# Methods for Corrosion Detection in Pipes Using Thermography: A Case Study on Synthetic Datasets
## 4 Case Study
### Data Augmentation with FEM  
To enhance the dataset and complement the experimental findings, this study's setup was replicated within the COMSOL Multiphysics environment. This simulation aimed to precisely model the steel pipes, fiberglass insulation, and aluminum cladding, incorporating defects similar to moisture ingress to thoroughly analyze their thermal impact. The simulation was based on the assumption of material homogeneity across all components, with boundary conditions set to no heat loss at the pipe ends, reflecting the \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Pipe ID** & **Length (mm)** & **Diameter (mm)** & **SCH** & **Thickness (mm)** \\ \hline
1 & 3200 & 50.8 & 40 & 3.91 \\ \hline
2 & 3200 & 50.8 & 80 & 5.54 \\ \hline
3 & 3200 & 76.2 & 40 & 5.49 \\ \hline
4 & 3200 & 76.2 & 80 & 7.62 \\ \hline
5 & 3200 & 152.4 & 40 & 7.11 \\ \hline
6 & 3200 & 152.4 & 80 & 10.97 \\ \hline \hline \end{tabular} Note: SCH (Schedule) refers to the wall thickness of the pipes.  
\end{table} 
Table 2: Dimension of the pipes. Figure 4: Defined ROI for the thermal image of pipe number 6 and 12.7 cm defect [51]. Figure 3: Experimental setup showing the moisture simulation process. (**a**) Cut of insulation at planned geometry [50]. (**b**) Installation of wet insulation in cut regions [51]. experimental setup. This approach ensured a focused analysis of the thermal behavior attributable to the introduced defects, aligning the computational model closely with the physical experiments. Defects were introduced in the simulation by substituting sections of the original insulation with new material representing wet insulation. This method simulated various moisture levels, expanding the range of defect sizes from as small as 0.1 inches to as large as 5 inches, aiming to understand the impact of defect size on thermal performance more comprehensively. Table 3 details the range of simulated defect sizes for each pipe ID. The simulations used steady-state conditions to mirror the experimental setup, focusing on achieving a uniform thermal regime. To accurately model the wet insulation's thermal properties, mixture rules were utilized. These rules allow for the calculation of effective thermal properties such as thermal conductivity (\(k\)), density (\(\rho\)), and specific heat capacity at constant pressure (\(c_{p}\)) for the insulation, taking into account varying moisture contents. The equations used are as follows:  
\[k_{wet}=V_{water}.k_{water}+V_{insulation}.k_{insulation} \tag{1}\]  
\[\rho_{wet}=V_{water}.\rho_{water}+V_{insulation}.\rho_{insulation} \tag{2}\]  
\[c_{p_{wet}}=\frac{V_{water}.\rho_{water}.c_{p_{water}}+V_{insulation}.\rho_{ insulation}.c_{p_{insulation}}}{\rho_{wet}} \tag{3}\]  
where  
* \(V_{water}\) and \(V_{insulation}\) are the volume fractions of water and insulation, respectively, satisfying \(V_{water}+V_{insulation}=1\). * \(k_{water}\), \(\rho_{water}\), and \(c_{p_{water}}\), are the thermal conductivity, density, and specific heat capacity at constant pressure of water, respectively. * \(k_{insulation}\), \(\rho_{insulation}\), and \(c_{p_{insulation}}\) are the corresponding properties of the insulation material. * This formulation provides a nuanced view of how moisture content influences the insulation's thermal properties. These formulations allowed us to accurately model the thermal behavior of insulation with 70% wetness levels, directly correlating with the experimental conditions. Table 4 presents the material properties used in the simulation, including the base properties of steel, fiberglass insulation, water, and aluminum. The conduction occurs between solid phases in each material and at contact surfaces. The conduction heat transfer is governed by \(q=-k(T_{ext}-T)\) where \(k\) is the conduction