Formula optimization method of high magnetic energy product high temperature resistant neodymium iron boron based composite plastic magnetic material

Abstract

This invention relates to the field of magnetic material formulation optimization technology, specifically a method for optimizing the formulation of high-energy-product, high-temperature-resistant NdFeB-based composite plastic magnetic materials. The method includes: collecting historical raw material ratio data and corresponding high-temperature magnetic performance test results for NdFeB magnetic powder, various heat-resistant modifiers, different molding aids, and binders; forming an original formulation-performance dataset; and generating formulation feature-performance vector pairs through normalization and structured coding. By processing the vectors through multi-dimensional spatial projection and principal component decomposition, a quantitative mapping model from formulation features to comprehensive performance is constructed based on a relational mapping network. Candidate formulations are obtained through global optimization in the formulation space, and target formulations are then screened through high-temperature thermodynamic stability simulation and microscopic magnetic structure calculation. This method can accurately quantify the correlation between formulation and high-temperature magnetic performance, improve formulation optimization efficiency, ensure the thermal stability and microscopic magnetic structure integrity of the optimized material, and adapt to the magnetic performance requirements under high-temperature conditions.

Description

Technical Field

[0001] This invention relates to the field of magnetic material formulation optimization technology, and in particular to a method for optimizing the formulation of high-energy-product, high-temperature-resistant neodymium iron boron-based composite plastic magnetic materials. Background Technology

[0002] Current formulation optimization of NdFeB-based composite magnetic materials largely relies on manual trial mixing. This involves collecting raw material ratio data for NdFeB magnetic powder, heat-resistant modifiers, molding aids, and binders, and then empirically adjusting the formulation based on single high-temperature magnetic performance test results. The correlation between formulation components and magnetic properties is established only through simple linear fitting, without standardized and structured processing of formulation and performance data. This type of formulation optimization can only adjust single performance indicators such as energy product and coercivity temperature coefficient, failing to integrate multi-dimensional high-temperature magnetic performance parameters into a unified evaluation standard. Furthermore, the proportional characteristics of formulation components cannot be systematically represented spatially, making it difficult to accurately characterize the nonlinear relationship between the formulation and overall high-temperature magnetic properties.

[0003] The current approach to formula selection, relying solely on experimental trial and error, fails to efficiently optimize within the complete formula space. Candidate formulas are screened only through macroscopic magnetic property testing, without simulation analysis of thermodynamic stability under high-temperature conditions or computational verification of the material's microscopic magnetic structure. This easily leads to problems such as excessively rapid magnetic property decay, substandard thermal stability, and defects in the microscopic magnetic structure at high temperatures. It is necessary to transform formula characteristics into a multidimensional spatial representation, extract comprehensive evaluation indicators for multidimensional performance, and construct a precise quantitative mapping model. Furthermore, after formula optimization, high-temperature thermodynamic simulation and microscopic magnetic structure calculations should be combined to complete formula selection, thereby improving the shortcomings of existing formula optimization methods. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by proposing a method for optimizing the formulation of high-energy-product, high-temperature-resistant NdFeB-based composite magnetic materials.

[0005] To achieve the above objectives, the present invention employs the following technical solution: a method for optimizing the formulation of high-energy-product, high-temperature-resistant neodymium iron boron-based composite plastic magnetic materials, comprising:

[0006] Historical raw material ratio data and corresponding high-temperature magnetic performance test results for neodymium iron boron magnetic powder, various heat-resistant modifiers, different molding aids and binders were collected to form an original formula-performance dataset;

[0007] The original formula-performance dataset is normalized and structured, and the component ratios of various raw materials are transformed into formula feature vectors. The magnetic energy product, coercivity temperature coefficient, and high-temperature magnetic performance test results corresponding to the magnetic performance decay rate at the highest working temperature are transformed into multi-dimensional performance vectors, and a set of formula feature-performance vector pairs is constructed.

[0008] Perform multidimensional spatial projection on the formula feature vector to generate an initial formula spatial representation, and perform principal component decomposition on the multidimensional performance vector to extract comprehensive performance evaluation indicators.

[0009] The initial formula space representation and the comprehensive performance evaluation index are input into a mapping network for iterative learning to establish a quantitative mapping relationship model from formula features to comprehensive performance.

[0010] Based on the quantitative mapping relationship model, global optimization is initiated in the formula space to generate a candidate formula list;

[0011] For each candidate formulation in the candidate formulation list, high-temperature thermodynamic stability simulation and micro-magnetic structure calculation are performed to screen out the target optimized formulation that meets the preset thermal stability threshold and micro-structure integrity.

[0012] As a further aspect of the present invention, multi-dimensional spatial projection is performed on the formula feature vector to generate an initial formula space representation, including:

[0013] The proportions of neodymium iron boron magnetic powder, various heat-resistant modifiers, and molding aids and binders are extracted from the formula feature vector as core components.

[0014] The core component is input into a preset multidimensional space transformation matrix, which maps the original proportional component to a set of mutually orthogonal basis vectors.

[0015] Calculate the projection coefficients in each basis vector direction after mapping, and combine all projection coefficients into a high-dimensional coordinate to form the initial formulation space representation that characterizes the intrinsic structure of the formulation components.

[0016] As a further aspect of the present invention, principal component decomposition is performed on the multidimensional performance vector to extract comprehensive performance evaluation indicators, including:

[0017] Calculate the covariance matrix among the various performance indicators in the multidimensional performance vector, including the magnetic energy product, coercivity temperature coefficient, and magnetic performance attenuation rate corresponding to the highest operating temperature.

[0018] The covariance matrix is ​​solved by eigenvalue and eigenvector calculation to obtain multiple principal component directions and their corresponding variance contributions;

[0019] Several principal component directions whose cumulative variance contribution exceeds a preset threshold are selected. The eigenvectors corresponding to the principal component directions are used as weights to linearly combine the original multidimensional performance vectors, generating a scalar value that characterizes the comprehensive high-temperature magnetic properties of the material, which serves as the comprehensive performance evaluation index.

[0020] As a further aspect of the present invention, the initial formula space representation and the comprehensive performance evaluation index input relationship mapping network are iteratively learned to establish a quantitative mapping relationship model from formula features to comprehensive performance, including:

[0021] The initial formula space representation is used as the input layer data of the relational mapping network, and the corresponding comprehensive performance evaluation index is used as the expected output target.

[0022] The relation mapping network is configured to contain multiple hidden layers, each containing a non-linear activation unit;

[0023] Using a forward propagation method, starting from the input layer, the feature representation of the initial formula space representation after nonlinear transformation of each hidden layer is calculated layer by layer until the output layer obtains a predicted comprehensive performance evaluation value.

