Multi-objective optimization hot work die steel design method

Abstract

The invention relates to a multi-objective optimization hot work die steel design method, belongs to the technical field of ferrous metallurgy, and solves the technical problem of limitation of single-objective optimization in the prior art. The multi-objective optimization hot work die steel design method comprises the steps that 1, data of hot work die steel are collected, null value filling is carried out, and an original data set is formed; 2, performing feature screening to form an initial data set; step 3, carrying out normalization processing on the characteristic values; 4, selecting a plurality of machine learning algorithms to perform model training; step 5, evaluating each model, and selecting a machine learning algorithm with an optimal training effect from the models so as to obtain a prediction model; step 6, performing multi-objective optimization by using an NSGA-II genetic algorithm to obtain multiple groups of optimal solutions; and step 7, determining components and heat treatment process parameters of the hot work die steel. Various optimization schemes are provided for material design, and different engineering requirements can be met.

Description

Technical Field

[0001] This invention belongs to the field of iron and steel metallurgy technology, and specifically relates to a multi-objective optimization design method for hot work die steel. Background Technology

[0002] Hot work die steel, as the core material for hot-working dies, plays a crucial role in modern industry. Because dies typically operate in harsh environments with high temperatures and pressures, the materials must possess excellent high-temperature strength, toughness, thermal fatigue resistance, and wear resistance, and also resist the formation of thermal fatigue cracks under alternating thermal stress caused by repeated heating and cooling. However, traditional hot work die steels, such as high-alloy steel 3Cr2W8V, medium-alloy steel H13, and low-alloy steel 5CrMnMoSiV, still have many shortcomings in terms of overall performance. For example, 3Cr2W8V steel has high hot strength but poor thermal conductivity and fatigue resistance, and insufficient low-temperature toughness; 5CrMnMoSiV steel has excellent low-temperature toughness, but its high-temperature yield strength is poor, and its room-temperature strength is average; although H13 steel is known as "universal hot work die steel" with good overall performance, its operating temperature is limited to below 600℃. Above 600℃, it will experience thermal softening, collapse, and deformation, indicating insufficient yield strength above 600℃. Therefore, as modern industry continues to increase its requirements for mold performance, optimizing a single performance is no longer sufficient to meet actual needs. It is urgent to achieve synergistic improvement in multiple key performance indicators, especially to simultaneously improve high-temperature yield strength above 600℃, room temperature strength, and low-temperature toughness.

[0003] In the areas of material property prediction and composition design, traditional theoretical calculations and experimental trial-and-error methods have significant limitations: the former has low computational efficiency, weak generalization ability, and difficulty in handling complex scenarios with multiple couplings; the latter is time-consuming, costly, and has a limited success rate. Given these limitations, there is an urgent need for a data-driven, highly efficient, multi-objective optimization method for steel design. Summary of the Invention

[0004] In view of the above-mentioned technical status, this invention provides a multi-objective optimization design method for hot work die steel. Based on historical data, a high-precision composition-process-performance mapping model is constructed through machine learning algorithms to achieve rapid and accurate prediction and synergistic optimization of three key performance indicators of hot work die steel: 700℃ yield strength, room temperature yield strength, and -40℃ impact energy. This provides a new method for the research and development of high-performance hot work die steel.

[0005] The objective of this invention is mainly achieved through the following technical solutions:

[0006] This invention provides a multi-objective optimization method for designing hot work die steel, comprising the following steps:

[0007] Step 1: Collect the composition content and heat treatment process parameters of hot work die steel, as well as the corresponding 700℃ yield strength data, room temperature yield strength data, and -40℃ impact energy data, and fill in the blanks to form the original datasets of 700℃ yield strength, room temperature yield strength, and -40℃ impact energy respectively.

[0008] Step 2: Feature screening of the composition and heat treatment process of the hot work die steel in Step 1 to identify the features that affect the yield strength at 700℃, the yield strength at room temperature, and the impact energy at -40℃. The data of the identified features, together with the corresponding data of the yield strength at 700℃, the yield strength at room temperature, and the impact energy at -40℃, are used to construct the initial datasets of the yield strength at 700℃, the yield strength at room temperature, and the impact energy at -40℃, respectively.

[0009] Step 3: Normalize the feature values ​​in the initial dataset from Step 2;

[0010] Step 4: Using the dataset after normalization in Step 3, select multiple machine learning algorithms to train the model.

[0011] Step 5: Evaluate each model and select the machine learning algorithm with the best training effect to obtain the 700℃ yield strength prediction model, the room temperature yield strength prediction model, and the -40℃ impact energy prediction model.

[0012] Step 6: Use the NSGA-II genetic algorithm to perform multi-objective optimization on the 700℃ yield strength, room temperature yield strength and -40℃ impact energy obtained by the prediction model in Step 5, and obtain multiple sets of optimal solutions;

[0013] Step 7: Determine the composition and heat treatment process parameters of the hot work die steel: Select the final composition and heat treatment process parameters of the hot work die steel from multiple optimal solutions.

[0014] Furthermore, the original dataset consists of several original data sets, each of which includes the contents of C, Si, Mn, P, S, Cr, Ni, Mo, V, Nb, Zr, W, and Al, the quenching temperature, the tempering temperature, and the yield strength at 700℃, the yield strength at room temperature, or the impact energy at -40℃.

[0015] Furthermore, in step 1, the null value filling is to directly fill with 0 when the hot work die steel does not contain this component; when the heat treatment process parameters of the hot work die steel do not exist, the average value of the quenching temperature or tempering temperature is used to fill.

