A two-stage model based on artificial neural networks to determine pitting corrosion status of 316L stainless steel

1 Introduction

Although the great corrosion resistance presented in austenitic stainless steel, localized corrosion is considered one of the most critical problems in this material. Based on the chemical composition of the alloy, one common way to analyze the corrosion resistance of austenitic stainless steel is by the pitting resistance equivalent number (PREN) (Lorenz & Medawar, 1969). In this expression, in addition to chromium, other alloying elements such as nitrogen and molybdenum are considered to evaluate pitting corrosion susceptibility of the material. Based on this expression, higher concentrations of chromium, molybdenum, and nitrogen lead to greater corrosion resistance of stainless steel. In this way, an alloy with a PREN value higher than 40 shows excellent corrosion resistance (Shin, Jang, Cho, & Park, 2012). However, this expression does not take into account the environmental conditions under which the material is exposed. To analyze the influence of the environment on corrosion behavior of stainless steel, electrochemical techniques have been applied by many authors (Jiang, Sun, Li, & Xu, 2014; Liu, Li, & Wang, 2010; Parsapour, Khorasani, & Fathi, 2012). These techniques include potentiodynamic, potentiostatic, and electrochemical noise measurements, among others. In the potentiodynamic technique, the potential is changed gradually at a constant rate to plot potential against current density values. One of the most important features obtained from these curves is the breakdown potential (E_b). This feature is defined as the potential at which the anodic current suffers an abrupt increase. Salvago, Magagnin, and Bestetti (2002) define this term as the potential value above which the material can be attacked by localized corrosion. Therefore, this parameter can be considered as an index to analyze the aggressiveness of the environment on pitting resistance. In general, larger values of this potential, greater resistance to pitting corrosion is presented by the material. Although electrochemical techniques have been used by many authors to evaluate the corrosion resistance of stainless steel, these techniques may present shortcomings (Moayed & Golestanipour, 2005). One of the most important aspects is that the value of the breakdown potential is influenced by the way in which the electrochemical test is carried out. In this sense, the authors exposed the need to repeat the test several times for a certain environmental conditions to assure reproducibility in the results (Man & Gabe, 1981). This leads to a too complex procedure when it is interesting to evaluate the corrosion resistance in a large range of environmental conditions. In addition, the breakdown potential is used as a general term to indicate the breakdown of the passive layer. This term is used independently of the reactions leading to the passive layer breakdown: pitting or transpassive corrosion (Alfonsson & Qvarfort, 1992). Thus, to confirm the type of attack, the researchers analyze the material surface microscopically after the polarization tests. Therefore, this visual interpretation of the surface may lead to subjectivity in the results. With the aim to solve these drawbacks, in addition to the need to get an effective and efficient model for analyzing corrosion behavior of materials, many authors have developed models based on artificial intelligence techniques because these models have been demonstrated to be an useful tool in material science applications (Roberge, 1997; Sha & Edwards, 2007; Yang, 2001). A chronological review of the application of artificial neural networks (ANNs) in corrosion studies is presented in this work.

Rosen and Silverman (1992) applied neural network techniques to predict the type of corrosion presented in the material in a certain ambient according to the polarization scans. Smets and Bogaerts (1992) applied ANN techniques to determine the chloride-induced stress corrosion risk automatically. The authors defined a transition region where the stress corrosion cracking risk increased, with values of temperature, chloride ion concentration, and oxygen content considered, whereas Trasatti and Mazza (1996) applied them to get rapid predictions of crevice corrosion performance of stainless steels and related alloys in near-neutral chloride-containing environments.

Related to pitting potential estimation, Cottis et al. (1999) presented a model with the ability to estimate this potential as a function of solution composition and temperature for AISI 304 stainless steel. Nesic and Vrhovac (1999) studied the corrosion prediction of steel in CO₂-containing solutions. In this case, the model demonstrated extrapolation capabilities comparable to a purely mechanistic electrochemical CO₂ corrosion model, improving the understanding of this type of corrosion. One of the most popular studies about ANN applications on corrosion problems was the one developed by Cai, Cottis, and Lyon (1999). These authors tried to model atmospheric corrosion of zinc and steel. In addition, the presented model was used to develop a sensitivity analysis to demonstrate the effects of the exposure time and the sulfur dioxide and chloride concentrations on atmospheric corrosion. This work was continued by Pintos, Queipo, de Rincon, Rincon, and Morcillo (2000), who designed an ANN model to determine the damage function of carbon steel. They measured the corrosion penetration as a function of cumulated values of the environmental variables.