[0024] Calculate the difference between the predicted comprehensive performance evaluation value and the expected output target, and adjust the connection weight parameters of each hidden layer in the relation mapping network according to the difference using the gradient backpropagation algorithm;

[0025] Repeat the forward propagation, difference calculation, and parameter adjustment process until the average difference between the network's predicted comprehensive performance evaluation value and the expected output target is less than a set threshold. At this point, the network's weight parameters are fixed, forming the quantitative mapping relationship model.

[0026] As a further aspect of the present invention, based on the quantitative mapping relationship model, a global optimization is initiated in the formulation space to generate a candidate formulation list, including:

[0027] Define a formulation search space that includes the upper and lower limits of the proportions of all components, including neodymium iron boron magnetic powder, various heat-resistant modifiers, molding aids, and binders;

[0028] Within the recipe search space, a large number of random recipe points are generated in a discrete or continuous sampling manner;

[0029] Each random recipe point is processed in the same way as the initial recipe space representation is constructed to generate a corresponding recipe space representation, which is then input into the established quantitative mapping relationship model.

[0030] The predicted comprehensive performance evaluation value corresponding to each random formula point is calculated using the quantitative mapping relationship model.

[0031] According to the predicted comprehensive performance evaluation value from high to low, all random formulation points are sorted, and the formulation points with the highest ranking and the sum of the component proportions being one are selected to form the candidate formulation list.

[0032] As a further aspect of the present invention, high-temperature thermodynamic stability simulation is performed on each candidate formulation in the candidate formulation list, including:

[0033] For each candidate formulation in the candidate formulation list, the molecular dynamics simulation system is invoked to set the initial atomic model according to the proportions of each component in the candidate formulation;

[0034] In the molecular dynamics simulation system, a preset high-temperature boundary condition is applied to the initial atomic model to simulate the atomic motion process of the material under the target high-temperature working environment;

[0035] During the simulation process, the mean square displacement of the atomic structure, energy fluctuations, and the breaking and formation of key chemical bonds within the material are monitored.

[0036] According to the preset thermal stability judgment criteria, if the mean square displacement of the atomic structure exceeds the critical value, or the energy fluctuation cannot be stabilized for a long time, or a large number of unexpected chemical bonds break, then the candidate formulation is determined to not meet the thermal stability requirements; otherwise, it meets the requirements.

[0037] As a further aspect of the present invention, microscopic magnetic structure calculations are performed on candidate formulations that meet thermal stability requirements to screen out target optimized formulations that meet preset microscopic structure integrity requirements, including:

[0038] To establish a microscopic magnetic domain model for candidate formulations that meet thermal stability requirements, the magnetocrystalline anisotropy parameters, exchange coupling constant, and initial magnetization distribution are set in the microscopic magnetic domain model.

[0039] A thermal perturbation field corresponding to a high-temperature environment is applied to the microscopic magnetic domain model, and the evolution of the magnetization state over time is calculated.

[0040] The average size of the domain structure, the clarity of the domain walls, and the directional consistency parameters of the overall magnetization intensity are extracted from the evolving magnetization state.

[0041] The average size, domain wall clarity, and orientation consistency parameters are compared with a preset microstructure integrity threshold. If all parameters are within the excellent range defined by the microstructure integrity threshold, the candidate formulation is determined to meet the microstructure integrity requirements and is included in the final screening results. From all candidate formulations that meet the thermal stability requirements and the microstructure integrity requirements, the formulation with the highest predicted comprehensive performance evaluation value is selected as the target optimized formulation.

[0042] As a further aspect of the present invention, the extraction of the average size of the magnetic domain structure, the clarity of the domain walls, and the directional consistency parameters of the overall magnetization intensity from the evolved magnetization state includes:

[0043] In the snapshot of the magnetization state during the stable evolution phase, a continuous region with basically consistent magnetization direction is identified, and this region is defined as a magnetic domain.

[0044] The area distribution of all identified magnetic domains is statistically analyzed using image processing techniques, and the average area of ​​all magnetic domains is calculated as the average size of the magnetic domain structure.

[0045] Magnetization direction gradient analysis is performed on the boundary region of adjacent magnetic domains to calculate the degree of change in magnetization direction when crossing the boundary, and the average gradient value is used as the clarity of the domain wall.

[0046] The average value of the cosine of the angle between the magnetization direction of all computational units in the computational model and the preset reference direction is used as the directional consistency parameter of the overall magnetization intensity.

[0047] As a further aspect of the present invention, the original formula-performance dataset is normalized and structured, and the component ratios of various raw materials are transformed into formula feature vectors, including:

[0048] The component proportion matrix in purely numerical form is extracted from the original formulation-performance dataset;

[0049] For each column in the component ratio matrix, i.e. the ratio data of each raw material, a maximum and minimum value normalization process is performed to map the ratio value to the interval between zero and one.

[0050] All the normalized raw material ratio values ​​are arranged in a fixed order to form a one-dimensional array, which serves as the formula feature vector describing a specific formula.

[0051] As a further aspect of the present invention, the covariance matrix among the performance indicators of magnetic energy product, coercivity temperature coefficient, and magnetic performance decay rate corresponding to the highest operating temperature in the multidimensional performance vector is calculated, including:

[0052] Extract the multidimensional performance vector of all samples from the set of formula feature-performance vector pairs, wherein each vector contains specific values ​​of magnetic energy product, coercivity temperature coefficient and magnetic performance decay rate corresponding to the highest operating temperature;

[0053] Calculate the mean values ​​of the magnetic energy product, the coercivity temperature coefficient, and the magnetic performance attenuation rate corresponding to the highest operating temperature, respectively.

[0054] For any two performance indicators among magnetic energy product, coercivity temperature coefficient and magnetic energy decay rate, calculate the deviation of the specific value of one indicator in multiple samples from its own mean, and at the same time calculate the deviation of the specific value of the other indicator in the same sample from its own mean.

[0055] Multiply the corresponding deviations of each pair of performance indicators across all samples, sum the products of all samples, and then divide by the total number of samples minus one to obtain the covariance between the two performance indicators.

[0056] The three performance indicators, namely magnetic energy product, coercivity temperature coefficient, and magnetic performance decay rate, are calculated in pairs to obtain a 3x3 symmetric matrix. Each element in the matrix is ​​the covariance between the corresponding pair of performance indicators. This symmetric matrix is ​​the covariance matrix.

