Data-driven multi-objective optimization design method for magnetic alloys

Abstract

The application provides a data-driven magnetic alloy multi-objective optimization design method, which comprises the following steps: establishing a composition-performance historical data set; establishing an initial feature pool; performing feature selection on the initial feature pool to form an optimization feature pool; training a machine learning model to perform regression prediction on a target performance; setting a search space; performing preliminary screening on the search space; calculating the expected improvement value of the target performance; calculating the Pareto optimal solution; if the generated Pareto optimal solution result does not converge, performing calculation on the Pareto optimal solution based on the density functional theory to obtain the theoretical values of a plurality of property parameters as supplementary material characteristics and incorporate them into the feature pool; performing calculation on all compositions in the composition-performance historical data set to obtain supplementary material characteristics and incorporate them into the feature pool; and repeating the above steps until the generated Pareto optimal solution result converges to obtain alloy composition recommendation results.

Description

Technical Field

[0001] This invention relates to the field of metallic material design technology, and in particular to a data-driven multi-objective optimization design method for magnetic alloys. Background Technology

[0002] Soft magnetic alloys are widely used in the cores of transformers and motors, and are an indispensable material in the electrification of human society. The soft magnetic properties of alloys refer to high saturation magnetization, high permeability, and low coercivity. The development of soft magnetic alloys has mainly revolved around practical application needs, resulting in the emergence of silicon steel, permalloy, amorphous alloys, nanocrystalline alloys, and the latest high-entropy alloys. While the performance of soft magnetic alloys is continuously optimized, their chemical composition is also becoming increasingly complex; amorphous alloys, nanocrystalline alloys, and high-entropy alloys can be collectively referred to as complex composition alloys.

[0003] Taking a typical five-element high-entropy alloy as an example, assuming the atomic percentage of each component element ranges from 5 to 35 (with a step size of 1), the possible alloy compositions exceed 550,000. Faced with such a vast space of alloy compositions, traditional trial-and-error methods for materials alloys clearly present a significant challenge. The optimal design of complex-composition magnetic alloys faces difficulties such as multi-element composition, complex structure, and diverse and unpredictable properties. However, current physical and chemical theories cannot accurately predict the properties of multi-element soft magnetic alloys, and simulation methods based on first-principles functional density theory suffer from computational complexity and are unsuitable for large-scale component screening. Furthermore, specific applications often impose comprehensive requirements on the multifaceted properties of complex-composition magnetic alloys, further increasing the difficulty of their optimal design.

[0004] Therefore, it is necessary to propose a data-driven multi-objective optimization design method for magnetic alloys to solve the above problems. Summary of the Invention

[0005] The purpose of this invention is to provide a data-driven multi-objective optimization design method for magnetic alloys, so as to improve the efficiency of performance prediction and composition optimization, and reduce the time cost and trial and error cost of multi-objective optimization design.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a data-driven multi-objective optimization design method for magnetic alloys, the method comprising the following steps:

[0007] S1. Establish a composition-performance history dataset based on the target performance of the magnetic alloy;

[0008] S2. Using the atomic molar percentage of chemical elements as the composition descriptor of the magnetic alloy, and establishing the initial feature pool of the magnetic alloy based on the theoretical values ​​of the property parameters of the elements in the composition descriptor.

[0009] S3. Based on the recursive feature elimination method, all features in the initial feature pool are voted on to carry out feature selection and form an optimized feature pool.

[0010] S4. Based on the component-performance historical dataset and the optimized feature pool, train a machine learning model to perform regression prediction on the performance of n targets;

[0011] S5. Set the search space for the magnetic alloy based on the material system and the atomic percentage range of each element;

[0012] S6. Set n target performances to be optimized and their corresponding expected value limits, use the machine learning model obtained in step S4 to predict the target performances of all alloy components in the search space, and perform preliminary screening of the search space according to the set expected value limits of the n target performances to form an optimized search space.

