Estimating pitting descriptors of 316 L stainless steel by machine learning and statistical analysis

The study addresses the long-standing challenge of extracting robust, quantitative pitting corrosion descriptors—particularly Epit (pitting potential) and Epass (passivation potential)—from potentiodynamic polarization (PP) data. Traditional definitions of Epit are qualitative or rely on fixed current-density thresholds, and experimental scatters are large and method-dependent. Prior work has shown pitting to be intrinsically stochastic, with events occurring over heterogeneous surfaces and varying with chloride concentration and scan rate. With the advent of high-throughput local electrochemical techniques such as SECCM, it becomes possible to gather statistically representative datasets capturing this variability. The research question is whether machine learning, combined with statistical density estimation and conditional quantile analysis, can accurately and robustly estimate pitting/passivity descriptors from large populations of micro-scale PP curves and provide reliable central tendencies for these descriptors across different corrosive conditions.

The paper situates the problem within extensive literature noting the variability and stochastic nature of pitting corrosion. Standards (ASTM G61, ISO 15158) give qualitative or fixed-threshold definitions of Epit, which can be problematic in highly variable datasets. Historical works (Nathan and Dulaney; Shibata and Takeyama) emphasized statistical analyses, challenging the notion of a sharp Epit threshold. Recent observations indicate current surges occur over ranges of potential, not at single values. Advances in SECM/SVET and especially SECCM enable high-throughput local electrochemical measurements that better capture heterogeneity. Data-driven approaches in localized corrosion remain relatively scarce, partially due to low-throughput traditions and complex feature engineering. The authors’ prior work showed uniform-like and heteroscedastic distributions of local current density in pitting regions, motivating large-sample, statistical, and ML-based analyses. The paper also references the growing role of ML in corrosion-related fields and the usefulness of quantile-based and robust methods when noise is non-normal and variance is non-constant.

Experimental: Electropolished 316L stainless steel was tested with SECCM (hopping-mode) to acquire high-throughput PP curves (log(j) vs E). Five conditions combined NaCl concentration and scan rate: 0.005 M–100 mV/s, 0.01 M–100 mV/s, 0.01 M–50 mV/s, 0.05 M–100 mV/s, 0.05 M–50 mV/s. Single-barrel borosilicate pipets (~2 µm internal diameter) were used. Potential swept from −0.5 V to 1.355 V vs Ag/AgCl. Datasets (955 curves total) were processed in Python; missing values were imputed using IterativeImputer (sklearn). For analysis, curves were sliced from 0.5 V upward (more positive than OCP). Where passivity/pitting occurred before/after this range or was absent within it, Epass and/or Epit were approximated as 0.5 V by default. Hybrid rule-based/ML estimator for descriptors: A deterministic linear regression (LR) rule-based algorithm first estimated Epit/log(jpit) and Epass/log(jpass) on individual curves. Two independent LR lines were fitted to smoothed data in low-E (~0.7 V) and high-E (~1.25 V) regions; the E location maximizing the sum of R² values defined Epit or Epass. Dataset-specific thresholds/classes guided the LR application, with visual validation of labels. In sets where LR underperformed (e.g., 0.05 M–100 mV/s and 0.005 M–100 mV/s), supervised ANNs were trained on curves with satisfactory LR labels and deployed on the challenging subsets to improve estimates. ANN design and training: Input features were engineered by slicing relevant curve regions (around target descriptors) and sparsely sampling every 40th–60th point, yielding 12–13 log(j) features equidistant in E. Potential values were treated as constant and not input. StandardScaler was applied to inputs and outputs. A Keras Sequential MLP with two hidden layers (12 and 11 nodes, ReLU activations) and a single output (Epit or Epass) was trained using Adam and MSE loss. 20-fold CV guided hyperparameter tuning; pruning (tensorflow_model_optimization) and additional validation (validation_split=0.1) followed, with 4500–6000 epochs and reduced learning rates (10⁻12–10⁻5). Final retraining used the entire labelled dataset. Reported final metrics included MSE and R²: for 0.005 M–100 mV/s (Epit) MSE 9.87×10⁵ (µA cm⁻²)², R² 0.9025; for 0.05 M–100 mV/s (Epass, Epit) MSE 1.35×10⁴ and 1.72×10⁴ (µA cm⁻²)², R² 0.9707 and 0.9653, respectively. ANN estimates were visually validated on individual curves. Ground truth central tendencies: Bivariate distributions of Epass/log(jpass) and Epit/log(jpit) (estimated per curve by the hybrid LR/ANN) were modelled using Gaussian KDE (scipy.stats). The maxima of these KDEs defined the ground-truth central tendencies for each descriptor per dataset. Normality of E distributions was assessed via Shapiro–Wilk, D’Agostino–Pearson, and Anderson–Darling tests (alpha=0.05). Proxy models (conditional mean/median): To simplify central tendency estimation without processing individual curves, conditional mean and conditional median curves of log(j) vs E were computed for each dataset. The same hybrid LR/ANN pipeline was then applied to these representative curves to estimate Epass/log(jpass) and Epit/log(jpit). Residuals were computed as (ground-truth KDE maxima − proxy estimates) for each descriptor to compare mean- vs median-based proxies.

