The use of artificial neural networks for modelling pitting corrosion behaviour of EN 1.4404 stainless steel in marine environment: data analysis and new developments

1 Introduction

The use of stainless steel in construction has grown significantly in recent years due to the excellent properties of this material (Lo et al. 2009). However, one of the most critical problems that may occur in this application is the corrosion attack, that may negatively affect the durability of the structure (Gadve et al. 2009; Ha et al. 2007; Pohjanne et al. 2008; Reale and O’Connor, 2012; Trethewey et al. 1998). Corrosion can be defined as the deterioration of a material as a result of the interaction between it and the environment (Fontana 2005). It is well known that both the type of material and the environmental conditions, determine the rate and form of deterioration. Pitting corrosion is a type of localized corrosion that leads to the creation of small holes in the surface of the metal (Sedriks 1996; Singh and Nakabayashi 2016). The “World Corrosion Organization” indicates that the annual cost of corrosion is around US $2.5 trillion, equivalent to roughly 3.4 percent of the global Gross Domestic Product (Hays 2010). The 2-year global study presented at the Corrosion 2016 Conference in Vancouver, B.C, analysed the cost of corrosion. This study concluded that implementing corrosion prevention best practices may lead to global savings of between 15 and 35 percent of the cost of damage. Therefore, it is necessary to make changes in how corrosion decisions are made. The complexity and the non-linearity of the corrosion process make prediction about corrosion behaviour of materials a very difficult task (Chew et al. 2013). For this reason, it is justified the interest in modelling corrosion behaviour of materials (Hu et al. 2019).

The models developed to predict corrosion behaviour of materials can be very useful since they become a tool to be applied for the assessment of the system life and the cost related to the degradation (Nazarnezhad-Bajestani et al. 2019; Saraswathy and Song 2007). Most of the predictive models found in the literature review are statistical regression models that try to find a specific mathematical function adjusted to the experimental data (Gelman and Hill 2007). However, the use of these models in corrosion problems is limited since the available information in this area has been demonstrated to be highly non-linear (Pohjanne et al. 2008). Therefore, it is necessary to develop generalized mathematical models to predict pitting corrosion behaviour of materials (Sharland 1987). Artificial Intelligence techniques, in particular artificial neural networks (ANNs), have proved to be very helpful in studying non-linear systems and solving complex problems (Farley et al. 2012; Rowshandel et al. 2018). These techniques try to simulate the ability of human brain to recognize patterns (Bishop 1995; Gurney 1997). ANNs are computational techniques inspired by the structure and functional aspects of biological neural networks. They can be considered as non-linear statistical data modelling tools that can be applied to analyse complex relationships between inputs and outputs. One of its greatest advantages is the fact that they can be undertaken to address many types of problems (Coşkun and Karahan 2018; Mousavifard et al. 2015). In the related field of corrosion protection, these techniques have been applied to solve multivariable problems. The following shows the most relevant studies about ANN models applied on corrosion analysis:

Barton et al. (1993) designed an ANN model to monitor the electrochemical signals produced by stainless steel samples during the initial stage of localized corrosion in order to classify the type of attack: pitting or crevice corrosion. Cottis et al. (1999) proposed a model to predict pitting corrosion behaviour of stainless steel as a function of solution composition and temperature. Pintos et al. (2000) presented a methodology based on ANN for modelling atmospheric corrosion process in order to predict the corrosion rate of carbon steel considering a variety of climatological and pollution conditions. Boucherit et al. (2008) illustrated the usefulness of ANN models to predict pitting corrosion of carbon steel in order to analyse the effect of different inhibitors. Diaz and Lopez (2007) designed a model based on ANNs to determine corrosion penetration of low carbon steel as a function of cumulated values of environmental variables. Ramana et al. (2009) developed an ANN model to determine pitting potential values of EN 1.4404 stainless steel in an aqueous environment for different environmental conditions. Kamrunnahar and Uriquidi-Macdonald (2010) developed a model based on ANNs to know the influence of certain parameters (i.e. pH, temperature, time of exposure, electrolyte composition, metal composition …) on electrochemical potentials and corrosion rates. Cavanaugh et al. (2010) applied these techniques for modelling pit growth as a function of temperature, pH and chloride ion concentration. The proposed models were used to characterize diameter distribution and pit depth. Martin et al. (2010) proposed ANN models to predict the influence of welding process on pitting corrosion behaviour of AISI 304 stainless steel. The corrosion resistance was estimated based on the pitting potential value, predicted according to the resistance spot welding parameters. Rolich et al. (2010) applied ANN technique to estimate the corrosion of steel guitar strings and concluded that this technique is a promising tool for estimation of corrosion process. Birbilis et al. (2011) presented an ANN model for predicting corrosion rate and yield strength analysing the effect of different alloying elements in magnesium alloys. Shi et al. (2014) proposed a model based on ANN to predict the crack growth rate of 304 stainless steels. Later, in 2015 (Shi et al. 2015), these authors applied this technique to model stress corrosion cracking in Alloy 600.