[0013] S7. Calculate the expected performance improvement in step S6 using a global optimization method. The calculation formula is as follows:

[0014]

[0015] In the formula, δ and f are the predicted value and uncertainty of the machine learning model for the target performance, respectively. max Let Φ(·) and φ(·) be the maximum value of the target performance in the component-performance historical dataset, and let Φ(·) and φ(·) be the standard normal distribution and its density function, respectively.

[0016] S8. For the n target performances set in step S6, calculate their EI as optimization targets, and calculate the Pareto optimal solution based on the optimized search space obtained in step S6 using the evolutionary algorithm.

[0017] S9. If the Pareto optimal solution does not converge, perform first-principles calculations on the Pareto optimal solution obtained in step S8 based on density functional theory to obtain theoretical values ​​of several property parameters as supplementary material features and include them in the feature pool; perform the same first-principles calculations on all components in the composition-performance history dataset obtained in step S1 to obtain supplementary material features and include them in the feature pool.

[0018] S10. Repeat steps S1 to S9 until the Pareto optimal solution converges, and obtain the recommended alloy composition of the magnetic alloy.

[0019] As a further improvement of the present invention, the composition-performance history dataset is obtained by collecting experimental data from publicly published literature, or by conducting experiments to prepare alloys and testing their properties.

[0020] The historical performance data includes the alloy chemical composition expressed as atomic percentages and the experimental saturation magnetization and hardness of the corresponding alloy samples.

[0021] As a further improvement of the present invention, in step S2, the theoretical value is obtained by calculating the weighted average value or mismatch degree of the element's property parameters; the element's property parameters include one or more of thermodynamic parameters, atomic structure parameters and electron migration parameters.

[0022] As a further improvement to the present invention, in step S2, the component descriptor is A. x B y C z D i E j …X n Where A, B, C, etc. are chemical elements, and x, y, z, etc. are the molar percentages of the elements.

[0023] As a further improvement of the present invention, in step S3, no less than three different machine learning kernels are selected to vote on all features in the feature pool, and features that receive more than half of the votes will be retained.

[0024] As a further improvement of the present invention, in step S4, the machine learning model includes one or more of linear regression, ridge regression, Lasso regression, support vector regression, multilayer perceptron, random forest, XGBoost and LightGBM.

[0025] As a further improvement of the present invention, in step S4, the average absolute percentage error of the trained machine learning model is not higher than 20%.

[0026] As a further improvement of the present invention, in step S5, the material system is a Fe-Co-Ni-Si-B magnetic alloy, and the atomic percentage of each element ranges from 5% to 35%, with a variation step of 1%.

[0027] As a further improvement to the present invention, in step S7, X = [X1, X2, ... X n To determine the atomic percentage of a certain alloy composition in the optimized search space, a machine learning model is used as a surrogate model to solve for the atomic percentage. And δ, and substitute them into the formula to obtain EI.

[0028] As a further improvement to the present invention, it also includes:

[0029] In step S11, alloy composition is selected from the Pareto optimal solution set for experimental preparation and testing. If the test results of the target performance do not meet the requirements, the experimental results are included in the composition-performance historical dataset and steps S1 to S10 are repeated.

[0030] Compared with existing technologies, this invention can achieve the following technical effects: when given multi-objective performance optimization requirements, it greatly reduces the alloy composition space, reduces the overall computational load, and improves the efficiency of performance prediction and composition optimization of complex magnetic alloys, thereby reducing the time cost and trial-and-error cost of multi-objective performance optimization design, meeting the research and development needs of new materials in scientific research and production, and realizing accurate and rapid design of complex magnetic alloys based on data-driven methods. Attached Figure Description

[0031] Figure 1 This is a flowchart of a data-driven multi-objective optimization design method for magnetic alloys proposed in this invention.

