<p>The applications of high-hardness refractory alloys in fields such as aerospace, nuclear energy, and the chemical industry are growing, driving the demand for new alloy designs. This paper aims to effectively predict the hardness of Ti-Zr-Nb-Ta alloys through the construction of machine learning models, so as to accelerate the development of new high-hardness alloys. The ETR model exhibits the highest prediction accuracy and the smallest error in both the training set and the test set, and shows good generalization ability on unknown data. Through PCC and MIC analysis, RMS_<i>R</i>, <i>T</i><sub>m</sub>, ENC, and APE are determined as the key features affecting the hardness of the alloy. Given that the small size of the original dataset affects the accuracy, data augmentation using a generative model was carried out, and the model accuracy was significantly improved when 200 generated data points were added. Subsequently, based on the high-precision model, the SHAP theory has been further introduced for interpretive analysis, and the results showed that the feature importance ranking is RMS_<i>R</i>, ENC, <i>T</i><sub>m</sub>, and APE. An increase in RMS_<i>R</i> and ENC, an elevation in <i>T</i><sub>m</sub>, and a decrease in APE all contribute to improving the hardness of the alloy. Based on the predictions of the machine learning model, it is determined that, in the Ti-Zr-Nb-Ta alloy, adding approximately 0.35&#xa0;at.% of Ta and 0.35–0.45&#xa0;at.% of Zr can achieve a hardness higher than 500&#xa0;HV. In addition, considering features such as atomic size difference, effective charge number, melting point, and electronegativity, Cr, Mo, W, and Hf have been finally selected as new alloying elements to construct the Ti-Zr-Nb-Ta-X (X = Cr, Mo, W, Hf) alloy system, so as to accelerate the design of new high-hardness alloys. These research results provide an important theoretical basis and practical guidance for the development of high-performance refractory alloys in the future.</p>

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Study on Hardness Prediction and Design of Ti-Zr-Nb-Ta Refractory Alloy Based on Interpretable Machine Learning and Generative Model

  • Chengcheng Liu,
  • Hang Su

摘要

The applications of high-hardness refractory alloys in fields such as aerospace, nuclear energy, and the chemical industry are growing, driving the demand for new alloy designs. This paper aims to effectively predict the hardness of Ti-Zr-Nb-Ta alloys through the construction of machine learning models, so as to accelerate the development of new high-hardness alloys. The ETR model exhibits the highest prediction accuracy and the smallest error in both the training set and the test set, and shows good generalization ability on unknown data. Through PCC and MIC analysis, RMS_R, Tm, ENC, and APE are determined as the key features affecting the hardness of the alloy. Given that the small size of the original dataset affects the accuracy, data augmentation using a generative model was carried out, and the model accuracy was significantly improved when 200 generated data points were added. Subsequently, based on the high-precision model, the SHAP theory has been further introduced for interpretive analysis, and the results showed that the feature importance ranking is RMS_R, ENC, Tm, and APE. An increase in RMS_R and ENC, an elevation in Tm, and a decrease in APE all contribute to improving the hardness of the alloy. Based on the predictions of the machine learning model, it is determined that, in the Ti-Zr-Nb-Ta alloy, adding approximately 0.35 at.% of Ta and 0.35–0.45 at.% of Zr can achieve a hardness higher than 500 HV. In addition, considering features such as atomic size difference, effective charge number, melting point, and electronegativity, Cr, Mo, W, and Hf have been finally selected as new alloying elements to construct the Ti-Zr-Nb-Ta-X (X = Cr, Mo, W, Hf) alloy system, so as to accelerate the design of new high-hardness alloys. These research results provide an important theoretical basis and practical guidance for the development of high-performance refractory alloys in the future.