According to the literature review, see Table 1, ANNs have been demonstrated to become a method capable of investigating non-linear correlation and predicting the corrosion behaviour of materials as a function of the environmental variables. In our previous works, the proposed ANN models were designed to predict pitting corrosion behaviour of EN 1.4404 stainless steel. A first attempt to model pitting corrosion behaviour of this material was presented in (Jiménez-Come et al. 2012). In this case, in order to determine the pitting corrosion status of EN 1.4404 stainless steel, the presented ANN model considered the most critical environmental variables with influence on the pitting corrosion resistance of the material according to the literature review: chloride ion concentration, pH and temperature. In addition, the breakdown potential values obtained from electrochemical tests were considered as input to the model. The results provided by the model were remarkably good and therefore, ANN models were proved to be a promising technique to predict pitting corrosion status of this material without resorting to optical metallographic studies. However, this design presented one disadvantage: in order to predict the corrosion status for a sample under new environmental conditions, it was necessary to require electrochemical polarization tests since the breakdown potential value obtained from these tests was considered as input for modelling. Therefore, the corrosion status prediction could not be performed automatically. With the aim to overcome this drawback, a second attempt was presented in (Jiménez-Come et al. 2014). In this case, the ANN model proposed to predict pitting corrosion behaviour of EN 1.4404 stainless steel was designed considering only the environmental variables, not taking into account the breakdown potential values. In this case, an automatic model to predict pitting status of the material based on environmental variables was obtained, however the predictive capability of the models was reduced compared to those obtained from the previous design where the breakdown potential was considered as input for modelling. This finding indicated that the breakdown potential has a great effect on pitting corrosion modelling and therefore, this parameter should be considered in corrosion behaviour predictions. Based on this fact, a third design is proposed in (Jiménez-Come et al. 2016). In this case, the model had two stages: in the first one, the ANN model was trained to estimate breakdown potential values according to the environmental variables and then, the estimated potential value, in addition to the environmental variables, were considered in the second stage to predict pitting corrosion status of the material. In this case, the model outperformed that model proposed in (Jiménez-Come et al. 2014), where only the environmental variables were considered as inputs for modelling. However, it did not achieve the precision obtained by the model proposed in (Jiménez-Come et al. 2012) where the experimental breakdown potential values were considered as input in addition to the environmental variables. In order to improve the results provided by the model presented in (Jiménez-Come et al. 2014) and to produce results more consistent with those presented in (Jiménez-Come et al. 2012), in this work, a three-stage model is presented. In this case, as it will be described in the following sections, a new step related to feature extraction technique is included. The objective of including this step is to derive new features from the original features in order to improve overall efficiency in the pitting corrosion modelling of EN 1.4404 stainless steel.

2 Materials and methods

2.1 The database

With the aim to analyse the influence of different environmental variables on pitting corrosion resistance of EN 1.4404 stainless steel, a project titled “Avoiding Catastrophic Corrosion Failure of Stainless Steel” – CORINOX (RFSRCT-2006-00022) – was developed by ACERINOX EUROPA S.A.U.

