Hardness prediction of WC-Co cemented carbide based on machine learning model

Song Rui; Liu Xue-Mei; Wang Hai-Bin; Lü Hao; Song Xiao-Yan

doi:10.7498/aps.73.20240284

Abstract

The hardness of cemented carbides is a fundamental property that plays a significant role in their design, preparation, and application evaluation. This study aims to identify the critical factors affecting the hardness of WC-Co cemented carbides and develop a high-throughput predictive model for hardness. A dataset consisting of raw material composition, sintering parameters and characterization results of cemented carbides is constructed in which the hardness of cemented carbide is set as the target variable. By analyzing the Pearson correlation coefficient, Shapley additive explanations (SHAP) results, WC grain size and Co content are determined to be the key characteristics influencing the hardness of cemented carbide. Subsequently, machine learning models such as support vector regression (SVR), polynomial regression (PR), gradient boosting decision tree (GBDT), and random forest (RF) are optimized to construct prediction models for hardness. Evaluations using 10-fold cross-validation demonstrate that the GBDT algorithm model exhibits the highest accuracy and strong generalization capability, making it most suitable for predicting and analyzing the hardness of cemented carbides. Based on predictions from GBDT algorithm model, PR algorithm model is established to achieve high-precision interpretable prediction of the hardness of cemented carbides. As a result, a quantitative relationship between hardness and Co content and WC grain size is obtained, demonstrating that reducing grain size and Co content is the key to obtaining high hardness of cemented carbide. This research provides a data-driven method for accurately and efficiently predicting cemented carbide properties, presenting valuable insights for the design and development of high-performance cemented carbide materials.

Keywords:

Authors and contacts

Key Laboratory of Advanced Functional Materials, Education Ministry of China, College of Materials Science and Engineering, Beijing University of Technology, Beijing 100124, China

Corresponding author: Liu Xue-Mei, liuxuemei@bjut.edu.cn ; Song Xiao-Yan, xysong@bjut.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 52271085, 92163107, 52171061).

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References

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Cited By

图 1 WC-Co硬质合金硬度预测的机器学习模型构建流程图

Figure 1. Hardness prediction workflow of WC-Co cemented carbides based on ML.

DownLoad: Full-Size Img PowerPoint

图 2 影响硬质合金硬度特征之间的皮尔逊线性相关系数

Figure 2. Pearson linear correlation coefficient of among the influence features on the hardness of cemented carbides.

DownLoad: Full-Size Img PowerPoint

图 3 目标变量为硬度时各特征SHAP值(a)和各特征平均SHAP的绝对值(b)的排序

Figure 3. SHAP values (a) and the absolute value of average SHAP (b) of each feature with target variable of hardness.

DownLoad: Full-Size Img PowerPoint

图 4 典型参数对GBDT算法模型的测试集准确率(R²)、偏差(Bias)和方差(Var)的影响　(a) 弱学习器数量; (b) 树的最大深度; (c) 叶子节点最少样本数; (d) 内部节点再划分所需最小样本数

Figure 4. Performance of typical parameters on the testing set in terms of accuracy (R²)、bias (Bias) and variance (Var) based on GBDT model: (a) Number of estimator; (b) max depth; (c) min sample leaf; (d) min sample split.

DownLoad: Full-Size Img PowerPoint

图 5 四种算法模型训练集学习效果　(a) SVR算法; (b) PR算法; (c) GBDT算法; (d) RF算法

Figure 5. Performance of four models on training set: (a) SVR algorithm; (b) PR algorithm; (c) GBDT algorithm; (d) RF algorithm.

DownLoad: Full-Size Img PowerPoint

图 6 四种算法模型测试集学习效果　(a) SVR算法; (b) PR算法; (c) GBDT算法; (d) RF算法

Figure 6. Performance of four models on testing set: (a) SVR algorithm; (b) PR algorithm; (c) GBDT algorithm; (d) RF algorithm.

DownLoad: Full-Size Img PowerPoint

图 7 不同机器学习算法模型测试集效果对比　(a) MSE和MAE; (b) 经10次10折交叉验证得到的R²

Figure 7. Performance of different machine learning algorithms on testing set: (a) MSE and MAE; (b) and R² score by 10-fold cross-validation.