Furthermore, Leifer and Mickalonis (2000) presented a model capable of predicting pit depth as a function of water pH, concentrations of carbonate, chloride ion concentration, and the storage time for the aluminum vessels storing spent nuclear fuels, whereas Parthiban et al. (2005) applied these technique to know embedded steel corrosion behavior in concrete. In this case, the model estimated the pitting potential accurately for different conditions. Ok, Pu, and Incecik (2007) developed ANN formulae to investigate the effects of pitting corrosion on strength reduction. In this case, the principal objective was to analyze the effect of corrosion and fatigue cracks on the structural integrity. Boucherit, Amzert, Arbaoui, Hanini, and Hammache (2008) studied the usefulness of inhibitors for the prevention of localized corrosion using neural networks. You and Liu (2008) developed a model to predict corrosion rate of stainless steel. The model was used to analyze the quantitative effects of the environmental parameters on the corrosion rate of the steel in seawater.

To understand the pitting corrosion process, Ramana et al. (2009) developed a model to predict pitting potentials of AISI type 316L stainless steel. Authors presented a model to simulate the intricate inter-relationships between this potential and various environmental parameters for austenitic stainless steel. Lajevardi, Shahrabi, Baigi, and Shafiei (2009) developed a neural network model to predict the time failure for 304 stainless steel as a result of stress corrosion cracking in aqueous chloride solution, analyzing the effect of temperature, chloride ion concentration, and applied stress. Cavanaugh, Birbilis, and Buchheit (2012) applied ANNs to model pit growth as a function of different environmental conditions: varying chloride ion concentration, pH, and temperature for different exposure times. The results demonstrated that the model could be considered as a powerful tool to predict the maximum pit depth as a function of the environmental conditions in aluminum alloys. Martin, De Tiedra, and López (2010) analyzed the influence of resistance spot welding (RSW) process on pitting corrosion behavior. In this case, authors used an ANN model as a predictive model to establish a relationship between the RSW process of AISI 304 and the pitting potential of the RSW joint. Kamrunnahar and Urquidi-Macdonald (2010) applied a supervised neural network model to predict the corrosion behavior of metal alloys. The model tried to find out the relationship between the composition of the alloy and the environmental conditions with the corrosion rate and the electrochemical potentials. Based on the high-quality results, these authors continued their studies, and in 2011, they applied ANN models to estimate the weight loss and the crevice repassivation potential of metals (Kamrunnahar & Urquidi-Macdonald, 2011). One of the most recent application of ANNs on corrosion studies was developed by Hodhod and Ahmed (2014). These authors presented an alternative approach based on neural networks to simulate the corrosion initiation time of slag concrete as a function of concrete cover depth, apparent chloride diffusion coefficient, chloride threshold value, and surface chloride concentration. The principal objective was to get a reliable prediction of the time to corrosion initiation of reinforced concrete structures. This is essential for the selection of durable and cost-efficient design of built structures, minimizing the life cycle costs.

According to the literature review, the utility of ANN techniques for any corrosion problem has been demonstrated. However, the studies about pitting corrosion status prediction of AISI 316L stainless steel are scarce in the literature. Focusing our attention on the pitting corrosion problem of this material, the authors have developed several studies. In a previous work (Jiménez-Come et al., 2012), a model based on ANNs was presented to determine the pitting corrosion status of the material. In this case, the pitting corrosion status was predicted, with environmental conditions considered, in addition to the breakdown potential values obtained from the polarization curves, but without requiring metallographic analysis of the surface. However, in this case, for new environmental conditions that had not been tested before, the presented model was not able to predict the pitting corrosion status of the material automatically, as polarization scans were required to determine the potential values used as inputs for modeling. With the aim to solve this drawback, a new study was presented (Jiménez-Come, Turias, Ruiz-Aguilar, & Trujillo, 2014). In this case, the pitting corrosion status of 316L was predicted based on the environmental conditions, not considering the breakdown potential values. In this way, the model could automatically distinguish the corrosion status of the material under different environmental conditions. However, comparing both studies (Jiménez-Come et al., 2012; Jiménez-Come et al., 2014), it can be pointed out that considering the breakdown potential values for predicting pitting corrosion status resulted in a more accurate estimation. Therefore, with the aim to develop a model to predict pitting corrosion status of 316L stainless steel automatically and accurately, a two-stage model based on ANNs is presented in this work. In the first stage, the breakdown potential of the material was estimated considering the influence of the critical environmental factors with influence on pitting corrosion behavior (pH, chloride ion concentration, and temperature), and then, the estimated values of the breakdown potentials, in addition to the environmental conditions, were used to obtain a model capable to determine the pitting corrosion status of 316L stainless steel automatically, not requiring the use of polarization tests. The combined model based on ANNs was trained using the experimental data obtained from the European project called “Avoiding Catastrophic Corrosion Failure of Stainless Steel”.