A total of 60 samples of austenitic stainless steel were subjected to polarization tests in order to determine the breakdown potential value and pitting corrosion status for different environmental conditions. Three variables were considered in this study: chloride ion concentration (0.0025–0.1 M), pH (3.5–8) and temperature (278 348 K). The composition of the alloys was: 1.6% Mn, 0.026% C, 0.37% Si, 0.01% S, 16.6% Cr, 2.4% Mo, 0.025% N, 0.032% P, and 10.2% Ni. For this project, all the samples were cut into 40 × 40 mm size. Before each test, the samples were prepared placing them in electrical contact with copper. All of them were polished down to #600 grit on silicon carbide paper. The potentiostatic tests were carried out using the equipment composed by a potentiostate “PARSTAT 2273” and a special design free-crevice cell described in (Merello et al. 2003). In this design, the cell has three electrodes: a graphite wire used as the counter electrode, the stainless steel sample with exposure area of 1 cm², as working electrode, in addition to a saturated calomel electrode (SCE) used as the reference electrode. During the experiment, the sodium chloride electrolyte was mechanically stirred into the cell and the oxygen was displaced from the system by nitrogen supplied from a feeding system. At the beginning of the experiment, each sample was immersed in the electrolyte during 30 min in order to stabilize the open circuit potential. Then, the sample was cathodically cleaned at a conditioning potential of −1300 mV versus SCE during 3 min. After that, the test was initiated at −1100 mV versus SCE setting a scan rate equal to 0.17 mV versus SCE/s. For each sample, the potential and current density values registered during the test were plotted with semi-logarithmic scale in order to obtain the polarization curve. Based on this curve, the breakdown potential value was defined as the potential at which current density reaches 100 μA/cm² for each condition (Alfonsson and Qvarfort 1992). In all cases, each environmental condition was carried out at least twice to ensure reproducibility in the results. At the end of the electrochemical tests, all samples were subjected to optical microscopy surface analysis in order to define the pitting corrosion status: one for samples suffering pitting attack and 0, otherwise (see Figure 1). For those cases, where pit could not be identified clearly, analyst required a cross-section micrograph. In this way, the experimental value obtained for the breakdown potential and the pitting corrosion status, in addition to the environmental variables, were used as database for modelling. The experimental results are collected in Table 2.

Figure 1:

Potentiodynamic polarization curve for EN 1.4404 stainless steel in NaCl and optical microscopy surface analysis: (a) no pitting corrosion, (b) pitting corrosion.

Table 2:

Experimental results for pitting corrosion modelling of EN 1.4404 stainless steel in marine environment.

Cl	pH	T (°C)	E b (mv vs. SCE)	Corrosion status
0.1	7.81	65	371.43	1
0.1	7.93	25	528.44	1
0.1	8.32	15	808.94	1
0.1	8.32	5	1330.04	0
0.05	8.02	50	560.20	1
0.05	8.1	25	706.99	1
0.05	8.1	15	882.49	1
0.05	8.28	5	1325.25	0
0.05	7.98	2	1360.45	0
0.01	8.37	75	666.56	1
0.01	8.37	25	799.77	1
0.01	7.95	15	1372.15	0
0.01	7.99	2	1440.00	0
0.005	7.86	45	774.00	1
0.005	7.86	35	1104.63	1
0.005	7.98	20	1308.00	0
0.005	8	15	1420.87	0
0.0025	8.26	55	826.25	1
0.0025	8.33	45	852.00	1
0.0025	8.35	35	1023.00	1
0.0025	7.79	25	1376.00	0
0.0025	8.26	15	1493.46	0
0.1	5.77	55	409.02	1
0.1	5.68	15	766.09	1
0.1	5.68	5	1307.28	0
0.05	5.85	75	345.35	1
0.05	5.42	25	715.02	1
0.05	5.42	15	957.80	1
0.05	5.47	5	1334.00	0
0.01	5.54	70	626.00	1
0.01	5.47	25	890.00	1
0.01	5.47	15	1369.00	0
0.005	5.61	75	680.58	1
0.005	5.52	45	894.73	1
0.005	5.52	35	985.24	1
0.005	5.61	25	1133.50	1
0.0025	5.45	75	795.00	1
0.0025	5.68	65	970.04	1
0.0025	5.68	55	1076.39	1
0.0025	5.68	45	1050.82	1
0.0025	5.86	30	1324.27	0
0.0025	5.73	20	1537.94	0
0.1	3.53	75	213.33	1
0.1	3.39	10	680.46	1
0.1	3.39	2	1324.50	0
0.05	3.42	75	247.74	1
0.05	3.53	20	657.38	1
0.05	3.53	10	1332.00	0
0.01	3.32	75	467.00	1
0.01	3.5	30	816.00	1
0.01	3.5	20	1032.77	1
0.01	3.5	10	1395.41	0
0.005	3.45	75	611.19	1
0.005	3.45	30	933.61	1
0.005	3.45	20	1368.98	0
0.0025	3.53	70	839.63	1
0.0025	3.41	60	967.52	1
0.0025	3.55	50	1031.32	1
0.0025	3.41	40	1313.00	1
0.0025	3.41	30	1415.00	0

