112 Chapter 5. Deterioration Modelling of Sewer Pipes via Discrete-Time Markov Chains: A Large-Scale Case Study in the Netherlands Sequential Least-Squares Programming to identify the DTMC parameter that best minimises the root mean weighted square error. Our results indicate that, for our case study, there is no significant di!erence between Chain ‘Multi’ and ‘Single’. However, the latter has fewer parameters and can be trained more easily. Our DTMCs are useful for comparing the cohorts via expected values. For instance, concrete pipes carrying mixed and waste content reach severe levels of surface damage more rapidly compared to concrete pipes carrying rainwater, which is a phenomenon typically observed in practice. 5.1 Introduction Sewer network systems are an important part of the civil infrastructure required to achieve an adequate level of social and economic welfare. The management of these systems has become increasingly challenging due to the need to cope with limited budgets, environmental changes, uncertainty about network deterioration, and a lack of rigorous deterioration analysis. This often leads to conservative approaches that result in the early replacement of sewer mains. Thus, aiming at finding a good trade-o! between maintenance costs and system performance, robust and reliable sewer main deterioration models are needed to prioritise pipes at high risk of failure for proactive maintenance, support decision making, and strategic rehabilitation planning (Scheidegger, Hug, Rieckermann, et al., 2011; Egger, Scheidegger, Reichert, et al., 2013). Moreover, there is a need in the research community for sharing existing case studies aiming at increasing the evidence on sewer main deterioration models (Tscheikner-Gratl, Caradot, Cherqui, et al., 2019). Concerning sewer main deterioration models, three types can be identified: those based on physics, Machine Learning, and probabilistic. A detailed review of the di!erent types of models used to predict the deterioration of sewer networks is presented in Hawari, Alkadour, Elmasry, et al., 2020. We are interested in Markov chain models, since they proved to be among the most reliable and widely used approaches to model the deterioration of a group of sewer mains (Kobayashi, Kaito, and Lethanh, 2012; Tscheikner-Gratl, Caradot, Cherqui, et al., 2019), and enable the modelling of sequential events, such as sewer mains deterioration (Ana and Bauwens, 2010). Several types of Markov Chains (MCs) have been implemented for the modelling of sewer networks, examples are discrete-time MC (Micevski, Kuczera, and Coombes, 2002; Baik, Jeong, and Abraham, 2006), continuous-time MC (Lin, Yuan, and Tovilla, 2019), non-Homogeneous MC (Le Gat, 2008), hidden-MC (Kobayashi, Kaito, and Lethanh, 2012), semi-MC (Scheidegger, Hug, Rieckermann, et al., 2011).
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