[0057] Compared with the prior art, the advantages and positive effects of the present invention are as follows:

[0058] Normalization and structured coding are performed on the original formula-performance dataset to transform the proportions of various raw material components into formula feature vectors and the test results of multiple high-temperature magnetic properties into multidimensional performance vectors. Multidimensional spatial projection is performed on the formula feature vectors to generate an initial formula spatial representation, and principal component decomposition is performed on the multidimensional performance vectors to extract comprehensive performance evaluation indicators. The initial formula spatial representation and comprehensive performance evaluation indicators are input into a relational mapping network to complete iterative learning. This allows the characteristics of the formula components to be presented in a standardized spatial form, and allows the dispersed high-temperature magnetic property parameters to form a unified evaluation dimension. The nonlinear correlation between formula features and comprehensive high-temperature magnetic properties can be fully captured, and the relationship between formula and performance can be accurately quantitatively correlated through model learning. This avoids the evaluation bias caused by comparing a single performance indicator and weakens the correlation judgment bias caused by human experience analysis.

[0059] Based on a quantitative mapping relationship model, a global optimization is performed in the formulation space to generate a candidate formulation list. For each candidate formulation, high-temperature thermodynamic stability simulation and micro-magnetic structure calculation are performed one by one. The screening is completed according to the preset thermal stability threshold and micro-structure integrity conditions. This allows the formulation optimization to cover the variation range of all formulation components, avoiding the optimization process being limited to local formulation combinations. The high-temperature adaptability of candidate formulations can be pre-judged through thermodynamic simulation, and the integrity of the material's micro-magnetic structure can be intuitively presented through calculation. The dual screening of thermal stability and micro-structure can eliminate formulation defects that cannot be identified by macroscopic performance testing, so that the final determined formulation can meet the magnetic structure stability requirements under high-temperature application scenarios. Attached Figure Description

[0060] Figure 1This is a state diagram of the formulation optimization method for high-energy-product, high-temperature-resistant NdFeB-based composite plastic magnetic materials according to the present invention;

[0061] Figure 2 A flowchart for generating the initial formulation space representation;

[0062] Figure 3 A flowchart for extracting comprehensive performance evaluation indicators. Detailed Implementation

[0063] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0064] In the description of this invention, it should be understood that the terms "length," "width," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings and are only for the convenience of describing the 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, and therefore should not be construed as a limitation of the invention. Furthermore, in the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0065] See Figure 1 This invention provides a method for optimizing the formulation of high-energy-product, high-temperature-resistant NdFeB-based composite plastic magnetic materials. The specific method includes:

[0066] Historical raw material ratio data and corresponding high-temperature magnetic performance test results for NdFeB magnetic powder, various heat-resistant modifiers, different molding aids, and binders were collected to form an original formula-performance dataset. This dataset underwent normalization and structured encoding, transforming the component ratios of various raw materials into formula feature vectors and converting high-temperature magnetic performance test results such as magnetic energy product, coercivity temperature coefficient, and magnetic performance decay rate at the highest operating temperature into multidimensional performance vectors, thus constructing a set of formula feature-performance vector pairs. Multidimensional spatial projection was performed on the formula feature vectors to generate an initial formula space representation reflecting the internal structure of the formula components. Simultaneously, principal component decomposition was performed on the multidimensional performance vectors to extract a scalar-form comprehensive performance evaluation index. The initial formula space representation and the comprehensive performance evaluation index were input into a relational mapping network for iterative learning to establish a quantitative mapping relationship model from formula features to comprehensive performance. Based on the established quantitative mapping relationship model, global optimization was initiated in the formula space to generate a list of candidate formulas with excellent predicted performance. For each candidate formulation in the candidate formulation list, high-temperature thermodynamic stability simulation and micro-magnetic structure calculation are performed to screen out the target optimized formulation that simultaneously meets the preset thermal stability threshold and micro-structure integrity requirements.

[0067] In one embodiment of the present invention, during the construction of the formula feature-performance vector pair set, the original formula-performance dataset is normalized and structured. A component proportion matrix in pure numerical form is extracted from the original formula-performance dataset. For each column of this matrix, i.e., the proportion data of each raw material, maximum and minimum value normalization is performed, mapping all proportion values ​​to the interval between zero and one. All the normalized raw material proportion values ​​are arranged in a predefined fixed order to form a one-dimensional array. This one-dimensional array serves as the formula feature vector describing a specific formula. For further analysis of the formula structure, see [reference needed]. Figure 2 The proportions of NdFeB magnetic powder, various heat-resistant modifiers, and molding aids and binders are extracted as core components from the feature vector of the formulation. These core components are then input into a pre-defined multidimensional space transformation matrix, which maps the original proportional components onto a set of mutually orthogonal basis vectors. The projection coefficients in each of the mapped basis vector directions are calculated, and all projection coefficients are combined into a high-dimensional coordinate system. This high-dimensional coordinate system forms the initial formulation space representation characterizing the intrinsic structure of the formulation components.

[0068] In practice, normalization and structured coding are performed to construct the formula feature vector. Multidimensional spatial projection is then applied to the formula feature vector to generate an initial formula spatial representation. This can begin with an original formula-performance dataset containing historical raw material ratio data. In practice, this dataset is stored in tabular form, with each row representing a historical formula sample and each column representing the component ratio of a raw material or a high-temperature magnetic property test result. A purely numerical component ratio matrix is ​​extracted from the original formula-performance dataset, where rows correspond to the number of samples and columns correspond to the number of raw material types. Maximum and minimum value normalization is performed on each column of data in the component ratio matrix. For any column of raw material ratio data, the maximum and minimum values ​​in that column are identified. For each original ratio value in that column, normalization is applied to map it to the interval between zero and one. After normalization, all raw material proportions are arranged in a predefined, fixed order: NdFeB magnetic powder proportion, first heat-resistant modifier proportion, second heat-resistant modifier proportion, molding aid proportion, and binder proportion. This arrangement forms a one-dimensional array, which serves as the formulation feature vector describing the corresponding sample. It can be understood that the dimension of the formulation feature vector is strictly equal to the number of raw material types, and the order of elements in the formulation feature vector remains consistent across all sample processing.