2.4 Computational procedure

As it was indicated in the introduction, ANNs have been demonstrated to become a method capable of investigating non-linear correlation and predicting the corrosion behaviour of materials as a function of the environmental variables. These techniques have as the advantage that no assumptions as to the underlying functional form of the model are required. In this sense, as a forecasting model, assumes that there is an underlying relationship between inputs and outputs. In this case, the main objective is to determine the relationship between the environmental conditions and the pitting corrosion behaviour of EN 1.4404 stainless steel.

According to the good performance of the models based on ANNs for both regression and pattern classification problems, in the present work, a feedforward artificial neural network model was selected and trained with corrosion data collected from the European Project called “Avoiding Catastrophic Corrosion Failure of Stainless Steel” in order to predict pitting corrosion status of EN 1.4404 stainless steel. The selected topology of the ANN model for the problem under study was a perceptron multilayer model with the following characteristics (see Figure 2):

Figure 2:

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

In the first step, where the system can be considered as a regression problem, the principal objective was to estimate breakdown potential values according to the environmental variables for EN 1.4404 stainless steel. In this case, the network presented three neurons in the input layer corresponding to each environmental parameter considered in this study: chloride ion concentration, pH and temperature. The number of neurons in the hidden layer was varied from 1 to 20 in order to evaluate the optimal configuration and finally, the output layer had one neuron corresponding to the breakdown potential value.

In the second step, the estimated value of breakdown potential, in addition to the environmental variables, were subjected to pre-processing techniques (PCA or LDA) selecting two new features. The obtained outputs were used as inputs in the third stage, where the network presented two units in the input layer, a hidden layer with different number of neurons (from 1 to 20) and two output neurons corresponding to the pitting corrosion status of the material surface (1 for pitting status and 0, otherwise).

In order to adjust the parameters involved in the model, Levenberg–Marquardt algorithm was used in this study. The training procedure was repeated until the predefined criteria was satisfied: measuring the root of the mean square error between the output provided by the model and the experimental data. In addition, with the aim to improve the network training process, the experimental data were preconditioned. To get it, previous to the feature extraction step, the original variables were standardized. This standardization was achieved through normalizing the attribute values. The need for this step lies in the fact that all the variables may be represented by different data types and each of them may present different range of values. Therefore, all the variables were normalized resulting in a transformed group of data with unit standard deviation and zeroed average. In this way, the same range of values for each input was obtained, leading to stable convergence of weight and biases. In this research, in order to avoid overfitting, 5-fold cross validation and early stopping have been applied for hyperparameter tuning where the scaled original data was randomly divided into three sets: training set, validation set and test set. The training set (60% of original patterns) was applied to fit the parameters of the ANN model. During training, the process was controlled by evaluating the validation set (20% of original patterns). When there is no improvement in the prediction capabilities of the ANN model considering this set, the training process is finished in order to avoid overfitting whereas the test set (20% of the original patterns) was used to estimate the performance of the model. This iterative process was repeated 20 times in order to ensure the generalization capability of the model.