The structure of the article is as follows: the next section, Materials and Methods, presents a brief introduction about pitting corrosion approach and how the database for modeling pitting corrosion status of stainless steel was obtained. The subsection Artificial Neural Networks presents a description of the methodology. In addition, the experimental procedure is included in this section. In the Results section, the goodness of the proposed model is evaluated and the principal remarks are exposed in the Conclusion section.

2 Materials and methods

2.2 The database

To analyze the effect of chloride ion concentration, pH, and temperature on pitting corrosion resistance of 316L stainless steel, a European project called “Avoiding Catastrophic Corrosion Failure of Stainless Steel” (CORINOX RFSR-CT-2006-00022) was developed partly in ACERINOX, known worldwide as the one of the most competitive groups in the world in stainless steel manufacturing. The composition of the alloy was <0.050% C, 0.20–0.70% Si, <0.014% S, <1.6% Mn, 16.5–17.5% Cr, 2.0–2.4% Mo, and 10–11% Ni. The breakdown potential values of 60 samples of the material were measured by potentiodynamic tests in different environmental conditions. The ranges of values evaluated for each environmental factor are collected in Table 1.

Table 1

Experimental conditions tested to evaluate the influence of environmental factors on pitting corrosion resistance of grade 316L austenitic stainless steel.

Chloride ion concentration (M)	pH	Temperature (°C)
0.1–0.05–0.01–0.005–0.0025	3.5	From 2 to 75
0.1–0.05–0.01–0.005–0.0025	5	From 2 to 75
0.1–0.05–0.01–0.005–0.0025	8	From 2 to 75

The experimental procedure is represented in Figure 1. Before the tests, all the samples were polished using a 600-grit abrasive paper. The equipment was composed by a potentiostat (PARSTAT 2273 “Advance Electrochemical System”, Princeton Applied Research, a subsidiary of AMETEK®, Inc., UK) and a special design free-crevice cell (Merello, Botana, Botella, Matres & Marcos, 2003). The cell had three electrodes: the sample of the alloy with exposure area of 1 cm² as working electrode, a graphite wire as the counter-electrode, and a saturated calomel electrode as the reference electrode. During the polarization tests, the voltammograms of the samples were traced in a chloride sodium solution by sweeping the potential from –1300 to –1100 mV. The potential was increased at a scan rate of 0.17 mV/s. The sodium chloride electrolyte was mechanically stirred, and a constant flow of pure nitrogen was used to displace the oxygen from the system. At the beginning of the experiment, the sample was immersed in the electrolyte for 30 min to stabilize the open circuit potential. Then, for 3 min, the specimen was cathodically polarized to –1300 mV.

Figure 1:

Experimental procedure to analyze pitting corrosion behavior of 316L stainless steel.

(A) Polishing, (B) free-crevice cell, and (C) metallographic analysis.

The value of the breakdown potential of the material for each condition was defined based on the polarization curve, defining it as the potential at which current density reached 100 μA/cm² (Figure 2). In all cases, each environmental condition was carried out at least twice to ensure reproducibility in the results. At the end of the polarization tests, all species were analyzed by optical microscope to check their pitting corrosion status. This way, all the samples were classified according to their pitting corrosion status determined by microscopy analysis: 1, samples where pits were observed on the surface; 0, otherwise. In this sense, each sample was characterized by the environmental conditions tested, the breakdown potential value obtained from the polarization curve, and its pitting corrosion status.