[0016] Furthermore, step 2 includes the following sub-steps:

[0017] Step 2.1: Manually discard data on the composition content and heat treatment parameters of hot work die steel that are small in volume or have a narrow range of variation;

[0018] Step 2.2: Perform correlation analysis on the composition data and heat treatment parameter data of the hot work die steel after manual rejection, and compare them with the yield strength data at 700℃, room temperature yield strength data, and impact energy data at -40℃, respectively, and screen out the common characteristics of the yield strength at 700℃, room temperature yield strength, and impact energy at -40℃.

[0019] Furthermore, in step 2.1, "small data volume" means that the data volume does not exceed 10% of the total data, and "narrow range of variation" means that the range of variation of the components is less than 0.1%.

[0020] Furthermore, in step 2.2, the correlation coefficient analysis involves deleting data with correlation coefficients greater than 0.95 between the component data and heat treatment parameter data of hot work die steel, and removing data with correlation coefficients less than 0.3 with the 700℃ yield strength, room temperature yield strength and -40℃ impact energy.

[0021] Furthermore, in step 2, the features include C, Si, Mn, Cr, Ni, Mo, V, quenching temperature, and tempering temperature.

[0022] Furthermore, step 4 includes the following sub-steps:

[0023] Step 4.1: First, shuffle the initial data groups in the normalized initial dataset as the smallest basic unit, arrange them randomly, and then divide them into training set and test set according to a 4:1 ratio.

[0024] Step 4.2: In the Python runtime environment, select four machine learning algorithms: LinearRegression, Support Vector Machine (SVR), RandomForest, and XGBoost. Import LinearRegression from the sklearn.linear_model library, SVR from the sklearn.svm library, RandomForestRegressor from the sklearn.ensemble library, and XGBoost from the xgboost library.

[0025] Step 4.3: Import the training and test set data into four models: LinearRegression, SVR, RandomForest, and XGBoost. Use C, Si, Mn, Cr, Ni, Mo, V, quenching temperature, and tempering temperature as feature values, and use the yield strength at 700℃, room temperature yield strength, or impact energy at -40℃ as target values, and train the models accordingly.

[0026] Furthermore, in step 5, the evaluation index is the coefficient of determination R. 2 The mean absolute error (MAE) is used to predict the yield strength at 700℃, which is based on the XGBoost algorithm; the room temperature yield strength prediction model is based on the RandomForest algorithm; and the -40℃ impact energy prediction model is based on the RandomForest algorithm.

[0027] Furthermore, step 6 includes the following sub-steps:

[0028] Step 6.1: Establish the objective function and boundary constraints of the decision variables, and initialize the NSGA-II parameters;

[0029] Step 6.2: Execute the NSGA-II optimization process and iterative optimization procedure;

[0030] Step 6.3: Extract the Pareto optimal solution set and obtain multiple sets of optimal solutions using the weighted sum method.

[0031] Compared with the prior art, the present invention can achieve at least one of the following technical effects:

[0032] (1) This invention combines the high-temperature yield strength, room-temperature yield strength and low-temperature toughness of hot work die steel for multi-objective optimization, which overcomes the limitations of single-objective optimization in traditional methods and achieves synergistic improvement of multiple key performance indicators of hot work die steel.

[0033] (2) This invention combines the high-temperature yield strength, room-temperature yield strength and low-temperature toughness of hot work die steel with machine learning algorithms and multi-objective optimization algorithms. Compared with traditional prediction methods, it can more accurately realize the composition design of hot work die steel, reduce the number of experiments to a certain extent, reduce the cost of experimental materials, equipment and manpower, provide a reference for the composition design and process optimization of hot work die steel, and improve R&D efficiency.

[0034] (3) This invention selects multiple machine learning algorithms such as Linear Regression, Support Vector Machine (SVR), RandomForest and XGBoost to construct a performance prediction model, ensuring the accuracy of the machine learning model.

[0035] (4) This invention combines machine learning prediction models with NSGA-II genetic algorithms and Pareto front analysis to provide a variety of optimization schemes for material design, which can meet different engineering needs. Attached Figure Description

[0036] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0037] Figure 1 This is a flowchart of the multi-objective optimization design method for hot work die steel of the present invention;

[0038] Figure 2 This is a comparison chart of the actual and predicted values ​​in the 700℃ yield strength prediction model established based on the XGBoost algorithm in an example.

[0039] Figure 3 This is a comparison chart of the actual and predicted values ​​in the room temperature yield strength prediction model established based on the RandomForest algorithm in the example.

[0040] Figure 4 This is a comparison chart of the actual and predicted values ​​in the -40℃ impact energy prediction model established based on the RandomForest algorithm, as an example. Detailed Implementation

[0041] The following detailed description of a multi-objective optimization method for hot work die steel design, with reference to specific embodiments, is provided. These embodiments are for comparative and illustrative purposes only, and the present invention is not limited to these embodiments.

[0042] The chemical composition of steel is its "innate genetic makeup," determining its mechanical properties. For example, higher carbon content leads to higher potential hardness and strength, but lower toughness and weldability. Alloying elements such as Si, Mn, Cr, Ni, Mo, V, and W provide solid solution strengthening, dispersion strengthening, and improve hardenability, wear resistance, red hardness, and toughness. Conversely, phosphorus (P) and sulfur (S), considered harmful elements, also affect the steel's mechanical properties. Heat treatment is a form of "post-treatment cultivation." Different heat treatment processes result in different microstructures, leading to steels with varying mechanical properties. Therefore, the same steel can exhibit vastly different mechanical properties depending on the heat treatment process.

[0043] Based on the above analysis, this invention proposes a multi-objective optimization design method for hot work die steel, comprising the following steps:

[0044] Step 1: Collect the composition content and heat treatment process parameters of hot work die steel from the existing data, as well as the corresponding 700℃ yield strength data, room temperature yield strength data, and -40℃ impact energy data, and fill in the blanks to form the original datasets of 700℃ yield strength, room temperature yield strength, and -40℃ impact energy respectively.

