Model construction of corrosion resistance of alloying elements for low alloy steel in marine atmospheric corrosive environment based on machine learning

2.1 Corrosion data

Corrosion rates for 108 low alloy steels were manually collected for 1 year using the marine atmospheric dataset from Chinese National Materials Corrosion and Protection Data Center (National Materials Corrosion and Protection Data Center 2023). The steel samples were cut into square slices of a few tens of millimeters and placed in the field at an angle of 45° to the horizontal. However, some of the raw corrosion data could not be directly composed into a dataset to build a model. For example, some of the samples in the collected dataset tables were unavailable to provide the complete content of the alloying elements (or are below the detection threshold), while others had a corrosion rate that was higher than a certain value (the specimen was fully corroded). Therefore, the raw dataset was preprocessed by correcting erroneous data (data cleaning) and filling in missing values to improve the accuracy of the machine learning model (Shin et al. 2019).

If a sample had an obviously higher corrosion rate than the others, we used the box plot shown in Figure 1 for detection and rejection. At the same time, elements without labeled content were assigned with the minimum value of the corresponding element. The data set after data processing is shown in Table 1. Seven metallic elements, four non-metallic elements, corrosion time, temperature and corrosion rate are included in each row of data. Feature scaling was used to adjust for alloying elements with a wide range of fluctuations prior to characterization and feature importance ranking.

Figure 1:

Box plot of the distribution of corrosion rate value points.

2.2 Machine learning algorithms

2.3 Model construction process

Spearman’s correlation analysis was used to evaluate the correlation between each feature and corrosion rate. Regression analysis was performed using the RF algorithm model and the features were ranked in order of importance. The SHAP method was also used to visually demonstrate the effect of features on the corrosion rate of low alloy steels (Liu and Li 2023). The feasibility of machine learning in corrosion data mining was demonstrated through the above steps. The original dataset was divided into a training set (for optimizing the corrosion rate model) and a testing set (for characterizing the model prediction accuracy) with several different division ratios (i.e. 40 %, 50 %, 60 %, 70 %, and 80 % of the training set data, and the rest of the test set data). K-fold cross validation technique was used to improve training effectiveness. The prediction performance of above machine learning models (RF, MLP, RR, KNN, LR and SVM) was compared. Finally, the generalization ability of the model was demonstrated by comparing the predictions of the model with several sets of newly collected corrosion rate data.

2.4 Performance evaluation of models

The fitting errors of the training and testing samples of the different models were simultaneously evaluated using the coefficient of determination (R²) and the root mean square error (RMSE) to assess the accuracy of the model’s prediction results. They are represented by the following formulas (Zhi et al. 2019):

where N denotes the sample size, f _n denotes the predicted corrosion rate, y _n denotes the measured value, and y ‾ denotes the average value. With R² approaching to the 1 and smaller RMSE, the better the predictive performance of the model.

3.1 Comparison of machine learning algorithms

In general, the larger the dataset is, the more information it is likely to contain. Possible relationships between input features and target attributes are better extracted by the model through large data sets. Figure 2 shows the results of the division of prediction accuracy with the proportion of training set. Clearly, as the proportion of training set increases, the accuracy of all six prediction models increases, and the MLP, LR and RF models has the highest prediction accuracy at 80 % of training set proportion. The accuracy of the algorithms for KNN, RR, and SVM decreases slightly as the division of the training set exceeds 75 %. This may be due to the reduced model generalization ability caused by overfitting of these algorithms (Deng et al. 2015). LR has large fluctuations in RMSE with less than 55 % division of the training set, which could also be overfitting or affected by randomness. The dataset of this study is relatively small, so 80 % training set and 20 % test set ratio was chosen.

Figure 2:

Comparison of the performance of random forest (RF), multilayer perceptron (MLP), ridge regression (RR), k-nearest neighbor model (KNN), logistic regression (LR), and support vector machine (SVM) for corrosion rate prediction with different training and test set partitioning ratios.

3.2 Key alloying elements description analysis and feature selection

Figure 3 reveals the relationship between 11 alloying elements and the Spearman’s correlation of marine atmospheric corrosion rates. Spearman’s coefficients are shown in each box, with the darker box color indicating that the element inhibits the corrosion strongly. As shown in Figure 3, the correlation between 11 elements and corrosion rate is as follows in descending order: Ni, Cu, Mo, C, Nb, Ti, Mn, Cr, Si, P, and S. Ni, Cu, Mo, Nb, Ti, Mn, Cr, and Si show negative correlation with corrosion rate, indicating that these elements inhibited the corrosion of low alloy steel. C and P are positively correlated with corrosion rate, revealing that C and P reduce their corrosion resistance. This result is in accordance with existing studies (Guo et al. 2012; Liu et al. 2014; Sun et al. 2014; Yang et al. 2023b, 2023c; Zhang et al. 2022, 2023a, 2023b; Zhou et al. 2013). Element S produces segregation at the oxide/matrix interface, weakening the oxide layer adhesion and thus reducing the oxidation resistance of the alloy (Zhan et al. 2023). The inhibition of corrosion rate shown in the thermogram may be due to the small amount of element S in the collected low alloy steels, which fluctuate over a small range. The same reason is for the P element. Adding P to steel could act as an anode depolarizer, allowing for more uniform dissolution of the steel surface during the corrosion process and faster transformation of Fe²⁺into Fe³⁺, which improved the rate of generation of α-FeOOH (Raghavan 2004; Stewart et al. 2000). The effect of alloying elements may be influenced by other elements and the environment in which the steel is used. Meanwhile, the small database may also lead to a slight deviation of the results, so further experimental validation is needed.

