## 3 Results and Discussion
### Machine Learning  
In this work, a total of 40 sets of spraying process parameters and microstructure and thermal cycle life data were selected to form a number set: 70% of the data set was taken as the training set, and 30% was taken as the prediction set to train and predict the machine learning model. The input is the spraying process parameters (powder feeding rate, distance between two powder feeders, and powder type), and the output is the content and thermal cycle life. The accuracy of predicting the microstructure and service life of the coating was explored to provide help for further improving the life of TBCs. In this work, a BP machine learning model, SVM machine learning model, and GA-SVM machine learning model were used to predict the microstructure and life data of EMAP TBCs, respectively, to explore the accuracy of three different machine learning models for predicting the MAP content and thermal cycle life of EMAP TBCs. Figure 9 shows the effectiveness of BP, SVM, and GA-SVM in evaluating the nonlinear relationship between spraying process parameters and the microstructure and thermal  
Figure 8: FCT life diagram of EMAP TBCs prepared by different plasma-spraying processes. (**a**) Effect of feeding rate1 on FCT life; (**b**) effect of feeder distance on FCT life; (**c**) the effect of the type of the first-phase powder on the FCT life; (**d**) FCT life comparison of two TBCs. cycle life data of EMAP TBCs. Among them, the dotted line of test values is the true value of the test set, while the dotted line values of BP, SVM, and GA-SVM are the predicted values of the MAP content and FCT life of the coatings. The better the fitting effect between the prediction results of the machine learning model and the test values, the better the evaluation effect. Among them, the GA-SVM algorithm has the best fitting effect and higher prediction accuracy for the MAP content data and thermal cycle life data of EMAP TBCs. As shown in Table 2, it is an evaluation index analysis table for the prediction results of the three models of EMAP TBCs life prediction. The regression coefficients R\({}^{2}\) of BP, SVM, and GA-SVM were 0.906, 0.959, and 0.979, respectively. The root mean square error (RMSE) of BP, SVM, and GA-SVM are 5.460, 3.125, and 2.563, respectively. The mean absolute errors (MAE) of BP, SVM, and GA-SVM are 4.345, 2.580, and 1.697, respectively. Through comparative analysis, it can be found that the regression coefficient R of the GA-SVM prediction model is the largest, and the prediction effect is the best. The error indexes RMSE and MAE of GA-SVM are the smallest, and its prediction accuracy is the highest. Similarly, as shown in Table 3, for the prediction of MAP content in EMAP TBCs, the error of the GA-SVM prediction model is the smallest, and R2 is the largest, which is 0.951. It shows that the GA-SVM prediction model has the best prediction effect in the prediction of the spraying process and microstructure data and thermal cycle life data of EMAP TBCs. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Forecasting Model** & \(\mathbf{R^{2}}\) & **RMSE** & **MAE** \\ \hline BP & 0.906 & 5.460 & 4.345 \\ SVM & 0.959 & 3.125 & 2.580 \\ GA-SVM & 0.979 & 2.563 & 1.697 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Coating lifetime prediction error analysis. Figure 9: MAP proportion and EMAP TBCs life prediction results fitting diagram. (**a**) MAP content prediction results fitting diagram; (**b**) fitting diagram of FCT life prediction results of EMAP TBCs. The results show that the machine learning method is used to predict the microstructure and thermal cycle life of EMAP TBCs, which has a good prediction effect. Among them, the GA-SVM machine learning model is used to predict the microstructure and life data of EMAP TBCs, and the prediction effect is the best. The prediction accuracy of BP, SVM, and GA-SVM is evaluated by combining the error index and regression coefficient R\({}^{2}\).