104 Part II: Multi-state deterioration modelling Figure II.5: Breda’s sewer network in the Netherlands (View of Breda 2024) comprises 25,594 pipes, totalling approximately 1,045 km in length. II.4.4 Deterioration modelling in sewer mains using Markov Chains Cherqui, Clemens-Meyer, Tscheikner-Gratl, et al., 2024 indicates that “for longterm assessments on relatively large cohorts of elements (i.e., at the scale of an entire catchment or urban area), statistical/data-driven models based on condition class data seem to present a usable tool”. As mentioned in Section 1.2.3, various Markov chains have been utilised to model the stochastic deterioration of sewer mains. This section provides a summary and overview of some models discussed in the literature. Inspection data are typically collected via CCTV along various sections of sewer mains. According to European standards EN 13508:1; EN 13508:2, damage codes and severities—ranging from 1 to 5—are then assigned. The need to explicitly model these severity levels as states in a Markov chain has led to the most common architectures found in the literature, as depicted in Figure II.7. Since severities are ranked from 1 to 5, the state space can be defined as S = ↔1,2,3,4,5↗ with an index k ↓S. The models in Figure II.7 represent sequential states frompristine condition (k =1) to severe deterioration (k =5) or functional failure (k =F). When accounting for functional failure, then S =↔1, 2, 3, 4, 5, F↗.
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