three-dimensional cloud map.

[0037] The beneficial effects of this invention are as follows:

[0038] 1. The method for rapid calculation of magnetic field for electromagnetic pulse welding disclosed in this invention reduces the dimensionality of high-dimensional time-varying spatial magnetic field data in the field of electromagnetic pulse welding, and transforms the high-dimensional magnetic field into the projected coordinates of low-dimensional space, which greatly reduces the calculation cost. At the same time, it can also play a certain role in noise reduction and filtering of magnetic induction intensity curve during the dimensionality reduction process.

[0039] 2. The rapid magnetic field calculation method for electromagnetic pulse welding disclosed in this invention constructs an efficient surrogate model between circuit parameters, structural geometric parameters, and the magnetic field. This surrogate model enables rapid calculation of the spatial magnetic field distribution of the magnet collector. Replacing the finite element model with a surrogate model solves the problems of insufficient accuracy in analytical methods and high computational complexity in numerical methods currently used for electromagnetic field analysis, while also achieving higher accuracy.

[0040] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0041] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0042] Figure 1 This is a flowchart of the rapid magnetic field calculation method for electromagnetic pulse welding according to the present invention;

[0043] Figure 2 This is a circuit structure diagram of the electromagnetic pulse welding principle in an embodiment of the present invention;

[0044] Figure 3This is a diagram illustrating the coupling structure of the magnet and coil in the electromagnetic pulse welding principle of this invention.

[0045] Figure 4 This is a training sample point map in an embodiment of the present invention;

[0046] Figure 5 This is a comparison chart of training values ​​and real values ​​in an embodiment of the present invention;

[0047] Figure 6 To construct an RBF model diagram for three training samples in this embodiment of the invention, Figure 6 (a) is the diagram of the first principal component RBF model; Figure 6 (b) is the RBF model diagram of the second principal component; Figure 6 (c) is the diagram of the third principal component RBF model;

[0048] Figure 7 This is a predicted sample point map in an embodiment of the present invention;

[0049] Figure 8 This is a comparison chart of predicted and actual values ​​in an embodiment of the present invention. Detailed Implementation

[0050] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0051] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0052] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0053] like Figure 1 The flowchart shows a method for rapid calculation of magnetic field for electromagnetic pulse welding. This method uses circuit parameters and structural geometric parameters as input variables and the distribution of the magnetic field in the inner ring of the magnet collector as the output.

[0054] Optimal Latin Hypercube Sampling (OHLS) is used in the input parameter space to calculate the magnetic field distribution at each sample point using a finite element model. Principal Components Analysis (PCA) is employed to reduce the dimensionality of the magnetic field calculation results, obtaining eigenvalues ​​and eigenvectors. Radial Basis Functions (RBF) are used to construct the mapping relationship between the input parameters and eigenvalues, ultimately yielding a computational model between the input parameters and the magnetic field.

[0055] The main function of PCA dimensionality reduction is to reduce the dimensionality of the initial samples, reproject these redundant data into mutually orthogonal coordinate systems, sort them according to the size of their contribution values ​​in the new coordinate system, and select the top few features to replace the original high-dimensional data while ensuring data accuracy, generating new low-dimensional samples. The new samples are then used as input to the training model of the RBF neural network to construct the RBF model.

[0056] Specifically, the following steps are included:

[0057] S1, Training Sample Sampling

[0058] In the input variable space consisting of circuit parameters and structural geometric parameters, m sample points are extracted using the optimal Latin hypercube method, denoted as X. m×q , where q represents the number of circuit parameters and structural geometric parameters;

[0059] S2, Call the finite element model

[0060] The finite element model of the electromagnetic pulse welding system is expressed as G(·), and the electromagnetic pulse welding finite element model is called once at each sample point to obtain the spatial distribution of the magnetic field strength of the magnetic concentrator, which is respectively denoted as M=G(X i ),i=1,2,…,m;