Figure 2:

Polarization curves measured for 316L stainless steel using sodium chloride as precursor salt (pH=5.5).

2.3 Artificial neural networks

ANNs are computational models that try to simulate human brain behavior. This technique has been proved to be a universal approximation, and it has been extended applied to solve many different problems, such as pattern recognition or non-function approximations (Hornik, Stinchcombe & White, 1989). The models based on ANNs are trained to understand the relationship existing between a set of pairs input-output obtained from any experimental process. These models have been considered as information processing systems with the ability to learn and generalize from training patterns.

A model based on ANNs is formed by several neurons located in different layers. The hidden layers represent the interaction between the input and the output layers. Some authors have investigated the optimal number of hidden layers, concluding that any continuous function can be represented using one-hidden layer neural network (Cybenko, 1989). In ANN models, a neuron can be defined as the unit that provides the map between the input and the output according to the activation function defined for each layer in the network. The activation function can be a linear or non-linear function. The transfer function provides an output corresponding to the weight summation of the inputs for each neuron. The weighted sum is defined as a function of weight and bias values. These parameters define the connections between the neurons of the different layers, and their values are adjusted in the training stage. The principal objective of the iterative training process is to minimize the error between the output provided by the model (s_i) and the target one (t_i), given by Eq. (1). The backpropagation algorithm is the most popular technique used in the training stage (Moré, 1978). This process involves two steps: the first stage, in which the signal from the input nodes is propagated forward through the hidden layer to compute the output signal in the output layer, and the second stage, when the difference between the computed output and the desired one is calculated. Based on this measurement, the connections between neurons are modified in the backward stage adjusting the weight values (see Figure 3). The backpropagation algorithm has been improved using different algorithms such as Levenberg-Marquardt (Bishop, 2006).

Figure 3:

Three-layer feed-forward ANN configuration using backpropagation algorithm.

The upper part shows the schematic description of the relationship between the input and the output for a hidden neuron.

(1) M S E = 1 N ∑ i = 1 N ( t i - s i ) 2  (1)

2.4 Experimental procedure

ANNs have been used successfully for both regression and classification problems. In this work, a two-stage model based on ANNs was presented to predict pitting corrosion status of 316L stainless steel. In the first step (the regression stage), the model was trained in order to estimate the breakdown potential values considering the most critical environmental factors with influence on pitting corrosion resistance of stainless steels: chloride ion concentration, pH, and temperature. In the second step (the classification stage), the aim was to predict the pitting corrosion status of austenitic stainless steel. To get it, the model was trained to assign an input pattern to one of the two classes: 1, patterns with pitting corrosion; 0, otherwise. In this stage, each pattern was defined considering the estimated pitting potential value from the first stage in addition to the environmental conditions. The schematic procedure is represented in Figure 4.

Figure 4:

Schematic description of the experimental procedure presented to predict pitting corrosion status of austenitic stainless steels by a two-stage model based on ANNs.

According to Figure 4, the topology of the ANN models presented in this study had one input layer, one hidden layer with hyperbolic tangent sigmoidal transfer function (“tansig”), and one output layer with linear transfer function (“purelin”) for both stages. The number of neurons in the input layers was set according to the features considered in each stage: three neurons in the first stage where the model was developed to estimate the breakdown potential values and four neurons for the second stage, where the model was presented to predict the pitting corrosion status. The output layer had one neuron in the first stage and two neurons in the second one. In addition, the influence of the number of hidden neurons on the model performance was analyzed. The supervised learning algorithm applied to train the network for both stages was the Levenberg-Marquardt backpropagation algorithm.

Cross-validation was used as the criterion to stop the training step. The principal objective was to maximize the generalization ability presented by the model. This is a crucial aspect to be considered because if the network is trained too much, the model learns the training set, memorizing the training patterns, and therefore, the generalization ability of the model will be reduced. In this case, 5-fold cross-validation was applied. The whole original data were divided into two parts: 80% for training set and 20% to test the generalization ability presented by the model. This process was repeated, 20 times, following a resampling procedure used successfully in our previous works (Jiménez-Come et al., 2014).