[0045] Step 2: Feature screening of the composition and heat treatment process of the hot work die steel in Step 1 to identify the features that affect the yield strength at 700℃, the yield strength at room temperature, and the impact energy at -40℃. The data of the identified features, together with the corresponding data of the yield strength at 700℃, the yield strength at room temperature, and the impact energy at -40℃, are used to construct the initial datasets of the yield strength at 700℃, the yield strength at room temperature, and the impact energy at -40℃, respectively.

[0046] Step 3: Normalize the feature values ​​in the initial dataset from Step 2;

[0047] Step 4: Using the dataset normalized in Step 3, select various machine learning algorithms to train the model, such as Linear Regression, Support Vector Machine (SVR), XGBoost, and Random Forest.

[0048] Step 5: Evaluate each model and select the machine learning algorithm with the best training effect to obtain the 700℃ yield strength prediction model, the room temperature yield strength prediction model, and the -40℃ impact energy prediction model.

[0049] Step 6: Use the NSGA-II genetic algorithm to perform multi-objective optimization on the 700℃ yield strength, room temperature yield strength and -40℃ impact energy obtained by the prediction model in Step 5, and obtain multiple sets of optimal solutions;

[0050] Step 7: Determine the composition and heat treatment process parameters of the hot work die steel: Select the final composition and heat treatment process parameters of the hot work die steel from multiple optimal solutions.

[0051] Figure 1 This is a flowchart illustrating the multi-objective optimization design method for hot work die steel according to the present invention.

[0052] Specifically, in step 1, the hot work die steel in this invention refers to steel with Fe as the base material, designed with "medium carbon (0.25%-0.60%) + multi-alloy element synergistic strengthening" (core elements are Cr, Ni, Mo, V, etc.), such as 4Cr5MoSiV, 4Cr3Mo3V, 5CrNiMo, etc. The composition of the hot work die steel includes C, Si, Mn, P, S, Cr, Ni, Mo, V, Nb, Zr, W, and Al. The heat treatment process parameters include quenching temperature and tempering temperature. These data are then processed separately... Corresponding to the data on yield strength at 700℃, yield strength at room temperature, and impact energy at -40℃, the original datasets for yield strength at 700℃, yield strength at room temperature, and impact energy at -40℃ are obtained. That is, the original datasets consist of several original data groups. Each original data group includes the contents of C, Si, Mn, P, S, Cr, Ni, Mo, V, Nb, Zr, W, and Al, the quenching temperature, the tempering temperature, and the yield strength at 700℃, the yield strength at room temperature, or the impact energy at -40℃, for a total of 16 data points. For example, with 0.32% C, 0.8% Si, 0.4% Mn, 0.005% P, 0.008% S, 2.2% Cr, 4.3% Ni, 1.6% Mo, 0.3% V, 0% Nb, 0% Zr, 0.65% W, 0% Al, a quenching temperature of 970℃, and a tempering temperature of 620℃, the corresponding yield strength at 700℃ is 302 MPa, the yield strength at room temperature is 1137 MPa, and the impact energy at -40℃ is 36 J.

[0053] It should be noted that null value filling refers to filling the blanks with 0 when the hot work die steel does not contain a certain component. For example, H13 steel does not contain Ni, Nb, Zr, W, or Al, so the content of these elements is 0. When the heat treatment process parameters of the hot work die steel are not available, such as when some heat treatment process parameter data is not publicly available, the average value of the quenching temperature or tempering temperature is used to fill the blanks. At the same time, the number of null values ​​for heat treatment process parameters needs to be controlled. If there are many null values ​​and all of them are filled with the average value, it will affect the model prediction results. In addition, the same data is collected only once. That is, within each dataset of the 700℃ yield strength original dataset, the room temperature yield strength original dataset, and the -40℃ impact energy original dataset, at least one data value is different between any two original datasets.

[0054] Furthermore, the quenching temperature of steel refers to the highest temperature reached when the workpiece to be quenched is heated, which is also the initial temperature at which it is cooled. The tempering temperature of steel refers to the temperature reached after quenching, when the workpiece is heated a second time to a certain temperature, held for a period of time, and then cooled.

[0055] In step 2, feature selection includes manual selection and correlation analysis, and the specific steps are as follows:

[0056] Step 2.1: Manually discard data on the composition content and heat treatment parameters of hot work die steel that are small in volume or have a narrow range of variation;

[0057] Step 2.2: Perform correlation analysis on the composition data and heat treatment parameter data of the hot work die steel after manual rejection, and compare them with the yield strength data at 700℃, room temperature yield strength data, and impact energy data at -40℃, respectively, and screen out the common characteristics of the yield strength at 700℃, room temperature yield strength, and impact energy at -40℃.

[0058] It should be noted that in step 2.1, "small data volume" means that the data volume does not exceed 10% of the total data, and "narrow variation range" means that the variation range of the composition is less than 0.1%. Specifically, for example, the variation range of P content in hot work die steel is 0.004%-0.016%, S content is 0.001%-0.011%, and Al content is 0.003%-0.033%. The data containing W accounts for less than 10% of the total data volume, so this invention excludes the content data of P, S, Al, and W. However, it should be noted that since P and S are harmful elements in steel, their content must be limited. Therefore, the P and S content of the final designed steel must be limited to the above-mentioned variation ranges.

