## 4 Experiments Results and Discussions
### Experiments and Analysis of Coating Lifetime Estimation  
As a durable part of the turbine blade, its economy should be considered in the real service process. The service lives of turbine blades can be greatly prolonged by removing coating and re-spraying. Therefore, it is also of significance to accurately estimate the TBCs lifetime to determine the operation decisions for gas turbines without causing irreparable damage to the hot components. In order to quantitatively evaluate the deviation between the predicted results and the ground truth, the Root Mean Square Error (RMSE) is adopted: which is defined as:  
\[RMSE=\sqrt{\frac{1}{n}\sum_{i}^{\overline{n}}(R_{i}-P_{i})^{2}} \tag{15}\]  
In Equation (15), \(n\) is the total number of predictions, \(R_{i}\) is the real RUL of the \(i_{th}\) sample. It is given by the finite element simulation results on the numericial model. \(P_{i}\) is the predicted RUL of the \(i_{th}\) sample using the lifetime prediction methods. The physical model, RVM model and information entropy fusion model are compared by predicting the RUL of the TBC. Table 5 lists the comparison of RUL prediction results using single method and weighted fusion algorithms. It can be seen that the fusion method based on information entropy has the best effect, which is superior to the other two methods in terms of the RMSE. The time cost of using the single detection method is shorter than that of the fusion method. However, all the time consumption periods for these methods are less than 2 s, which is acceptable for on-line monitoring of coatings with a low sampling rate. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Class\textbackslash\{Method}** & **Proposed** & **Faster R-CNN** & **YOLOv4** & **SSD** & **MMTLNet** & **SegNet** \\ \hline Non-crack & **0.821** & 0.747 & 0.764 & 0.783 & 0.665 & 0.626 \\ Large-scale cracks & **0.864** & 0.814 & 0.802 & 0.726 & 0.699 & 0.638 \\ \hline Small-scale cracks & **0.712** & 0.650 & 0.668 & 0.677 & 0.640 & 0.606 \\ Average & **0.806** & 0.739 & 0.747 & 0.732 & 0.673 & 0.627 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Algorithms comparison in crack detection accuracy. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Class\textbackslash\{Method}** & **Proposed** & **Faster R-CNN** & **YOLOv4** & **SSD** & **MMTLNet** & **SegNet** \\ \hline Non-crack & **0.915** & 0.822 & 0.825 & 0.819 & 0.754 & 0.726 \\ Large-scale cracks & **0.923** & 0.850 & 0.861 & 0.830 & 0.780 & 0.731 \\ \hline Small-scale cracks & **0.848** & 0.763 & 0.767 & 0.714 & 0.552 & 0.509 \\ Average & **0.898** & 0.819 & 0.823 & 0.782 & 0.698 &The lifetime estimation result calculated by the fusion model is depicted in Figure 7. The result reveals that the effect of crack length on coating lifetime is nonlinear. When the crack length is between 20 \(\upmu\)m and 200 \(\upmu\)m, the coating lifetime fraction does not increase significantly, but when the crack length is above 220 \(\upmu\)m, the coating lifetime has entered a sharp downturn, which reflects that the crack length has an exponential effect on the internal stress. This conclusion is basically consistent with the detection accuracy given by Figure 5 since when the crack length is more than 220 \(\upmu\)m, the detection accuracy also sees a great improvement. The error rate of different porosities and temperature legends in variation of crack lengths is also described in the figure. The temperature legend represents the range of the whole picture. When the temperature legend is set larger and the shooting range remains (as is the case in this study), its resolution will be lower, providing disturbance for lifetime prediction. The temperature legend in this lifetime prediction experiment is set between 1020 \({}^{\circ}\)C and 1080 \({}^{\circ}\)C initially, and expanded to between 940 \({}^{\circ}\)C and 1080 \({}^{\circ}\)C. The porosity is set at 25% initially, and decreased to 5% by the end. From the figure it can be seen that all detection conditions of the error rates are below 15%.