[0069] In some embodiments, a multidimensional spatial projection is performed on the formulation feature vector to generate an initial formulation spatial representation. Specifically, the proportions of NdFeB magnetic powder, various heat-resistant modifiers, and the molding aid and binder system are extracted from the formulation feature vector as core components, forming a low-dimensional vector. The core component vector is input to a preset multidimensional spatial transformation matrix. The dimension of the multidimensional spatial transformation matrix is ​​predefined based on the length of the core component vector and the dimension of the target projection space. The multidimensional spatial transformation matrix maps the original core component vector to a set of mutually orthogonal basis vectors. The projection coefficients in the direction of each basis vector after mapping are calculated. These projection coefficients are obtained by the dot product operation between the core component vector and each basis vector. All projection coefficients are combined to form a high-dimensional coordinate. The initial formulation spatial representation is fully defined by this high-dimensional coordinate, and the dimension of the initial formulation spatial representation is equal to the number of mutually orthogonal basis vectors. The multidimensional spatial transformation matrix is ​​applied to the core component vector. Obtain the projection coefficient vector The process is described by the following linear transformation:

[0070]

[0071] Where: symbol This represents the core component vector consisting of the proportions of NdFeB magnetic powder, various heat-resistant modifiers, and the molding aids and binder system. The symbol is... Represents the preset multidimensional space transformation matrix, symbol This represents the calculated projection coefficient vector. This is the initial formula space representation. It can be understood that this is a multidimensional spatial transformation matrix. The row vectors are composed of a set of pre-selected mutually orthogonal unit basis vectors. Optionally, the multidimensional space transformation matrix can be pre-trained based on statistical analysis of historical formulation data to ensure that the projected space can effectively distinguish different formulation characteristics. In some embodiments, the core components can be selected based on the chemical properties and functions of the raw materials, rather than being strictly limited to extraction by position index from the formulation feature vectors. Optionally, mutually orthogonal basis vectors can be obtained by performing principal component analysis on a large number of historical formulation feature vectors, thereby ensuring that the projection direction has maximum variance representativeness. In a specific implementation, through the above process, the formulation feature vector of each historical formulation sample is transformed into a point in a higher-dimensional or more abstract space, i.e., the initial formulation space representation, which is used as the input to the subsequent relational mapping network.

[0072] In one embodiment of the present invention, principal component decomposition is performed on the multidimensional performance vector during the process of refining comprehensive performance evaluation indicators. (See also...) Figure 3 This requires calculating the covariance matrix between the performance indices in the multidimensional performance vector. Multidimensional performance vectors are extracted from the formula feature-performance vector pair set for all samples. Each vector contains the magnetic energy product value, the coercivity temperature coefficient value, and the magnetic performance decay rate corresponding to the highest operating temperature. The mean values ​​of the magnetic energy product, coercivity temperature coefficient, and magnetic performance decay rate are calculated separately. For any two of the three performance indices, the deviation of one index's value across all samples from its own mean is calculated, and the deviation of the other index's value from its own mean in the same samples is also calculated. The corresponding deviations of each pair of performance indices across all samples are multiplied, and the sum of the products is divided by the total number of samples minus one, thus obtaining the covariance between the two performance indices. This calculation process is repeated pairwise for each of the three performance indices, resulting in a 3x3 symmetric matrix. Each element in the matrix represents the covariance between a corresponding pair of performance indices. This symmetric matrix is ​​the required covariance matrix. The covariance matrix is ​​solved by eigenvalues ​​and eigenvectors to obtain multiple principal component directions and their corresponding variance contributions. Several principal component directions whose cumulative variance contributions exceed a preset threshold are selected. The eigenvectors corresponding to these principal component directions are used as weights to linearly combine the original multidimensional performance vectors, generating a scalar value that characterizes the material's comprehensive high-temperature magnetic properties. This scalar value is the comprehensive performance evaluation index.

[0073] In practice, principal component decomposition is performed on the multidimensional performance vectors to extract comprehensive performance evaluation indicators. The covariance matrix among the performance indicators—magnetic energy product, coercivity temperature coefficient, and magnetic performance decay rate at the highest operating temperature—is calculated. Multidimensional performance vectors for all samples are extracted from the formula feature-performance vector pair set. Each multidimensional performance vector is a row vector containing three elements: the magnetic energy product value, the coercivity temperature coefficient value, and the magnetic performance decay rate at the highest operating temperature value. Assuming the formula feature-performance vector pair set contains N samples, N multidimensional performance vectors will be extracted. The mean values ​​of the magnetic energy product, coercivity temperature coefficient, and magnetic performance decay rate at the highest operating temperature are calculated for each of the N samples. For any two of the three performance indicators—magnetic energy product, coercivity temperature coefficient, and magnetic performance decay rate at the highest operating temperature—calculate the deviation of one performance indicator's value in N samples from its mean. Simultaneously, calculate the deviation of the other performance indicator's value in the same N samples from its mean. Multiply the corresponding deviations of each pair of performance indicators in each sample, sum the products of the N samples, and divide by N-1 to obtain the covariance between the two performance indicators. Repeat the above calculation process pairwise for each of the three performance indicators—magnetic energy product, coercivity temperature coefficient, and magnetic performance decay rate at the highest operating temperature—to obtain a 3x3 symmetric matrix. It can be understood that the element value in the i-th row and j-th column of the symmetric matrix is ​​equal to the element value in the j-th row and i-th column, and the elements on the diagonal are the variances of each performance indicator. This symmetric matrix is ​​the required covariance matrix. Calculate the covariance matrix. The Middle Line 1 Column elements The process can be described as follows:

[0074]

[0075] Where: symbol Represents the covariance matrix The Middle Line 1 Column elements, symbols Represents the total number of samples, symbol Indicates the first The sample at the th The values ​​and symbols for each performance indicator. Indicates the first The mean of a performance metric across all samples, with sign... Indicates the first The sample at the th The values ​​and symbols for each performance indicator. Indicates the first The mean of each performance metric across all samples.

[0076] In some embodiments, eigenvalues ​​and eigenvectors are solved for the covariance matrix. For a 3x3 covariance matrix, eigenvalues ​​and eigenvectors are obtained, resulting in three eigenvalues ​​and their corresponding eigenvectors, each being a three-dimensional column vector. The magnitude of the eigenvalue represents the magnitude of the data variance along the corresponding eigenvector direction. Several principal component directions whose cumulative variance contribution exceeds a preset threshold are selected. The proportion of each eigenvalue to the sum of all eigenvalues ​​is calculated as the variance contribution. The eigenvalues ​​are sorted from largest to smallest, and their corresponding variance contributions are accumulated sequentially. When the cumulative contribution first exceeds a preset threshold, the eigenvectors corresponding to all eigenvalues ​​up to this point are selected as principal component directions. Using the eigenvectors corresponding to the selected principal component directions as weights, the original multidimensional performance vectors are linearly combined to generate a scalar value characterizing the comprehensive high-temperature magnetic properties of the material. This scalar value is the comprehensive performance evaluation index. The specific linear combination method involves centering the original multidimensional performance vector, performing a dot product with the eigenvectors of each selected principal component direction to obtain a projection scalar, and then weighting and summing these projection scalars using the variance contribution of each principal component direction as the weight. The final result is the comprehensive performance evaluation index. Optionally, the preset threshold can be set to 85% or 90%. In some embodiments, if only one principal component direction with the largest variance contribution is selected, the comprehensive performance evaluation index is the projection value of the original multidimensional performance vector in that principal component direction. Optionally, the comprehensive performance evaluation index can also be calculated without weighting, by directly adding the projection values ​​of multiple selected principal component directions.

