Markov Chain Models for the Stochastic Modeling of Pitting Corrosion

Abstract

The stochastic nature of pitting corrosion of metallic structures has been widely recognized. It is assumed that this kind of deterioration retains no memory of the past, so only the current state of the damage influences its future development. This characteristic allows pitting corrosion to be categorized as a Markov process. In this paper, two different models of pitting corrosion, developed using Markov chains, are presented. Firstly, a continuous-time, nonhomogeneous linear growth (pure birth) Markov process is used to model external pitting corrosion in underground pipelines. A closed-form solution of the system of Kolmogorov's forward equations is used to describe the transition probability function in a discrete pit depth space. The transition probability function is identified by correlating the stochastic pit depth mean with the empirical deterministic mean. In the second model, the distribution of maximum pit depths in a pitting experiment is successfully modeled after the combination of two stochastic processes: pit initiation and pit growth. Pit generation is modeled as a nonhomogeneous Poisson process, in which induction time is simulated as the realization of a Weibull process. Pit growth is simulated using a nonhomogeneous Markov process. An analytical solution of Kolmogorov's system of equations is also found for the transition probabilities from the first Markov state. Extreme value statistics is employed to find the distribution of maximum pit depths.

Markov chain modelling for time evolution of internal pitting corrosion distribution of oil and gas pipelines

“…where N represents the number of states the pipeline wall is divided, Pi(t) is the probability that the pit depth is at i th state at time t and can be determined by measuring the pit depth distribution at such a time or by expert knowledge [1,8 ].…”

“…Manipulating Equation (14) will give the Kolmogorov forward and backward equations, however, for a continuous time non-homogenous linear growth Markov process which the pit depth is assumed to follow in this research, the probability that a process at state i will be in state j for j≥i at a later time follows Kolmogorov forward equation shown in Equation (15) [1,8,13].…”

“…Pitting process can be metastable in nature -a situation in which a pitting process starts and stops after a while or immediately [1,2] or it can be a stable pitting that nucleates and grows indefinitely. Stable pits generally show stochastic behaviour [1,3] and are the focus of many researches.…”

“…Stable pits generally show stochastic behaviour [1,3] and are the focus of many researches. Pitting corrosion is initiated due to:…”

“…The work of Valor et al [1] focused on pitting corrosion of underground pipelines and corrosion coupons.…”