## 3 Results and Discussion
### Development and Training of the Regression Model  
Figure 8 presents the experimental results, showing the relationship between the factors (temperature and flow velocity) and the response variable (CR, MPY). This study aimed to determine whether these relationships are linear or non-linear and to establish the relative importance of each factor in the regression model. The results indicate that CR increases non-linearly with flow velocity, exhibiting behavior close to second-order trends. Additionally, the effect of temperature on the CR follows an exponential trend, consistent with the Arrhenius equation [31]. These findings demonstrates the necessity of incorporating interaction terms in the regression model to account for the combined influence of temperature and flow velocity on corrosion behavior. The regression models developed using the data from the commercial LPR sensor and the potentiostat are expressed as follows:  
\[MPY_{com.}=22.3+0.9666 temp+3.84 vel+1.826 temp*vel\left(R^{2}=0.9764\right) \tag{8}\]  
\[MPY_{pstat.}=20.17+0.992 temp+5.28 vel+1.676 temp*vel\left(R^{2}=0.9672\right) \tag{9}\]  
These equations reflect the contributions of temperature, flow velocity, and their interaction (temp-vel) to the MPY values. Here, temp is expressed in degrees Celsius, and vel in meters per second. The interaction term addresses the non-linear relationship between the two factors, showing how their combined effect differs from their individual  
Figure 7: Three-dimensional surface profiles of corrosion coupons tested in a 3.5% NaCl solution with pH fixed at 7 and flow velocity at 1.6 m/s: (**a**) 25 \({}^{\circ}\)C for 48 h, (**b**) 25 \({}^{\circ}\)C for 60 h, (**c**) 40 \({}^{\circ}\)C for 48 h, (**d**) 40 \({}^{\circ}\)C for 60 h. (**e**) Surface analysis of profile for (**d**). contributions. This approach helps better represent the complex corrosion dynamics in environments such as marine cooling systems. The coefficient of determination (R2) for each model, calculated using Equation (10), evaluates the model's performance:  
\[R^{2}=1-\frac{\sum\left(y_{i}-\hat{y_{i}}\right)^{2}}{\sum\left(y_{i}-\overline{ y}\right)^{2}} \tag{10}\]  
where \(y_{i}\) represents the actual MPY values, \(\hat{y_{i}}\) is the predicted values from the model, and \(\overline{y}\) is the mean of the responses. An R2 value close to one indicates that the models explain most of the variability in the data, confirming their reliability. Both models demonstrate high R2 values (0.9764 for the LPR sensor and 0.9672 for the potentiostat), indicating a strong fit with the training data. Moreover, the constants and weights in both models are nearly identical, further validating the consistency of the data obtained from the two measurement methods. This consistency supports the use of LPR sensors as practical alternatives to the three-electrode corrosion cells, offering comparable accuracy in monitoring CR in real-time. To enhance the model's robustness and reduce overfitting, the datasets from both techniques were combined into an integrated regression model with 54 samples:  
\[MPY_{model}=21.26+0.977 temp+4.54 vel+1.725 temp*vel\ (R^{2}=0.9733) \tag{11}\]  
The integrated model provides a balanced prediction of CR by drawing on data from both measurement techniques. The interaction term in the model remains significant, emphasizing the importance of simultaneously accounting for both temperature and flow velocity when predicting corrosion behavior. With an R2 of 0.9733, the integrated model explains almost all variability in the data, demonstrating its reliability for practical applications. The stepwise regression process ensured that only statistically significant terms were retained, resulting in a more interpretable model. Higher-order terms were excluded, as they did not meaningfully contribute to the predictions. The final models confirm that  
Figure 8: CR measured by potentiostat as a function of flow velocity and temperature.