In-line inspection (ILI) data is commonly used in corrosion growth models (CGMs) to predict the corrosion growth in energy pipelines. A hierarchical stochastic corrosion growth model is considered in this paper which considers the variations in the corrosion growth, both spatially and temporally, the inherent measurement error of the ILI tools as well as the model uncertainties. These uncertainties are represented as unknown model variables and are often inferred using a Bayesian method ,  and samples of the unknown parameters’ posterior probability density functions (PDFs) are obtained using Markov Chain Monte Carlo (MCMC) sampling techniques .
ILIs can result in massive data sets. In order for MCMC-based inference techniques to yield reasonably accurate results, many samples (approaching infinity) are required. This fact in addition to the massive data sets exponentially increases the scale of the inference problem from an attainable solution to a potentially impossible one that is limited by today’s computing power. For this reason, MCMC-based inference techniques can become inefficient in the cases where ILI datasets are large. The objective is to propose variational inference (VI) as an alternative to MCMC to determine a Bayesian solution for the unknown parameters in complex stochastic CGMs. VI produces approximations of the posterior PDFs by treating the inference as an optimization problem. Variational inference emerged from machine learning for Bayesian inference of large data sets; therefore, it is an appropriate tool to use in the analysis of mass pipeline inspection data–.
This paper introduces VI to solve the inference problem and provide a solution for a hierarchical stochastic CGM to describe the defect-specific corrosion growth experienced in pipelines based on excessively large ILI datasets. To gauge the accuracy of the VI implementation in the model, the results are compared to a set of values generated using a stochastic gamma process that represents the corrosion growth process experienced by the pipe.