According to Figure 3, the modelling process proposed in this study may be described in the following steps: (i) partitioning of the original data set into three subsets: training, validation and test sets, (ii) pre-processing data, (iii) ANN model architecture training, (iv) model testing; and (v) application.

Figure 3:

Modelling procedure proposed for ANN models.

3 Results and discussion

The described model in this study, based on artificial neural network, was presented to predict pitting corrosion status of EN 1.4404 stainless steel considering the most critical environmental variables involved in this process: chloride ion concentration, pH and temperature. In this work, the influence of different dimension reduction techniques on the performance of the ANN models was analysed.

As it has been introduced in the methodology section, the presented model can be defined as a three-step model. At the first stage, the model was trained to estimate the breakdown potential value according to the environmental variables considered in the study. At the second stage, the environmental variables, in addition to the breakdown potential value estimated in the previous step, were pre-processed by using two different feature reduction techniques: PCA and LDA. Finally, the two new features obtained from this step were considered as inputs in following stage where the model was trained to predict the pitting corrosion status of the material.

The first stage can be considered as a regression problem. The results obtained in this case are collected in (Jiménez-Come et al. 2014). The ANN structure used to predict breakdown potential value according to the environmental variable is illustrated in Figure 2. In this case, the optimal configuration was obtained using three hidden neurons (3:3:1). In order to offer a clear vision of the predicted values versus the experimental ones, Figure 4 shows the correlation plots for training data (blue points), validation data (red crosses) and testing data (black triangles) respectively, considering a random iteration.

Figure 4:

Estimated values of breakdown potential provided by ANN model [3:3:1] versus experimental ones considering the most relevant environmental variables involved in pitting corrosion behaviour of stainless steel: chloride ion concentration, pH and temperature.

According to the figure, the ANN model not only performed well for training and validation sets (R = 0.99 for training set and R = 0.95 for validation set, respectively), but also the model provided good results for the test set (R = 0.92). The good correlation between the experimental and estimated values, reflects the capacity of the proposed ANN model to estimate the breakdown potential value through the knowledge of specific environmental factors: chloride ion concentration, pH and temperature. The estimated values of breakdown potential provided by the optimal configuration of ANN model in the first stage were considered as inputs in addition to the environmental variables in the second step.

In the second step, all the inputs were pre-processed. In this case, the principal objective was to improve the performance of the ANN model to predict pitting corrosion behaviour of EN 1.4404 stainless steel, leading to faster and more efficient predictor. This pre-processing step is crucial to avoid irrelevant and redundant variables. In this study, two different techniques were proposed: PCA tries to reduce the dimensionality of the original problem preserving the maximum variance of the original features, whereas LDA retains as much discriminatory information as possible. Figure 5a shows the projection of the original patterns provided by PCA preserving as much information in the data as possible where the combinations of the original variables that account for the most variance are identified. This technique projects the patterns along the direction where the data varies most. In this case, the original patterns are represented in a new dimensional space considering two principal components. These new directions are determined by the eigenvectors of the covariance matrix corresponding to the largest eigenvalues. The magnitude of the eigenvalues represents the variance of the original data along the eigenvector directions. U1 is the direction of the greatest variability whereas U2 represents the next orthogonal direction of higher variability. The variance retained for each dimension is represented by the eigenvalues: 39.86% in U1 and 32.87% in U2, respectively.

Figure 5:

(a) Principal component analysis 2D plot of corrosion (red) and no corrosion (black) data sets. The first two components are represented by the axes of the plot and capture the most variance of the data. (b) Linear discriminant analysis 2D plot of corrosion (red) and no corrosion (black) data sets onto the first two linear discriminants maximizing the separation between classes.

Based on the findings from Figure 5a, it can be seen that the projection along the two principal components separates most of the patterns corresponding to each class. In relation to LDA technique, it tries to identify those variables that account for the most variance between classes. In this case, in contrast to PCA, this technique is a supervised method that used the original class labels to define the latent variables minimizing the variance within the group whereas the variance between classes is maximal. Figure 5b shows the linear discriminant analysis 2D plot of the experimental data for a random iteration of the simulations.