[0032] Figure 2 The atomic percentages of Fe, Co, Ni, Si, and B elements, as well as M, in the composition-performance history dataset. s Correlation matrix diagram of H.

[0033] Figure 3 The predictive capabilities of 6 different machine learning models.

[0034] Figure 4 The Pareto front corresponding to the obtained Pareto optimal solution set. Detailed Implementation

[0035] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0036] 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.

[0037] This invention provides a multi-performance collaborative optimization method for designing high-entropy alloy compositions based on machine learning. This embodiment takes a complex Fe-Co-Ni-Si-B magnetic alloy system as an example, requiring collaborative optimization of saturation magnetization (M... s The invention aims to obtain a complex-composition magnetic alloy of Fe-Co-Ni-Si-B with both high saturation magnetization and high hardness (H) using the proposed design method. Specifically, the atomic percentages of Fe, Co, Ni, Si, and B range from 5% to 35%, with a variation step of 1%, and the required M is to be predicted.s Alloy composition with ≥100 emu / g and H≥500 HV.

[0038] like Figure 1 As shown, the method includes the following steps:

[0039] Step S1: Establish a composition-performance history dataset based on the target properties of the magnetic alloy. In this embodiment, firstly, experimental data is collected from publicly published literature, including the alloy chemical composition expressed as atomic percentages and the experimental saturation magnetization and hardness of the corresponding alloy samples. The collection of experimental data is not limited to the Fe-Co-Ni-Si-B alloy system; relevant data from similar alloy systems such as Fe-Co-Ni-Al-Si can also be included in the composition-performance history dataset to enrich the dataset. Please refer to... Figure 2 As shown, in this embodiment, the experimental data in the composition-performance history dataset are organized into atomic percentages of Fe, Co, Ni, Si, and B elements, as well as M. s Correlation matrix diagram of H.

[0040] Step S2: Using the atomic molar percentage of chemical elements as the composition descriptor of the magnetic alloy, and based on the theoretical values ​​of the element property parameters in the composition descriptor, establish the initial feature pool of the magnetic alloy. In this embodiment, the composition descriptor is set to A. x B y C z D i E j …X n Where A, B, C, etc. are chemical elements, and x, y, z, etc. are the molar percentages of the elements. The theoretical values ​​of the elemental property parameters are obtained by calculating the weighted average or mismatch of the elemental property parameters; the elemental property parameters include, but are not limited to, mixing entropy and mixing enthalpy related to thermodynamics, atomic radius and molar volume related to atomic structure, and valence electron concentration and electronegativity related to electron migration.

[0041] Step S3: Based on the recursive feature elimination method, vote on all features in the initial feature pool to perform feature selection and form an optimized feature pool. In Step S3, select no fewer than three different machine learning kernels to vote on all features in the feature pool, and features that receive more than half of the votes will be retained.

[0042] Step S4: Based on the component-performance historical dataset and optimized feature pool, train a machine learning model to perform regression predictions on the performance of n targets, obtain the prediction capabilities of different machine learning models, and thus train machine learning models for Ms and H. The machine learning models include one or more of the following: linear regression, ridge regression, Lasso regression, support vector regression (SVR), multilayer perceptron (MLP), random forest (RF), XGBoost (eXtreme Gradient Boosting), and LightGBM (Light Gradient Boosting Machine).

[0043] Please refer to Figure 3 As shown, this embodiment selects six different machine learning models for prediction, and the evaluation metric is the Mean Absolute Percentage Error (MAPE). In this embodiment, the MAPE of the machine learning model trained is no higher than 20%.

[0044] Step S5: Set the search space for the magnetic alloy based on the material system and the atomic percentage range of each element. In Step S5, the material system is set to an Fe-Co-Ni-Si-B magnetic alloy, and the atomic percentage range of each element is set to 5% to 35%, with a variation step of 1%.