[0061] The welding process is a transient time-varying process, and the magnetic field M is also a quantity that changes with time. For the convenience of description, a point P( at a position 1mm away from the inner ring surface of the magnetic concentrator is selected Figure 3 marked position) whose z-direction magnetic induction intensity is taken as the magnetic field M;

[0062] S3. Constructing the RBF proxy model

[0063] At each sample point X i , a magnetic induction intensity curve with respect to time can be obtained. A time period [0,t] is selected and discretized into d time instants, so that an m×d magnetic induction intensity matrix can be obtained, which is denoted as

[0064]

[0065] Centralizing the matrix B

[0066]

[0067] Calculating the covariance matrix of the centralized matrix B *

[0068] Performing eigenvalue decomposition on the covariance matrix C, arranging the eigenvalues in descending order as λ1,λ2,…,λ d , and the corresponding eigenvectors

[0069] The contribution rate of the i-th principal component is

[0070] The cumulative contribution rate of the first k principal components is

[0071] The cumulative contribution rate is selected and determined according to the actual situation to obtain the first k (k<<d) principal components, and the projection coordinates of the original d-dimensional magnetic induction intensity data B in the k-dimensional coordinate system are

[0072]

[0073]

[0074] The corresponding eigenvectors Thus, the magnetic induction intensity B is equivalently represented in the low-dimensional space as

[0075] It can be seen that the input variable X​m×q The mapping relationship with magnetic induction intensity B can be transformed into the input variable X. m×q and projected coordinates α m×k The mapping relationship between them yields k sets of interpolation nodes.

[0076] S4, Magnetic Field Prediction

[0077] The input variable X is constructed based on k sets of interpolation nodes. m×q and projection coefficient α i RBF proxy model between

[0078]

[0079] In the formula, ω i Represents the interpolation weights, φ represents the radial basis function kernel, and ||XX i || represents the distance from the predicted point X to the sample point X. i The Euclidean distance between them. Commonly used radial basis function kernels include the Gaussian kernel, cubic kernel, and polynomial kernel, etc. Input variable X m×q The mapping relationship with magnetic induction intensity B is expressed as follows:

[0080]

[0081] Input variable X m×q The time-varying curve of magnetic induction intensity B is represented as {t,B(X)}.

[0082] Example

[0083] The circuit structure in the principle of electromagnetic pulse welding is as follows: Figure 2 As shown, during the charging stage: when switch S is closed, power supply U charges the capacitor; after charging is complete, switch S is opened, and the capacitor capacity is 140 microfarads. During the discharging stage: the TVS switch is turned on, and the capacitor discharges. The capacitor, line inductance L = 1.6 microhenries, line resistance r = 26 milliohms, and welding coil constitute an RLC oscillating circuit, generating an oscillating current in the welding coil. The coupling structure of the magnet collector and the coil is as follows: Figure 3 As shown in the figure, the figure is an axisymmetric geometric model. Under the action of high-frequency current in the welding coil, the magnetizer induces a high-frequency magnetic field, providing a strong magnetic field condition for the welding workpiece.

[0084] The feasibility of this method is verified below using an engineering example:

[0085] use Figure 2 Circuit structure and Figure 3An axisymmetric geometric model of a magnetizer coil is constructed, using the charging voltage U and the number of turns N as input variables. The voltage affects the amplitude of the coil current, and the number of turns affects the coil inductance; both together influence the magnitude and frequency of the magnetic field. 30 sample points are sampled from the input variable space using the optimal Latin hypercube. Figure 4 As shown, call Figure 3 The finite element model yielded 30 training curve samples of the z-direction magnetic induction intensity at point P. Using the method presented in this paper, an RBF model with 3 training samples was constructed as follows: Figure 6 As shown, Figure 6 (a) is the diagram of the first principal component RBF model; Figure 6 (b) is the RBF model diagram of the second principal component; Figure 6 (c) is the diagram of the third principal component RBF model; the comparison diagram of training values ​​and true values ​​is shown below. Figure 5 As shown, the training values ​​and the true values ​​are basically consistent when using this fast magnetic field calculation method.