Figure 3:

Spearman’s correlation plot for alloying elements. Spearman’s correlation coefficients are shown in each box, with darker colors indicating stronger corrosion rate inhibition by the element.

SHAP can be used to analyze the mechanism of action of individual alloying elements. Figure 4 shows the overall distribution of SHAP values for the main features of all the samples. These features are arranged on the vertical axis from highest to lowest importance. Red and blue colors indicate higher and lower values of the features (Roy et al. 2023). More positive SHAP values indicate higher corrosion rate. From the figure, it can be seen that Ni has the greatest effect on the corrosion rate. The lower the content of Ni, the more positive the value of SHAP, which indicates that Ni reduces the corrosion rate. Similarly, Ni, Mo and Cr all improve the corrosion resistance of low alloy steels, which is consistent with the findings obtained in Figure 3. The remaining features such as S, P and Ti present less effect on corrosion.

Figure 4:

Importance plot of SHAP variables for corrosion data. Each point represents a sample and these points are colored from low (blue) to high (red) by the corresponding eigenvalue. Positive SHAP values represent the ability to increase corrosion rate and negative SHAP values represent the ability to decrease corrosion rate. The features are listed from top to bottom on the vertical axis in order of their functional importance.

The RF model was used to further determine feature importance. Figure 5 shows the importance ranking of the 11 alloying elements based on the RF model. The order of importance of the 11 alloying elements is Ni, Cu, Mo, Nb, Cr, C, Mn, Si, S, P, and Ti. This is generally consistent with the ordering of importance given in Figures 3 and 4. The top eight features (Ni, Cu, Mo, Nb, Cr, C, Mn, and Si) with the highest importance were chosen to ensure the generalization ability of the model. Due to the limitations of the sample size, the content of the elements S, P, and Ti varied little and did not have a significant effect on the corrosion rate. Therefore, in the subsequent model selection, the first eight features were chosen to ensure the accuracy of the model. And S, P, and Ti were excluded from the model inputs.

Figure 5:

Order of importance of elemental content on corrosion rate.

3.3 Modeling of corrosion rate prediction

Ni, Cu, Mo, Nb, Cr, C, Mn, and Si were used as input features to select the best model. RMSE and R² were used to evaluate the reliability of the six machine learning models (RF, MLP, RR, KNN, LR and SVM) used. A comparison of the accuracy of the models is shown in Figure 6 and their specific values are shown in Table 2. Figure 6a shows the difference between the R² of the six models in the training and test sets. The models all have slightly higher R² on the training set than on the test set. From the model comparison, RF, SVM and LR have higher R² values, resulting in better model fit results. The R² of KNN has a larger accuracy gap between the training set and the test set, which may be due to overfitting. Figure 6b shows the results of the RMSE comparison of the six models. RMSE values of RF, SVM, MLP and LR are smaller compared to the RMSE of KNN and RR. Figure 6a and b indicates that RF, SVM and LR have lower model error and higher fitting accuracy.

Figure 6:

(a) R² for the training and test sets of six chosen models. (b) RMSE for training and test sets of six chosen models. The dataset is randomly divided into 80 % training set and 20 % test set.

Figure 7 compares the predicted values and actual values of the RF, SVM, and MLP models on the training and test sets. The vertical axis represents the predicted corrosion rate, the horizontal axis represents the true corrosion rate as a function of the true corrosion rate, and the diagonal line is the true prediction line. If all data points tend towards the 45° diagonal distribution in the graph, the model tends to be more perfect (Zhi et al. 2019). Figure 7a1, b1, c1 shows the results of the model on the training set, while Figure 7a2, b2, c2 shows the results on the test set. The RF model has a smaller RMSE and a larger R² on the training set than on the test set. This indicates that the model has slightly higher model accuracy on the training set. Similar to the RF results, both SVM and MLP have slightly higher prediction accuracy on the training set than on the test set. On the comparison of the models on the training set, the three models are ranked in order of accuracy as RF, SVM, and MLP. R² is 0.93, 0.82, and 0.79 and RMSE are 0.05, 0.10, and 0.10. The model accuracy ranking for the test set is the same as the results in the training set, with R² being 0.85, 0.77, and 0.71, and RMSE being 0.11, 0.10, and 0.11. It can be seen that the RF model has the lowest fitting error with RMSE and R² of 0.05 and 0.93 on the training set and 0.11 and 0.85 on the test set.