Finally, the criterion used to select the optimal configuration for the ANN model varied according to the considered stage. In the first one, where the model was presented to estimate the breakdown potential values, the selected criterion was the correlation coefficient (R) and the root mean square error (RMSE) [see Eqs. (2) and (3)], whereas for the second stage, where the model was used to predict pitting corrosion status, receiver operating characteristic (ROC) curves in addition to area under the curve (AUC) values were selected to estimate the discrimination capability of the model (Fawcett, 2006).

(2) R = 1 p ∑ i = 1 p ( t i - t m ) ( o i - o m ) 1 p ∑ i = 1 p ( t i - t m ) 2 1 p ∑ i = 1 p ( o i - o m ) 2 ,  (2)

(3) R M S E = 1 p ∑ i = 1 l ( t i - o i ) 2 ,  (3)

where p is the total number of data points, t and o are the target and experimental values, respectively, whereas t_m and o_m are their mean values, respectively.

3 Results and discussion

To develop an automatic system to predict pitting corrosion status of 316L stainless steel, a model based on ANNs is presented in this research. In the first step, the ANNs model was trained to estimate the breakdown potential values as a function of the principal environmental factors considered in this study: chloride ion concentration, pH, and temperature. To determine the optimal configuration of the model, different numbers of hidden neurons were tested. Figures 5 and 6 show the influence of the number of hidden neurons on the regression performance in terms of correlation coefficient and root mean square error, respectively. In these figures, the mean values for each metric are collected for the different sets considered in cross-validation technique: training, validation, and test sets. However, to evaluate the generalization ability of the model to estimate the breakdown potential values as a function of the environmental conditions, the results obtained using the test subset are the most relevant, because they reflect the capability of the model to predict breakdown potential values when new environmental conditions, different from those used to train the model, are presented to the model.

Figure 5:

Influence of the number of hidden neurons on the correlation coefficient.

The mean value for each case is represented (20 repetitions with 5-fold cross-validation).

Figure 6:

Influence of the number of hidden neurons on the RMSE.

The mean value for each case is represented (20 repetitions with 5-fold cross-validation).

According to these figures, on the one hand, it can be assessed that large numbers of hidden neurons provided poor regression results: values of correlation coefficient decreased and values of RMSE increased when 10 and 20 hidden neurons were used. On the other hand, to determine the optimal configuration for the ANN models (number of hidden neurons), a multiple comparison analysis was developed. In this sense, two statistical tests, Friedman and Fisher’s least significant difference (LSD) post hoc tests were presented. The influence of the number of hidden neurons was analyzed on the regression performance to identify the models with similar behavior providing the optimal results. In this case, models using 10 and 20 hidden units were not considered in the analysis because, as has been exposed before, these models did not provide the optimal performance. In this way, reducing the number of models to be compared, the error type 1 (wrongly rejecting null hypothesis) was reduced. The results obtained from the multiple comparison tests, with correlation coefficient and RMSE values considered, are collected in Table 2.

Based on the results collected in Table 2, the optimal models considering the correlation coefficient were ANNs using 3 or 4 hidden neurons. In this case, the R-value was 0.903. Meanwhile, based on RMSE, the optimal models showing minimum value of this error (RMSE=148.193) were ANN models using 2, 3, or 4 hidden neurons. Thus, combining criterions, the regression coefficient, and the RMSE, the optimal models to estimate the breakdown potential values of stainless steel may be obtained using 3 or 4 hidden neurons. Based on these results and according to the principle of parsimony (the simplest model is the preferred one, Occam’s razor), the topology using 3 hidden neurons for ANN models was selected as the optimal model in the first stage of the model to estimate the breakdown potential values of 316L stainless steel.

The estimated values of the breakdown potentials using 3 hidden neurons are represented in Figure 7 plotted against the experimental values. These estimated values, in addition to the environmental conditions, were used as inputs in the second stage of the combined model to predict pitting corrosion status of the material.

Figure 7:

Estimated values of the breakdown potential vs. the experimental ones using ANNs with 3 hidden neurons.

In the second stage, the set of estimated values of the breakdown potential obtained from the first step was used as input for modeling in addition to the environmental conditions considered in this study: chloride ion concentration, temperature, and pH values. In this stage, the model based on ANNs was trained to predict pitting corrosion status of 316L stainless steel. In this step, the model was presented to classify the patterns into one of the two classes according to the corrosion behavior: pitting corrosion patterns and no-corrosion patterns.