[0086] To verify the accuracy of the surrogate model, 20 sample points were selected for testing. Figure 7 For the predicted sample points, the actual values ​​of the finite element response and the predicted values ​​of the surrogate model response are compared at 20 sample points. Figure 8 As shown, the predicted value and the actual value are basically consistent when using this fast magnetic field calculation method. Therefore, it can be seen that this calculation method can reduce the amount of calculation while also achieving high calculation accuracy.

[0087] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for rapid calculation of magnetic field for electromagnetic pulse welding, characterized in that, Includes the following steps: S1, Training Sample Sampling Optimal Latin hypercube decimation in the input variable space comprised of circuit parameters and structural geometry parameters. m There are 1 sample points, denoted as _ . X m×q ,in q Indicates the number of circuit parameters and structural geometric parameters; S2, Call the finite element model The finite element model of the electromagnetic pulse welding system is represented as follows: G ( At each sample point, the electromagnetic pulse welding finite element model is called once to obtain the spatial distribution of the magnetic field strength of the magnet collector, denoted as follows: ; S3. Construct the RBF proxy model Each sample point X i A magnetic flux density curve with respect to time is obtained, taking a time interval [0, ... t Discretized into d At that moment, I got a m × d The magnetic flux density matrix is ​​denoted as matrix B Centralization Calculate the centering matrix B covariance matrix For covariance matrix C Perform eigenvalue decomposition and arrange the eigenvalues ​​in descending order: λ1, λ2, ... …, λ d The corresponding feature vector φ 1, φ 2, …,φ d No. i The contribution rate of each principal component is forward k The cumulative contribution rate of each principal component is Based on the actual situation, select and determine the cumulative contribution rate to obtain the top ranking. k ( k << d ) principal components, original d Magnetic induction intensity data B exist k The projected coordinates in the 3D coordinate system are corresponding feature vector Therefore, magnetic induction intensity B In low-dimensional spaces, the equivalent representation is: ; Therefore, we can know Input variables X m×q With magnetic induction intensity B The mapping relationship is transformed into input variables. X m×q and projected coordinates α m×k The mapping relationship between them is obtained. k Group interpolation nodes Principal component analysis was used to reduce the dimensionality of the magnetic field calculation results, obtain eigenvalues ​​and eigenvectors, and radial basis functions were used to construct the mapping relationship between input parameters and eigenvalues. S4, Magnetic Field Prediction according to k The group interpolation nodes construct the input variables respectively. X m×q and projection coefficient α i RBF proxy model between In the formula, ω i Indicates the interpolation weight value. Represents the radial basis kernel function. Indicates the prediction point X to sample point X i The Euclidean distance between them; Input variables X m×q With magnetic induction intensity B The mapping relationship is represented as Input variables X m×q With magnetic induction intensity B The time-varying curve is represented as .

2. The method for rapid calculation of magnetic field for electromagnetic pulse welding as described in claim 1, characterized in that, In step S3, PCA dimensionality reduction reduces the dimensionality of the initial samples by reprojecting these redundant data into mutually orthogonal coordinate systems. The data is sorted according to the contribution value in the new coordinate system. While ensuring data accuracy, the top few features are selected to replace the original high-dimensional data, generating new low-dimensional samples. These new samples are then used as inputs to the training model of the RBF neural network to construct the RBF model.

3. The method for rapid calculation of magnetic field for electromagnetic pulse welding as described in claim 1, characterized in that, Radial basis kernel function in step S4 It is one of the Gaussian kernel function, cubic kernel function, and polynomial kernel function.

4. The method for rapid calculation of magnetic field for electromagnetic pulse welding as described in claim 1, characterized in that, Magnetic induction intensity in steps S3 and S4 B It can be in the form of a curve, a two-dimensional cloud map, or a three-dimensional cloud map.

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