[0077] In one embodiment of the present invention, a quantitative mapping relationship model from formulation features to overall performance is established. An initial formulation space representation and an overall performance evaluation index are input into a mapping network for iterative learning. The initial formulation space representation is used as the input layer data of the mapping network, and the corresponding overall performance evaluation index is used as the desired output target. The mapping network is configured to contain multiple hidden layers, each containing a nonlinear activation unit. Using a forward propagation method, starting from the input layer, the feature expression of the initial formulation space representation after nonlinear transformation through each hidden layer is calculated layer by layer until the output layer obtains a predicted overall performance evaluation value. The difference between the predicted overall performance evaluation value and the desired output target is calculated, and the connection weight parameters of each hidden layer in the mapping network are adjusted based on this difference using a gradient backpropagation algorithm. The forward propagation, difference calculation, and parameter adjustment process is repeated until the average difference between the network's predicted overall performance evaluation value and the desired output target is less than a set threshold. At this point, the network's weight parameters are fixed, forming a quantitative mapping relationship model. Based on the trained quantitative mapping relationship model, global optimization is initiated in the formulation space to generate a candidate formulation list. A formulation search space is defined, encompassing the upper and lower limits of the proportions of all components, including NdFeB magnetic powder, various heat-resistant modifiers, molding aids, and binders. Within this search space, a large number of random formulation points are generated using discrete or continuous sampling. Each random formulation point is processed using the same method as constructing the initial formulation space representation, generating a corresponding formulation space representation, which is then input into an established quantitative mapping model. The predicted comprehensive performance evaluation value corresponding to each random formulation point is calculated using the quantitative mapping model. All random formulation points are sorted from highest to lowest according to their predicted comprehensive performance evaluation values, and the top-ranked formulation points that satisfy the condition that the sum of the proportions of all components is one are selected to form a candidate formulation list.

[0078] In practical implementation, a quantitative mapping model from formulation features to comprehensive performance is established. The initial formulation space representation and the comprehensive performance evaluation index are input into the mapping network for iterative learning. The initial formulation space representation serves as the input layer data of the mapping network, and the corresponding comprehensive performance evaluation index serves as the expected output target. The mapping network is configured to contain multiple hidden layers, each containing a nonlinear activation unit. In practical implementation, the mapping network can have a structure of one input layer, three hidden layers, and one output layer. The number of nodes in the input layer is the same as the dimension of the initial formulation space representation. The output layer contains one node to output the predicted comprehensive performance evaluation value. Each hidden layer can contain 64, 32, or 16 nodes, and the nonlinear activation unit can use the ReLU function. Using a forward propagation method, starting from the input layer, the feature expression of the initial formulation space representation after nonlinear transformation of each hidden layer is calculated layer by layer until the output layer obtains a predicted comprehensive performance evaluation value. During the forward propagation process, the output of each layer is the product of the previous layer's output and the weight matrix, plus the bias vector, and then transformed by the nonlinear activation function. The difference between the predicted comprehensive performance evaluation value and the expected output target is calculated. This difference is quantified by a loss function, commonly the mean squared error function. Based on the difference, the connection weight parameters of each hidden layer in the relation mapping network are adjusted using the gradient backpropagation algorithm. The gradient backpropagation algorithm calculates the gradient of the loss function with respect to the weights of each layer in the network and updates the weight parameters in the reverse direction of the gradient according to the learning rate. This process of forward propagation, difference calculation, and parameter adjustment is repeated until the average difference between the network's predicted comprehensive performance evaluation value and the expected output target is less than a set threshold. At this point, the network's weight parameters are fixed, forming a quantitative mapping relationship model. The weight parameter update process can be described as follows:

[0079]

[0080] Where: symbol Indicates the updated weight parameters, symbol Indicates the weight parameters before the update, symbol Indicates the preset learning rate, symbol Represents the loss function In weight parameters The gradient at that point.

[0081] In some embodiments, based on a trained quantitative mapping relationship model, global optimization is initiated in the formulation space to generate a candidate formulation list. A formulation search space is defined, encompassing the upper and lower limits of the proportions of all components, including NdFeB magnetic powder, various heat-resistant modifiers, molding aids, and binders. The formulation search space is defined by the allowed mass percentage range for each raw material. For example, a formulation search space containing five raw materials is defined as shown in Table 1.

[0082] Table 1: Definition of Recipe Search Space

[0083]

[0084] Within the formulation search space, a large number of random formulation points are generated using discrete or continuous sampling. In practice, Latin hypercube sampling can be used to generate 10,000 random formulation points to ensure uniform coverage of the entire formulation search space. Each random formulation point is processed using the same method as the initial formulation space representation: first, normalization and structured encoding are performed to generate a formulation feature vector; then, multidimensional spatial projection is performed to generate the corresponding formulation space representation, which is then input into the established quantitative mapping relationship model. The predicted comprehensive performance evaluation value corresponding to each random formulation point is calculated using the quantitative mapping relationship model. All random formulation points are sorted from highest to lowest according to their predicted comprehensive performance evaluation values, and the top-ranked formulation points that satisfy the condition that the total component ratio is 100% are selected to form a candidate formulation list. The specific number of top-ranked selections can be set according to actual needs; for example, the top 100 formulation points in terms of predicted comprehensive performance evaluation values ​​can be selected for the candidate formulation list. Optionally, during sorting and filtering, an absolute threshold for the predicted comprehensive performance evaluation value can be set, selecting only formulation points exceeding this threshold. In some embodiments, for random formulation points where the sum of the component proportions is not 100%, normalization correction can be performed to make the sum 100% before prediction and sorting. Optionally, when generating random formulation points, constraints can be introduced so that the sum of the component proportions of the generated random formulation points is automatically 100%, thereby simplifying subsequent screening steps.