To evaluate the classification performance, the ROC space was presented (Fawcett, 2006). Based on this technique, the optimal model is selected based on the tradeoff between hit and false alarm rates of the classification models. When an instance is presented to a binary classification model, four are the possible outcomes provided by the model: if the instance is positive and it is classified correctly by the model, it is considered true positive (TP); otherwise, when it is wrong classified, it is false negative (FN). On contrary, if the instance is negative and the model classifies it correctly, it is considered as true negative (TN), whereas if it is wrong classified, it will be considered as false positive (FP). According to these terms, two metrics can be defined: the true-positive ratio (TPR) or sensitivity defined by Eq. (4) and the false-positive ratio (FPR) given by Eq. (5), which can be expressed as 1-specificity.

Representing sensitivity against (1-specificity), the ROC graphic is obtained (see Figure 8). This graphic can be presented as a technique for selecting classifiers based on their performances. The ROC graph depicts relative tradeoff between the TP and the FP patterns. Each classifier can be represented by a single point in the ROC space. In this graphic, the point (0, 1) represents a perfect classification. Therefore, the models located on the upper left-hand side on the ROC graph provide the best classification performance. According to Figure 8, the ANN model using 10 hidden neurons provided the best classification performance because this model was the closest to the left upper corner, providing a value of 0.980 for sensitivity and 0.956 for specificity, respectively. However, to conclude if this model is only better by chance or whether its performance was truly significant (Forman, 2002), a methodology based on ROC curve was presented.

Figure 8:

ROC space for the ANN models using different hidden neurons: 1, 2, 3, 4, 5, 10, and 20.

The ANN models applied to classification tasks are considered as probabilistic models. These models provide a score representing the grade to which a pattern belongs to a class. Based on these scores given by the model, the ROC curve can be represented considering one of the classes. ROC curve represents a complete analysis of TPR/FPR to evaluate the classification performance. Figure 9 shows some of the curves obtained for the different configurations of the ANN models presented in this work.

Figure 9:

ROC curves for one of the 20 repetitions using 5-fold cross-validation to evaluate classification performance of the combined model using 1, 2, 4, and 10 hidden neurons, respectively.

Each point of the ROC curve represents pairs of sensitivity-specificity values for a certain decision threshold. Therefore, the closer the curve is to the upper left corner, the greater is classification performance shown by the model. In this sense, the AUC can be used to measure the ability of the model to classify a pattern into the right group: an AUC value of 1 represents a perfect classification performance, whereas a value of 0.5 represents a worthless classification test. The influence of the number of hidden units for the ANN models on AUC values is represented in Figure 10.

Figure 10:

Influence of the number of hidden neurons on the AUC values for the ANN models in the second stage.

Mean values were calculated for the 20 repetitions with 5-fold cross-validation.

According to Figure 10, it can be stated that the range of AUC values obtained for all the configurations varies from 0.972 (using 5 hidden neurons) to 0.994 (using 10 hidden neurons). The values of AUC close to 1 provided by the ANN model using 10 hidden neurons revealed the ability of the model to identify those samples that will suffer corrosion accurately. Therefore, this result was in agreement with those obtained from ROC space.

The selection of the optimal model based on ROC space, in addition to AUC values, ensured the selection of the optimal model as the one with the capacity not only to predict the samples that will suffer corrosion correctly, but also to predict those samples that will show resistance to pitting attack. The ability of the model to predict both cases, corrosion and no-corrosion samples, is essential from the point of view of the material design because prior knowledge of the CORROSION behavior of the material may save costs related to maintenance and repair operations.

Considering the two-stage model based on ANNs, the frontier between corrosion and no-corrosion patterns predicted by the optimal model (using 3 hidden neurons in the first stage and 10 for the second one) can be represented in Figure 11. This figure shows the limit between these regions as a function of the environmental factors considered in this study. According to the figure, the two-stage model based on ANN presented in this work was able to determine the pitting corrosion status of the material according to the environmental conditions automatically.

Figure 11:

Modeling of pitting corrosion behavior using a combined model based on ANNs with 3 hidden neurons for breakdown potentials estimation and 10 hidden neurons for pitting corrosion behavior prediction.

The frontier between the corrosion and the no-corrosion areas is represented by the gray surface. The upper region belongs to corrosion area whereas the lower region corresponds to the no-corrosion area.