[0045] Step S6: Set n target performances to be optimized and their corresponding expected value limits. Use the machine learning model obtained in step S4 to predict the target performances of all alloy components in the search space. Based on the set expected value limits of the n target performances, perform preliminary screening of the search space to form an optimized search space. Specifically, in this embodiment, the expected value limits of the target performances are set as follows: M s ≥100 emu / g and H≥500 HV. Based on the MAPE results, SVC and LightGBM were selected as M... s The prediction model for H predicts all components of the search space, thereby excluding M. s Components with <100 emu / g and H <500 HV.

[0046] Step S7: Calculate the expected improvement (EI) of the target performance from Step S6 using the efficient global optimization (EGO) method. The calculation formula is as follows:

[0047]

[0048] In the formula, δ and f are the predicted value and uncertainty of the machine learning model for the target performance, respectively. max Let Φ(·) and φ(·) be the maximum value of the target performance in the composition-performance history dataset, respectively, and let Φ(·) and φ(·) be the standard normal distribution and its density function, respectively. The remaining alloy composition in the optimized search space is calculated based on the EI calculation formula. Define X = [X1, X2, ... X... n To determine the atomic percentage of a certain alloy composition in the optimized search space, a machine learning model is used as a surrogate model to solve for the atomic percentage. And δ, and substitute them into the formula to obtain EI.

[0049] Step S8: For the n target performances set in step S6, calculate their EI as optimization targets. Calculate the Pareto optimal solution based on the optimized search space obtained in step S6 using an evolutionary algorithm. In this embodiment, the multi-objective evolutionary algorithm NSGA-II is specifically used to solve for the Pareto optimal solution set. Please refer to... Figure 4 As shown, the Pareto front corresponding to the Pareto optimal solution set obtained in the optimized search space is displayed. Further, it is determined whether the Pareto optimal solution results converge.

[0050] Step S9: If the generated Pareto optimal solution does not converge, then perform first-principles calculations on the Pareto optimal solution obtained in step S8 based on density functional theory (DFT) to obtain theoretical values ​​for several property parameters, such as the average atomic magnetic moment. Curie temperature and other supplementary material features are added to the feature pool. Simultaneously, the same first-principles calculations are performed on all components in the composition-performance history dataset obtained from S1 to obtain supplementary material features, which are then included in the feature pool.

[0051] Step S10: Repeat steps S1 to S9 until the Pareto optimal solution converges, and finally obtain the recommended alloy composition of the magnetic alloy.

[0052] Step S11: In the face of a specific application scenario, the decision-maker can select some alloy components from the Pareto optimal solution set to conduct experiments and tests. If the test results of the target performance do not meet the requirements, the experimental results are included in the composition-performance historical dataset and steps S1 to S10 are repeated until the recommended alloy composition of the magnetic alloy that meets the requirements is obtained.

[0053] In summary, compared with the prior art, the present invention can achieve the following technical effects: when given multi-objective performance optimization requirements, it greatly reduces the alloy composition space, reduces the overall computational load, and improves the efficiency of performance prediction and composition optimization of complex magnetic alloys, thereby reducing the time cost and trial-and-error cost of multi-objective performance optimization design, meeting the research and development needs of new materials in scientific research and production, and realizing accurate and rapid design of complex magnetic alloys based on data-driven methods.

