Comparing Homogeneous And Inhomogeneous Time Markov Chains For Modelling Degradation In Sewer Pipe Networks

TL;DR

This paper compares homogeneous and inhomogeneous Markov chains for sewer pipe degradation modeling, finding that inhomogeneous chains better capture nonlinear degradation patterns despite higher complexity and over-fitting risks.

Contribution

It provides a large-scale empirical comparison of Markov chain types for sewer pipe degradation, highlighting the advantages of inhomogeneous models with Gompertz distribution.

Findings

Inhomogeneous Markov chains better model nonlinear degradation.

Gompertz distribution is most suitable for inhomogeneous models.

Inhomogeneous models require improved parameter inference methods.

Abstract

Sewer pipe systems are essential for social and economic welfare. Managing these systems requires robust predictive models for degradation behaviour. This study focuses on probability-based approaches, particularly Markov chains, for their ability to associate random variables with degradation. Literature predominantly uses homogeneous and inhomogeneous Markov chains for this purpose. However, their effectiveness in sewer pipe degradation modelling is still debatable. Some studies support homogeneous Markov chains, while others challenge their utility. We examine this issue using a large-scale sewer network in the Netherlands, incorporating historical inspection data. We model degradation with homogeneous discrete and continuous time Markov chains, and inhomogeneous-time Markov chains using Gompertz, Weibull, Log-Logistic and Log-Normal density functions. Our analysis suggests that, despite their higher computational requirements, inhomogeneous-time Markov chains are more appropriate for modelling the nonlinear stochastic characteristics related to sewer pipe degradation, particularly the Gompertz distribution. However, they pose a risk of over-fitting, necessitating significant improvements in parameter inference processes to effectively address this issue.