- Conditional median vs mean as proxy: Across datasets, conditional median curves of log(j) vs E provided notably more accurate and robust central tendency estimates for Epass/log(jpass) and Epit/log(jpit) than conditional mean curves. Mean curves often failed to represent typical PP behavior and, in the most aggressive condition (0.05 M NaCl, 50 mV/s), could not yield Epass at all. Median curves generally intersected or closely approached KDE maxima (targets); only Epit at 0.05 M NaCl, 50 mV/s deviated appreciably. - Residual analysis: For passivity descriptors, the median proxy had consistently smaller residuals than the mean proxy; at 0.05 M NaCl, 100 mV/s, median reduced residuals for log(jpass) and Epass by 54.2% and 73.2%, respectively, relative to mean. For pitting descriptors, median reduced log(jpit) residuals by 89.5%, 77.4%, 53.8%, 25.8%, and 97.1% with increasing aggressiveness; Epit was generally better with median, except at 0.05 M NaCl, 50 mV/s (median underperformed but with preferred negative bias—i.e., underestimation of Epit). - Outlier influence and heteroscedasticity: High-log(j) outliers at high E skewed conditional means upward relative to medians, especially at more aggressive conditions (E > ~1.15 V). KDEs and quantile curves showed heteroscedastic log(j) distributions with increasing variance vs E, and positive skewness intensified with corrosiveness. Descriptor histograms confirmed means exceeded medians due to high outliers (except one case with more low outliers at 0.05 M, 100 mV/s). - Descriptor distributions and normality: Epass and Epit distributions were continuous, roughly unimodal, broadened with aggressiveness, and became near-uniform at 0.05 M, 50 mV/s. Normality tests consistently rejected normality for E distributions across all conditions (p-values ≤ alpha), even after outlier exclusion. - Corrosiveness trends and passivity range: With increasing aggressiveness, Epass distributions shifted to more positive values while Epit stayed roughly constant at lower aggressiveness but decreased sharply at the most aggressive condition. Overall passivity range shrank primarily due to increasing Epass (delayed passive film stabilization) rather than early breakdown (decreasing Epit), aligning with chloride-induced film thinning and inhibited repassivation. - Coefficients of variation (CV): For Epit across conditions, CVs were 4.3%, 1.8%, 11.1%, 11.4%, and 32.7%; excluding default 0.5 V assignments: 2.6%, 1.8%, 3.0%, 7.0%, and 7.9%. These CVs were generally lower than the 9.6% reported for macro-scale PP of 316, possibly due to better surface finish, less aggressive chloride, and larger sample sizes (>100 per set). CVs for log(jpit) (excluding 0.5 V cases) were higher: 10.0%, 8.1%, 10.3%, 21.8%, and 17.1%, explaining why E-based descriptors were estimated more accurately than log(j)-based ones. - Extreme (top-activity) curves: Selecting the top 4 highest-activity curves per dataset showed that higher aggressiveness led to lower Epit and higher log(jpit), corroborating the weakest-link perspective that the most active sites drive macroscopic behavior. In some highly active curves Epit could not be determined (assigned 0.5 V by default).

The study demonstrates that robust statistical proxies—specifically conditional medians—better capture central tendencies of pitting and passivity descriptors in heterogeneous, heteroscedastic, and positively skewed electrochemical datasets than conditional means. This directly addresses the challenge of deriving reliable Epit/Epass values from noisy, high-variance PP data. Median-based estimates resist upward bias from high outliers (metastable/stable pitting at high E) and align closely with density maxima of descriptor distributions. Residual analyses quantify improved accuracy and, where deviations occurred, showed a preferred negative bias for Epit (safer underestimation in predictive contexts). The observed shortening of the passivity range with aggressiveness is primarily controlled by shifts in Epass, implying delayed passive film stabilization in chloride environments, rather than earlier breakdown—consistent with mechanistic evidence (film thinning and hindered repassivation by chloride). The approach yields statistically supported insights into how aggressiveness modulates descriptor distributions and underscores that E-based descriptors are more stable and predictable than current-density-based ones. These outcomes suggest quantile/robust regression as promising modeling choices for localized corrosion, with conditional medians serving as effective set-level proxies when analyzing large populations of micro-scale curves.

The work contributes: (1) a robust hybrid rule-based/ML framework (LR plus supervised ANN) to estimate Epit/log(jpit) and Epass/log(jpass) from individual SECCM-derived PP curves on 316L; (2) a simplified, accurate proxy approach using the conditional median of log(j) vs E to estimate central tendencies of descriptor distributions without processing every curve; and (3) mechanistic insights indicating that shrinking passivity ranges with aggressiveness are mainly driven by increased Epass (delayed passive film stabilization) rather than decreased Epit. The code and datasets are publicly available to support reproducibility and reuse across corrosion and other electrochemical applications. Future work should validate median-based proxies and the hybrid estimator on macro-scale PP data, additional alloys/environments, and alternative protocols; explore quantile/robust regressions and CNNs for feature extraction; and expand structured databases for localized corrosion to enhance model generalizability.

- Generalizability: The rule-based LR component is dataset-specific (thresholds/classes) and may not generalize without adaptation; the ANN was trained on subsets with satisfactory LR labels and deployed on challenging sets, limiting applicability beyond the training domain. - Ground truth dependence: KDE-based central tendencies are derived from descriptors estimated by the LR/ANN pipeline; thus, ground truth depends on the upstream estimation quality. - Experimental scope: Only electropolished 316L in NaCl at five condition pairs was studied using SECCM (micro-scale). Self-passivation at OCP was not considered; curves were analyzed from 0.5 V upwards. Some descriptors were defaulted to 0.5 V where features fell outside the analyzed range or were uncertain. - Most aggressive conditions: Estimation accuracy decreased at high aggressiveness (e.g., 0.05 M NaCl, 50 mV/s), with the mean proxy failing to yield Epass and the median proxy underperforming for Epit in that set. - Potential feature exclusion: Potential (E) was treated as constant and not provided as an explicit input feature to ANN; alternative architectures might benefit from joint E–j representations.