DownLoad: Full-Size Img PowerPoint

图 8 硬质合金硬度随WC晶粒尺寸和Co含量的变化　(a) 原始数据; (b) GBDT模型预测

Figure 8. Hardness of cemented carbides as a function of WC grain size and Co content: (a) Original data; (b) data predicted by GBDT model.

DownLoad: Full-Size Img PowerPoint

图 9 PR算法模型训练及预测效果的评估　(a) 训练集与测试集预测的MAE, MSE; (b) PR算法模型测试集预测准确率

Figure 9. Evaluation of the PR model: (a) MSE and MAE for the training and testing sets; (b) R² for the testing set.

DownLoad: Full-Size Img PowerPoint

图 10 PR算法模型的硬质合金硬度预测结果　(a) 硬度随WC晶粒尺寸、Co含量变化的三维图; (b) 硬度在WC晶粒尺寸和Co含量构成平面上的投影图

Figure 10. Hardness of cemented carbides predicted by the PR model: (a) Hardness varing with WC grain size and Co content; (b) hardness projection on the plane of WC grain size and Co content.

DownLoad: Full-Size Img PowerPoint

图 11 硬度大于1800 kgf/mm²区域的硬质合金硬度预测结果　(a) 硬度随WC晶粒尺寸的变化; (b) 硬度随Co含量的变化

Figure 11. Prediction of hardness in a range of hardness higher than 1800 kgf/mm²: (a) Hardness varying with WC grain size; (b) hardness varying with Co content.

DownLoad: Full-Size Img PowerPoint

图 12 不同WC晶粒尺寸下硬度变化率随Co含量的变化

Figure 12. Hardness slope with different variables with Co content under different WC grain size.

