8 8.2. Markov Process-based Prognostics: Multi-state deterioration modelling 181 lowering model performance. Moreover, deterioration in sewer mains is a slow process spanning decades. During this time, context may significantly change as cities evolve e.g., demands in the sewer mains shift, sewer main properties improve due to advances in material science and construction techniques, etc. E!ective deterioration models, among others, must consider the context and its evolution. Known additional challenges include the absence of maintenance records in sewer inspection data, which complicates the assessment of their impact on degradation behaviour. Functional failures are infrequent, making it di"cult to construct models that can accurately predict them. The interval-censored nature of the data (Duchesne, Beardsell, Villeneuve, et al., 2013) introduces biases and uncertainties, which must be considered in e!ective models. Synthetic data, as proposed by Scheidegger, Hug, Rieckermann, et al., 2011, may o!er a promising alternative to cope with some of these limitations. However, improving the quality of inspection data remains an open issue. Data management and quality control for sewer assets are discussed in detail in Auger, Besnier, Bijnen, et al., 2024. Having acknowledged all these challenges in the inspection data, there are also mathematical assumptions in deterioration models that must be discussed, some of which address dataset limitations, while others prioritise simplicity. We elaborate on this in the next section. Assumptions on deterioration modelling of sewer mains via Markov chains Among the various models for long-term sewer main condition assessment, we focus on Markov chains due to their intuitive representation of severities and wellestablished mathematical properties. Markov chains assume that the degradation process follows the Markov property, where future states depend solely on the current state, disregarding previous states. The suitability of this assumption for sewer mains has been discussed in Timashev and Bushinskaya, 2015 and is not addressed in this dissertation; however, corroborating this property for larger schemes using multiple case studies is still worth exploring. This part of the dissertation focuses on the structure of Markov chains, the assumption of homogeneity, interval-censored data, and parameter inference. We assess typical Markov chain structures from the literature and observe that, under regular conditions—excluding rare events such as explosions or accidents—their performance is comparable. However, more complex structures, with additional parameters, tend to exhibit undesired behaviours, including the formation of unwanted absorbing states. Adding a functional failure state is necessary, as high severity does not indicate failure. Although the architecture we proposed including functional failure state produced reasonable results, further evaluation is necessary due to the scarcity of functional failure data, hindering validation.
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