Figure 7:

(a1) RF, (b1) SVM and (c1) MLP model fits to the training samples, and (a2) RF, (b2) SVM and (c2) MLP model fits to the test samples.

At the same time, the fitting abilities of RR, KNN, and LR were compared in Figure 8a1, b1, c1, and Figure 8a2, b2, c2. The RR, KNN and LR models all have smaller RMSE and larger R² on the training set than on the test set. Figure 8b1 and 8b2 show that the RMSE and R² of the KNN model on the training set is 0.11 and 0.75, while on the test set is 0.16 and 0.58. The KNN has a low model accuracy on the test set, and there is a large difference in the accuracy of the model between the test set and the training set. This may be due to the fact that although KNN can handle nonlinear data, it requires a large sample size to train the model (Zhang 2016). Therefore, the model accuracy of KNN is not good enough to obtain relatively reliable results with fewer training samples. Comparing the models on the training set, the three models are ranked in order of accuracy as LR, RR, and KNN. The R² is 0.80, 0.76, and 0.75, and the RMSE is 0.10, 0.10, and 0.11. The ranking of the models in order of accuracy on the test set is the same as the results on the training set, with the R² being 0.76, 0.66, and 0.58, and the RMSE being 0.12, 0.14, and 0.16. It can be seen that the LR model has the lowest fitting error with RMSE and R² of 0.10 and 0.80 for the training set and 0.12 and 0.76 for the test set. R² and RMSE can be used to evaluate the prediction accuracy (Diao et al. 2021). However, the prediction accuracy of the models shown in Figures 7 and 8 is lower on the test set than on the training set, which may be due to the insufficient amount of data to adequately reflect the elemental versus corrosion rate relationship.

Figure 8:

(a1) RR, (b1) KNN and (c1) LR model fit results for the training samples, and (a2) RR, (b2) KNN and (c2) LR model fit results for the test samples.

From the results in Figures 7 and 8, it is clear that the RF predictions are generally accurate, with only a few cases deviating from the 45-degree diagonal. This indicates that the RF model is reliable in dealing with corrosion datasets characterized by small samples, steep flow patterns, and nonlinearities. Meanwhile, K-fold cross-validation was also used to improve the training of the model (Figures S6 and S7). The results indicated that the RF model still has the highest prediction accuracy and the smallest error under K5-fold and K10-fold cross-validation. In summary, RF is able to achieve better performance than five other commonly used machine learning algorithms in predicting the corrosion rate of steel.

3.4 Generalization capabilities of machine learning models

To further validate the model accuracy, 10 rows of low alloy steel corrosion data (from National Materials Corrosion and Protection Data Center (National Materials Corrosion and Protection Data Center 2023)) independent of the previous dataset were collected as a validation set. The newly collected low alloy steel has different elemental content from the steel used in the training model. Therefore, these 10 rows of data can be used to verify the generalization ability of the model. The corrosion data are listed in Table S1. After inputting the elements of the new steel grade into the six models, the corrosion rate of each sample was predicted. Then compare the predicted corrosion rate with the actual corrosion rate. The results of the comparison of RF with the remaining five models (SVM, MLP, RR, KNN, LR) are documented in Figure 9 and Figures S1–S5. The results demonstrate that RF possesses higher predictive power than the other five models. In Figure 9, blue color represents the measured corrosion rate and red color represents the corrosion rate predicted by the model. Sample 8 had a slightly larger difference between the actual and predicted corrosion rates, and the rest of the samples had a small difference. This indicates that the RF model has high prediction accuracy and excellent generalization capability.

Figure 9:

Comparison between test-measured corrosion rates and corrosion rates predicted by the RF machine learning model. Using 10 new rows corrosion data.

In the feature selection process, some metallic elements (Ni, Cu, Mo, and Cr) and non-metallic elements (C, P, Si) which have a large influence on corrosion are used as input features in the feature selection process. In previous studies, corrosion rate prediction models have also used elements as input features, but the models are limited to certain steels because of the low alloy content and the lack of some elements that have an impact on corrosion (Wei et al. 2021). Zhi et al. (2020) applied a deep forest algorithm to construct a prediction model based on the collected corrosion data of 17 steels. However, the model was also trained using a dataset missing an important element (Mo) that affects the corrosion resistance of low alloy steels as an input feature. This greatly limits the ability to generalize the predictive model. The RF corrosion rate prediction model constructed in this study uses 11 elements as feature inputs for the first time and performs well in terms of model generalization ability in marine atmospheric environments. At the same time, we also screened out the alloying elements with the largest corrosion-influenced rates in the marine atmospheric environment. Finally, as shown in Table 3, five low alloy steel compositions with the best corrosion resistance were selected by the RF model. This is a great reference for guiding the development of corrosion-resistant materials and the design of related experiments.