Model calibration and uncertainty quantification of cellular automata-based pitting corrosion model

Abstract

This study presents a Bayesian framework for calibrating cellular automata (CA) models of pitting corrosion. A high-fidelity two-dimensional CA model is used to simulate pit morphology evolution under coupled electrochemical and mass transport processes, incorporating eight uncertain model parameters related to metal dissolution, hydrolysis, diffusion, and sedimentation. Key geometric indicators—maximum pit depth and pit aspect ratio—are extracted from the simulation outputs and reduced to interpretable scalar features using power-law fitting. Correlation analysis is conducted to assess linear relationships between model parameters and power-law coefficients. Gaussian Process Regression (GPR) surrogate models are constructed using Latin Hypercube Sampling (LHS) to emulate the high-fidelity CA model. Global sensitivity analysis (GSA) using Sobol’ indices is performed by utilizing the trained surrogate models; it identifies sedimentation and ionic diffusion as the dominant contributors to output feature variability, with significant nonlinear interactions. The trained surrogates are integrated into a Bayesian inference framework using Metropolis-Hastings Markov Chain Monte Carlo (MH-MCMC) sampling to infer posterior distributions of the uncertain model parameters. The posterior samples are further propagated through the surrogates to quantify the output uncertainty, and the prediction is evaluated using a distance-based probabilistic model validation metric. Two numerical examples related to API-5L X65 steel pipelines are presented, demonstrating that incorporating multiple geometric features—both pit depth and aspect ratio—improves predictive accuracy. The proposed framework supports uncertainty-aware modeling and decision-making for structural health assessment and maintenance planning in corrosion-critical infrastructure.