The AH-32 grade carbon steel used in this study had the following chemical composition (wt.%): C 0.18, Si 0.5, Mn 0.9-1.6, S 0.035, Cr 0.2, Mo 0.08, Ni 0.4, Cu 0.35, Nb 0.02, V 0.05, and Fe balance. Specimens for corrosion tests were machined to dimensions of 20 mm x 20 mm. The surface of each specimen was polished sequentially using emery paper, finishing with #600 grit paper. After polishing, they were thoroughly cleaned with acetone and subsequently dried in a drying oven.

In the electrochemical evaluation, a potentiodynamic polarization technique was employed using a three-electrode setup in an electrochemical workstation (Bio-logic, VSP). The working electrode (WE) configuration involved a specimen with an electroactive surface area of 1 cm². A specific electrolyte volume-tospecimen area ratio was maintained at 5 mL/mm². The counter electrode (CE) was realized using a platinum mesh of dimensions 20 mm x 20 mm, while an Ag/AgCl electrode, saturated with KCl, served as the reference electrode (RE). Electrochemical equilibrium was ensured by stabilizing the system until the potential drift was limited to below 2 mV/h or for a maximum duration of one hour. The potentiodynamic sweep was then executed from -250 mV to +250 mV with respect to the open circuit potential (OCP) at a scan rate of 5 mV/s.

The corrosion experiment was designed using a three-factor full factorial design, as shown in Table 1. Each factor was set at three distinct levels, resulting in a total of 27 experiments. Table 2 presents the full factorial design details. The experimental factors were chosen based on previous relevant studies [6]-[8] and practical considerations in ship operations [9]-[11].

The corrosion current density was determined using the Tafel extrapolation method applied to potentiodynamic curves [12]. By extrapolating the anodic and cathodic slopes from the linear polarization region, the intersection point was identified to determine the corrosion current density, as illustrated in Figure 1. This analysis was facilitated by the EC-Lab^® Software integrated into the electrochemical equipment. The corrosion rate, expressed in mils penetration per year (mpy), was then computed using Equation (1) following Faraday's law.

Figure 1: 
Tafel extrapolation for determining electrochemical corrosion parameters

where λ is 1.2688×10⁵, I_corr. is corrosion current density, ρ is the density (7.86g/cm³), and ϵ is the equivalent weight (27.56).

This study utilized potentiodynamic data from polarization curves. Each curve consists of 100 data points representing potential versus current density. A single polarization curve is characterized by four inputs: temperature, pH, salinity concentration, and polarization potential, with the output being the current density. Consequently, the dataset used in this study includes a total of 2700 columns of input and output variables. Each input variable has been normalized to have a value between 0 and 1, as per Equation (2).

where X is the normalized value, x is the unnormalized value, and x_max and x_min denote the maximum and minimum values for each level, respectively.

The ANN model employs supervised learning through the back-propagation algorithm. In this study, it is designed to accept four inputs: temperature, pH, salinity concentration, and polarization potential. It then produces an output corresponding to the corrosion current density. As illustrated in Figure 2, the ANN architecture is a multilayer perceptron, consisting of an input layer with four nodes, several hidden layers, and a single-node output layer. The activation function used in each hidden layer is the hyperbolic tangent (tanh) as given by Equation (3).

Figure 2: 
Schematic diagram for ANN architecture

For the ANN, the data was split into training, validation, and test sets in proportions of 80%, 10%, and 10%, respectively. This division was randomly executed during the training phase. The ANN was implemented in Python 3.7, using the TensorFlow 2.0 library.

To generate training data for the ANN model, potentiodynamic tests were performed with factor combinations, as listed in Table 2. The results for the 27 conditions are depicted in Figure 3. All curves illustrate a rapid increase in the current density in the anodic range, which is attributed to the oxidation reaction on the WE. Some curves displayed stagnation in the corrosion current density in the cathodic section owing to oxygen concentration limitations. This phenomenon is known as "oxygen concentration polarization,” indicating that the current density plateaus approximately at 10^-1 mA/cm², which results from oxygen diffusion constraints within the cathodic range [13]. Consequently, the polarization curves revealed complex patterns influenced by factor variables and electrochemical reactions.