[0059] In step 2.2, if Pearson correlation coefficient analysis is performed, data with correlation coefficients greater than 0.95 between the composition data and heat treatment parameter data of hot work die steel are deleted. This aims to eliminate high linear redundancy among features and avoid the negative impact of multicollinearity on model performance. Simultaneously, to ensure the normal operation of subsequent optimization algorithms, the input parameters of each established machine learning model should remain consistent. Therefore, only data with correlation coefficients less than 0.3 with the 700℃ yield strength, room temperature yield strength, and -40℃ impact energy are removed. Based on this standard, features Nb and Zr with correlation coefficients less than 0.3 with the target variable are deleted. Specifically, the correlation coefficients of Nb with the 700℃ yield strength, room temperature yield strength, and -40℃ impact energy are -0.24, 0.0023, and -0.22, respectively, and the correlation coefficients of Zr with the 700℃ yield strength, room temperature yield strength, and -40℃ impact energy are -0.29, -0.16, and -0.28, respectively. Ultimately, the common characteristics of the yield strength at 700℃, the yield strength at room temperature, and the impact energy at -40℃ include nine features: C, Si, Mn, Cr, Ni, Mo, V, quenching temperature, and tempering temperature.

[0060] It should be noted that in step 3, due to the large difference in magnitude between the eigenvalues, a normalization method is used to process each eigenvalue to eliminate the difference in dimensions between them. The normalization calculation formula used in this invention is: Xnew =(X max -X) / (X max -X min In the formula, X new These are the normalized eigenvalues, and their range is 0 ≤ X. new ≤1; X is the eigenvalue before normalization, X max X is the largest eigenvalue within this feature. min It is the smallest eigenvalue within this feature.

[0061] Specifically, step 4 includes the following sub-steps:

[0062] Step 4.1: First, shuffle the initial data groups in the normalized initial dataset as the smallest basic unit, arrange them randomly, and then divide them into training set and test set according to a 4:1 ratio.

[0063] Step 4.2: In the Python runtime environment, such as Python 3.8, select four machine learning algorithms: LinearRegression, Support Vector Machine (SVR), RandomForest, and XGBoost. Import LinearRegression from the sklearn.linear_model library, SVR from the sklearn.svm library, RandomForestRegressor from the sklearn.ensemble library, and XGBoost from the xgboost library.

[0064] Step 4.3: Import the training and test set data into four models: LinearRegression, SVR, RandomForest, and XGBoost. Use C, Si, Mn, Cr, Ni, Mo, V, quenching temperature, and tempering temperature as feature values, and use the yield strength at 700℃, room temperature yield strength, and impact energy at -40℃ as target values. Train the models separately, for a total of 12 models.

[0065] It should be noted that in step 4.1, the normalized initial dataset consists of several initial data groups. Each original data group includes the contents of C, Si, Mn, Cr, Ni, Mo, V, Nb, and Zr, the quenching temperature, the tempering temperature, and the yield strength at 700℃ or the yield strength at room temperature or the impact energy at -40℃, for a total of 9 data points.

[0066] Specifically, in step 4, the LinearRegression algorithm does not require setting hyperparameters. The SVR algorithm's hyperparameters for constructing the 700℃ yield strength prediction model, the room temperature yield strength prediction model, and the -40℃ impact energy prediction model are all set to kernel = 'rbf', C = 100, gamma = 0.1, and epsilon = 0.1. When constructing the 700℃ yield strength prediction model, the RandomForest algorithm's hyperparameters are set to n_estimators = 80 and max_depth = 10, while the XGBoost algorithm's hyperparameters are set to n_estimators = 100, learning_rate = 0.1, and max_depth = 5. When constructing the room temperature yield strength prediction model, the hyperparameters of the RandomForest algorithm are set to n_estimators = 100 and max_depth = 10, and the hyperparameters of the XGBoost algorithm are set to n_estimators = 120, learning_rate = 0.1, and max_depth = 5. When constructing the -40℃ impact energy prediction model, the hyperparameters of the RandomForest algorithm are set to n_estimators = 70 and max_depth = 10, and the hyperparameters of the XGBoost algorithm are set to n_estimators = 80, learning_rate = 0.1, and max_depth = 3.

[0067] Specifically, in step 5, the evaluation metric for model performance is the coefficient of determination R. 2 and Mean Absolute Error (MAE), R 2 R is a statistical indicator used to characterize the goodness of fit of a regression model. 2 The closer the value is to 1, the better the model fits; the smaller the MAE value, the lower the model error.

[0068] The coefficient of determination R 2 The calculation formula is: In equation (1), n ​​is the number of training data sets in the test data, and y i This represents the yield strength at 700℃, the yield strength at room temperature, or the impact energy at -40℃ for the i-th data set in the test data. This refers to the numerical value of the yield strength at 700℃, the yield strength at room temperature, or the impact energy at -40℃ for the i-th data set predicted by the model. It is the average of the yield strength at 700℃, the yield strength at room temperature, or the impact energy at -40℃ for n training data groups in the test data.

[0069] The formula for calculating the Mean Absolute Error (MAE) is: In equation (2), n is the number of data sets in the test data, and yi This represents the yield strength at 700℃, the yield strength at room temperature, or the impact energy at -40℃ for the i-th data set in the test data. This represents the value of the yield strength at 700℃, the yield strength at room temperature, or the impact energy at -40℃ for the i-th data set predicted by the model.

[0070] By comparing the training effects of various algorithms, the model with the highest accuracy among the four machine learning algorithms was selected according to the evaluation criteria. Among them, the XGBoost algorithm for predicting the 700℃ yield strength showed the best learning effect, with R... 2 The value is 0.86, and the MAE value is 30.9, confirming it as the 700℃ yield strength prediction model; the room temperature yield strength prediction model shows the best learning effect from the RandomForest algorithm, R 2 With a value of 0.87 and a MAE value of 35.8, it is determined to be the room temperature yield strength prediction model; the RandomForest algorithm has the best learning effect for the -40℃ impact energy prediction model. 2 With an accuracy of 0.75 and an MAE of 3.39, it was determined to be the -40℃ impact energy prediction model. The -40℃ impact energy dataset is small in sample size, and the model accuracy largely depends on data quality. Therefore, adjusting parameters has a limited impact on improving model accuracy. After multiple parameter adjustments, the best-performing model was selected as the -40℃ impact energy prediction model. Parameter tuning for the -40℃ impact energy prediction model mainly focused on the RandomForest algorithm, which has shown good learning performance. Specifically, the parameters n_estimators were adjusted between 50 and 200, and max_depth between 3 and 10, and then the prediction accuracy of the model was compared.

