# Innovative Approach Integrating Machine Learning Models for Coiled Tubing Fatigue Modeling
## 7 Correlation Analysis  
### Heatmap Correlation  
The correlation heatmap (Figure 10) provides valuable insights into the mechanistic influence of various parameters on the fatigue life of coiled tubing, as measured in N cycles. A detailed examination of the correlation values allows us to identify key factors that either enhance or degrade fatigue resistance in the material.  
Among the positively correlated features, wall thickness (+0.26) shows a moderate correlation with fatigue life, suggesting that increasing the wall thickness improves fatigue resistance. Mechanistically, thicker walls mitigate stress concentrations, delaying the initiation and propagation of fatigue cracks. Similarly, the absence of welds (Weld_Type_none, +0.37) significantly enhances fatigue life, as welding often introduces discontinuities, residual stresses, and metallurgical defects that can act as crack initiation sites. Additionally, bending radius (+0.30) exhibits a positive correlation, indicating that a larger bending radius reduces strain-induced damage, thereby extending fatigue life.  
Conversely, several features exhibit a negative correlation with fatigue life, indicating detrimental effects. Coiled tubing diameter (\(-0.29\)) negatively affects fatigue performance, which can be attributed to the fact that larger diameters undergo greater bending stresses during repeated coiling and uncoiling operations, accelerating crack growth. Similarly, manual welding (\(-0.39\)) has the strongest negative correlation, highlighting the adverse effects of inconsistencies in manually welded sections, which introduce defects such as porosity, incomplete fusion, and higher residual stresses that reduce fatigue resistance. Even orbital welding (\(-0.16\)), which is generally more consistent than manual methods, exhibits a negative correlation due to the heat-affected zone (HAZ) altering material properties and reducing fatigue resistance. Other parameters demonstrate weaker correlations with fatigue life. Material grade (\(+0.24\)) shows a slight positive influence, suggesting that higher-strength materials offer improved resistance to cyclic loading, likely due to their refined microstructure and better fatigue crack resistance. Operating pressure (\(-0.06\)), despite being a crucial factor in wellbore operations, exhibits a weak negative correlation, implying that bending loads dominate fatigue damage mechanisms more than internal pressure fluctuations.  
Table 3 presents a summary of the impact of mechanistic features on the fatigue life of CT.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{3}{c}{**Mechanistic Summary**} \\ \hline
**Feature** & **Correlation with N Cycle** & **Mechanistic Explanation** \\ \hline Wall Thickness & 0.26 & Thicker walls reduce stress concentration, \\ Weld\_Type\_none & 0.37 & No welds = No defects, better fatigue resistance. \\ CT Diameter & \(-0.29\) & Larger diameter \(\rightarrow\) Higher bending stress \(\rightarrow\) Lower fatigue life. \\ Weld\_Type\_manual & \(-0.39\) & Manual welding introduces defects and residual stress, reducing fatigue life. \\ Weld\_Type\_orbital & \(-0.16\) & Orbital welding still causes some HAZ effects, \\ Grade & 0.24 & Higher grades offer better fatigue resistance. \\ Pressure & \(-0.06\) & Weak influence; bending loads dominate over \\ Radius & 0.3 & Larger bending radius reduces strain, increasing \\ \hline \hline \end{tabular}
\end{table}
Table 3: Summary of mechanistic feature impact on fatigue life of CT.  
Figure 10: Correlation analysis between features and N cycle.  
In conclusion, this analysis highlights the influence of welding methods, tubing diameter, and bending radius on fatigue life. Strategies to improve fatigue resistance should emphasize minimizing welding defects, optimizing tubing geometry, and increasing bending radius to reduce cyclic strain.