From this figure, it can be seen that this technique provides a representation where most of the experimental patterns belonging to each class are grouped together. This representation demonstrates the utility of this technique to determine the directions for maximum discrimination between classes, in addition to reduce the dimensionality of the original data.

Once the new two features were selected in the second step, in the next one, an ANN model was presented with the aim to define the pitting corrosion status of EN 1.4404 stainless steel by an automatic way. The global results, in terms of sensitivity and specificity, are collected in the following table according to the proposed structure of the ANN model. For all the configurations, the model presented two neurons in the input layer corresponding to those variables obtained from the second step, two neurons in the output layer that represent the corrosion status of the material, whereas the number of hidden neurons varied from 1 to 20 in order to determine the optimal configuration.

According to the table, when no pre-processing technique was used, the maximum values in terms of sensitivity and specificity were 0.983 and 0.952, respectively. Based on the collected data, it can be noted that the use of feature extraction techniques has an important effect on the performance of the model. Considering the use of PCA, the maximum values were 0.954, and 0.646 for sensitivity and specificity, respectively; whereas for LDA, the best results provided by the model were 0.992 and 0.956, respectively. One important observation that need to be noted is that the optimal results were obtained by using LDA.

When LDA is applied, new directions along which the classes are best separated are found. In this new projection, the distance between the differences classes is maximized, as can be seen in Figure 5b.

With the aim to know the optimal configuration of ANN model for the proposed application, the Receiver Operating Characteristics (ROC) graph is presented in Figure 6. This technique has become a useful technique for visualizing, organizing and selecting classification models based on the performance even when skewed class distribution is presented (Fawcett 2006). In this graph, TP rate is plotted on the Y axis and FP rate, on the X axis. This figure shows all the proposed configurations represented in a ROC space, considering different number of hidden neurons and different feature extraction techniques. The perfect classification is represented by the point (0, 1). The models represented on the upper region have the capability to detect those patterns that will suffer from pitting corrosion attack correctly. According to ROC space, one point is better than another when it is located near the upper-left corner of the graphic. In this case, according to Figure 6, the models using LDA show better performance overcoming those models where no-pre-processing techniques were applied. The results achieved by using LDA are superior to those obtained considering PCA since the model tries to find out the low-dimensional representation of the observations focussing on the most discriminant feature extraction.

Figure 6:

Sensitivity and specificity plotted in ROC space for all the configurations proposed to model pitting corrosion behaviour of EN 1.4404 stainless steel.

According to Figure 6, the selection of the optimal configuration for the proposed model is not a simple task since most of LDA models are located close together in the graphic. In order to determine the optimal structure for LDA models, a statistical analysis is proposed applying Friedman and LSD post hoc tests considering TPR and FPR values. Based on the information obtained from the statistical analysis, the equivalent LDA models providing the best results in terms of TPR were the ANN models using 3, 4, 5 and 20 hidden neurons, whereas according to FPR, the optimal configurations that resulted to be equivalent were those models with 4 and 20 hidden neurons. From these findings, it can be noted that LDA-ANN model using four neurons in the hidden layer can be considered the best configuration for the presented study.

Moreover, with the aim to analyse the influence of the pre-processing techniques on pitting corrosion modelling, in addition to compare the predictive capacity of the model presented in this work with those provided by other models proposed in our previous studies, Table 3 shows the most relevant results considering the area under the ROC curve (AUC), sensitivity and specificity values as indicators to estimate the discrimination capability of each model. In this case, AUC has been considered since it is a measure of how well a parameter can distinguish between two different classes (corrosion/ no corrosion).

The 4-input model represents the case where the environmental variables in addition to the experimental breakdown potential value were considered as inputs for modelling. In this case, in order to predict the pitting corrosion status for new environmental conditions, it is necessary to resort to electrochemical tests, leading to a no-automatic process. With the aim to solve this disadvantage, the 3-input model was proposed. In this case, only the environmental variables were considered as inputs to ANN model. In this way, the pitting corrosion status of the material could be predicted automatically without resorting to the use of electrochemical techniques. However, according to the results, a decrease in the prediction performance of the model is observed, showing the importance of considering the breakdown potential in corrosion modelling. For this reason, the combined model was proposed analysing the influence of different pre-processing techniques to achieve an accurate predictive model.