[0071] Specifically, step 6 includes the following sub-steps:

[0072] Step 6.1: Establish the objective function and boundary constraints of the decision variables, and initialize the NSGA-II parameters;

[0073] Step 6.2: Execute the NSGA-II optimization process and iterative optimization procedure;

[0074] Step 6.3: Extract the Pareto optimal solution set and obtain multiple sets of optimal solutions using the weighted sum method;

[0075] In step 6.1, the three performance indicators—yield strength at 700℃, room temperature yield strength, and impact energy at -40℃—are defined as objective functions. C, Si, Mn, Cr, Ni, Mo, V, quenching temperature, and tempering temperature are defined as decision variables, and upper and lower bounds for each decision variable are set according to the composition and process requirements of the target product. NSGA-II parameters include population parameters, such as population size; genetic operation parameters, such as crossover probability, crossover distribution index, mutation probability, and mutation distribution index; and termination condition parameters, such as maximum number of iterations, convergence threshold, and maximum running time.

[0076] The typical range for population size is 50-500. For problems with continuous and simple frontiers, a smaller population, such as 100, is sufficient. The typical range for binary crossover probability is 0.7-0.9, with 0.9 being a reliable and widely used value. The typical range for crossover distribution index is 5-20. The larger the value, the closer the offspring are to the parent. 20 or 50 are commonly used. The typical range for multinomial mutation probability is 1 / n-2 / n, where n is the number of decision variables. In this invention, it is 9. The typical range for mutation distribution index is 20-100. The larger the value, the smaller the perturbation. 20 or 50 are commonly used. The maximum number of iterations depends on the problem complexity and population size, with a typical range of 100-1000.

[0077] First, use typical values ​​of the above parameters as a starting point, then run the algorithm, observe the final Pareto front plot and convergence index curve, and then adjust the population size, crossover index, and variation index.

[0078] Ultimately, this invention sets the population size to 100 individuals, the maximum number of generations to 200, and sets the objective function tolerance to 0.25% as an early termination condition; it employs a simulated binary crossover operator with a crossover probability of 0.9 and a distribution exponent of 15; and it uses a polynomial mutation operator with a mutation probability of 0.1 and a distribution exponent of 20.

[0079] It should be noted that since NSGA-II defaults to a minimization problem, while the goal of this invention is to find a steel composition and quenching and tempering temperature with good comprehensive performance of yield strength at 700℃, room temperature yield strength and impact energy at -40℃, the higher the mechanical performance index, the better. Therefore, the maximization problem is transformed into a minimization problem, that is, to comprehensively measure the negative yield strength at 700℃, negative room temperature yield strength and negative impact energy at -40℃ to obtain the minimum value.

[0080] In step 6.2, an initial population is first generated, with each individual representing a combination of C, Si, Mn, Cr, Ni, Mo, V, quenching temperature, and tempering temperature. This process is then iterated until a termination condition is met. For each generation, the following steps are performed:

[0081] A. Evaluate the objective function value for each individual in the population;

[0082] B. Perform non-dominated ranking on the population, dividing individuals into multiple non-dominated layers;

[0083] C. Calculate the crowding distance for each individual to measure the distribution density of individuals in the same non-dominated layer;

[0084] D. Generate an inherent population through tournament selection, crossover, and mutation;

[0085] E. Merge parent and offspring populations and select the next generation population based on non-dominated ordering and crowding distance.

[0086] In step 6.3, the weighted sum method combines the 700℃ yield strength, room temperature yield strength, and -40℃ impact energy into a single comprehensive objective function through linear weighting, such as MinF(X)=-[af1(X)+bf2(X)+cf3(X)], where F(X) represents the comprehensive objective of the 700℃ yield strength, room temperature yield strength, and -40℃ impact energy, and MinF(X) represents the optimal comprehensive objective; f1(X) represents the predicted value of the 700℃ yield strength prediction model, f2(X) represents the predicted value of the room temperature yield strength prediction model, and f3(X) represents the predicted value of the -40℃ impact energy prediction model; a, b, and c are the weight coefficients of the objective function. For example, according to the importance of performance, the weight of the 700℃ high-temperature yield strength is set to 0.4, and the weights of the room temperature yield strength and -40℃ impact energy are each set to 0.3; X is the decision variable, namely C, Si, Mn, Cr, Ni, Mo, V, quenching temperature, and tempering temperature. It should be noted that after the calculated decision variables are denormalized, the output X is the data format before normalization.

[0087] In step 7, the final C, Si, Mn, Cr, Ni, Mo, and V composition ranges in the steel, as well as the quenching and tempering temperatures, are selected from the multiple optimal solutions obtained in step 6. Furthermore, the P and S content in the steel is limited to the variation range statistically determined in step 2.1.

[0088] Finally, based on the obtained hot work die steel content data and heat treatment process parameters, actual smelting and heat treatment were carried out, and the mechanical properties of the obtained hot work die steel samples were tested. The test results showed that the sample met the target performance requirements, indicating that the method of the present invention can accurately realize the composition design of hot work die steel.

