數(shù)據(jù)挖掘
Making predictions of the lattice misfit rapidly and accurately is therefore of much practical importance, especially for costly and time-consuming material design by trial and error.So, we provide a machine learning approach to predict misfit using relevant material descriptors including the chemical composition, dendrite information and measurement temperature and so on. We perform support vector regression, sequential minimal optimization regression and multilayer perceptron algorithms with linear and poly kernels on experimental dataset for appropriate model selecting, and multilayer perceptron model works well for its distinguished prediction performance with high correlation coefficient and low error values. The approach is validated by comparing the predicted lattice misfit with a widely used empirical formula and experimental observation with respect to prediction accuracy.
The composition of superalloys in this dataset contains 13 elements, like Ni, Al, Co, Cr, Mo and so on, where Ni is dominated. The lattice misfits of the 136 instances are all measured by CBED after standard heat treatment of the specified alloy grand. The natural lattice misfit of c and c0 phase is depicted in Fig. 1(a). As it is illustrated in the published literatures , lattice misfit is definitely different in dendrite center and interdendrite, so we consider the measurement position of dendrite as an factor for lattice misfit during data collection, as shown in Fig. 1(b).
Here we set k = 10. Let D be our training set, and we split D into 10 mutually exclusive folds D1, D2; ... ;D10 of approximately equal size with 13 or 14 instances randomly. The regression algorithms are performed 10 times, and for each time 9 folds are used for training and leave one fold for testing. The performance of model training is shown in Fig. 2 with measured misfit on horizontal axis and predicted misfit on vertical axis. The predicted misfit values generated by the above five models are plotted as a function of the measured. The more closely the plots align along the 45 diagonal line, the more consistent the predicted misfits are with the measured. We can see that the MLP model performs a perfect fitting intuitively by Fig. 2(e).
Fig. 3 shows the correlation coefficient of the five machine learning models, and the MLP model has the highest value with 0.9794. The MAE and RMSE are means of difference evaluation between two continuous variables [28], given in Eqs. (6) and (7) respectively where jeij is the standard difference between the measured misfit and the predicted.
The values of MAE and RMSE are depicted in Fig. 4, where the blue1 bars represent RMSE and the green bars are MAE. We can see the MLP model has the lowest MAE and RMSE value with 0.178 and 0.2307. So we choose MLP as the selected model to predict lattice misfit on Ni-based single crystal superalloys quantitatively, for its distinguished correlation degree and minimal error.
The actual measured misfits by CBED, the calculated misfits by WATANABE (1957) model and our predicted misfits by MLP are compared in Fig. 5. It is obviously that for instance 2#, 3# and 4#, our MLP misfit model achieves the same accuracy as WATANABE (1957), both highly consistent with the measured misfit actually. And for instance 1#, the difference between our MLP predicted misfit and the measured value is 2.425, smaller than 2.703 between WATANABE (1957) and the measured value, and our MLP model has a high agreement with the measured in misfit sign (positive or negative) prediction, which is better than WATANABE (1957) model.
Conclusion
The informatics approach integrated with machine learning algorithms provides a novel methodology during material design, especially for lattice misfit of Ni-based single crystal superalloys. In this paper, we accumulate relevant dataset manually from open access literatures and construct a dedicated Ni-based single crystal superalloys database for data reuse. After data preprocessing is performed, we train misfit models by SVR, SMOreg and MLP machine learning algorithms with linear and poly kernels for appropriate model selecting. Finally we choose MLP model for its distinguished prediction performance with high correlation coefficient and low MAE and RMSE values. In addition, we compare the prediction accuracy between our MLP misfit model and the well-known empirical formula, and our method performs better. Therefore, machine learning assisted approach accelerates the misfit prediction procedure quantitatively with little experiment and measurement. It is of great importance to reduce the time and cost during alloy design. In the present study, we have considered the effects from composition, dendrite information, shape and size of specimen and temperature. However, other factors, including the effects of different heat treatment parameters and stress constraints, which are also critical to determine misfit, are to be resolved in the follow-on work. The explicit rules of factors to the desired misfit, which is suitable for creep and fatigue properties, are also expected to serve for inverse design of Ni-based single crystal superalloys.
相關(guān)工作已發(fā)表：Jiang, X., Yin, H. Q. (2018). An materials informatics approach to Ni-based single crystal superalloys lattice misfit prediction. Computational Materials Science, 143, 295-300.