Based on the findings from Table 4, it can be noted that according to the indices considered in this study to evaluate the capability of ANN models to predict the corrosion behaviour of EN 1.4404 stainless steel (specificity, sensitivity and AUC), as it has been introduced previously, the use of LDA as dimension reduction technique improved the prediction capability for the proposed combined model of three steps. In this case, the reached values for the quality ratios are 0.992 for sensitivity, 0.956 for specificity and 0.987 for AUC, respectively. These values lead to an increase in the reliability and accuracy of the model compared with the combined model without pre-processing step. The higher quality results provided by LDA-combined model compared with those values provided by 3-input model, reflects the key role of the breakdown potential for modelling pitting corrosion behaviour of stainless steel. The configuration of LDA-combined model became a more effective option leading to a 4, 3 per cent increase in sensitivity; 12, 47 per cent in specificity and 3, 76 per cent in AUC terms, respectively compared to those obtained from 3-input model.

Finally, based on the results provided by the ANN model with four inputs, considering chloride ion concentration, pH, temperature and the experimental breakdown potential obtained from electrochemical tests, it can be concluded that the use of the proposed LDA-combined model, where the breakdown potential value is estimated by the model itself, becomes an efficient option to obtain a completely automated model to determine pitting behaviour of stainless steel. In this case, although the quality indices decrease slightly comparing with those values obtained from 4-input model (4.4 per cent in specificity and 1.3 per cent in AUC values, respectively), the proposed model presents the advantage that the pitting status prediction of the material for new conditions is not based on the results obtained from electrochemical tests since the model is capable to predict the breakdown potential value accurately, considering this value to model pitting corrosion behaviour. The LDA-combined model predicts pitting corrosion status with rigorous precision of 99.2%, becoming a fundamental tool to determine corrosion behaviour of EN 1.4404 stainless steel since according to the environmental condition, the model predicts the pitting corrosion status of the material. One of the limitations that can be found in the proposed model is that it is useful only for the range of experimental conditions tested. In addition, the model is suitablefor the study of corrosion attack for this type of material, EN 1.4404 stainless steel. The use as a generalized tool to study the behaviour of any grade of stainless steel will be the subject of future works. Figure 7 shows the frontier between corrosion and no corrosion patterns according to values of chloride ion concentration and temperature provided by the LDA-combined model.

Figure 7:

Pitting corrosion modelling based on LDA-ANN combined model according to chloride ion concentration and temperature (pH value equal to 5.5). The black solid line represents the frontier between corrosion and no-corrosion patterns. The original no-corrosion patterns are represented with black colour and corrosion patterns with red stars.

4 Summary

Artificial neural networks have become a powerful tool for the prediction of corrosion behaviour of materials. In this work, a combined model based on ANN is presented to predict pitting corrosion status of EN 1.4404 stainless steel, considering the most critical environmental variables involved in this process. The proposed model consists of three steps: (i) estimation of breakdown potential values, (ii) dimension reduction using PCA or LDA, and (iii) prediction of pitting corrosion status of EN 1.4404 stainless steel. The data used to train, validate and test the model in each stage were obtained from the European project called “Avoiding Catastrophic Corrosion Failure of Stainless Steel”. The results show high precision in terms of sensitivity (99.2%). This values demonstrated the improvement obtained by considering the LDA-combined model in comparison with our previous studies where no feature selection technique was considered. This result reflected the effectiveness of the proposed model, becoming a very useful tool to determine pitting corrosion behaviour of EN 1.4404 stainless steel without resorting to electrochemical corrosion testing. This model may be effectively used to prevent pitting corrosion damage in EN 1.4404. In future works, it would be useful to analyse the influence of the chemical composition of the alloy on the pitting corrosion behaviour in order to get a global model capable to predict pitting corrosion status for any stainless steel grade.