[0089] Example

[0090] A multi-objective optimization method for hot work die steel design includes the following steps:

[0091] Step 1: Collect the composition content and heat treatment process parameters of hot work die steel, as well as the corresponding 700℃ yield strength data, room temperature yield strength data, and -40℃ impact energy data, and fill in the blanks to form the original datasets of 700℃ yield strength, room temperature yield strength, and -40℃ impact energy respectively.

[0092] The original dataset consists of several raw data sets. Each raw data set includes the contents of C, Si, Mn, P, S, Cr, Ni, Mo, V, Nb, Zr, W, and Al, quenching temperature, tempering temperature, and yield strength at 700℃, room temperature yield strength, and impact energy at -40℃, totaling 16 data points. Because not all literature data simultaneously measured the yield strength at 700℃, room temperature yield strength, and impact energy at -40℃ for hot-work die steels, the amount of data in the original datasets varies. The 700℃ yield strength dataset contains 82 data points, the room temperature yield strength dataset contains 95 data points, and the -40℃ impact energy dataset contains 64 data points.

[0093] Step 2: Feature screening of the composition and heat treatment process of the hot work die steel in Step 1 to identify the features that affect the yield strength at 700℃, the yield strength at room temperature, and the impact energy at -40℃. The data of the identified features, together with the corresponding data of the yield strength at 700℃, the yield strength at room temperature, and the impact energy at -40℃, are used to construct the initial datasets of the yield strength at 700℃, the yield strength at room temperature, and the impact energy at -40℃, respectively.

[0094] Step 2.1: Manually discard data on the composition content and heat treatment parameters of hot work die steel that are small in volume or have a narrow range of variation;

[0095] Among them, the amount of W data accounts for less than 10% of the total data. The variation range of P content in hot work die steel is 0.004%-0.016%, the variation range of S content is 0.001%-0.011%, and the variation range of Al content is 0.003%-0.033%. Their composition variation range is less than 0.1%, so the content data of P, S, Al and W are excluded.

[0096] Step 2.2: Perform correlation analysis on the composition data and heat treatment parameter data of the hot work die steel after manual rejection, and compare them with the yield strength data at 700℃, room temperature yield strength data, and impact energy data at -40℃, respectively, and screen out the common characteristics of the yield strength at 700℃, room temperature yield strength, and impact energy at -40℃.

[0097] Among them, the correlation coefficients between Nb and the yield strength at 700℃, the yield strength at room temperature, and the impact energy at -40℃ were -0.24, 0.0023, and -0.22, respectively; and the correlation coefficients between Zr and the yield strength at 700℃, the yield strength at room temperature, and the impact energy at -40℃ were -0.29, -0.16, and -0.28, respectively. Finally, the common characteristics of the yield strength at 700℃, the yield strength at room temperature, and the impact energy at -40℃ include nine features: C, Si, Mn, Cr, Ni, Mo, V, quenching temperature, and tempering temperature.

[0098] Table 1 shows the distribution of the initial dataset of yield strength at 700℃ in this embodiment; Table 2 shows the distribution of the initial dataset of yield strength at room temperature in this embodiment; Table 3 shows the distribution of the initial dataset of impact energy at -40℃ in this embodiment.

[0099] Step 3: Normalize the feature values ​​in the initial dataset from Step 2;

[0100] The formula for normalization is: X new =(X max -X) / (X max -X min In the formula, X new These are the normalized eigenvalues, and their range is 0 ≤ X. new ≤1; X is the eigenvalue before normalization, X max X is the largest eigenvalue within this feature. min It is the smallest eigenvalue within this feature.

[0101] Step 4: Using the dataset normalized in Step 3, select various machine learning algorithms to train the model, such as Linear Regression, Support Vector Machine (SVR), XGBoost, and Random Forest.

[0102] Step 4.1: First, shuffle the initial data groups in the normalized initial dataset as the smallest basic unit, arrange them randomly, and then divide them into training set and test set according to a 4:1 ratio.

[0103] Step 4.2: In the Python 3.8 runtime environment, select four machine learning algorithms: LinearRegression, Support Vector Machine (SVR), RandomForest, and XGBoost. Import LinearRegression from the sklearn.linear_model library, SVR from the sklearn.svm library, RandomForestRegressor from the sklearn.ensemble library, and XGBoost from the xgboost library.

[0104] Step 4.3: Import the training and test set data into four models: LinearRegression, SVR, RandomForest, and XGBoost. Use C, Si, Mn, Cr, Ni, Mo, V, quenching temperature, and tempering temperature as feature values, and use the yield strength at 700℃, room temperature yield strength, or impact energy at -40℃ as target values. Train the models separately, for a total of 12 models.

[0105] The LinearRegression algorithm requires no hyperparameter settings. The SVR algorithm, when constructing the 700℃ yield strength prediction model, the room temperature yield strength prediction model, and the -40℃ impact energy prediction model, has hyperparameters set to kernel = 'rbf', C = 100, gamma = 0.1, and epsilon = 0.1. When constructing the 700℃ yield strength prediction model, the RandomForest algorithm's hyperparameters are set to n_estimators = 80 and max_depth = 10, while the XGBoost algorithm's hyperparameters are set to n_estimators = 100, learning_rate = 0.1, and max_depth = 5. When constructing the room temperature yield strength prediction model, the hyperparameters of the RandomForest algorithm are set to n_estimators = 100 and max_depth = 10, and the hyperparameters of the XGBoost algorithm are set to n_estimators = 120, learning_rate = 0.1, and max_depth = 5. When constructing the -40℃ impact energy prediction model, the hyperparameters of the RandomForest algorithm are set to n_estimators = 70 and max_depth = 10, and the hyperparameters of the XGBoost algorithm are set to n_estimators = 80, learning_rate = 0.1, and max_depth = 3.

