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Introduction
Predicting pitting corrosion remains a challenge despite advancements in predictive modeling. This study addresses the difficulty of accurately estimating relevant pitting descriptors (like pitting potential, *E*<sub>pit</sub>, and passive potential, *E*<sub>pass</sub>) from experimental data, a problem often handled qualitatively in literature. Potentiodynamic polarization (PP) curves are widely used, but existing standards for extracting *E*<sub>pit</sub> are vague, relying on subjective interpretations of a "sharp rise" in current. The variability inherent in PP curves, previously attributed to experimental error, is now recognized as an intrinsic property of pitting corrosion, emphasizing the need for statistical analysis. The dynamic nature of pitting corrosion, occurring at a nanoscale, coupled with the influence of aggressive species like Cl⁻ and surface heterogeneities, contributes to the difficulty in obtaining a generalized value for *E*<sub>pit</sub>. Advanced techniques like SECCM provide high-throughput data generation, crucial for capturing the high variance expected in pitting features. Data-driven approaches, though scarce in localized corrosion research, offer a promising path forward. This work uses SECCM to obtain high-throughput data and develops a methodology to accurately estimate *E*<sub>pass</sub> and *E*<sub>pit</sub> from these data.
Literature Review
The authors review existing literature on pitting corrosion modeling, highlighting the challenges and limitations of traditional methods. They discuss the use of potentiodynamic polarization curves and the ambiguities in defining and extracting pitting potential from these curves. The limitations of relying on qualitative descriptions of pitting potential are emphasized, alongside the shortcomings of existing quantitative definitions. The review underscores the importance of statistical approaches to account for the inherent variability in pitting corrosion data, citing relevant studies that have challenged the concept of a sharp threshold value for pitting initiation. The development of advanced scanning electrochemical techniques, such as SECCM, is highlighted as a means to collect statistically representative high-throughput data to improve pitting corrosion research. The limited use of data-driven approaches in localized corrosion is also discussed, attributing it to the traditional reliance on low-throughput data generation and complex feature engineering challenges.
Methodology
This study uses five datasets of log(j) vs. E (PP) curves obtained from high-throughput SECCM measurements on 316L stainless steel under varying NaCl concentrations and scan rates. A hybrid approach, combining a rule-based linear regression (LR) algorithm with artificial neural networks (ANNs), was developed to estimate *E*<sub>pass</sub> and *E*<sub>pit</sub>. The LR algorithm provided initial estimates by fitting two linear regression lines to smoothed polarization curves. This rule-based method, however, produced unsatisfactory results for some datasets, necessitating the use of ANNs. The ANNs were trained on datasets with satisfactory LR estimates and then used to refine estimates on datasets where the LR method had performed poorly. Feature engineering was employed to select input features representative of the target behavior (passivity or pitting), including a data reduction step to reduce the number of data points used as input features. A sequential model (multi-layer perceptron) was used, with hyperparameter tuning and pruning to optimize performance. The accuracy of the estimations was assessed using mean squared error (MSE) and R². Additionally, non-parametric density estimation was used to determine the central tendencies of the *E*<sub>pit</sub>/log(*j*<sub>pit</sub>) and *E*<sub>pass</sub>/log(*j*<sub>pass</sub>) distributions. The conditional mean and median curves were calculated to provide proxy estimations of the central tendencies, and these were compared with the values obtained from non-parametric density estimations. Various normality tests (Shapiro-Wilk, D'Agostino and Pearson's, and Anderson-Darling) were applied to the *E* descriptor distributions.
Key Findings
The conditional median of log(j) provided more accurate estimations of the central tendencies of the pitting descriptors than the conditional mean. The conditional median approach proved more robust to high outliers, common in pitting corrosion datasets. The study showed a trend of passive range shortening with increasing testing aggressiveness, primarily due to delayed stabilization of the passive film rather than early passivity breakdown. Analysis of the most active pitting sites (high outliers) corroborates the observation that *E*<sub>pit</sub> decreases significantly with increasing corrosiveness. The coefficient of variation (CV) values for *E*<sub>pit</sub> were relatively low compared to those reported in literature, likely due to the high number of samples in this study. The CVs calculated for log(*j*<sub>pit</sub>) were significantly higher than those for *E*<sub>pit</sub>, indicating higher variability in the log(*j*<sub>pit</sub>) distributions. The hybrid LR/ANN approach effectively estimated pitting corrosion descriptors, with high R² values achieved after model training and pruning. The conditional median of log(j) served as a robust proxy for estimating the central tendency of pitting descriptors.
Discussion
This study demonstrates the effectiveness of using a hybrid rule-based/ML approach to estimate pitting descriptors from high-throughput SECCM data. The use of conditional median curves proves superior to conditional means for estimating central tendencies, especially in the presence of high outliers characteristic of pitting corrosion. The finding that passive range shortening is more strongly influenced by delayed passive film stabilization than by early passivity breakdown offers valuable insights into the corrosion mechanisms. The analysis of high-activity pitting sites supports the "weakest link" theory in predicting overall corrosion behavior. The generally low CV values for *E*<sub>pit</sub>, compared to previous literature, highlight the advantage of using high-throughput data to obtain more representative distributions. The success of the hybrid model suggests that combining rule-based and ML methods can be an effective approach for analyzing complex electrochemical data.
Conclusion
This research presents a robust hybrid ML-based method for estimating pitting descriptors from polarization curves, a proxy model using conditional median for efficiently estimating the central tendencies of descriptor distributions, and insights into localized corrosion mechanisms. The superior performance of the conditional median model highlights the value of quantile regression in analyzing heteroscedastic and non-normal data in pitting corrosion. Future work should focus on validating the model's generalizability across a wider range of experimental conditions and extending the approach to macro-scale polarization curves and other electrochemical processes.
Limitations
The model's generalizability might be limited by the specific experimental conditions and 316L grade used in the study. The accuracy of the estimations may also depend on the quality of the SECCM data and the effectiveness of the data preprocessing steps. The rule-based portion of the model requires some manual adjustments for different classes of curves, limiting its fully automated applicability. Further research is needed to validate the approach on macro-scale polarization curves and expand its application to other alloys and corrosive environments.
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