## 2 Materials and Methods
### Full Factorial Design  
The full factorial design was employed to investigate the complex interactions among three factors: temperature, flow velocity, and pH. The design involved three levels for each factor as shown in Table 2, and it was structured to simulate the conditions inside open circuit seawater cooling pipes. Each factor and their levels were set as follows:  
(1) Temperature ranges [17]:  
The temperature was set to reflect the surface seawater temperatures encountered during actual ship sailing, which generally range from 10 \({}^{\circ}\)C to 35 \({}^{\circ}\)C. However, within the seawater cooling system, the coolant temperature can rise up to 40 \({}^{\circ}\)C.  
(2) Flow velocity ranges:  
The flow velocity was set considering the actual conditions of seawater cooling pipes (max. 3.0 m/s) and the limitations of the experimental setup.  
(3) pH ranges:  
The pH of seawater typically ranges from 7.7 to 8.3, showing a slightly alkaline nature. However, due to increasing atmospheric CO\({}_{2}\) levels, ocean acidification is progressing, resulting in a downward trend in average seawater pH. Therefore, the pH range was set to 6-8.  
Training, validation, and test data for the regression model were obtained using a full factorial design with three factors at three levels as shown in Table 2. The factor level was selected with consideration of the conditions inside seawater cooling pipes. This design incorporates experiments for all factor-level combinations as shown in Table 3, allowing identification of main effects and interactions. In Table 3, CR\({}_{\text{Com}}\) and CR\({}_{\text{Pstat}}\) represent the CR measured using the commercial sensor and potentiostat, respectively, and henceforth, CR values will be expressed as MPY for practical purposes.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline  & & & & & & & & & & & \\ \hline
**C** & **Si** & **Mn** & **P** & **S** & **Cu** & **Ni** & **Cr** & **Mo** & **Al** & **Fe** \\ \hline
0.19 & 0.13 & 0.62 & 0.02 & 0.007 & 0.01 & 0.01 & 0.01 & 0.01 & 0.031 & Bal. \\ \hline \end{tabular}
\end{table}
Table 1: Chemical composition (wt. %) of mild steel used for specimen preparation.  
A 3.5% NaCl solution was prepared using reagent-grade NaCl to replicate the typical seawater composition used in cooling systems. The temperature of the solution was controlled using a double-jacketed beaker connected to an external chiller, while the pH of the solution was adjusted with hydrochloric acid (HCl) and sodium hydroxide (NaOH) to achieve the desired pH levels. To simulate flow velocity, a 5 cm diameter of magnetic stir bar was rotated at three different speeds (80, 300, and 600 RPM) in a 1 L beaker containing 700 mL of NaCl solution using a high-speed stirrer. The flow velocity corresponding to each stirring speed was estimated using following equations:  
\[\omega=RPM\times 2\pi/60 \tag{1}\]  
\[v=\omega\times\gamma \tag{2}\]  
where \(\omega\) is the angular velocity, \(\gamma\) is the radial distance from the stir bar to beaker wall, and \(v\) is the linear velocity. The calculated flow velocities were approximately 0.2, 0.8, and 1.6 m/s. These values are approximations, as the calculation assumes simplified fluid dynamics, excluding factors such as beaker geometry, fluid viscosity, and turbulence.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Factors** & **Unit** & & **Level** & **Response** \\ \hline Temperature & \({}^{\circ}\)C & 10 & 25 & 40 \\ pH & & 6 & 7 & 8 \\ Flow velocity & m/s & 0.2 & 0.8 & 1.6 \\ \hline \end{tabular}
\end{table}
Table 2: Experimental factors (temperature, flow velocity, and pH) and their levels used in the full factorial design.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**No.** & **Temperature** & **pH** & **Flow Velocity** & **CR\({}_{\text{Com.}}\), MPY** & **CR\({}_{\text{Pstat}}\), MPY** \\ \hline
1 & 10 & 6 & 0.2 & 37 & 37 \\
2 & 10 & 6 & 0.8 & 56 & 52 \\
3 & 10 & 6 & 1.6 & 65 & 62 \\
4