[0106] Step 5: Evaluate each model and select the machine learning algorithm with the best training effect to obtain the 700℃ yield strength prediction model, the room temperature yield strength prediction model, and the -40℃ impact energy prediction model.

[0107] The performance evaluation metric for the model is the coefficient of determination R. 2 and Mean Absolute Error (MAE), R 2 R is a statistical indicator used to characterize the goodness of fit of a regression model. 2 The closer the value is to 1, the better the model fits; the smaller the MAE value, the lower the model error.

[0108] Among them, the XGBoost algorithm for predicting yield strength at 700℃ showed the best learning performance, R 2 The value is 0.86, and the MAE value is 30.9, confirming it as the 700℃ yield strength prediction model; the room temperature yield strength prediction model shows the best learning effect from the RandomForest algorithm, R 2 With a value of 0.87 and a MAE value of 35.8, it is determined to be the room temperature yield strength prediction model; the RandomForest algorithm has the best learning effect for the -40℃ impact energy prediction model. 2 With a value of 0.75 and a MAE value of 3.39, it is determined to be the -40℃ impact energy prediction model.

[0109] Figure 2 This is a comparison chart of the actual value and the predicted value in the 700℃ yield strength prediction model established based on the XGBoost algorithm in this embodiment.

[0110] Figure 3 This is a comparison chart of the actual value and the predicted value in the room temperature yield strength prediction model established based on the RandomForest algorithm in this embodiment.

[0111] Figure 4 This is a comparison chart of the actual and predicted values ​​in the -40℃ impact energy prediction model established based on the RandomForest algorithm in this embodiment.

[0112] Step 6: Use the NSGA-II genetic algorithm to perform multi-objective optimization on the 700℃ yield strength, room temperature yield strength and -40℃ impact energy obtained by the prediction model in Step 5, and obtain multiple sets of optimal solutions;

[0113] Step 6.1: Establish the objective function and boundary constraints of the decision variables, and initialize the NSGA-II parameters;

[0114] The three performance indicators of yield strength at 700℃, yield strength at room temperature, and impact energy at -40℃ are defined as objective functions; C, Si, Mn, Cr, Ni, Mo, V, quenching temperature, and tempering temperature are defined as decision variables, and the upper and lower bounds of each decision variable are set according to the composition and process requirements of the target product. Table 4 shows the upper and lower bound setting standards for each decision variable in this embodiment.

[0115] In this embodiment, the NSGA-II parameter settings are as follows: the population size is set to 100 individuals, the maximum number of generations is 200, and the objective function tolerance is set to 0.25% as an early termination condition; a simulated binary crossover operator is used, with a crossover probability of 0.9 and a distribution exponent of 15; a polynomial mutation operator is used, with a mutation probability of 0.1 and a distribution exponent of 20.

[0116] Step 6.2: Execute the NSGA-II optimization process and iterative optimization procedure;

[0117] First, an initial population is generated, with each individual representing a combination of C, Si, Mn, Cr, Ni, Mo, V, quenching temperature, and tempering temperature. This process is then iterated until a termination condition is met. For each generation, the following steps are performed:

[0118] A. Evaluate the objective function value for each individual in the population;

[0119] B. Perform non-dominated ranking on the population, dividing individuals into multiple non-dominated layers;

[0120] C. Calculate the crowding distance for each individual to measure the distribution density of individuals in the same non-dominated layer;

[0121] D. Generate an inherent population through tournament selection, crossover, and mutation;

[0122] E. Merge parent and offspring populations and select the next generation population based on non-dominated ordering and crowding distance.

[0123] Step 6.3: Extract the Pareto optimal solution set and obtain multiple sets of optimal solutions using the weighted sum method;

[0124] The yield strength at 700℃, the yield strength at room temperature, and the impact energy at -40℃ are combined into a single comprehensive objective function through linear weighting: MinF(X)=-[af1(X)+bf2(X)+cf3(X)], where F(X) represents the comprehensive objective of the yield strength at 700℃, the yield strength at room temperature, and the impact energy at -40℃, and MinF(X) represents the optimal comprehensive objective; f1(X) represents the predicted value of the 700℃ yield strength prediction model, and f2(X) represents the predicted value of the room temperature yield strength prediction model. f3(X) represents the predicted value of the -40℃ impact energy prediction model. In this embodiment, the room temperature yield strength is required to reach 1350MPa, the 700℃ yield strength is required to reach 300MPa, and the -40℃ impact energy is required to be as high as possible. a, b, and c are the weight coefficients of the objective function. According to the importance of the performance, the weight of the 700℃ high temperature yield strength is set to 0.4, and the weights of the room temperature yield strength and the -40℃ impact energy are each set to 0.3. X is the decision variable, namely C, Si, Mn, Cr, Ni, Mo, V, quenching temperature, and tempering temperature.

[0125] Step 7: Determine the composition and heat treatment process parameters of the hot work die steel: Select the final composition and heat treatment process parameters of the hot work die steel from multiple optimal solutions.

[0126] Based on the optimal solution output by the model, material composition and heat treatment process parameters are selected. Table 5 shows the material composition and heat treatment process parameters selected from the optimal solution set in this embodiment.

[0127] Finally, based on the obtained hot work die steel content data and heat treatment process parameters, actual smelting and heat treatment were carried out, and the mechanical properties of the obtained hot work die steel samples were tested. The measured mechanical properties are shown in Table 6.

[0128] Table 1. Distribution of initial dataset of yield strength at 700℃ in Example 1

[0129]

[0130] Table 2. Distribution of initial dataset for room temperature yield strength in the embodiments.

[0131]

[0132]

[0133] Table 3. Distribution of the initial dataset of impact energy at -40℃ in Example 3

[0134]

[0135] Table 4. Upper and lower bound setting standards for each decision variable in the example.