[0054] The above embodiments are only used to illustrate the present invention and are not intended to limit the technical solutions described in the present invention. The understanding of this specification should be based on those skilled in the art. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still make modifications or equivalent substitutions to the present invention. All technical solutions and improvements that do not depart from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1. A data-driven multi-objective optimization design method for magnetic alloys, characterized in that, The method includes the following steps: S1. Establish a composition-performance history dataset based on the target performance of the magnetic alloy; S2. Using the atomic molar percentage of chemical elements as the composition descriptor of the magnetic alloy, and establishing the initial feature pool of the magnetic alloy based on the theoretical values ​​of the property parameters of the elements in the composition descriptor. S3. Based on the recursive feature elimination method, all features in the initial feature pool are voted on to carry out feature selection and form an optimized feature pool. Among them, no less than three different machine learning kernels are selected to vote on all features in the feature pool, and features with more than half of the votes will be retained. S4. Based on the component-performance historical dataset and the optimized feature pool, train a machine learning model to perform regression prediction on the performance of n targets; S5. Set the search space for the magnetic alloy based on the material system and the atomic percentage range of each element; S6. Set n target performances to be optimized and their corresponding expected value limits, use the machine learning model obtained in step S4 to predict the target performances of all alloy components in the search space, and perform preliminary screening of the search space according to the set expected value limits of the n target performances to form an optimized search space. S7. Calculate the expected performance improvement in step S6 using a global optimization method. The calculation formula is as follows: In the formula, and These are the machine learning model's predicted performance and its uncertainty, respectively. The maximum value of the target performance in the component-performance historical dataset. and These are the standard normal distribution and its density function, respectively. S8. For the n target performances set in step S6, calculate their EI as optimization targets, and calculate the Pareto optimal solution based on the optimized search space obtained in step S6 using the evolutionary algorithm. S9. If the Pareto optimal solution does not converge, perform first-principles calculations on the Pareto optimal solution obtained in step S8 based on density functional theory to obtain theoretical values ​​of several property parameters as supplementary material features and include them in the feature pool; perform the same first-principles calculations on all components in the composition-performance history dataset obtained in step S1 to obtain supplementary material features and include them in the feature pool. S10. Repeat steps S1 to S9 until the Pareto optimal solution converges, and obtain the recommended alloy composition of the magnetic alloy.

2. The data-driven multi-objective optimization design method for magnetic alloys according to claim 1, characterized in that, The composition-performance history dataset is obtained by collecting experimental data from publicly published literature, or by conducting experiments to prepare alloys and testing their properties. The historical performance data includes the alloy chemical composition expressed as atomic percentages and the experimental saturation magnetization and hardness of the corresponding alloy samples.

3. The data-driven multi-objective optimization design method for magnetic alloys according to claim 1, characterized in that, In step S2, the theoretical value is obtained by calculating the weighted average or mismatch degree of the element's property parameters; the element's property parameters include one or more of thermodynamic parameters, atomic structure parameters, and electron migration parameters.

4. The data-driven multi-objective optimization design method for magnetic alloys according to claim 1, characterized in that, In step S2, the component descriptor is A x B y C z D i E j … X n Where A, B, and C are chemical elements, and x, y, and z are the molar percentages of the elements.

5. The data-driven multi-objective optimization design method for magnetic alloys according to claim 1, characterized in that, In step S4, the machine learning model includes one or more of the following: linear regression, ridge regression, Lasso regression, support vector regression, multilayer perceptron, random forest, XGBoost, and LightGBM.

6. The data-driven multi-objective optimization design method for magnetic alloys according to claim 1, characterized in that, In step S4, the mean absolute percentage error of the trained machine learning model is no higher than 20%.

7. The multi-objective optimization design method for magnetic alloys according to claim 1, characterized in that, In step S5, the material system is an Fe-Co-Ni-Si-B magnetic alloy, with the atomic percentage of each element ranging from 5% to 35%, and the variation step size being 1%.

8. The data-driven multi-objective optimization design method for magnetic alloys according to claim 1, characterized in that, In step S7, define To optimize the atomic percentage of a certain alloy composition in the search space, a machine learning model is used as a surrogate model to solve for the atomic percentage. and And substitute it into the formula to obtain EI.

9. The data-driven multi-objective optimization design method for magnetic alloys according to claim 1, characterized in that, Also includes: Step S11: Select alloy composition from the Pareto optimal solution set for experimental preparation and testing. If the test results of the target performance do not meet the requirements, the experimental results are included in the composition-performance historical dataset and steps S1 to S10 are repeated.

Images