## 3 Methodology
### Stage 3: ANOVA Test  
The ANOVA Test is used to analyze the differences among the means of different groups using variance and to prove which groups are statistically significant. To prove that the performance is significantly different for various ML models, an ANOVA test [24] is implemented in this work. Figure 3 represents the probability plot of performance measures of the ML model obtained by executing the Python codes. It is understood that the values of R\({}^{2}\) and RMSE of both training and testing are within the 95% confidence interval and that their probability values are greater than 0.005. This shows that the experimentation results are acceptable for crack length prediction. Similarly, for crack depth and crack width, the \(p\)-value shown in Figure A1 and Table A6 is greater than 0.005, which reveals that the experimental results obtained are acceptable. The main and interaction effect plots of parameters are depicted in Figure 4a-h for crack length prediction. It is inferred from Figure 4a,b that the mean value of R2 Tr is higher when the parameters are MIS, 15, and XGB, whereas in R2 Tt the parameters are FS and 18, respectively. It is understood from Figure 4c,d, that for getting the lower mean value of RMSETr and RMSETt, the parameters are to be set in a different way than R2 Tr and R2 Tt. From Figure 4e,f, it is noted that increasing the NoF value decreases the R2 Tr value for all ML models, whereas in R2 Tt except MLM and DT in all other models, it increases. Using XGB, a lower RMSE is reported in Figure 4g,h. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**E.No.** & **FSM** & **MLM** & **NoF** & **R2 Tr** & **R2 Tt** & **RMSETr** & **RMSETt** & **Deng’s Value** \\ \hline
1 & FS & DT & 15 & 0.2619 & 0.3737 & 0.9684 & 1.4000 & 0.4569 \\
2 & FS & DT & 17 & 0.1998 & 0.4572 & 1.0000 & 1.3000 & 0.4771 \\
3 & MIS & DT & 19 & 0.6100 & 0.1434 & 1.0278 & 1.6440 & 0.4879 \\
4 & MIS & DT & 21 & 0.5940 & 0.1429 & 1.0282 & 1.6446 & 0.5040 \\
5 & FS & LiR & 15 & 0.9596 & 0.6091 & 0.2346 & 1.2090 & 0.4434 \\
6 & FS & LiR & 17 & 0.9592 & 0.6209 & 0.2389 & 1.1815 & 0.4616 \\
7 & MIS & LiR & 19 & 0.9221 & 0.6109 & 0.3917 & 1.1977 & 0.4643 \\
8 & MIS & LiR & 21 & 0.9078 & 0.5437 & 0.4225 & 1.2860 & 0.4248 \\
9 & MIS & LoR & 15 & 0.6002 & 0.1449 & 0.8200 & 1.6425 & 0.5484 \\
10 & MIS & LoR & 17 & 0.6120 & 0.1441 & 0.8150 & 1.6433 & 0.5360 \\
11 & FS & LoR & 19 & 0.5860 & 0.1434 & 0.8008 & 1.6441 & 0.5324 \\
12 & FS & LoR & 21 & 0.3960 & 0.1430 & 0.8400 & 1.6445 & 0.5408 \\
13 & MIS & XGB & 15 & 0.8652 & 0.8646 & 0.4410 & 0.6942 & 0.6073 \\
14 & MIS & XGB & 17 & 0.8757 & 0.8705 & 0.4055 & 0.6869 & 0.6444 \\
15 & FS & XGB & 19 & 1.0000 & 0.5988 & 0.0005 & 1.1801 & 0.6263 \\
16 & FS & XGB & 21 & 1.0000 & 0.5841 & 0.0006 & 1.2013 & 0.6326 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: L16 OA—Performance of ML for Crack Length. Figure 3: _Cont._Figure 4: _Cont._  
Figure 3: Probability Plot of Performance Measures of ML Models in Crack Length. (**a**) Probability Plot for Crack Length-R\({}^{2}\)Tr. (**b**) Probability Plot for Crack Length-R\({}^{2}\)Tr. (**c**) Probability Plot for Crack Length-RMSETr. (**d**) Probability Plot for Crack Length-RMSETt. The main and interaction effects plots for crack depth and width are shown in Figures 15a-15a and 15a-15b. It is observed that different parameter settings are required for getting an individual's optimum response value. Hence, in this work, [PERSON]'s method is introduced to select the best parameter settings based on R2 Tr, R2 Tr, RMSETr, and RMSETt values. It is inferred that FS, 19, and XGB are the optimum parameters for the highest [PERSON]'s value, which will give optimum response values. The \(p\)-values of factors and their interactions for the training dataset, except for the interaction between FSM and MLM, are all greater than 0.05 in Table 5, which confirms that none of the factors and their interactions influence the performance of ML Models. In the testing dataset, it is identified that NoF and MLM are the influencing parameters.