[0136]

[0137] Table 5 shows the material composition and heat treatment process parameters selected from the optimal solution set in the examples.

[0138] Table 6. Measured Mechanical Properties of Hot Work Die Steel in Examples

[0139]

[0140] As shown in Table 6, the measured yield strength at 700℃ and room temperature yield strength are 1370MPa and 310MPa, respectively, both higher than the target performance of 1350MPa and 300MPa. The impact energy at -40℃ is 25J, which is close to the average value and meets the target performance requirements.

[0141] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method of designing a hot work die steel for multi-objective optimization, characterized by, The method comprises the following steps: Step 1, collecting the component content and heat treatment process parameters of hot work die steel, and corresponding 700 DEG C yield strength data, room temperature yield strength data, -40 DEG C impact energy data, and performing null value filling to form 700 DEG C yield strength original data set, room temperature yield strength original data set and -40 DEG C impact energy original data set respectively; Step 2, performing feature screening on the components and heat treatment processes of the hot work die steel in step 1 to determine the features that have influence on 700 DEG C yield strength, room temperature yield strength and -40 DEG C impact energy, and forming 700 DEG C yield strength initial data set, room temperature yield strength initial data set and -40 DEG C impact energy initial data set together with the determined features and corresponding 700 DEG C yield strength data, room temperature yield strength data and -40 DEG C impact energy data respectively; Step 3, performing normalization processing on the feature values in the initial data set in step 2; Step 4, using the data set after normalization processing in step 3, selecting a plurality of machine learning algorithms to perform model training respectively; Step 5, evaluating each model to select the machine learning algorithm with the optimal training effect, thereby obtaining 700 DEG C yield strength prediction model, room temperature yield strength prediction model and -40 DEG C impact energy prediction model; Step 6, using NSGA-II genetic algorithm to perform multi-objective optimization on the 700 DEG C yield strength, room temperature yield strength and -40 DEG C impact energy obtained through the prediction model in step 5 to obtain a plurality of optimal solutions; Step 7, determining the components and heat treatment process parameters of the hot work die steel: selecting and determining the final components and heat treatment process parameters of the hot work die steel from the plurality of optimal solutions.

2. The method of claim 1, wherein, In the step 1, the original data set is composed of a plurality of original data groups, and each original data group includes the contents of C, Si, Mn, P, S, Cr, Ni, Mo, V, Nb, Zr, W and Al, quenching temperature, tempering temperature and 700 DEG C yield strength or room temperature yield strength or -40 DEG C impact energy.

3. The method of claim 1, wherein, In the step 1, the null value filling is to directly fill 0 when the hot work die steel does not contain the component, and to fill the average value of quenching temperature or tempering temperature when the heat treatment process parameters of the hot work die steel do not exist.

4. The method of claim 1, wherein, The step 2 comprises the following sub-steps: Step 2.1, performing artificial elimination on the component content data and heat treatment parameter data of the hot work die steel with smaller data volume or narrower variation range; Step 2.2, performing correlation analysis on the component data and heat treatment parameter data of the hot work die steel after artificial elimination and 700 DEG C yield strength data, room temperature yield strength data and -40 DEG C impact energy data respectively to screen out the common features of 700 DEG C yield strength, room temperature yield strength and -40 DEG C impact energy.

5. The method of claim 4, wherein, In the step 2.1, the smaller data volume refers to that the data volume is not more than 10% of the total data, and the narrower variation range refers to that the component variation range is less than 0.1%.

6. The method of claim 4, wherein, In step 2.2, the correlation coefficient analysis is to delete the data with the correlation coefficient between the data of each component of the hot work die steel and the data of each parameter of the heat treatment greater than 0.95, and to eliminate the data with the correlation coefficient with the yield strength at 700 DEG C, the yield strength at room temperature and the impact energy at-40 DEG C all less than 0.

3.

7. The method of claim 1, wherein, In step 2, the characteristics include C, Si, Mn, Cr, Ni, Mo, V, quenching temperature and tempering temperature.

8. The method of claim 1, wherein, The step 4 comprises the following sub-steps: Step 4.1, first, the initial data set in the initial data set after normalization is taken as the minimum basic unit and is randomly arranged, and then is divided into a training set and a test set according to the quantity ratio of 4:1; Step 4.2, under the running environment of Python, four machine learning algorithms of linear regression (LinearRegression), support vector machine (SVR), RandomForest and XGBoost are selected, LinearRegression is imported from the sklearn.linear_model library, SVR is imported from the sklearn.svm library, RandomForestRegressor is imported from the sklearn.ensemble library, and XGBoost is imported from the xgboost library; Step 4.3, the training set and the test set data are imported into the four models of LinearRegression, SVR, RandomForest and XGBoost, C, Si, Mn, Cr, Ni, Mo, V, quenching temperature and tempering temperature are taken as characteristic values, and the yield strength at 700 DEG C or the yield strength at room temperature or the impact energy at-40 DEG C is taken as the target value, and model training is carried out respectively.

9. The method of claim 1 wherein, In step 5, the evaluation index of the evaluation is the coefficient of determination R 2 and the mean absolute error MAE; the 700℃ yield strength prediction model is a model based on the XGBoost algorithm, the room temperature yield strength prediction model is a model based on the RandomForest algorithm, and the -40℃ impact energy prediction model is a model based on the RandomForest algorithm.

10. The method of claim 1, wherein, The step 6 comprises the following sub-steps: Step 6.1, the objective function and the boundary constraint condition of the decision variable are established, and the NSGA-II parameters are initialized; Step 6.2, the NSGA-II optimization execution process and the iterative optimization process are executed; Step 6.3, the Pareto optimal solution set is extracted, and multiple groups of optimal solutions are obtained according to the weighted sum method.

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