DownLoad: Full-Size Img PowerPoint

DownLoad: Full-Size Img PowerPoint

[1]	丁业章, 叶寅, 李多生, 徐锋, 朗文昌, 刘俊红, 温鑫 2023 物理学报 72 068703 Google Scholar Ding Y Z, Ye Y, Li D S, Xu F, Lang W C, Liu J H, Wen X 2023 Acta Phys. Sin. 72 068703 Google Scholar
[2]	Useldinger R, Schleinkofer U 2017 Int. J. Refract. Met. Hard Mater. 62 170 Google Scholar
[3]	Springs G E 1995 Int. J. Refract. Met. Hard Mater. 13 241 Google Scholar
[4]	Ghasali E, Orooji Y, Tahamtan H, Asadian K, Alizadeh M, Ebadzadeh T 2020 Ceram. Int. 46 29199 Google Scholar
[5]	Ezquerra B L, Lozada L, Berg H V D, Wolf M, Sánchez J M 2018 Int. J. Refract. Met. Hard Mater. 72 89 Google Scholar
[6]	Sun L, Yang T E, Jia C C, Xiong J 2011 Int. J. Refract. Met. Hard Mater. 29 147 Google Scholar
[7]	Ding Q J, Zheng Y, Ke Z, Zhang G T, Wu H, Xu X Y, Lu X P, Zhu X G 2020 Int. J. Refract. Met. Hard Mater. 87 105166 Google Scholar
[8]	Hu H X, Liu X M, Chen J H, Lu H, Liu C, Wang H B, Luan J H, Jiao Z B, Liu Y, Song X Y 2022 J. Mater. Sci. Technol. 104 8 Google Scholar
[9]	Yu S B, Min F L, Ying G B, Noudem J G, Liu S J, Zhang J F 2021 Mater. Charact. 180 111386 Google Scholar
[10]	Tang Y Y, Wang S N, Xu F Y, Hong Y K, Luo X, He S M, Chen L Y, Zhong Z Q, Chen H, Xu G Z, Yang Q M 2021 J. Alloy Compd. 882 160638 Google Scholar
[11]	Jafari M, Enayati M H, Salehi M, Nahvi S M, Park C G 2014 Ceram. Int. 40 11031 Google Scholar
[12]	Wang H, Zeng M Q, Liu J W, Lu Z C, Shi Z H, Ouyang L Z, Zhu M 2015 Int. J. Refract. Met. Hard Mater. 48 97 Google Scholar
[13]	Singla G, Singh K, Pandey O P 2014 Ceram. Int. 40 5157 Google Scholar
[14]	Liu W H, Wu Y, He J Y, Nieh T G, Lu Z P 2013 Scripta Mater. 68 526 Google Scholar
[15]	Liu X M, Song X Y, Wei C B, Gao Y, Wang H B 2012 Scripta Mater. 66 825 Google Scholar
[16]	Song X Y, Gao Y, Liu X M, Wei C B, Wang H B, Xu W W 2013 Acta Mater. 61 2154 Google Scholar
[17]	Bonache V, Salvador M D, Fernández A, Borrell A 2011 Int. J. Refract. Met. Hard Mater. 29 202 Google Scholar
[18]	Fang Z , Maheshwari P, Wang X, Sohn H Y, Griffo A, Riley R 2005 Int. J. Refract. Met. Hard Mater. 23 249 Google Scholar
[19]	Fang Z Z, Wang X, Ryu T, Hwang K S, Sohn H Y 2009 Int. J. Refract. Met. Hard Mater. 27 288 Google Scholar
[20]	Liu K, Wang Z H, Yin Z B, Cao L Y, Yuan J T 2018 Ceram. Int. 44 18711 Google Scholar
[21]	赵世贤, 宋晓艳, 刘雪梅, 魏崇斌, 王海滨, 高杨 2011 金属学报 47 1188 Google Scholar Zhao S X, Song X Y, Liu X M, Wei C B, Wang H B, Gao Y 2011 Acta Metall. Sin. 47 1188 Google Scholar
[22]	Roy A, Babuska T, Krick B, Balasubramanian G 2020 Scripta Mater. 185 152 Google Scholar
[23]	Chanda B, Jana P P, Das J 2021 Comp. Mater. Sci. 197 110619 Google Scholar
[24]	George K, Haoyan D, Chanho L, Samaei A T, Tu P, Maarten J, Ke A, Dong M, Peter K L, Wei C 2019 Acta Mater. 181 124 Google Scholar
[25]	Bakr M, Syarif J, Hashem I A T 2022 Mater. Today. Commun. 31 103407 Google Scholar
[26]	Ozerdem M S, Kolukisa S 2009 Mater. Design 30 764 Google Scholar
[27]	Sun Y, Zeng W D, Han Y F, Ma X, Zhao Y Q, Guo P, Wang G, Dargusch M S 2012 Comp. Mater. Sci. 60 239 Google Scholar
[28]	Zhang X Y, Dong R F, Guo Q W, Hou H, Zhao Y H 2023 J. Mater. Res. Technol. 26 4813 Google Scholar
[29]	Catal A A, Bedir E, Yilmaz R, Swider M A, Lee C, El-Atwani O, Maier H J, Ozdemir H C, Canadinc D 2024 Comp. Mater. Sci. 231 112612 Google Scholar
[30]	Guan Z H, Tian H X, Li N, Long J Z, Zhang W B, Du Y 2023 Ceram. Int. 49 613 Google Scholar
[31]	Guan Z H, Li N, Zhang W B, Wang J J, Wang C B, Shen Q, Xu Z G, Peng J, Du Y 2022 Int. J. Refract. Met. Hard Mater. 104 105798 Google Scholar
[32]	Rahadian H, Bandong S, Widyotriatmo A, Joelianto E 2023 Alex. Eng. J. 82 304 Google Scholar
[33]	Zhong L, Guo X, Ding M, Ye Y C, Jiang Y F, Zhu Q, Li J L 2024 Comput. Electron. Agr. 217 108627 Google Scholar
[34]	Someh N G, Pishvaee M S, Sadjadi S J, Soltani R 2020 J. Eval. Clin. Pract. 26 1498 Google Scholar
[35]	Cervantes J, Lamont F G, Mazahua L R, Lopez A 2020 Neurocomputing 408 189 Google Scholar
[36]	Tsai C Y, Kim J, Jin F, Jun M, Cheong M, Yammarino F J 2022 Leadership Quart. 33 101592 Google Scholar
[37]	Khakurel H, Tanfique M F N, Roy A, Balasubramanian G, Ouyang G, Cui J, Johson D D, Devanathan R 2021 Sci. Rep. 1117149 Google Scholar
[38]	Genuer R, Poggi J M, Malot C T, Vialaneix N V 2017 Big Data Res. 9 28 Google Scholar

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