Figure 3: 
Potentiodynamic curves with corrosion parameter combination

Table 3 lists the I_corr., E_corr., and mpy values obtained using the Tafel extrapolation method. The samples exhibited an mpy range from a minimum of 9.7 to a maximum of 192.8. Factors had varying influences based on the mean and variance of the response. The order is as follows: factor B (pH), factor A (temperature), and factor C (salt conc.).

This suggests that each factor and its level affect both the polarization curve and the corrosion characteristics. Consequently, they can serve as inputs for the ANN to produce significant outputs.

Determining the optimal parameters for the ANN model is significant to ensure superior performance during the training, validation, and test phases. These parameters can depend on various factors including the network structure, activation function, learning rate, and data acquisition. Finding the optimal combination typically involves multiple iterations and adjustments. In our study, we employed an ANN with a 4-50-50-1 architecture. The mean squared error (MSE), as presented in Equation (4), was the chosen loss function for training the model.

where, n is the number of outputs for the training set, X(t) is the actual value, and X′(t) is the predicted value. The MSE is used as a loss function for the regression results in the ANN model and represents the difference between the actual and predicted values. Consequently, one of the primary objectives of model training is to minimize MSE through iterative learning.

Figure 4 depicts the MSE in relation to the number of epochs for the ANN model. The MSE decreased sharply up to 100 epochs, after which the reduction proceeded more gradually. At a maximum of 500 epochs, the MSE values were found to be 0.0018 and 0.0016, with no further significant decline beyond more epochs. This trend suggests that the ANN model reached an optimal level of training at approximately 100 epochs, where additional training did not markedly enhance the performance.

Figure 4: 
MSE in relation to the number of epochs for the ANN model

Figure 5 illustrates both the actual and predicted curves. For a total of 27 polarization curves, the ANN presented curves that closely resembled the actual shape, as Figure 5(a)-(c).

Figure 5: 
Experimental and ANN predicted potentiodynamic curves for some condition

However, as observed in experiments no. 6 and 19, there were slight deviations at some data points. The ANN showed a very high learning performance on the entire training dataset; however, the cathode region exhibited a slightly lower learning performance than the anode region. Given that ANN models are trained to minimize the loss function, they may emphasize learning in certain regions over others, depending on the range or distribution of the output value [14]. In this study, the output of the ANN model was the current density. The current density in the anodic region in the data was up to two orders of magnitude higher than that in the cathodic region. Therefore, it is possible that the ANN model was trained to preferentially reduce the MSE for the data in the anode region.

Figure 6 illustrates the correlation between the actual values and ANN’s predictions, providing empirical evidence of the model's performance across the training, validation, and test data. Most data points were concentrated near the best-fit regression line (Y=T), demonstrating a high correlation, with a coefficient of determination close to 1. The correlation coefficients R² for the training, validation, and test phases were 0.999, 0.9847, and 0.984, respectively, indicating a robust model fitness. Although there are minor deviations between the actual and predicted data at specific points, the overall predictions were consistent and reliable. This indicates the potential of the ANN model to learn the pattern of the polarization curve in complex combinations of factors.

Figure 6: 
Actual value vs. ANN predicted values for log(i)

However, a high degree of correlation coefficient might indicate a potential risk of overfitting. Overfitting means that the model might be too closely tailored to the training data, leading to decreased performance with new data. Therefore, external validation using datasets that are not included in the training phase is essential.

Figure 7 shows a comparison of the actual polarization and prediction curves from the ANN model for the new test conditions excluded from the ANN training data. For Test Condition 3 in Figure 7(c), the ANN generated a polarization curve that was very similar to the actual curve. In addition, E_corr. and I_corr. also showed very similar values, and the actual and predicted mpy values were found to be 42.109 and 35.369, respectively. In contrast, test conditions 1 and 2, illustrated in Figure 7(a, b), exhibited similar E_corr. values However, a noticeable deviation in the current density between the anode and cathode is evident. This deviation is further emphasized by the significant mpy variation displayed in Figure 7(d). Such outcomes underline the capacity of the ANN model to yield precise predictions for certain Test Conditions, while also revealing its limitations under other conditions, such as Test Conditions 1 and 2.

Figure 7: 
Actual and ANN curves (These conditions not included in Table 2)

The observed discrepancies can be attributed to inherent differences or potential noise in the test conditions, suggesting the need for more extensive data collection and model optimization. In summary, the ANN model in its present configuration demonstrates considerable capability in corrosion prediction, particularly in reproducing polarization curves, while emphasizing the need for ongoing optimization to enhance its wider application.