[0085] In one embodiment of the present invention, high-temperature thermodynamic stability simulation is performed on each candidate formulation in the candidate formulation list. For each candidate formulation in the candidate formulation list, a molecular dynamics simulation system is invoked to set an initial atomic model according to the proportions of each component in the candidate formulation. In the molecular dynamics simulation system, preset high-temperature boundary conditions are applied to the initial atomic model to simulate the atomic motion process of the material under the target high-temperature working environment. The mean square displacement, energy fluctuation, and the breaking and formation of key chemical bonds of the internal atomic structure of the material are monitored during the simulation. According to the preset thermal stability judgment criteria, if the mean square displacement of the atomic structure exceeds a critical value, or the energy fluctuation cannot stabilize for a long period of time, or a large number of unexpected chemical bond breaks occur, the candidate formulation is determined to not meet the thermal stability requirements; otherwise, it meets the requirements.

[0086] In practice, high-temperature thermodynamic stability simulations are performed on each candidate formulation in the candidate formulation list. For each candidate formulation, a molecular dynamics simulation system is invoked to execute the simulation. The molecular dynamics simulation system can utilize the appropriate modules from LAMMPS, GROMACS, or MaterialsStudio. In practice, an initial atomic model is set based on the proportions of each component in the candidate formulation. The initial atomic model is constructed based on the known crystal structure or molecular force field parameters of each component. According to the mass percentage or atomic percentage given in the candidate formulation, the initial positions of the atoms of each component are randomly or orderly assigned in the simulated supercell. In the molecular dynamics simulation system, preset high-temperature boundary conditions are applied to the initial atomic model. These preset high-temperature boundary conditions typically include the target temperature, pressure, simulation time step, total simulation time, and the statistical ensemble used. The target temperature is set to the material's expected maximum operating temperature or higher for accelerated testing. The atomic motion process of the material under the target high-temperature operating environment is simulated. The atomic motion process is iteratively updated by numerically solving Newton's equations of motion to determine the positions and velocities of all atoms. The simulation monitors the mean square displacement, energy fluctuations, and the breaking and formation of key chemical bonds within the material's internal atomic structure. The mean square displacement is obtained by calculating the average squared displacement of all atoms over a given simulation period. Energy fluctuations are assessed by monitoring the standard deviation of the system's total kinetic energy, total potential energy, or total energy. The breaking and formation of key chemical bonds are determined by statistically analyzing whether the distance between specific atomic pairs changes over time beyond a bond length threshold. According to a pre-defined thermal stability criterion, if the mean square displacement of the atomic structure exceeds a critical value, or if energy fluctuations fail to stabilize over a long period, or if a large number of unexpected chemical bond breaks occur, the candidate formulation is deemed not to meet thermal stability requirements; otherwise, it is deemed to meet them. It is understood that the critical value, the criteria for stable energy fluctuations, and the specific threshold for "a large number of unexpected chemical bond breaks" all need to be predefined based on the material system and application requirements. In some embodiments, the pre-defined high-temperature boundary conditions can be specifically set using a parameter table, see Table 2:

[0087] Table 2: Simulation parameters for high-temperature thermodynamic stability

[0088]

[0089] In practical implementation, the mean square displacement is calculated. The process can be described as follows:

[0090]

[0091] Where: symbol Indicates the time interval Mean square displacement within, sign Represents the total number of atoms in the simulated system, symbol Indicates the first Atoms in time Position vector at time, sign Indicates the first The position vector of each atom at the initial time (time 0), symbol This indicates the calculation of the Euclidean norm. It can be understood that the slope of the region where the mean square displacement increases linearly with time is related to the diffusion coefficient. Preset thermal stability criteria may include: in the later stages of the simulation, the slope of the mean square displacement-time curve should be below a critical slope value. In some embodiments, if energy fluctuations cannot be stabilized over a long period, this can be determined by calculating the standard deviation of the total potential energy of the system within a 100 ps time window after the simulation and determining whether this standard deviation consistently exceeds a set threshold. Optionally, key chemical bonds can be defined as neodymium-iron bonds, iron-boron bonds, or metal-oxygen bonds in specific heat-resistant modifiers. Optionally, the interatomic interaction potentials (force fields) used in the molecular dynamics simulations must be applicable to all involved constituent elements.

[0092] In one embodiment of the present invention, microscopic magnetic structure calculations are performed on candidate formulations that meet thermal stability requirements to screen out target optimized formulations that meet preset microscopic structural integrity requirements. A microscopic magnetic domain model is established for candidate formulations that meet thermal stability requirements, setting magnetocrystalline anisotropy parameters, exchange coupling constants, and initial magnetization distribution in the model. A thermal perturbation field corresponding to a high-temperature environment is applied to the microscopic magnetic domain model, and the evolution of the magnetization state over time is calculated. The average size of the magnetic domain structure, the clarity of the domain walls, and the directional consistency parameters of the overall magnetization intensity are extracted from the evolved magnetization state. In a snapshot of the magnetization state during the stable evolution stage, a continuous region with basically consistent magnetization direction is identified, and this region is defined as a magnetic domain. The area distribution of all identified magnetic domains is statistically analyzed using image processing techniques, and the average area of ​​all magnetic domains is calculated as the average size of the magnetic domain structure. A magnetization direction gradient analysis is performed on the boundary regions of adjacent magnetic domains to calculate the drastic change in magnetization direction when crossing the boundary, and the average gradient value is used as the clarity of the domain walls. The average value of the cosine of the angle between the magnetization direction of all computational units within the calculation model and the preset reference direction is used as the directional consistency parameter of the overall magnetization intensity. The calculated average size, domain wall clarity, and directional consistency parameter are compared with a preset microstructure integrity threshold. If all parameters are within the excellent range defined by the microstructure integrity threshold, the candidate formulation is determined to meet the microstructure integrity requirement and is included in the final screening results. From all candidate formulations that simultaneously meet the thermal stability and microstructure integrity requirements, the formulation with the highest predicted comprehensive performance evaluation value is selected as the target optimized formulation.

[0093] In practical implementation, microscopic magnetic structure calculations are performed on candidate formulations that meet thermal stability requirements. Target optimized formulations that satisfy the preset microscopic structural integrity are selected, and a microscopic magnetic domain model is established for these candidate formulations. In this implementation, the candidate formulations that meet thermal stability requirements are derived from the formulation verified by molecular dynamics simulations in Example 4. A microscopic magnetic domain model is established for such a candidate formulation. In this model, magnetocrystalline anisotropy parameters, exchange coupling constants, and initial magnetization distribution are set. The magnetocrystalline anisotropy parameters are set according to the properties of the NdFeB main phase and each added phase in the candidate formulation. The exchange coupling constant describes the interaction strength between the spins of adjacent atoms. The initial magnetization distribution can be set so that the magnetization direction of all computational units is along the same easy axis. A thermal perturbation field corresponding to a high-temperature environment is applied to the microscopic magnetic domain model. This thermal perturbation field is simulated by superimposing a random magnetic field fluctuation on each computational unit, and the evolution of the magnetization state over time is calculated.