Finally, to demonstrate the advantage of considering the breakdown potential in the corrosion status prediction, Figures 12–14 show a comparison between the results obtained from the model presented in this article and those obtained from our previous study (Jiménez-Come et al., 2014). These figures collect the results in terms of sensitivity, specificity, and AUC values obtained from both works. In the first work (Jiménez-Come et al., 2014), the ANN models were presented to predict pitting corrosion status of 316L stainless steel not considering the breakdown potential values. In this case, the pitting corrosion status of the material was predicted according to the environmental variables (chloride ion concentration, pH, and temperature). These factors were identified as the inputs for modeling, whereas in the case of the combined model presented in the present article, as has been explained in the experimental procedure, the breakdown potential values were estimated in the first stage, and then, these estimated values, in addition to the environmental conditions, were considered as inputs in the second stage to model pitting corrosion status of the material.

Figure 12:

Comparison of sensitivity results obtained using the two-stage model (four inputs: [Cl^–], pH, T, and estimated E_b) and the simple model, not considering values of breakdown potentials (three inputs: [Cl^–], pH, and T).

Mean values were calculated for the 20 repetitions with 5-fold cross-validation.

Figure 13:

Comparison of specificity results obtained using the two-stage model (four inputs: [Cl^–], pH, T, and estimated E_b) and the simple model, not considering values of breakdown potentials (three inputs: [Cl^–], pH, and T).

Mean values were calculated for the 20 repetitions with 5-fold cross-validation.

Figure 14:

Comparison of AUC results obtained using the second-stage model (four inputs: [Cl^–], pH, T, and estimated E_b) and the simple model, not considering values of breakdown potentials (three inputs: [Cl^–], pH, and T).

Mean values were calculated for the 20 repetitions with 5-fold cross-validation.

On the one hand, according to these figures, the range of values obtained for the simple model presented in our previous study (Jiménez-Come et al., 2014), not considering the influence of the breakdown potential values, were 0.915–0.958 for sensitivity, 0.791–0.841 for specificity, and 0.884–0.954 for AUC. On the other hand, for the two-stage model proposed in the present article, as has been exposed in the discussion, the ranges of these metrics were 0.973–0.981 for sensitivity, 0.917–0.956 for specificity, and 0.972–0.994 for AUC. According to these values, it can be concluded that considering the breakdown potentials, the prediction performance was improved for all the ANN configuration models. Therefore, the combined model can be presented as an accurate and effective tool to predict pitting corrosion status automatically. These results demonstrated the crucial role of considering breakdown potentials for the prediction of pitting corrosion behavior of 316L stainless steel. The use of this technique in corrosion studies may save costs, leading to optimal material selection according to environmental conditions.

4 Conclusions

The knowledge of corrosion behavior of stainless steel is crucial to get an effective use of this material. The prediction of the pitting corrosion resistance of stainless steel as a function of the environmental conditions guarantees the optimal performance and cost-effective option of this material in building and structures. Among the different types of corrosion, pitting corrosion is one of the most important corrosion types in material design. In this case, chloride ion concentration, pH, and temperature are the main environmental variables that influence corrosion behavior.

Motivated to reduce the costs incurred due to corrosion, a two-stage model based on ANNs was presented to predict the pitting corrosion status of austenitic stainless steel automatically way. The breakdown potential values were estimated in the first step, and the estimated values, in addition to the environmental conditions, were considered in the second step for modeling pitting corrosion status of 316L stainless steel.

The performance of the two-stage model was evaluated based on ROC space and AUC values. Based on these results, it can be concluded that the ANNs model using 3 hidden neurons in the first stage and 10 hidden units in the second stage resulted to the optimal configuration. This model provided great values of sensitivity and specificity: 0.980 and 0.956, respectively, and 0.994 for the AUC value. These results demonstrated the utility of the combined model to predict the pitting corrosion status of the material accurately. Furthermore, the important role of the breakdown potentials in pitting corrosion status prediction of stainless steel has been verified because the combined model presented to predict corrosion behavior, with the estimated values of the breakdown potential considered, outperformed the model where breakdown potential values were not considered. Therefore, the two-stage model based on ANNs can be considered as an effective tool in automatically predicting the pitting corrosion status of austenitic stainless steel according to the environmental conditions, without having to use polarization tests, thus becoming a tool of great importance in corrosion studies.