[0094] The average size of the domain structure, the sharpness of the domain walls, and the directional consistency parameters of the overall magnetization intensity are extracted from the evolving magnetization state. In snapshots of the magnetization state during the stable evolution phase, continuous regions with essentially consistent magnetization directions are identified. In practice, a magnetization direction deviation angle threshold is set, and the simulated region is discretized into multiple computational units. A clustering algorithm groups adjacent computational units with magnetization direction deviations less than the angle threshold into the same region, defining this region as a domain. Image processing techniques are used to statistically analyze the area distribution of all identified domains, and the average area of ​​all domains is calculated as the average size of the domain structure. Magnetization direction gradient analysis is performed on the boundary regions of adjacent domains to calculate the drastic change in magnetization direction when crossing the boundary. In practice, a sampling path is set along the direction perpendicular to the domain wall, and the rate of change of the angle between the magnetization directions of adjacent computational units along the path is calculated. This calculation is performed on all identified domain wall boundaries, and the average value is taken as the sharpness of the domain wall. The average value of the cosine of the angle between the magnetization direction of all computational units within the microscopic magnetic domain model and a preset reference direction is calculated and used as the directional consistency parameter of the overall magnetization intensity. The calculation method is as follows:

[0095]

[0096] Where: symbol The parameter representing the directional uniformity of the overall magnetization, with the symbol... Represents the total number of computational units in the microscopic magnetic domain model, with the symbol... Indicates the first The angle between the magnetization direction vector of each computing unit and the preset reference direction vector.

[0097] In some embodiments, the preset reference direction is typically set to the direction of the material's easy magnetization axis. It can be understood that the orientation consistency parameter... The closer the value is to 1, the more consistent the magnetization direction of all computational units is with the reference direction. The calculated average size, domain wall sharpness, and orientation consistency parameters are compared with preset microstructure integrity thresholds, which define the lower or upper limit of the optimal range for each parameter. If the average size of the magnetic domain structure is greater than the preset lower threshold, the domain wall sharpness is greater than the preset lower threshold, and the orientation consistency parameter is greater than the preset lower threshold, then the candidate formulation is determined to meet the microstructure integrity requirements and is included in the final screening results. From all candidate formulations that meet the thermal stability and microstructure integrity requirements, the formulation with the highest predicted comprehensive performance evaluation value is selected as the target optimized formulation.

[0098] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments that can be applied to other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for optimizing the formulation of high-energy-product, high-temperature-resistant NdFeB-based composite plastic magnetic materials, characterized in that, The method includes: Historical raw material ratio data and corresponding high-temperature magnetic performance test results for neodymium iron boron magnetic powder, various heat-resistant modifiers, different molding aids and binders were collected to form an original formula-performance dataset; The original formula-performance dataset is normalized and structured, and the component ratios of various raw materials are transformed into formula feature vectors. The magnetic energy product, coercivity temperature coefficient, and high-temperature magnetic performance test results corresponding to the magnetic performance decay rate at the highest working temperature are transformed into multi-dimensional performance vectors, and a set of formula feature-performance vector pairs is constructed. Perform multidimensional spatial projection on the formula feature vector to generate an initial formula spatial representation, and perform principal component decomposition on the multidimensional performance vector to extract comprehensive performance evaluation indicators. The initial formula space representation and the comprehensive performance evaluation index are input into a mapping network for iterative learning to establish a quantitative mapping relationship model from formula features to comprehensive performance. Based on the quantitative mapping relationship model, global optimization is initiated in the formula space to generate a candidate formula list; For each candidate formulation in the candidate formulation list, high-temperature thermodynamic stability simulation and micro-magnetic structure calculation are performed to screen out the target optimized formulation that meets the preset thermal stability threshold and micro-structure integrity.

2. The method for optimizing the formulation of high-energy-product, high-temperature-resistant NdFeB-based composite plastic magnetic material according to claim 1, characterized in that, Perform a multidimensional spatial projection on the formula feature vector to generate an initial formula space representation, including: The proportions of neodymium iron boron magnetic powder, various heat-resistant modifiers, and molding aids and binders are extracted from the formula feature vector as core components. The core component is input into a preset multidimensional space transformation matrix, which maps the original proportional component to a set of mutually orthogonal basis vectors. Calculate the projection coefficients in each basis vector direction after mapping, and combine all projection coefficients into a high-dimensional coordinate to form the initial formulation space representation that characterizes the intrinsic structure of the formulation components.

3. The method for optimizing the formulation of high-energy-product, high-temperature-resistant NdFeB-based composite plastic magnetic material according to claim 1, characterized in that, Principal component decomposition is performed on the multidimensional performance vector to extract comprehensive performance evaluation indicators, including: Calculate the covariance matrix among the various performance indicators in the multidimensional performance vector, including the magnetic energy product, coercivity temperature coefficient, and magnetic performance attenuation rate corresponding to the highest operating temperature. The covariance matrix is ​​solved by eigenvalue and eigenvector calculation to obtain multiple principal component directions and their corresponding variance contributions; Several principal component directions whose cumulative variance contribution exceeds a preset threshold are selected. The eigenvectors corresponding to the principal component directions are used as weights to linearly combine the original multidimensional performance vectors, generating a scalar value that characterizes the comprehensive high-temperature magnetic properties of the material, which serves as the comprehensive performance evaluation index.

4. The method for optimizing the formulation of high-energy-product, high-temperature-resistant NdFeB-based composite plastic magnetic material according to claim 1, characterized in that, The initial formula space representation and the comprehensive performance evaluation index are input into a mapping network for iterative learning to establish a quantitative mapping model from formula features to comprehensive performance, including: The initial formula space representation is used as the input layer data of the relational mapping network, and the corresponding comprehensive performance evaluation index is used as the expected output target. The relation mapping network is configured to contain multiple hidden layers, each containing a non-linear activation unit; Using a forward propagation method, starting from the input layer, the feature representation of the initial formula space representation after nonlinear transformation of each hidden layer is calculated layer by layer until the output layer obtains a predicted comprehensive performance evaluation value. Calculate the difference between the predicted comprehensive performance evaluation value and the expected output target, and adjust the connection weight parameters of each hidden layer in the relation mapping network according to the difference using the gradient backpropagation algorithm; Repeat the forward propagation, difference calculation, and parameter adjustment process until the average difference between the network's predicted comprehensive performance evaluation value and the expected output target is less than a set threshold. At this point, the network's weight parameters are fixed, forming the quantitative mapping relationship model.

5. The method for optimizing the formulation of high-energy-product, high-temperature-resistant NdFeB-based composite plastic magnetic material according to claim 4, characterized in that, Based on the quantitative mapping relationship model, global optimization is initiated in the formulation space to generate a candidate formulation list, including: Define a formulation search space that includes the upper and lower limits of the proportions of all components, including neodymium iron boron magnetic powder, various heat-resistant modifiers, molding aids, and binders; Within the recipe search space, a large number of random recipe points are generated in a discrete or continuous sampling manner; Each random recipe point is processed in the same way as the initial recipe space representation is constructed to generate a corresponding recipe space representation, which is then input into the established quantitative mapping relationship model. The predicted comprehensive performance evaluation value corresponding to each random formula point is calculated using the quantitative mapping relationship model. According to the predicted comprehensive performance evaluation value from high to low, all random formulation points are sorted, and the formulation points with the highest ranking and the sum of the component proportions being one are selected to form the candidate formulation list.

6. The method for optimizing the formulation of high-energy-product, high-temperature-resistant NdFeB-based composite plastic magnetic material according to claim 5, characterized in that, High-temperature thermodynamic stability simulations were performed on each candidate formulation in the candidate formulation list, including: For each candidate formulation in the candidate formulation list, the molecular dynamics simulation system is invoked to set the initial atomic model according to the proportions of each component in the candidate formulation; In the molecular dynamics simulation system, a preset high-temperature boundary condition is applied to the initial atomic model to simulate the atomic motion process of the material under the target high-temperature working environment; During the simulation process, the mean square displacement of the atomic structure, energy fluctuations, and the breaking and formation of key chemical bonds within the material are monitored. According to the preset thermal stability judgment criteria, if the mean square displacement of the atomic structure exceeds the critical value, or the energy fluctuation cannot be stabilized for a long time, or a large number of unexpected chemical bonds break, then the candidate formulation is determined to not meet the thermal stability requirements; otherwise, it meets the requirements.

7. The method for optimizing the formulation of high-energy-product, high-temperature-resistant NdFeB-based composite plastic magnetic material according to claim 6, characterized in that, Microscopic magnetic structure calculations were performed on candidate formulations that met thermal stability requirements to screen out target optimized formulations that met the preset microstructural integrity requirements, including: To establish a microscopic magnetic domain model for candidate formulations that meet thermal stability requirements, the magnetocrystalline anisotropy parameters, exchange coupling constant, and initial magnetization distribution are set in the microscopic magnetic domain model. A thermal perturbation field corresponding to a high-temperature environment is applied to the microscopic magnetic domain model, and the evolution of the magnetization state over time is calculated. The average size of the domain structure, the clarity of the domain walls, and the directional consistency parameters of the overall magnetization intensity are extracted from the evolving magnetization state. The average size, domain wall clarity, and orientation consistency parameters are compared with a preset microstructure integrity threshold. If all parameters are within the excellent range defined by the microstructure integrity threshold, the candidate formulation is determined to meet the microstructure integrity requirements and is included in the final screening results. From all candidate formulations that meet the thermal stability requirements and the microstructure integrity requirements, the formulation with the highest predicted comprehensive performance evaluation value is selected as the target optimized formulation.

8. The method for optimizing the formulation of high-energy-product, high-temperature-resistant NdFeB-based composite plastic magnetic material according to claim 7, characterized in that, The extraction of parameters from the evolving magnetization state, including the average size of the domain structure, the clarity of the domain walls, and the directional consistency of the overall magnetization, includes: In the snapshot of the magnetization state during the stable evolution phase, a continuous region with basically consistent magnetization direction is identified, and this region is defined as a magnetic domain. The area distribution of all identified magnetic domains is statistically analyzed using image processing techniques, and the average area of ​​all magnetic domains is calculated as the average size of the magnetic domain structure. Magnetization direction gradient analysis is performed on the boundary region of adjacent magnetic domains to calculate the degree of change in magnetization direction when crossing the boundary, and the average gradient value is used as the clarity of the domain wall. The average value of the cosine of the angle between the magnetization direction of all computational units in the computational model and the preset reference direction is used as the directional consistency parameter of the overall magnetization intensity.

9. The method for optimizing the formulation of high-energy-product, high-temperature-resistant NdFeB-based composite plastic magnetic material according to claim 1, characterized in that, The original formula-performance dataset is normalized and structured, and the component ratios of various raw materials are transformed into formula feature vectors, including: The component proportion matrix in purely numerical form is extracted from the original formulation-performance dataset; For each column in the component ratio matrix, i.e. the ratio data of each raw material, a maximum and minimum value normalization process is performed to map the ratio value to the interval between zero and one. All the normalized raw material ratio values ​​are arranged in a fixed order to form a one-dimensional array, which serves as the formula feature vector describing a specific formula.

10. The method for optimizing the formulation of high-energy-product, high-temperature-resistant NdFeB-based composite plastic magnetic material according to claim 3, characterized in that, Calculate the covariance matrix among the various performance indices in the multidimensional performance vector, including the magnetic energy product, coercivity temperature coefficient, and magnetic performance decay rate corresponding to the highest operating temperature, as well as: Extract the multidimensional performance vector of all samples from the set of formula feature-performance vector pairs, wherein each vector contains specific values ​​of magnetic energy product, coercivity temperature coefficient and magnetic performance decay rate corresponding to the highest operating temperature; Calculate the mean values ​​of the magnetic energy product, the coercivity temperature coefficient, and the magnetic performance attenuation rate corresponding to the highest operating temperature, respectively. For any two performance indicators among magnetic energy product, coercivity temperature coefficient and magnetic energy decay rate, calculate the deviation of the specific value of one indicator in multiple samples from its own mean, and at the same time calculate the deviation of the specific value of the other indicator in the same sample from its own mean. Multiply the corresponding deviations of each pair of performance indicators across all samples, sum the products of all samples, and then divide by the total number of samples minus one to obtain the covariance between the two performance indicators. The three performance indicators, namely magnetic energy product, coercivity temperature coefficient, and magnetic performance decay rate, are calculated in pairs to obtain a 3x3 symmetric matrix. Each element in the matrix is ​​the covariance between the corresponding pair of performance indicators. This symmetric matrix is ​​the covariance matrix.

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